{ "id": 2670, "name": "make_k_subarray_sums_equal", "difficulty": "Medium", "link": "https://leetcode.com/problems/make-k-subarray-sums-equal/", "date": "1679097600000", "task_description": "You are given a **0-indexed** integer array `arr` and an integer `k`. The array `arr` is circular. In other words, the first element of the array is the next element of the last element, and the last element of the array is the previous element of the first element. You can do the following operation any number of times: Pick any element from `arr` and increase or decrease it by `1`. Return _the minimum number of operations such that the sum of each **subarray** of length _`k`_ is equal_. A **subarray** is a contiguous part of the array. **Example 1:** ``` **Input:** arr = [1,4,1,3], k = 2 **Output:** 1 **Explanation:** we can do one operation on index 1 to make its value equal to 3. The array after the operation is [1,3,1,3] - Subarray starts at index 0 is [1, 3], and its sum is 4 - Subarray starts at index 1 is [3, 1], and its sum is 4 - Subarray starts at index 2 is [1, 3], and its sum is 4 - Subarray starts at index 3 is [3, 1], and its sum is 4 ``` **Example 2:** ``` **Input:** arr = [2,5,5,7], k = 3 **Output:** 5 **Explanation:** we can do three operations on index 0 to make its value equal to 5 and two operations on index 3 to make its value equal to 5. The array after the operations is [5,5,5,5] - Subarray starts at index 0 is [5, 5, 5], and its sum is 15 - Subarray starts at index 1 is [5, 5, 5], and its sum is 15 - Subarray starts at index 2 is [5, 5, 5], and its sum is 15 - Subarray starts at index 3 is [5, 5, 5], and its sum is 15 ``` **Constraints:** `1 <= k <= arr.length <= 105` `1 <= arr[i] <= 109`", "public_test_cases": [ { "label": "Example 1", "input": "arr = [1,4,1,3], k = 2", "output": "1 " }, { "label": "Example 2", "input": "arr = [2,5,5,7], k = 3", "output": "5 " } ], "private_test_cases": [ { "input": [ [ 411440961, 479228108, 846536696, 213956621, 470440189, 934283870, 816468685, 128150573, 574634398, 659692438, 79758305, 563138399, 686036189, 665529921, 862521737, 481410313, 839015142, 249292132, 288804789, 307705039, 446331679, 354111445, 917646518, 962828142, 333103734, 908012949, 677380949, 881051872, 460929623, 782392800, 419195114, 223923727, 551525158, 872154567, 135817892, 621664472, 353233727, 31824251, 981065410, 147304333, 17585577, 746889299, 862255106, 73008661, 46262541, 135792575, 935110240, 387764398, 466996699, 322706743, 187960783, 62287312, 961828456, 547630691, 539689560, 765308759, 832576711, 540537192, 285506088, 437828317, 728602027, 59256060, 265966843, 957112996, 395985823, 454148576, 769932206, 434840317, 626955623, 722304152, 568567840, 939646556, 536578703, 918534422, 420248102, 24023376, 286300182, 273565932, 633345447, 237533964, 19548965, 67980915, 486668873, 179749426, 710372310, 857286861, 531306236, 217553011, 441238863, 385834280, 612711373, 285670325, 89878076, 970894336, 440917621, 190156638, 984858046, 995129067, 818979732, 104563954, 927968761, 672454647, 783779886, 339897130, 126840412, 552384557, 596098398, 176032313, 554197604, 187411113, 790813264, 274173072, 825520585, 694792095, 120928078, 876997342, 84062240, 686574622, 822794220, 155667759, 268743546, 895861465, 646878505, 21243771, 968168737, 566517603, 446050877, 644865734, 131051580, 575986906, 774358671, 482333577, 14040565, 12265169, 290850457, 189492849, 431697112, 342531939, 695659154, 532601470, 672633286, 242326115, 56289760, 198108648, 347050247, 619645252, 592819676, 680288137, 752472839, 428132254, 926400391, 771958312, 914197093, 546374340, 982644798, 45115623, 722389028, 122577488, 372212401, 987155086, 45797650, 70467832, 543270055, 768226971, 563795039, 618335520, 166141660, 406014741, 199122076, 679024672, 306584986, 477067751, 313075592, 74932157, 872769544, 467748164, 74224912, 12174610, 587003510, 612110732, 595100349, 703608841, 238960736, 427502681, 278412755, 831127173, 746331197, 152746269, 753043711, 420226680, 936805781, 72194759, 786865874, 466622456, 391745764, 6698817, 166143953, 976228096, 278039841, 15158032, 379135303, 140621147, 619839114, 95986429, 686159841, 486076036, 184821594, 31851974, 298442084, 833028855, 139318079, 282987553, 962990068, 847617703, 859808600, 356552410, 870061725, 878475029, 455288489, 398201414, 752317002, 563701784, 944692142, 673369820, 130568435, 536344089, 106894423, 216694599, 286950831, 680150024, 470831976, 364806102, 552884862, 476676178, 1626818, 550083272, 679081181, 477289138, 982206264, 936954599, 549986676, 973646835, 815595931, 860729001, 394473182, 175252248, 927213428, 501410554, 25642230, 6152236, 615584871, 200019792, 610002867, 374888239, 746725412, 358820088, 416301399, 947662203, 546362674, 854531475, 787659243, 769461637, 898732183, 597121970, 861830350, 635788670, 946625619, 326889503, 665044048, 710873419, 568874218, 391089180, 570024849, 233174876, 641427240, 678615219, 130713275, 247869982, 576959077, 474472073, 852583665, 783333704, 576702618, 587410566, 174940696, 904424717, 211923305, 715197497, 606620470, 213029872, 935890571, 208233288, 133930357, 269043243, 443137695, 532680335, 285690854, 24518569, 107134390, 275734675, 579860100, 188455138, 574414796, 618951458, 454247506, 679479893, 506261949, 768108403, 260679689, 644700545, 528329237, 582363907, 787890473, 341990083, 176182176, 212324967, 993208708, 83917574, 107207810, 821957922, 678605436, 923866901, 655452017, 663297817, 577424582, 363435038, 391069651, 701906219, 962386337, 538956780, 197939812, 26521837, 966717119, 804242964, 79884982, 861887663, 33756559, 953352641, 339709398, 149134852, 415893964, 44829955, 926923820, 888602183, 723261807, 409989756, 352744414, 127483033, 519478813, 171972553, 899430942, 823409443, 59883104, 226198984, 363140451, 57440029, 232350703, 185817193, 482461433, 653966308, 405085111, 641221489, 97601138, 659214003, 30829699, 651252931, 456330970, 590766322, 702309276, 806425889, 603017229, 416084199, 305549586, 989865352, 775700388, 880579796, 948026252, 60638483, 620746150, 190225466, 98390270, 747443604, 43821425, 592397183, 281864415, 524023054, 872715386, 596670892, 255412709, 447187389, 907253462, 69557782, 593032428, 975462436, 693500776, 163826138, 441106965, 579817014, 897726023, 775907845, 881053393, 216784316, 850770236, 736912373, 714299511, 255274508, 585749111, 235695518, 874507851, 72708321, 177155623, 535582507, 519381564, 121670950, 947947582, 600131374, 795366962, 243888894, 105305485, 859920186, 822757367, 637328909, 954697532, 520030336, 73289802, 485172757, 320867907, 867615825, 514418960, 892459396, 924225750, 831049416, 766979196, 907575258, 339918142, 17290942, 773783162, 939423480, 723972779, 770813101, 814047546, 117241439, 56182887, 802862833, 145796885, 212954607, 70664251, 619535490, 323191491, 479103640, 558532746, 327410600, 558502590, 931867550, 15737519, 472120462, 823686703, 971527004, 506453277, 536483711, 739479919, 189237457, 116183162, 948523751, 516019115, 789355453, 426841436, 798976137, 470228492, 841723856, 69197200, 608686238, 674517798, 104288236, 518203123, 414434930, 722738632, 250905486, 531800733, 461952015, 506622256, 49208180, 2622081, 980190774, 878340739, 367790125, 352577320, 358134531, 863019754, 113946868, 352889547, 336570977, 218456871, 218133863, 48642062, 98790093, 26351692, 331518183, 682522211, 520807549, 780535041, 464749698, 184861610, 513588249, 1501173, 973871425, 307313802, 43222119, 352644571, 591862699, 855293459, 89630539, 960821582, 198827553, 935777437, 783883772, 953207177, 166245923, 259621220, 329060048, 661048108, 309347781, 370819311, 246972652, 897167426, 432430735, 515534868, 51740856, 198764303, 164200238, 274097608, 132683763, 382879041, 150336180, 612739325, 998999088, 291758365, 796501452, 451919634, 731130610, 592883723, 77174566, 192584847, 768611121, 598395691, 241406080, 981174537, 135905725, 925490638, 406034827, 843660964, 772148529, 374056142, 3524859, 778181322, 607840141, 213186611, 340603420, 861459506, 944768233, 380210002, 461894600, 692428773, 430676938, 546099657, 293245147, 503336833, 956811125, 68991680, 847829901, 170987306, 352809302, 740962208, 961122259, 507018565, 142133847, 804783693, 572230871, 322257471, 58795786, 730410820, 30322200, 762206543, 341313383, 574773442, 385512449, 484365975, 350664582, 521677305, 690291515, 330941985, 604351194, 989383495, 473719063, 548366242, 69306172, 244567585, 214913647, 661382155, 553527092, 867736222, 898930135, 500749515, 466734525, 3405609, 440519282, 584024350, 83458685, 496727167, 821287665, 129873241, 576145317, 893884878, 486989372, 859053384, 256255385, 369670507, 349461593, 519411579, 397384300, 263401802, 61931949, 732954092, 608826910, 485483901, 81638228, 168895314, 550258556, 904324538, 904999854, 906393530, 409810068, 241238785, 987625565, 642986110, 34043797, 16571610, 843634769, 2584287, 770482042, 107598752, 879244688, 477497274, 201664757, 322454183, 491275445, 70468187, 584280610, 860615442, 394142273, 534760472, 346886771, 117402434, 830703442, 433088025, 501403275, 13632422, 948643201, 720266656, 400174016, 851119303, 13016773, 286003683, 407587362, 235928068, 951605022, 570913217, 683826540, 376618000, 275438825, 559165875, 205919076, 152614737, 978135548, 640332318, 421120589, 265523534, 76170172, 697301634, 676820502, 702326500, 273523132, 730328258, 737685291, 954016197, 875656361, 250019215, 125837497, 472251960, 595414622, 698886744, 91748064, 751735012, 641547618, 497883423, 249583172, 775084501, 110020937, 186701741, 114533253, 58484844, 240537108, 493947804, 997689668, 63120075, 241513620, 638905293, 772528490, 66474915, 271911251, 354332159, 898980166, 519363490, 544706534, 629192369, 860529639, 818361495, 301369890, 508481630, 911947314, 619875444, 491247397, 468385062, 484892345, 744024341, 492722995, 907155466, 443521530, 575020033, 832769669, 24558334, 510983921, 417244787, 724510171, 872189254, 310858609, 842369675, 107692487, 753655557, 269038386, 270571059, 666564549, 180159135, 99824096, 759146014, 667114344, 635583828, 587770388, 539569407, 942007914, 721994015, 277533542, 424252243, 895458692, 200702632, 251239081, 725939735, 527861353, 481397336, 363823328, 857603325, 375027886, 471550781, 312003884, 368361742, 521495886, 897270666, 538498640, 664260857, 963077367, 715698931, 103038723, 370362563, 330075203, 5142864, 835525880, 95258768, 685454933, 332458853, 704698274, 591470750, 724601440, 689178188, 870746839, 582768625, 945015310, 472248780, 186440349, 462107119, 65225333, 438217211, 359212894, 59997095, 492569052, 635966289, 262166333, 299622431, 28479094, 555521906, 433186053, 114565728, 409663330, 438093782, 339265476, 626272942, 892879188, 395624515, 362183670, 885660557, 170752855, 173192117, 999420761, 577325702, 193215941, 836881653, 128075188, 4960570, 595426591, 708732823, 223526966, 911502008, 360164603, 641730441, 337161594, 525053772, 562701661, 805400209, 463986398, 666361276, 961341542, 989917307, 617962872, 749969092, 240713867, 222600583, 186057539, 762552186, 137174788, 899429739, 67343258, 115851677, 805536081, 206193835, 649455006, 418984225, 406372781, 997679134, 627551414, 898699371, 699263157, 645975126, 851023515, 934034879, 536909623, 30169690, 647279900, 66949236, 158784031, 133472230, 438291896, 307596392, 938071760, 294139932, 928875626, 787134064, 559468443, 174916272, 318468744, 883558331, 364754329, 589298445, 254267584, 514710521, 956374326, 448082387, 177689787, 508574274, 176262630, 661606651, 729501195, 964466975, 582875062, 249813596, 615246205, 461358298, 691872609, 31636528, 608960386, 615010228, 204032299, 285009759, 619660031, 884382459, 170980864, 449744588, 748675087, 335692017, 373449744, 545133940, 705370511, 538192808, 255717663, 284261351, 185989412, 607322661, 444013208, 529256403, 52398032, 324196177, 447647146, 599112701, 108070355, 379075405, 840857128, 765815028, 181209043, 47106782, 606526800, 364922560, 602208379, 404754111, 658232061, 507457071, 35561974, 745072381, 665446727, 624435580, 902985985, 554942377, 92722119, 489569642, 268522098, 265591319, 144531424, 242692738, 961203935, 156923920, 924786023, 213682065, 694389484, 767909119, 850862120, 155694968, 686887102, 742966963, 548884899, 231100067, 889900267, 334875652, 1340482, 770040954, 511347189, 6901754, 346512666, 504684297, 50134256, 285427015, 937166999, 680961708, 428432138, 602197105, 398954939, 208651287, 867533139, 367696322, 214302738, 741561969, 926630044, 687385718, 424941910, 417836104, 156863801, 296807872, 242918234, 123430565, 700319331, 285227381, 121236011, 868420892, 944411645, 124499555, 456644648, 227152950, 608987962, 235783233, 757317257, 125613814, 235474057, 659298290, 763873241, 242163008, 814414699, 306049999, 218278472, 536273376, 422503438, 263712950, 487183460, 824504463, 502713740, 808250124, 795526049, 158726329, 422288261, 925182101, 472660037, 171373062, 911109881, 455962917, 463734694, 396433595, 402528698, 625583704, 477062730, 451977912, 169792895, 194564871, 511852516, 519612391, 865349780, 984429653, 682800746, 321244569, 728493337, 97692115, 393154648, 666899328, 400829530, 780200741, 924437085, 12725956, 941893160, 929579052, 793474147, 583027416, 232375075, 660706804, 157383937, 241897451, 147510837, 798642072, 317754538, 398782194, 620196064, 756279926, 271307327, 873164355, 717614452, 396815730, 735063024, 534205724, 304163692, 757095919, 344487066, 818700967, 994412210, 876455615, 835195986, 243406647, 292444142, 754981866, 228408724, 497969836, 925808364, 620637197, 999300308, 732581752, 118811375, 239013886, 349488870, 891069732, 328781827, 338306387, 527417621, 556618167, 152895540, 585020087, 217922062, 298885059, 573356994, 228836050, 98843916, 958815741, 231438283, 716693124, 629149901, 870746521, 322823020, 776489881, 322434932, 921801487, 391508756, 322711160, 905302766, 120888706, 672086657, 455669394, 975468466, 834535579, 1806321, 904037306, 266918337, 563799199, 211547578, 4395985, 989799300, 307725121, 333075852, 253014978, 43214106, 275913413, 886960596, 644549773, 761786026, 699227511, 630066058, 220125502, 743199455, 530854934, 175829204, 583254123, 543446228, 872214639, 764858809, 804952436, 768037522, 382616551, 220040494, 281092076, 220453048, 444509953, 789493672, 471086301, 562844538, 653155510, 428520525, 744436418, 396947170, 376886981, 981400677, 245671546, 520167730, 820496245, 182623219, 814343336, 659678480, 891803433, 139756004, 194251118, 952389792, 625324858, 993582486, 191962477, 503596309, 844287095, 255743285, 39275198, 973089497, 28362435, 610637262, 777967753, 9050354, 673659440, 349039666, 392053687, 242866186, 707768667, 608210082, 952128061, 422054420, 591284004, 513389854, 478592705, 819165905, 156921956, 673254710, 49618286, 80168575, 652145509, 520864136, 279037710, 388352568, 292139242, 840467836, 160083207, 715823480, 434519566, 419364916, 981104195, 293964625, 7506806, 228804079, 492928716, 684562404, 122630849, 676617492, 948608502, 249325139, 756561772, 129464328, 104007835, 731530449, 964681120, 719432833, 549411721, 22378495, 556006523, 916376844, 578999517, 112965813, 433591107, 803007593, 839393687, 953750223, 943541004, 668003488, 68400371, 134144880, 753762991, 398675015, 559454744, 820720114, 261410610, 142092084, 809884694, 627798803, 180575184, 260274545, 244536837, 148399718, 914472082, 123543231, 755869125, 658127976, 856915253, 967444860, 149956, 221177710, 562984637, 555464898, 630757206, 385588477, 145759043, 189098318, 532935619, 122184183, 443139011, 647052931, 702571699, 261148776, 365488472, 507837889, 283764591, 844812151, 120951959, 466716762, 518156811, 839730127, 475359299, 473852820, 172125727, 865159752, 184730990, 428989532, 852410581, 128787930, 478802197, 874143982, 267803272, 996018496, 726757410, 589759263, 809735654, 124331339, 323439770, 116236428, 422722804, 103044510, 581135106, 631155018, 598150801, 490884435, 139784676, 164604511, 19601210, 589435970, 597303246, 573516660, 752888458, 528539047, 261825822, 996301657, 489478834, 873292365, 476422356, 581092059, 726917430, 620854987, 737477983, 513889003, 962631708, 286861933, 889305697, 646558177, 906127865, 662972063, 604030138, 958615417, 407408506, 408368242, 103093389, 732435574, 600782928, 262351758, 919872253, 45010672, 152741292, 401887936, 498607244, 752278762, 816743339, 197821469, 530335578, 70319669, 11176347, 47098181, 338901031, 166333159, 41721769, 72400364, 927006875, 317782540, 634934283, 716599783, 883694682, 729303821, 341122570, 776647323, 590995094, 937827449, 479571712, 672849788, 913786921, 55530946, 596976728, 496961847, 623491445, 937453435, 925471050, 617733046, 169746216, 3478133, 927638151, 238978549, 4827111, 630180319, 379089106, 586599281, 94816718, 728418466, 397107274, 402003453, 614741078, 301017329, 998407075, 706463435, 932406267, 667404122, 549740143, 639976029, 459447791, 526784819, 940992221, 2356304, 637621724, 86299623, 289691442, 38135766, 251098842, 794943842, 130177254, 203287127, 928610223, 860203740, 276323772, 504438462, 875671075, 491224359, 838882334, 435058999, 268011834, 706312707, 985696765, 356729779, 303217513, 57075275, 220118413, 521622563, 358143017, 455380327, 862909677, 964262558, 355058033, 677388364, 473525881, 960698555, 383954106, 985547693, 884288462, 229075710, 51931504, 685035187, 316282738, 927783366, 94368330, 194686270, 902511988, 400783811, 796760511, 175165240, 787370544, 744147119, 366899380, 409496175, 109083138, 353716775, 399920760, 489034858, 931276138, 983663265, 97810645, 604333231, 856699885, 42875929, 206602590, 730895152, 820158391, 480592523, 25014760, 206066214, 714711772, 842637314, 965402309, 261269516, 657054435, 790562854, 726999626, 102082446, 251726858, 647624064, 64339953, 65238890, 390721475, 144211131, 231601714, 988017368, 139467977, 137465919, 142907258, 484877553, 486353225, 681309010, 533798619, 374360225, 617910480, 541245127, 940375619, 892236066, 733162024, 504999900, 92591602, 105116857, 534635812, 190080173, 13994612, 51764842, 343823359, 687011586, 995190239, 310983511, 482122901, 974137858, 385814879, 819862156, 353766652, 67971199, 882358158, 777997984, 606743936, 271097483, 372156251, 236014618, 214067044, 879265126, 568370701, 411474137, 214768543, 719589076, 573135843, 29122381, 395941309, 710495429, 487482368, 97139823, 202546798, 208717183, 705300793, 993762795, 916539110, 848606598, 976447341, 689981927, 577443185, 28205596, 836621047, 724926492, 514217699, 305838928, 815579848, 604734901, 664262420, 622014896, 995920273, 371129946, 149957503, 45093702, 477968832, 957136597, 449996771, 19248895, 289795770, 393564033, 508856672, 835492040, 439286802, 825010125, 315357714, 124802801, 401281567, 309024705, 676871766, 791411968, 389013729, 40617547, 833390003, 313780570, 729219456, 246335751, 602352939, 637600583, 595890007, 36790350, 433479082, 21480327, 327411128, 720615711, 205506403, 461178496, 130040520, 184551100, 595040951, 475325931, 570397808, 656232801, 582591246, 800368049, 830978606, 378254050, 781726119, 729159967, 439091588, 195936820, 831564752, 111446367, 273926970, 4752655, 79676433, 778809652, 265556207, 84654375, 398315553, 606859426, 175350055, 501450627, 546397222, 15352183, 397168877, 803026025, 913312547, 333959597, 125073417, 489636448, 347839425, 9837946, 651095501, 451031524, 773987106, 640868466, 29655762, 668413663, 212151494, 768059225, 200334803, 970045883, 180226491, 291357798, 724190205, 722037313, 310836176, 477475754, 924798517, 883471007, 760978627, 185950417, 359318678, 463791686, 2746975, 388635546, 438990155, 401943826, 612075920, 103950207, 32352662, 557734786, 28407353, 987775599, 517778701, 839383256, 944928240, 249897489, 475739982, 558393371, 550396228, 434247145, 378784887, 269571841, 286113160, 403234329, 193257137, 478380234, 737311827, 956918861, 453242260, 835616795, 670516648, 757124286, 607211025, 486185018, 21265080, 807376348, 925197826, 595591908, 314367521, 750491945, 281811845, 999827901, 673024591, 533472334, 840577071, 494353286, 83814531, 992122277, 280990601, 813254613, 118208148, 895306529, 828413246, 571375757, 424881030, 405112021, 806743705, 89196479, 430812867, 811963429, 951304790, 305214832, 498022420, 243563574, 392121172, 692621718, 839523515, 744075701, 350789688, 460925655, 825431994, 665320320, 333536572, 983486992, 77587771, 781429248, 307232190, 538802716, 660952900, 492625000, 987859062, 297004004, 585098137, 297261474, 528994901, 782282918, 460950970, 599068383, 757384718, 581247644, 817425671, 374094826, 12327075, 562760152, 785889674, 843336489, 500254298, 633854204, 616230223, 860975321, 677959761, 932576274, 817704756, 984298080, 756693560, 344975239, 615590856, 33434371, 34834966, 907216599, 158103771, 849382934, 600296730, 926481913, 193215196, 274404616, 34192178, 783203188, 434192395, 965624251, 163638657, 370454464, 515026799, 941511127, 193580293, 87488014, 613920106, 261210570, 717510772, 846447382, 997009835, 153136999, 38448190, 986961738, 626625552, 928893505, 965814096, 828925304, 347126812, 707534821, 83737151, 686998485, 810914042, 230353004, 466080521, 681356578, 82831176, 324105268, 280401641, 109157090, 764228712, 160669267, 487096794, 291789121, 98908353, 378640828, 178380065, 579254794, 967381985, 773410205, 788637260, 424235545, 586562478, 108928953, 827102729, 590403176, 598819945, 456990286, 450718829, 687739398, 850244072, 85376370, 529391101, 816157174, 185546797, 77592788, 318145026, 438255730, 385475607, 131083746, 955737534, 985559145, 485119547, 9798379, 28077006, 118594867, 690245630, 37799664, 613027259, 862745127, 811780855, 249263594, 656289031, 686239829, 255449572, 716129690, 620861349, 871780638, 867689422, 899924839, 882286793, 823805003, 547158973, 107479306, 417897062, 407253394, 134730111, 797262592, 439406698, 981053999, 859666643, 782158485, 280034806, 399402618, 501834711, 760750393, 916115593, 521755806, 873369803, 699435220, 761522523, 561756594, 479787240, 192924891, 743562393, 403912194, 507571073, 521930993, 739827733, 393668992, 935791973, 683803788, 723184170, 755188728, 26405352, 494819617, 201207498, 833280044, 608347999, 782692259, 346817384, 90370068, 589319211, 964067977, 295077374, 833938215, 814494485, 904004455, 26347034, 566766557, 224471467, 377132903, 955778578, 863256538, 595036577, 361568462, 926929839, 689616642, 421709870, 114481715, 497218985, 201830063, 271115629, 772263678, 494051843, 341020848, 308525365, 978699545, 224694046, 327356888, 338094016, 444473538, 171091888, 113733399, 625857162, 62883633, 650785778, 49015249, 983707100, 755304390, 12461097, 954362162, 578956320, 311384631, 158102726, 376853173, 894796275, 898880187, 566178601, 480766254, 820350658, 190849305, 70624050, 812234281, 161645630, 360245215, 541673833, 501352129, 446655478, 745667373, 784591301, 391390983, 699885891, 713234564, 237085180, 934533497, 316395897, 489883766, 26507000, 519300073, 67106408, 367056862, 153373275, 877309871, 539539323, 651412018, 956815129, 788051672, 582518761, 112310599, 334701586, 688788040, 16550452, 494104395, 18712321, 4136702, 666963826, 938440133, 791337767, 937270343, 642831948, 55297949, 272849038, 544257952, 171270310, 286516182, 622957589, 110687212, 563556902, 679344843, 593511708, 60296827, 274502565, 865485201, 814275810, 248910413, 853630958, 85546966, 249292839, 577732814, 373893376, 442248106, 140020474, 427645961, 792856224, 996278005, 376593658, 241237627, 326168251, 389067872, 5481802, 960260838, 313451781, 693884899, 740982042, 938454567, 544342359, 984734470, 595090296, 811603195, 240104310, 416468547, 781694016, 267498077, 724222380, 770273080, 82097027, 59482326, 111040714, 234057408, 576587265, 618820393, 158931812, 95083445, 585530294, 458045413, 891532356, 948544424, 244302662, 439304459, 397663519, 352612906, 298913589, 378716512, 602857004, 470859691, 796921705, 95435768, 207957056, 931471064, 871939085, 786111901, 249049901, 719016784, 249447109, 590146496, 949341526, 88257887, 539183883, 357342700, 254522589, 799466281, 173187130, 964406721, 623144183, 494755083, 597608501, 837438765, 237671103, 140122002, 744531721, 804086196, 589091686, 395114, 110054957, 731863357, 602848190, 578639363, 877393074, 704221424, 855161536, 375183423, 478125395, 61348859, 731496951, 156512427, 992761577, 995981072, 715933642, 149262051, 327549318, 559345432, 163987641, 267969534, 213476708, 186098668, 209734318, 399126680, 122293205, 423217721, 819686498, 163083497, 688568431, 944108506, 838002007, 28296223, 152449399, 411156803, 175227385, 374970670, 876771201, 987002132, 763562410, 737625060, 32666318, 925296412, 472426729, 683768975, 156836597, 473397409, 467469938, 210527683, 869776236, 516183472, 872372752, 602157693, 383518736, 39379796, 3276789, 641924158, 370262485, 761777926, 33418538, 572491338, 165153142, 14439713, 183592187, 890963507, 919359102, 965859615, 63568713, 412554668, 904461130, 900830275, 538142897, 414435579, 296086894, 724413056, 847270466, 451345178, 168047566, 707460687, 700139744, 398053616, 698242895, 632060683, 773329472, 20256878, 738153030, 709872760, 632143852, 804318652, 726881841, 649343161, 670782123, 602970218, 894153292, 752075479, 240568642, 901492159, 528033037, 726092727, 155504798, 907522341, 445381433, 765135778, 242071005, 978456664, 398152014, 972229208, 355116419, 791531867, 919965654, 197179161, 701487492, 616349210, 946812356, 113409012, 935617306, 932775029, 413493555, 542253367, 329630509, 414213587, 590686844, 498701498, 482581243, 879796186, 509898550, 265434616, 150086378, 647598608, 605425847, 56409514, 411728619, 910997384, 986492389, 40978433, 58342601, 86110400, 594005270, 974106692, 102488980, 75856359, 727994018, 57153366, 512172835, 561529982, 828388304, 163858954, 277153970, 194694515, 170439850, 175175179, 859179243, 967503743, 631868473, 471443621, 481137510, 53172701, 166130971, 840428282, 179736189, 556608199, 495330092, 752256246, 911633835, 136157488, 514882791, 17190155, 964527409, 303007339, 568605159, 314643341, 453255105, 591070130, 651077901, 650567954, 753339531, 776103401, 508376680, 1920537, 30312305, 124122024, 299381308, 632400312, 4982442, 701240069, 147472313, 334797788, 62793431, 591930372, 753081027, 718751344, 599470451, 883078652, 265070486, 588439416, 784096474, 305994828, 999822778, 745461861, 489321298, 192566946, 64508589, 817910206, 326742631, 333797486, 231511297, 414046517, 995605756, 551441490, 105854519, 706780101, 660909677, 184146659, 814422728, 992046954, 454707583, 828694591, 398731091, 334367482, 390086848, 655657262, 687963274, 670998735, 681555168, 276842026, 16986973, 566834182, 819738100, 758955043, 181519234, 893731527, 90580289, 86373090, 44214070, 272326979, 278948562, 121311083, 840445600, 953123005, 515826697, 881359712, 761797808, 51221023, 332681581, 15911045, 364938440, 332317906, 781778208, 977628000, 873229580, 663127461, 468162496, 487822888, 669671716, 505743076, 695503866, 310230516, 274096208, 502578561, 290932695, 184769454, 930003822, 473950007, 355877397, 1757076, 954305951, 15789664, 318599999, 324332374, 593360158, 218355334, 208378581, 348600530, 358075406, 894395692, 952807678, 519720888, 633228875, 755000691, 58446159, 114391456, 326302931, 986591671, 936518004, 641262333, 741626036, 133106091, 634667700, 174345352, 667722820, 675554589, 960786264, 246147579, 556030855, 411350930, 383177586, 284949798, 298033127, 580745258, 328684334, 742420825, 588909705, 807847344, 922959131, 44030082, 964046922, 2193424, 188044837, 50394972, 742896059, 941606460, 335282628, 279888916, 975485362, 429233363, 402906177, 895887501, 153196075, 533531026, 106201021, 229270729, 54946534, 924026182, 385416942, 175559801, 149607416, 552902046, 744968966, 145222242, 644879759, 510746317, 449500485, 340957612, 38885003, 887472557, 122206854, 256602494, 79686669, 466831179, 771572762, 706364266, 124624210, 602803214, 979561990, 842748399, 36141397, 247638223, 165671540, 572586785, 93949907, 723593244, 484250657, 738664178, 443734705, 325339855, 294598588, 896502690, 314342868, 27069395, 204017095, 293824, 969953939, 554048927, 223519315, 190938951, 839034620, 574862998, 802539004, 559777050, 654931932, 855525136, 661853822, 494058556, 783969270, 136517165, 433365624, 943142596, 881260973, 727341, 463659830, 453038603, 302673836, 803399794, 39966683, 856101199, 49977577, 993011813, 515637276, 833630145, 282449150, 756598217, 531301783, 53942831, 408607913, 698058155, 214794558, 843965911, 876282116, 229470120, 408210857, 174031831, 145156133, 807361571, 330447312, 8605756, 185169557, 990326947, 378017075, 518183167, 731470524, 971045862, 237954793, 709397205, 780104285, 607475606, 428428602, 604920496, 277656942, 863371096, 308279810, 491436495, 495893890, 263843670, 342838114, 560219380, 209682957, 432632911, 449175456, 176418302, 641645133, 591552697, 598421689, 106590632, 151401684, 102459556, 888061572, 163139035, 442004920, 736113394, 75721040, 852964437, 141530035, 524890056, 166622994, 68377110, 575823613, 664371842, 394466301, 497331680, 676646216, 414426085, 173961656, 945349538, 533456984, 171360894, 898833502, 753913374, 221208457, 431399664, 247577197, 158682619, 377079725, 669839932, 594381424, 72388812, 697812973, 117625486, 227900701, 616242364, 445602490, 857149515, 276572172, 147559157, 852452103, 414228975, 145661045, 520291278, 220123441, 8474369, 859847243, 644707830, 365983411, 694083409, 140233901, 1703976, 297738159, 550792067, 370894600, 721374266, 644004155, 55769433, 754380864, 121123185, 165325918, 244642327, 132244333, 695354880, 598004748, 128338628, 129398067, 417846885, 871400644, 441762523, 93571555, 271023545, 815907299, 402220567, 803195476, 977391337, 24246994, 85867963, 424531123, 251908398, 830213750, 629957894, 589516225, 240891250, 191879405, 487518379, 224706156, 65374175, 563972762, 168428668, 44623469, 734168090, 881504290, 164601467, 644795727, 333806811, 222395543, 840098758, 961984800, 907931261, 904085122, 245834743, 493498924, 163911749, 335919548, 281001420, 540194890, 151091538, 164337766, 174717383, 772158619, 694349070, 493573277, 913785007, 885980013, 664556505, 972466553, 2837253, 748279838, 769920665, 979661627, 863548641, 767748267, 505177644, 547936242, 614730310, 724587320, 723044897, 745777480, 324065826, 138268123, 614790528, 879232782, 110256047, 330234695, 903123024, 750554629, 598830955, 998602614, 463612908, 6594568, 340237443, 953985911, 356977473, 828036537, 238889546, 267818865, 568902925, 653189204, 729291666, 61727186, 671050097, 181855545, 368283330, 123957967, 222968571, 668644630, 458108711, 964543092, 772240045, 787417949, 949587017, 419773003, 825834401, 841662756, 712272013, 221006020, 923345697, 757268320, 569864556, 87044218, 982986132, 322353483, 400762295, 54059316, 555816190, 342563512, 686754020, 386459531, 146853281, 786013568, 7264888, 417612216, 273646380, 560460398, 80669526, 896825814, 440826335, 424124132, 295322769, 29134467, 993410807, 924462362, 652508218, 281366539, 832909549, 521787508, 469241500, 554124145, 679628184, 18097053, 657296603, 995834926, 728466903, 707165549, 963356341, 430644486, 936003447, 597457398, 434922402, 102729801, 448735572, 677005207, 372518453, 332548368, 555837549, 510186580, 943073884, 88805188, 79833605, 945956666, 562718198, 107847539, 679577823, 160754374, 744668487, 994207997, 145514502, 891273147, 687608119, 491380244, 211975630, 172440742, 547203268, 682643165, 356772320, 514470979, 471535887, 578176987, 945924637, 451796553, 383974950, 292672983, 525258597, 495972, 864856099, 689782690, 662817254, 215878519, 877386598, 865624900, 427749180, 258233068, 159723477, 10103164, 291595646, 883781035, 712558095, 378528318, 139002769, 399904434, 611301675, 92137669, 118186720, 474074055, 662648926, 71895120, 454662493, 4297548, 705448702, 909405393, 655665715, 63184168, 3384075, 227511771, 186367013, 885447368, 745268761, 369548680, 552583347, 996637300, 912366168, 30797017, 281469707, 622287420, 288525594, 276022047, 999171754, 853133787, 880816018, 268572063, 747128738, 336352465, 342371069, 354364134, 621582109, 364998052, 864553736, 34607824, 277324042, 923175039, 690458425, 70519068, 281895146, 31420383, 983415693, 136250034, 345316469, 699368095, 478412467, 577569706, 160437926, 549054225, 521873413, 805394308, 395330319, 187099953, 981758999, 211692263, 727924621, 511522601, 324680274, 767295566, 618927834, 54660901, 773752696, 820056339, 655004725, 580512590, 116334270, 649405116, 742566991, 824151673, 687923877, 497218612, 191576445, 982972503, 664310059, 465295568, 215552454, 662854503, 909027919, 104380915, 996998653, 282037863, 474477206, 513963832, 685467790, 572934050, 110414930, 890370753, 32645928, 633003663, 339812736, 962257585, 298454749, 61675608, 27020346, 264222600, 816150692, 501401086, 497442151, 283783280, 321277858, 756669808, 200854946, 742410874, 243788741, 192709368, 495348988, 789071778, 655983072, 784261313, 240148171, 717191196, 22089376, 478321694, 637706809, 829675822, 489607509, 973820701, 269565017, 616773197, 855797765, 929048487, 409702267, 286824016, 213679687, 25203231, 840850092, 766508414, 432459652, 286213607, 779935173, 691601410, 14181201, 191626883, 513546164, 884008318, 357472363, 228008851, 396364072, 901610779, 452264846, 321252209, 244736360, 530609939, 740645440, 994397707, 399598167, 446822698, 703206232, 383692319, 320726852, 927462802, 911023096, 657809126, 816693568, 336727199, 409239462, 755158033, 781372057, 534016523, 296235627, 918891691, 937777558, 904276926, 693762875, 689021171, 327479373, 53971446, 187477982, 703662528, 611022098, 731198243, 449383115, 104578280, 783411158, 856733721, 630943725, 192527239, 952421308, 799530980, 274786917, 61083973, 228999277, 670309282, 265410878, 747580765, 433046294, 369622350, 322630536, 412077607, 930977240, 151304138, 798826188, 128347755, 595492329, 763408588, 257219490, 904490922, 24486375, 882292321, 466894141, 451486330, 520880331, 92162305, 178220396, 141771829, 89730386, 358066806, 513863190, 81320443, 907314220, 961252552, 405046085, 938133196, 465242476, 159492798, 568287907, 173274896, 474895270, 454489988, 755474111, 928009294, 456597269, 423944009, 751226483, 627023767, 717947810, 783684376, 317647279, 805351953, 476305057, 717694553, 882919481, 283912465, 872682086, 93221568, 515116462, 256175072, 975639368, 82617117, 378497040, 655631924, 965671001, 144203990, 335806548, 123249443, 63527776, 895698405, 475824060, 567072038, 137265268, 963292706, 954381209, 412235551, 924156489, 887427162, 429487777, 285461420, 966086908, 118949581, 764870510, 354131231, 220523234, 423666836, 925511091, 753121596, 537985462, 566409553, 83219156, 716410956, 867303855, 119720943, 740517300, 965631507, 87314176, 898006594, 353457659, 885602443, 546666607, 406784653, 607023021, 225759096, 766818089, 382042897, 27911841, 242567531, 466745053, 809815655, 563351152, 388634560, 283452896, 436215114, 998779925, 503849577, 889905836, 74792420, 348324872, 260036603, 272896830, 774114600, 993939017, 477096229, 4571903, 403478529, 240618528, 137505206, 982839659, 312070716, 79083630, 896806202, 976677543, 972061960, 468936937, 470937927, 68786537, 279944694, 630964049, 494435874, 593914949, 498599671, 246297475, 856414646, 816052135, 746287055, 595301204, 253067170, 631570131, 88354447, 399833966, 594553510, 595260339, 374993879, 781557343, 511859884, 441366632, 93073704, 137331906, 248481703, 876919383, 680831905, 685420679, 694225791, 552923193, 305654094, 249088554, 283043404, 1829461, 102032157, 655353847, 755349826, 903198308, 804676156, 663773444, 324907232, 98370580, 588790739, 242302195, 424330059, 450593272, 539570845, 492981651, 834325505, 76492147, 491706997, 506687412, 429904230, 271979021, 912518941, 180002410, 796140037, 395549543, 753361607, 69970501, 896358935, 390491291, 78514376, 102749161, 963474262, 906786869, 809607389, 288750244, 4763112, 328199486, 321187208, 733808562, 194278088, 294280843, 613391164, 170969601, 810861867, 754209026, 473001065, 122034577, 327865585, 704187363, 731816444, 276829111, 302045167, 4258026, 902628244, 637632700, 104523681, 641484220, 721628925, 144465843, 368643631, 577826546, 992813567, 360101710, 168981831, 202163772, 978933917, 790750915, 538963699, 43175445, 447898100, 652517958, 233681607, 758402119, 766640537, 210237060, 448079510, 462881991, 961953062, 187873909, 227002597, 204633350, 814734284, 800941761, 390894391, 735575862, 340865821, 144515773, 306790328, 364147752, 440368672, 285275969, 314148011, 705111438, 67041695, 404431235, 296078973, 948220341, 290929031, 548178605, 951791705, 464091181, 210280341, 722177841, 215876183, 600144803, 968105037, 786607197, 381378578, 611466579, 741125853, 455002490, 320037575, 682443216, 531262925, 294990837, 837085734, 831520967, 468109005, 591366098, 191468757, 510325270, 254459741, 464304441, 172157946, 398046780, 21789531, 969066479, 966254718, 492241651, 409912969, 252278845, 504894846, 149217617, 426363669, 958743437, 98313352, 619178559, 779813942, 558458641, 867096688, 626144827, 650261950, 58565310, 357070252, 610585475, 735259624, 469065990, 710378770, 702559714, 99855570, 440032901, 840425460, 830449261, 502437736, 786691159, 631879084, 697806841, 292321011, 285504082, 174652637, 440735492, 153812341, 126217055, 523074597, 1939399, 335938334, 77490048, 688511693, 878241750, 436364360, 158284717, 948399327, 219411648, 765028984, 953229156, 450920384, 561156589, 102055474, 646043567, 536617556, 860081847, 807809969, 313899023, 330760167, 242632744, 699317595, 764375655, 625898779, 14509813, 577109005, 533342299, 609159717, 364260842, 990476209, 855231256, 576345396, 631002959, 634637126, 515721722, 812113592, 891004162, 608994744, 705599258, 461345009, 323913637, 104898158, 557844424, 842984143, 150280138, 240954612, 324358858, 473889492, 167267135, 279602006, 928627890, 402419513, 922528154, 340825907, 538901585, 209112550, 853547786, 468510174, 833752441, 40553589, 260300690, 308760197, 906565955, 319336036, 344754081, 402884015, 52026367, 298823191, 506566440, 247659199, 569347482, 103211596, 103292388, 81781317, 853742747, 332000097, 238416562, 39144145, 340241277, 210786992, 694594791, 492692865, 285278942, 920654010, 110638523, 370636141, 674639592, 266986737, 760553647, 973088879, 926204966, 883060534, 582113496, 822338145, 908872596, 602263643, 267949694, 351252702, 321913605, 804649491, 111681668, 391789730, 330727049, 315894211, 539563659, 281329101, 946789781, 297945487, 858114615, 110271640, 766951459, 993808758, 558864358, 759125097, 28697537, 850797765, 591574361, 586311642, 32946649, 570690070, 106361774, 295140262, 138984288, 457070784, 873265579, 996796021, 267649769, 977624140, 832326537, 48593898, 626322616, 30682, 229534577, 868077107, 164594713, 320166522, 787429613, 600337871, 543940858, 376790872, 189771573, 592194684, 727201300, 435358013, 474134542, 828584635, 910555817, 624842058, 254089594, 593447829, 199428764, 516443797, 655747144, 123506143, 554408357, 909441916, 958233099, 44826880, 859100032, 97302379, 260896802, 643868330, 71644299, 302279695, 504360550, 743419894, 856381348, 533198547, 65950391, 507282365, 574592116, 450124595, 316633971, 795162297, 643067152, 556768317, 345468557, 132021678, 932451456, 454930630, 259159020, 641514802, 359622408, 323314339, 828466393, 747493150, 507148266, 846782792, 848527690, 563415107, 870390910, 388604845, 546880732, 282167810, 15107628, 535963319, 859771524, 369293647, 753599875, 909124325, 121018345, 857807491, 646454571, 16591420, 765389109, 541515196, 547347374, 352352252, 196119145, 690509199, 315258206, 6079642, 288110182, 33436360, 868179442, 945435424, 646593275, 554216338, 416866979, 983293539, 268956588, 427441435, 866990355, 487785268, 569488934, 149122000, 794764755, 308133897, 805384514, 393278440, 135432050, 119317818, 918493986, 436810316, 122829337, 867723707, 705903044, 405684431, 522329249, 754278800, 302947746, 565230529, 407693939, 678002598, 17400594, 225821562, 933091741, 398910101, 400234795, 361714240, 102242964, 426367043, 480451497, 544735801, 346581089, 859002007, 894187752, 247883326, 243546208, 761725216, 17915241, 218093092, 408676837, 499950771, 15501624, 628857849, 153999794, 469711017, 480772625, 552316693, 621872102, 335333820, 112822796, 262054742, 278581289, 650845255, 925969854, 687286276, 272822533, 720331742, 405752882, 400005355, 28738824, 750724601, 967199721, 823039024, 789985658, 556715088, 877184306, 560374953, 712582142, 266613813, 460818803, 597875383, 602978525, 455417983, 497273813, 481480285, 262749088, 252714093, 272963124, 462827582, 65652244, 45004088, 545601116, 697260166, 221135030, 929920691, 574367035, 563562282, 818643681, 58875489, 395080876, 217619571, 587477824, 362805161, 99610714, 211296560, 576908736, 542239982, 65063920, 653126939, 340106832, 260356005, 224827498, 764660420, 903892871, 97064079, 552362175, 888742816, 959724223, 777659997, 953644972, 68810744, 72525239, 73552999, 635134685, 359438131, 459531949, 949868602, 519682424, 363594324, 972535093, 631386724, 271567696, 999248083, 1926202, 94140507, 106526953, 919484822, 689075670, 723284852, 714364734, 170023230, 762992795, 844284486, 527217857, 697840735, 471174302, 408776936, 331706233, 287399134, 6539362, 192751255, 337259134, 165810953, 632911856, 642632955, 281550038, 510277331, 240631219, 228098714, 330472945, 105822289, 139285032, 12800135, 803498222, 750458337, 982281925, 685303077, 236603470, 775327174, 385297524, 996139554, 946312339, 46412125, 635751145, 137260359, 58464390, 333154086, 803543126, 344838851, 936992345, 989306706, 133634736, 291674778, 16418504, 339927331, 645337902, 389535507, 677422429, 225177299, 405489690, 410646427, 551030135, 593597676, 293017188, 290577426, 168769192, 718536121, 410147385, 236572727, 502694188, 583625129, 440634290, 673838196, 202316940, 483893992, 580504817, 507123594, 950257154, 562602883, 789764063, 529330779, 304534682, 843022499, 530129473, 643029022, 270385847, 643176063, 102808302, 962212541, 846614444, 867357541, 965000681, 676264748, 228619347, 152346518, 342405492, 297599831, 769466833, 639842487, 591081501, 820783661, 358930066, 744903576, 49251677, 209466722, 78208322, 89260254, 194576817, 984874814, 440752870, 543813821, 83512994, 999351451, 80263744, 861118604, 43983607, 770005559, 891705069, 652229716, 411606022, 219905559, 494503698, 755092009, 403357319, 945912722, 136798759, 540179309, 154099636, 713755829, 668720867, 469815464, 913903031, 343706362, 807157470, 58711073, 216188022, 495363945, 567373432, 449633165, 4922534, 828349638, 523464578, 948869302, 982686119, 264228438, 671033137, 653688600, 993030141, 462072149, 820620115, 27965661, 804960385, 842717908, 489528002, 326833031, 496223803, 86484537, 708479943, 41357695, 713661045, 435753387, 766580678, 153102298, 762026052, 308023164, 175546496, 216133816, 993635723, 487656590, 289008816, 853031144, 571246707, 156635766, 547270343, 514351471, 649756835, 238519676, 944644754, 844740884, 316446665, 240348726, 491080396, 446421148, 407921219, 110108534, 378177172, 422565746, 430491176, 453795832, 598049738, 570828998, 220796708, 831111815, 810272397, 432424680, 769705590, 222120712, 684424194, 373088613, 359537932, 937630979, 26152823, 670454285, 574531817, 771139355, 61973041, 302030001, 391483696, 10082251, 537642952, 889040964, 216452150, 120021630, 762334534, 930489851, 194341810, 862702576, 928739933, 960934594, 386284063, 406999985, 150034127, 167683738, 333184172, 209367726, 649679943, 676716126, 273865169, 240496025, 430684936, 157382171, 335672554, 428932216, 234587442, 448899685, 190579050, 367278972, 952753644, 321498302, 389968603, 692187240, 236856678, 192416466, 89977048, 770539746, 414640043, 7651233, 996236029, 940436189, 753798979, 643420377, 650920912, 727125495, 869403597, 821160203, 537605773, 239280905, 616771774, 818316851, 930690008, 770207829, 418341235, 290366617, 115563595, 527554460, 190809946, 379832961, 321980979, 806187852, 797800906, 333582309, 41416332, 824424386, 602389548, 224684537, 525197717, 584981972, 859395306, 15287887, 273847338, 74052455, 544196577, 716392081, 459426152, 830163640, 403683982, 999057672, 731318298, 198239613, 377529705, 755198655, 814059242, 426442194, 679515494, 505160386, 502535502, 508124479, 78256809, 409794132, 324171778, 259305087, 419327455, 950641350, 254114593, 147858530, 54048054, 356119022, 404836207, 508999759, 223317277, 312471929, 885604868, 829729928, 699879697, 608175743, 846023879, 630241070, 523643655, 736079230, 114534447, 662039184, 536522176, 82737532, 416069352, 311254533, 731005871, 679603697, 663139146, 339110778, 861064781, 757720217, 40948326, 767078038, 391166721, 161356339, 189305693, 23473227, 363609073, 74157856, 212461416, 65979204, 944100088, 533928920, 44439488, 115776887, 380174368, 256834026, 356090119, 963326087, 736851091, 670761535, 608725063, 937453827, 451628462, 486510224, 286611978, 531367161, 533355834, 91366653, 53229168, 195351796, 512147903, 622982041, 242064776, 669807856, 1842058, 732151225, 295366995, 112792246, 934962980, 480747754, 995825102, 113742270, 617383359, 521090969, 836105843, 688915823, 344954502, 977594652, 767442323, 837341883, 501947426, 891631115, 186513601, 217003928, 724307725, 9594130, 481935566, 890173314, 101022772, 846048524, 917135027, 669296615, 146638242, 194159334, 110337315, 885147311, 434475818, 661566808, 63731597, 851833655, 744463629, 853586046, 717285163, 641398120, 660630199, 816654125, 879688101, 198916017, 598048038, 799558807, 193628139, 82561518, 82084793, 966822259, 233423536, 488873351, 380094440, 79682253, 680954053, 666463842, 75772857, 561097420, 351575976, 885366388, 86203520, 214947048, 713670325, 250389627, 145574289, 198347301, 239373088, 421309372, 533785051, 521034766, 813451900, 585478457, 987612922, 876395949, 35609269, 702624402, 547621708, 779228675, 292752202, 363686501, 867435889, 607166262, 174893599, 14361811, 21292373, 754699002, 927097091, 74757099, 492213500, 135451460, 699548286, 601410998, 989477874, 89264375, 61430685, 205604189, 866548288, 87067383, 336585975, 915874898, 588262817, 793848568, 972201323, 226706548, 505523746, 231874291, 400997044, 146498133, 519337751, 922421907, 167799115, 229790349, 385481043, 999479041, 255049018, 82002084, 697291880, 872499055, 127870952, 720385598, 518638045, 440098373, 79341506, 414614113, 562908771, 929654996, 535833227, 477451313, 923301878, 660394817, 532269155, 395844420, 998975676, 905487786, 9454149, 728324835, 785648547, 992810002, 927872329, 843025175, 618705654, 550938283, 163697005, 407807862, 508115313, 123746151, 969497119, 138144706, 686558529, 647419409, 681582313, 867460124, 277598895, 781744166, 356802676, 850426812, 127694659, 933649636, 19493818, 190454335, 855065303, 927336480, 109917784, 373392833, 739604552, 411008120, 545229146, 585595132, 318679006, 887140942, 48777753, 586289486, 826244632, 721833380, 478797049, 225303004, 437966191, 604953847, 998803715, 592091234, 306832817, 348022658, 976857764, 74503300, 65902651, 264665160, 144389282, 299296552, 629876465, 62848791, 957129774, 587921600, 564517438, 918335125, 332322696, 251709640, 784476034, 638749527, 390896136, 938170937, 993389178, 870992343, 281233335, 770275075, 500363634, 43986245, 995384522, 485669794, 3523325, 847340895, 904328385, 888175145, 204890984, 500395570, 907081800, 214686670, 104852636, 498305738, 970937539, 191973376, 812026917, 167313221, 507722266, 77805464, 146216574, 18143035, 197424825, 281617576, 910394426, 597923990, 138288084, 953536299, 44297535, 201162475, 600043723, 188703901, 358976920, 948697073, 823611746, 636711998, 474881126, 830108038, 748867766, 379609689, 816623357, 479025384, 929169406, 507558120, 605723564, 642158493, 950119071, 249858662, 537697483, 369069725, 575130274, 12365513, 201431001, 942374848, 234276391, 380884920, 122714064, 843829589, 931052258, 749497894, 926526749, 462582069, 334298556, 236275801, 336777665, 868211976, 549042080, 179221589, 17385055, 586198247, 595824024, 64727787, 910465941, 763778966, 475711901, 897533054, 99173013, 22474517, 741583048, 351305465, 886060953, 21062318, 83212314, 542816007, 551216526, 972651206, 536730510, 246601011, 472106135, 935320877, 300739979, 317632018, 993918333, 98757780, 698667827, 682246720, 520242575, 638608158, 536097112, 252478737, 437467513, 835419858, 772940950, 693030446, 490042637, 563371806, 936549678, 845905762, 911544139, 883887556, 743737661, 810733158, 64143094, 655718393, 415159079, 946801425, 985280004, 554759600, 43806358, 356298514, 635502874, 770731635, 125875950, 507657310, 878160072, 263180927, 176152857, 233996725, 961916103, 586995794, 823108935, 751674599, 613541989, 327537073, 612473807, 267838973, 616178035, 154469147, 844804056, 825204661, 84195593, 35606347, 859331989, 164744119, 131557920, 135547974, 714916334, 757974163, 468261260, 667970546, 132249304, 946669731, 588827079, 452530827, 543295848, 771893074, 433427711, 285494107, 60244607, 383925020, 297552597, 784774076, 886890580, 925388703, 678498169, 528090148, 508577320, 171763147, 229662328, 72323578, 659442414, 929421848, 887901830, 862693477, 691330749, 778141820, 570106681, 554187449, 364767436, 825526208, 660431110, 976408434, 84442097, 886367173, 624968225, 266720132, 400291729, 186630426, 77053759, 363725638, 195790797, 160983407, 704386244, 756038256, 295964050, 832996139, 648498539, 677131343, 212662518, 5435040, 610739726, 819470166, 690706442, 560143800, 106907243, 218729509, 232563862, 886914915, 44657466, 718958311, 848490382, 304301366, 302722444, 495952207, 508381504, 849165653, 672760064, 101956648, 666269137, 366311726, 690128565, 962026475, 846156817, 558849410, 981435065, 377895726, 192106495, 786691624, 234456803, 855137058, 480882988, 437677607, 399243386, 598840838, 406683409, 935366688, 179495542, 269662170, 186739028, 265327333, 919090915, 128901975, 978174206, 193012718, 153037131, 495160415, 43201033, 833626178, 680169799, 960547131, 730747877, 643755694, 283805891, 126492523, 614874743, 77524225, 986786419, 313629465, 641621460, 446925484, 395411545, 436220543, 673031817, 738564418, 214854594, 208857712, 624045701, 771587615, 780563366, 305511691, 450393449, 308464653, 66139247, 611118837, 732806164, 23020247, 583297408, 861840412, 592753855, 216578136, 222932529, 552600902, 22897951, 267938867, 554966945, 552461036, 642380559, 471127499, 292249532, 608278895, 28346782, 198489944, 582153689, 415779911, 397334343, 879912668, 136888292, 967943779, 100588048, 132749410, 559970791, 804945341, 466189408, 482793749, 925621160, 100638947, 790395293, 844784738, 18938367, 505770424, 557618544, 450328425, 716370241, 759578751, 185060038, 858843534, 588718217, 833784128, 934505682, 563249218, 660061059, 221514780, 951311511, 186556200, 621695437, 216781554, 405244817, 944116808, 299734376, 432840875, 114107397, 534899554, 445531166, 663365014, 764791780, 637511538, 309461378, 811172934, 385146550, 603517425, 446719863, 536526332, 26936081, 624440756, 170514963, 490441111, 396920652, 899199415, 79726687, 409980840, 321339006, 621382155, 521703791, 255782089, 784093680, 628678392, 460105115, 93505233, 966328267, 27646906, 439124206, 473112109, 326534260, 913178217, 865141730, 360479855, 636205343, 351727965, 789264657, 720852343, 227367540, 235818264, 310594737, 163875045, 537505565, 985081734, 402954812, 209513235, 477234386, 525506214, 373375674, 720462381, 278125256, 594881922, 445814130, 930808648, 597523494, 97433514, 37758340, 75699721, 321326040, 243556641, 838984487, 961929914, 303673826, 913620765, 365634463, 91060276, 239644516, 370975564, 756038955, 920576342, 701768420, 538888719, 198999452, 127999938, 543051959, 72485035, 609785681, 684196147, 568085698, 756152471, 941696713, 899167339, 996600008, 297432768, 390996490, 434039576, 493234670, 815072625, 500860235, 814230875, 49050519, 564090359, 564989784, 524587686, 834160154, 181278955, 361733943, 25240326, 620297821, 573997685, 374851093, 934233526, 72932044, 135092903, 102317600, 651368406, 485374549, 653528366, 398215751, 186449357, 459702482, 865908436, 92549021, 491662656, 48928669, 501148705, 158864124, 453473840, 374314242, 780140926, 318062978, 78376616, 653865863, 626392436, 285999991, 151740466, 623012035, 578414595, 393481124, 200868360, 510663605, 891762204, 150453887, 153953526, 318674332, 381561446, 354658449, 935671760, 624088299, 841780027, 461177833, 670719048, 32324209, 110913879, 388388333, 131766961, 283631158, 750922951, 192329580, 111828316, 691670115, 407815310, 595778304, 923438144, 804291348, 422161066, 446155834, 484846725, 608764685, 423084102, 42224088, 832596578, 179541762, 920949901, 360875266, 334472985, 475794929, 565088206, 671495431, 953176169, 944257022, 751155113, 890485843, 513860593, 101817939, 624194008, 650243669, 683629264, 166158272, 219740081, 45160365, 913269060, 136502109, 923422673, 242607717, 89916102, 939585369, 404927235, 958767160, 669214087, 781337246, 397612136, 859960288, 322207044, 249677846, 965907037, 170864039, 25580278, 744820638, 92693075, 746856998, 243759507, 619853604, 649855106, 83735990, 458782681, 543361942, 356471142, 364492570, 513911388, 466559729, 817202380, 480331372, 300133043, 481297218, 845399338, 968735243, 55035602, 853827712, 822201621, 24417472, 283382113, 50103600, 60396748, 296917335, 81311798, 663744339, 749949069, 393852532, 817523409, 708660894, 712663536, 998271707, 698425109, 416332816, 39839334, 870825750, 38201719, 363379677, 40826354, 415302865, 213480118, 53867689, 970391010, 603590635, 303606292, 204492643, 844445803, 426463212, 416860035, 892348210, 465282965, 867889524, 607850229, 123363915, 660111734, 195359828, 960123821, 11487944, 772718316, 356992665, 471312742, 623971450, 768075985, 513878156, 276069183, 236706316, 334057788, 662262649, 842470166, 180244473, 564082472, 282947792, 185139792, 808193330, 191130238, 414128397, 671986045, 934364513, 296597645, 637446001, 800149461, 401471944, 363058679, 300972070, 28941575, 813411979, 141484010, 53981469, 45470744, 732350664, 534482478, 926860160, 284590844, 216203730, 197748753, 490093034, 388874155, 772706738, 549536499, 219190630, 375425369, 435278662, 372696395, 461672941, 414217425, 63850793, 926250526, 298659634, 750371826, 149598366, 289438975, 582545303, 441207555, 766200995, 661247329, 985260140, 124169928, 513331820, 907779974, 698846348, 391351382, 596710059, 574956073, 60063045, 309570233, 787818214, 861566747, 863603128, 770821740, 636968826, 695689009, 880735200, 772817380, 723344897, 966506260, 712626242, 390772949, 249061302, 796577736, 551797226, 514680345, 410296323, 616062160, 534357474, 996593858, 110285463, 628757546, 82836762, 291250627, 22237963, 85302286, 333944181, 783537939, 311625523, 423842654, 21949383, 83223633, 210236693, 510007796, 582553397, 829811567, 672078306, 693137969, 149337917, 273349058, 9042752, 194922448, 952833580, 660643536, 871539256, 418505561, 904637135, 695467256, 421370966, 348359539, 956634586, 202903506, 879393412, 416503050, 232332388, 423215715, 211718966, 440527757, 379074424, 159096447, 366386608, 450785981, 398036563, 107900828, 877696556, 858369534, 544502572, 169357924, 197623635, 589459192, 406002599, 58069304, 423891915, 391984819, 321562799, 210296505, 34613729, 128632602, 775486942, 733941858, 718609480, 990702883, 673442775, 810971393, 439515013, 528271260, 43337050, 702804698, 373491545, 49354295, 673511658, 266053659, 499396197, 826386204, 326901795, 433068797, 260343360, 15667745, 910845320, 51725606, 626449793, 447348824, 641357612, 689795052, 233139457, 989044871, 847609005, 139692417, 215959589, 45203911, 265775574, 696975898, 246860866, 713623581, 146181986, 203239232, 454871740, 126993667, 994346109, 311512223, 775758866, 657171900, 980725534, 254311235, 258709968, 361397276, 344916023, 897407692, 126366136, 212383031, 212019559, 417372429, 998148581, 956325150, 264253948, 33590669, 82065470, 949951218, 463432787, 99232198, 633191748, 293734637, 185445809, 3103559, 89587992, 327624147, 138122094, 192040941, 861824826, 812629735, 458477237, 672615573, 762021832, 431366363, 31284777, 69146135, 672811501, 918313936, 779198338, 545138351, 763066793, 255463672, 941222959, 594938457, 815777044, 140362127, 298587235, 494419794, 845554532, 882910034, 742907117, 981981559, 991316822, 426437342, 748358447, 93046716, 862466640, 569870698, 338416545, 123042571, 931242974, 322828411, 435800591, 769271501, 954167756, 576919801, 32816130, 562507094, 325807552, 361199762, 236402907, 480684255, 63803638, 91570587, 321794455, 219912775, 546381381, 968601153, 825945445, 960501653, 30961976, 443424480, 503249034, 631220243, 14877224, 588796984, 163490085, 757900595, 280931792, 29613647, 620795224, 336021228, 880665765, 880595302, 392785864, 516224144, 678109464, 730830643, 592077431, 935118132, 147779397, 239099719, 991993869, 5566994, 837322667, 960082930, 615484355, 808188713, 523126951, 601528856, 866164816, 584567895, 639192649, 449200963, 185513441, 115714881, 699999015, 746081519, 407845211, 73155022, 730367008, 464948993, 930881024, 714992299, 827303585, 201922696, 473034251, 639528218, 88305752, 549788994, 343099806, 492796819, 856935974, 890714317, 24669591, 363251631, 330641852, 589249080, 167388518, 442439455, 573260690, 172688770, 929544250, 885228308, 273014389, 608634169, 159777778, 232507443, 200675087, 84758459, 623264759, 918650063, 659928678, 67078261, 762607698, 892633084, 390258166, 112393827, 336079227, 937966593, 720717893, 686186838, 798727670, 512118277, 320132154, 194535183, 185026542, 36528515, 930994289, 73671658, 830119997, 858521502, 30064500, 125615356, 199966158, 984589306, 614636082, 849552501, 683583529, 326070411, 526534524, 388438, 277916606, 291724251, 937857866, 735945897, 12858698, 521771965, 826447982, 957516979, 578631835, 676168238, 269599937, 158978567, 663490859, 86759457, 443257668, 491740830, 997561606, 238840899, 764825763, 612991040, 965150277, 190829450, 476998403, 944032172, 743987791, 927867151, 299938865, 968054578, 631526919, 134554335, 67512818, 560803409, 323553725, 925481767, 711872632, 751602163, 665387441, 919594082, 104160907, 603711264, 297938438, 111620226, 537570901, 37444192, 277481701, 531228618, 495816133, 261345947, 918013033, 496403966, 627823303, 349767264, 69028944, 347069920, 930484492, 434838714, 272910752, 848781994, 313522523, 350018074, 824966133, 708210980, 594535339, 388403946, 957875830, 425314093, 692695434, 487477494, 358584202, 70545958, 775588434, 281681888, 313001225, 4533498, 360495839, 37831432, 170565052, 618399464, 813316948, 694968969, 587996048, 307900900, 450634362, 183494389, 274017533, 829001946, 604695686, 352043774, 146859412, 926282213, 712661574, 337011622, 878976981, 384466155, 193990233, 952814838, 319611311, 228170911, 301487624, 8853421, 430831345, 62466636, 340612693, 160119222, 298384783, 35414434, 843948731, 367989409, 209371080, 223421489, 620652596, 398520940, 934861553, 812379356, 933833407, 136012408, 655192815, 611210542, 336054877, 864315849, 140453246, 177332840, 830061373, 660214992, 830401654, 778763938, 481450657, 854578197, 593979065, 39792516, 296739919, 587693305, 983496185, 695375558, 279994777, 651087730, 860688016, 366228093, 878806098, 305541152, 483518518, 73209663, 353434009, 540712244, 739521601, 869126895, 316926783, 914550599, 374967762, 899603722, 472188856, 78940259, 894064492, 280799570, 218974005, 910042175, 384638630, 435878651, 546119109, 120039586, 819205843, 948203448, 816333657, 219575889, 721592157, 877882520, 391529916, 820581968, 553183134, 783866997, 669231175, 904798007, 646098460, 382350081, 720704237, 847180186, 925168715, 29879916, 4431887, 346193399, 23097760, 690750480, 177316265, 746829829, 663919541, 522899626, 935121249, 180173667, 58930754, 436713336, 832002993, 146025400, 778585417, 149031879, 435356924, 306786784, 97034349, 921410063, 981891197, 356722217, 658776890, 15703077, 866939840, 258246305, 740633045, 124342414, 720966046, 541629324, 733506387, 951698654, 610357891, 395423548, 354528554, 983983043, 242712162, 213837026, 734536878, 684017438, 260830998, 555534881, 747994348, 313321187, 373865716, 252230265, 902978935, 205270512, 326978658, 100622611, 179895574, 788511943, 390794075, 174221400, 959191046, 820105048, 890550431, 412009277, 64651320, 182668255, 886553352, 608581155, 135400238, 989885019, 110720307, 828071656, 363940054, 753084082, 879796188, 965518600, 856110929, 585757132, 139051171, 160347765, 699450231, 128411303, 128752426, 318669594, 683596055, 285766661, 818146503, 704968110, 700941026, 386587236, 752563041, 50971206, 640284855, 775053678, 471703759, 320631638, 889225932, 280731535, 564685394, 178250846, 723725998, 431920557, 990493728, 272941303, 739458686, 635796168, 715505825, 154318528, 552196569, 847120680, 721625184, 452892143, 551200595, 169728145, 329181356, 675593987, 742192394, 19519592, 82812300, 248115103, 24525658, 460366825, 128376746, 582910600, 634778504, 9683652, 925576550, 475928090, 818520829, 414674557, 522383243, 54112554, 507671004, 990924787, 380338908, 713204965, 755305068, 608683403, 278728826, 324781077, 65533452, 671482644, 905720671, 881190653, 607700617, 689177397, 452087835, 286710038, 834117958, 702149987, 875591651, 204088187, 851962194, 973154815, 385471058, 794488483, 51417180, 647886346, 89847567, 511585184, 652971140, 472914258, 455273138, 623606477, 640830240, 510807653, 149119949, 270362251, 307095184, 472043219, 590420834, 562834984, 909739653, 758524025, 165236316, 584802916, 249065815, 218024805, 443691470, 350677798, 685892626, 719246088, 93096871, 709390032, 835816224, 203418740, 335662909, 675181865, 977076343, 771792263, 503900795, 71385509, 934096430, 21463226, 772159205, 35285388, 526081419, 611193738, 82097220, 495475524, 945734442, 743945969, 5616715, 647507015, 889886200, 81062391, 142582390, 611805879, 401500402, 4746197, 138883329, 754040776, 489846091, 554793290, 787851159, 992676880, 778852362, 491731911, 49643413, 196655948, 525477536, 135440525, 530102974, 631329059, 370854462, 157306152, 59614579, 273335949, 408185774, 298335123, 653265207, 215927563, 971004105, 165538104, 418918789, 459736069, 815289256, 811174457, 242045926, 748596851, 419981393, 155713991, 63074235, 537282734, 561187049, 21440817, 367182220, 732067241, 693654772, 883262227, 476377599, 610776001, 676081274, 124186975, 28081059, 776142297, 59997980, 725224763, 292739458, 93135471, 853900690, 597216416, 878934917, 832932137, 278674505, 273705894, 306762142, 597070992, 484319513, 242317658, 243427282, 263397648, 411034295, 845490104, 913496588, 691758428, 125733033, 294399672, 284506597, 583235583, 653131637, 622054293, 278877766, 764117601, 433407427, 41127260, 744335657, 216937511, 418012383, 917463992, 411902352, 91293266, 50450081, 791513372, 947339604, 453187911, 845216742, 801001309, 385781788, 217429058, 634567832, 992152772, 55252593, 759510903, 991984836, 843462974, 759662579, 877067605, 948330763, 133040074, 220823858, 376763631, 490361780, 884551121, 46088839, 257805230, 622311837, 535330420, 181202001, 795837694, 660673318, 166116701, 475487672, 559407483, 859351160, 374598427, 757053115, 17576781, 883478760, 459072946, 855662115, 296742152, 256318576, 844052537, 389441445, 231051886, 51606726, 22625896, 614026700, 587140755, 910156819, 661147981, 44720900, 423614780, 814117239, 822133699, 82627777, 378409810, 837628717, 494818267, 402329143, 843985156, 987759904, 154644522, 816790292, 447829122, 605068245, 248056842, 799603577, 22988890, 761870363, 96684875, 105591493, 282219277, 473560777, 780315410, 970108594, 435346684, 536776416, 495377892, 54786963, 257904355, 960286614, 845230058, 198397662, 953930800, 718170800, 306648479, 233112670, 607579206, 837434527, 291271423, 88783872, 365210715, 305292226, 18111312, 339921603, 399368060, 150683871, 327738458, 92069162, 115751882, 859463198, 234121086, 873114379, 423184834, 722608529, 998974865, 428806693, 303615485, 357577658, 327964944, 51434772, 521886661, 886875355, 439053455, 902418057, 383366708, 649881392, 443780156, 326881039, 177029057, 630926335, 754040330, 402412883, 894037300, 920239390, 670525898, 394260814, 530115350, 412265745, 127320361, 525833339, 579469289, 947225292, 972022125, 376794453, 958304109, 904305578, 644531426, 576224579, 881418621, 569203069, 841254735, 370089192, 753365989, 717511672, 777195014, 678861456, 529767444, 282038591, 163520492, 427592046, 487546775, 399487948, 323337114, 806806729, 705921049, 395941260, 616431868, 474036222, 994777233, 311448396, 891699455, 964569870, 53595875, 4014016, 239101724, 487593700, 756542391, 126085342, 337026556, 90048699, 283326396, 94622440, 325104196, 973841375, 303089821, 259740685, 24891314, 243920420, 798539499, 207998466, 110020434, 540287132, 973396020, 824953754, 406236986, 990942032, 138058263, 329206595, 313468554, 516745511, 260998537, 562057174, 750559747, 422840307, 370033683, 47298316, 327374574, 879572400, 971967618, 654088043, 231760481, 865668070, 855238104, 47129608, 546289224, 117558771, 322494499, 18121485, 406116247, 38215824, 311044872, 642043568, 175061113, 222457305, 569593399, 609353990, 468583167, 305517127, 806031935, 842516894, 221872993, 573436030, 462656730, 701667112, 207844070, 276662018, 202716565, 877582246, 798482777, 397104314, 501308736, 616773845, 747225792, 228974617, 965901058, 210499374, 926147243, 338979935, 708169227, 184526333, 512638962, 372612737, 314455349, 911342409, 373782830, 906518424, 737262198, 302742446, 385819679, 514739715, 923361053, 451989515, 715592485, 508547141, 53560868, 330759768, 155344905, 143199220, 281961281, 94268018, 201482214, 408120915, 170437946, 807690455, 308533595, 706309640, 45553020, 318075027, 874395117, 520863664, 975462666, 75780500, 726986616, 662756857, 861485793, 381227396, 853543476, 782754, 770224821, 326377004, 311168469, 770085120, 127798331, 630167848, 473403043, 969278237, 986110696, 621356169, 804823104, 32116242, 18168800, 998511932, 734204914, 527187098, 98226304, 132804692, 512548591, 906530835, 225339304, 834193880, 595268101, 974081242, 28467635, 360946083, 284889982, 85246030, 461628273, 979055968, 139887389, 86097207, 73278773, 568420247, 950277642, 371210119, 241976758, 530662665, 387185299, 713608090, 497412120, 649407654, 387617322, 116101026, 514641617, 543512904, 535467766, 52581617, 668006258, 312329866, 813411015, 527619629, 564065700, 353599699, 609143938, 991778175, 390690061, 940486642, 102203991, 412979453, 300181077, 905552090, 444765110, 896507073, 587101795, 241463837, 40134240, 201212314, 485924095, 187499457, 458330215, 871124788, 329340835, 367393136, 138162740, 265559360, 121929229, 115718047, 521753180, 543576270, 258596048, 573177235, 308585070, 511756151, 458064156, 526313768, 956583525, 918034217, 900956747, 345138766, 142387016, 151927827, 977574846, 502510841, 995066958, 376103608, 969681355, 922771616, 135517164, 351814238, 373592278, 91730353, 730595779, 745945677, 532658200, 89288829, 738546972, 35784370, 743004468, 482324059, 144206837, 67262287, 302988667, 311708374, 647826175, 568653622, 830935593, 859899989, 90258897, 813587947, 394271779, 253440189, 903241272, 645014336, 241349725, 739767450, 710154497, 282622434, 320119791, 958945055, 660624537, 82613661, 809785156, 738682188, 611986711, 768212194, 549472386, 707360654, 199104766, 195735425, 525286395, 772288226, 676513548, 375124473, 398868694, 265407826, 291238967, 7168840, 937876380, 740543061, 826991581, 419946099, 933598791, 285759759, 483705386, 678028754, 659465371, 615444640, 404266705, 308815719, 461770397, 820439643, 780902197, 435790144, 969625645, 796050815, 397371168, 29464602, 364572530, 582771494, 854179208, 364322021, 442753420, 944899734, 850293424, 630915618, 81916609, 597875106, 322124747, 109982763, 778346539, 55709433, 868453061, 952588901, 305466677, 748175802, 672785802, 102513699, 237481498, 311948651, 689319121, 489398288, 551453837, 803459108, 226643553, 961477086, 179714659, 272647232, 998362738, 542119910, 110950537, 106869004, 661003829, 60684105, 750132060, 314469908, 754151400, 556709028, 441416713, 894601852, 800089305, 700546146, 164283266, 907010280, 406193745, 283161488, 998754570, 937881113, 353941581, 382630272, 223586980, 516811060, 2883000, 878422778, 520504330, 878070928, 873917806, 470242959, 724865973, 768536433, 39777277, 253715401, 809031384, 884905050, 994503925, 690085531, 723551594, 699248246, 487272798, 865134670, 553309392, 483098734, 903377019, 801287830, 809903059, 532691461, 244538917, 113129018, 97447463, 60546295, 130920689, 47590156, 321787883, 496187164, 890924416, 505494221, 433522779, 457593549, 822922182, 387957167, 501649250, 123539857, 470979184, 351595300, 349630746, 148243291, 535809410, 743271392, 613303277, 430768721, 115942625, 3045482, 721565347, 49232622, 5601393, 680845483, 853333523, 638928235, 878318219, 493666849, 491375411, 677462154, 637304116, 957152964, 392734547, 986500605, 356095153, 352557334, 828028905, 665069370, 229075427, 764218830, 897328805, 980639115, 678580415, 770674211, 597215015, 732698259, 617410836, 711327824, 17208255, 8329691, 952019665, 949707241, 903124976, 353714552, 871581404, 763316424, 738976936, 55462626, 491651592, 307125498, 130064960, 937002199, 874725493, 373585248, 940446448, 877253636, 39344684, 304565671, 641692934, 887374084, 187139007, 86733682, 197591355, 111216142, 881975907, 414815959, 865858683, 861490156, 507172211, 952111184, 610046311, 373635818, 794556641, 289458391, 177454924, 533749344, 811758624, 160860389, 299077769, 500603728, 4226929, 166326686, 564398271, 996685090, 98313385, 891889641, 359706621, 624739294, 911011874, 414554233, 484113836, 552445325, 114541830, 981508432, 509254103, 938793278, 941460432, 813238630, 976101884, 295839054, 355422755, 332917391, 792752327, 929107350, 689881696, 97502045, 728045229, 287370010, 4536485, 436932626, 521748908, 540648222, 796819348, 329032481, 456817747, 531799486, 861479506, 946266000, 68091475, 44624761, 359335808, 792222879, 659323420, 479656248, 768892712, 178004428, 723927485, 250437489, 819360217, 455264396, 276021672, 399415624, 742153143, 551666664, 124174908, 421268055, 749532567, 65019, 207762598, 545311435, 167577431, 337154033, 655126340, 822680614, 160876409, 592889781, 631148636, 334537810, 513190170, 854989033, 127998653, 709385333, 440855537, 335813755, 130495432, 387834340, 678721269, 557575730, 454282182, 919113789, 688840804, 657140832, 15682261, 15744374, 668053060, 803759509, 366514919, 634198747, 727651488, 585449893, 511077406, 197907064, 908098558, 418070093, 638384418, 307763909, 784445866, 295799667, 417402736, 523704287, 82754881, 259449755, 23824483, 934387734, 58530717, 781593766, 748278720, 976167307, 216123107, 963937327, 15494583, 678929600, 13321289, 550106275, 714607521, 167631755, 926294536, 528801701, 559775602, 128505632, 767682095, 342915564, 83534633, 113320046, 765725708, 959354492, 667055284, 283738190, 267134737, 24064652, 311035093, 278539159, 391734437, 193773864, 875164664, 391130875, 267380589, 874719850, 701910306, 418448872, 516121693, 467255790, 239976488, 666829401, 83314430, 46657944, 648425063, 59540285, 820257313, 231905014, 625777542, 169714065, 459425360, 29710645, 340699480, 941609396, 493088593, 285261275, 121843050, 447209999, 967455739, 394820062, 301394762, 769622169, 487069233, 898256146, 789167169, 742369750, 909946832, 471555490, 684758991, 151873899, 138771974, 594629056, 581207949, 619796243, 119229457, 546370905, 555438233, 302073724, 158988383, 772820457, 324022294, 480540269, 379490427, 298625475, 986581731, 627085550, 505733439, 88589501, 171955541, 207743671, 715599588, 314574011, 194768905, 588059650, 219101285, 959311897, 207538420, 213946236, 790161249, 951543550, 361103257, 66546611, 295979734, 567800564, 489580795, 321468397, 742827226, 607333805, 131591932, 767255417, 535206653, 431444942, 373555747, 93081705, 656352225, 382535564, 199034540, 780968263, 866820835, 831199134, 266201614, 187306957, 154823039, 420589510, 461669418, 24886849, 821612147, 448303250, 178333127, 541079238, 558611099, 327854548, 518089023, 448257548, 826675333, 152856066, 752949396, 487337498, 961610688, 187523584, 233142732, 998010767, 250612241, 293398041, 914072828, 962604704, 811179329, 924468633, 794387297, 955135804, 713108639, 640971108, 768003635, 331779580, 301561675, 194010155, 79325647, 123580153, 15717164, 570508172, 386636885, 328766793, 578365067, 673760713, 351088399, 582312968, 102246354, 813330167, 753733060, 624597903, 957701949, 338234134, 162297851, 299221610, 412307608, 76981375, 257607406, 411393590, 436653725, 231543002, 888564199, 78527658, 456207668, 110159559, 394818932, 823759723, 463348451, 350616241, 269565085, 223917040, 406562037, 166415440, 890137832, 962140012, 308019795, 114997760, 535415304, 106676294, 120545742, 854452048, 502267369, 585714196, 751391703, 386611114, 532528064, 62691564, 196897728, 653240244, 871121100, 866030053, 544249032, 85321387, 432140043, 690530201, 286035957, 707669050, 8252207, 127147370, 207837637, 343558257, 718497670, 911443967, 494364710, 520996916, 738852972, 146648763, 795184357, 586058960, 621257188, 712192808, 596821376, 945100875, 306124643, 183775958, 134590852, 291630289, 329183227, 707478593, 967971501, 232281702, 841203700, 881537944, 780605858, 930550149, 867986963, 910616230, 752931422, 786930100, 896020302, 567669038, 394984356, 846080157, 333257865, 974850294, 146415072, 843576001, 974033983, 658929607, 852254422, 517859113, 885063570, 627246119, 271142076, 431758604, 96085561, 569395084, 302956924, 322226944, 431632931, 759444477, 422516635, 72589192, 611935741, 867236990, 56836745, 909277622, 79336072, 368024029, 64978965, 793574106, 79590880, 760321439, 785656830, 830022134, 918006998, 543240714, 304566929, 448777158, 794435285, 146170112, 853889014, 964388098, 264987455, 553391726, 27309448, 876115454, 706837771, 861573547, 393376701, 765277365, 556054168, 478260689, 505451791, 4343084, 301964753, 789186433, 405236132, 912409817, 558599010, 367269070, 182040182, 880955826, 746797124, 915458278, 340845819, 50721277, 123990867, 256645998, 557347689, 131142465, 343387046, 869761688, 534442163, 633332242, 616938804, 115104486, 371841631, 67264881, 738909987, 87504930, 547413228, 539653634, 254731591, 979041485, 640042427, 824711827, 580608001, 228177802, 98925147, 701480355, 762264196, 807812689, 641842390, 236136802, 677776934, 963409770, 693431124, 52838040, 421685151, 377768604, 739493791, 223819128, 142180757, 293961311, 895300195, 981046157, 782491584, 179536608, 954235260, 847769606, 860781137, 327222969, 19924607, 407040030, 409423075, 183333285, 979281210, 396003512, 347071436, 232469045, 694227615, 625110577, 320046148, 252379812, 670541280, 882212350, 96705953, 32617534, 780046683, 945600088, 684643107, 863459257, 752400600, 888055151, 288667307, 679191485, 514632822, 361029365, 270538172, 569618480, 977479715, 913008269, 724312494, 579005618, 710045878, 220529400, 627837133, 355742074, 240988265, 53109503, 717841720, 73734176, 162258387, 395486622, 53053043, 393844046, 745586, 930001256, 647330777, 36009710, 573856556, 858609561, 191587071, 704965350, 921454613, 991307037, 488500955, 395106246, 171649207, 191632761, 294296729, 735636476, 364222033, 794995909, 372929344, 852201006, 111935520, 12255903, 817933176, 301596657, 118209289, 691390595, 137469728, 37705148, 422444837, 296289991, 442767494, 753948103, 346526490, 300509627, 957819191, 993928886, 418553703, 500500176, 301792018, 968700131, 93648671, 359392089, 593625973, 324056609, 354463202, 622625704, 231705282, 41489695, 467908218, 622749683, 466023001, 778896654, 318711957, 72442305, 433715996, 406064920, 214633238, 423166338, 140534083, 121016501, 959411630, 747571786, 647624625, 300405536, 921486649, 784578829, 538992517, 470526355, 170532657, 211344352, 697000108, 840845822, 265214843, 90040136, 27600943, 932597666, 333574690, 91412612, 260899273, 756328591, 294145045, 634909180, 507557500, 939924917, 313875643, 905966104, 773863875, 325625893, 994042479, 310439416, 866005187, 50731679, 62246566, 684245785, 107998324, 92802810, 817325495, 291834939, 811459392, 326651202, 920215439, 821619835, 904613460, 507191321, 45811584, 271631126, 248383931, 447652475, 349057944, 966096301, 478603921, 50474200, 996597765, 548799844, 303068400, 937129472, 857386476, 634818216, 632504237, 626533070, 803346390, 137507699, 544516760, 580924320, 419865088, 322177277, 861098, 969119580, 344253700, 411303382, 693091008, 686638222, 444371202, 771369253, 287964550, 583148002, 786301123, 316923858, 661080529, 354906011, 206025319, 321484888, 416396428, 590453619, 674457703, 55955389, 146578851, 821280699, 628189038, 390916647, 287297859, 290204350, 250315571, 387676437, 649438554, 725716681, 633758467, 330770904, 205847598, 992493730, 655522505, 967208578, 14920931, 726156459, 151451305, 966414743, 166674254, 493940308, 452753423, 329192446, 927797263, 501223147, 908075596, 703535191, 155951738, 446458856, 754859926, 445906350, 913221643, 897563745, 899984604, 448492847, 962650086, 117921807, 553930506, 142766093, 977438654, 782252141, 739242477, 366264887, 972239562, 253925465, 816637315, 116370660, 860797354, 382845500, 386782808, 511983341, 317319229, 718566051, 500624557, 650169595, 109130321, 801221807, 851407962, 732533448, 116588022, 489478866, 956662078, 131303947, 947630286, 953664301, 705792140, 481322425, 966969142, 354112515, 83251152, 496758364, 637705349, 758822655, 39694720, 681687557, 921388365, 376377874, 918270075, 864616063, 198275810, 463999482, 890303311, 145366188, 287654255, 599587930, 680441537, 875484125, 33172438, 780428530, 613422754, 307423915, 960429716, 394693056, 6475618, 48817564, 402591508, 658909741, 572367008, 712493648, 243221380, 633447262, 994644086, 137229954, 621237382, 558871342, 582280030, 610651966, 776340530, 594381773, 799055438, 592689777, 758517664, 980785464, 337289762, 477338592, 86983399, 93128909, 875827315, 673348989, 791799256, 687194400, 626309905, 419314619, 739021293, 892839528, 59559579, 691361057, 771592488, 568836572, 627838, 444550923, 904537035, 978863119, 972982629, 910219644, 404011494, 703324448, 16300446, 144666973, 411993535, 830740137, 892133979, 223060304, 676581012, 385420928, 339583561, 993906340, 965291764, 911537287, 390343531, 12343151, 29938686, 10148201, 930405285, 512312976, 925289638, 625800005, 258232519, 583271816, 145771073, 833935584, 140822082, 52147791, 876277201, 125822980, 674375845, 723539694, 912562956, 426973942, 706824545, 449436972, 759766341, 692483222, 636285053, 62767683, 33102328, 534501875, 925075, 243085350, 996557025, 916948445, 545206703, 249634055, 113469589, 322574898, 530971318, 651751471, 994844575, 97847038, 87069690, 283529511, 987335628, 51286227, 404214240, 802688548, 191421044, 480178742, 691204771, 686314792, 568462622, 251313409, 407808390, 780679600, 218690387, 70778300, 4854471, 906109773, 875910534, 833358805, 785382145, 553495974, 103056391, 2628016, 923409841, 999578736, 285049820, 454813439, 963234746, 643355367, 912672858, 698862772, 924673198, 284171367, 418319142, 807845182, 359325123, 154371631, 563832556, 930896225, 688691917, 455271573, 964435140, 972437953, 118357684, 26102585, 900224881, 960995219, 193238372, 419298698, 89275017, 906939260, 338617138, 742291028, 142674553, 513340558, 753752301, 285981883, 698475391, 189761281, 545025266, 664787500, 83694786, 752754464, 954059241, 623688293, 790078634, 574024711, 764099242, 170615761, 273088522, 445710609, 178464209, 844348886, 417672168, 648449485, 270451393, 625814040, 433442112, 229467318, 522043719, 720266468, 893268554, 230173507, 765224652, 529702293, 34756868, 86908627, 767156588, 149279044, 869183611, 761680504, 836819746, 966393733, 306633109, 451534679, 447065720, 271305351, 630875398, 820755976, 177633720, 475162987, 30272309, 788813744, 894972478, 326781649, 78096045, 768442091, 27795176, 64004706, 967174814, 577463647, 78678626, 728006817, 343429755, 303918074, 673113395, 602153923, 952638994, 451088175, 228380164, 589810157, 619297304, 884795515, 185954077, 993882760, 922966573, 593245049, 383339054, 100174488, 348123355, 90284549, 439604218, 525952992, 206699034, 800993825, 687985843, 694837, 176749197, 618147919, 155721181, 518203155, 411256277, 668669815, 545967819, 143667793, 843840630, 538498965, 341897618, 98158767, 565825723, 966609363, 961637383, 332729474, 278865662, 795012431, 366880784, 290470462, 210314032, 879971665, 383635151, 455671584, 671909769, 158755579, 717512154, 269125074, 538606111, 210744876, 852972531, 285101201, 327702061, 531486778, 454546131, 114338677, 107182764, 409685141, 556246405, 501214505, 509604590, 894598546, 821141790, 83641689, 175271070, 727991227, 442759804, 456165984, 970934644, 665377950, 299920047, 626332150, 258353717, 161534920, 900240759, 854512135, 424355852, 31482650, 256516898, 959618397, 828598997, 49395900, 457794415, 827104991, 924737319, 790980741, 591725045, 40782007, 354432887, 609724642, 345079824, 242322636, 508955559, 773036143, 790177500, 232695613, 674597886, 443350816, 308555462, 165291649, 679706210, 538071859, 303228828, 964313449, 124776083, 793628671, 83517980, 735637265, 947607189, 780433076, 1788029, 331828020, 886347685, 418552938, 559597155, 514028371, 33706151, 820334052, 416102667, 484842392, 887793039, 897039845, 489388942, 259129001, 769372909, 406658697, 251352030, 573446857, 231902859, 547095606, 357585533, 691624466, 693069732, 695153600, 494617292, 265779252, 380073942, 772302431, 456511216, 76219039, 199283731, 330843729, 842811891, 390537876, 276315746, 723548987, 440005316, 918166194, 342419067, 740291465, 900279724, 786866030, 114537099, 79081391, 288744928, 500226952, 735903674, 853172604, 409220973, 983462319, 754942590, 39786216, 281042488, 538046619, 943309807, 217118833, 705844819, 818438009, 501810334, 37657039, 445712290, 393767649, 262508052, 675292499, 769827768, 560873423, 35589088, 373092777, 634272456, 329925942, 820890298, 226240707, 435615014, 49830465, 647328887, 442595695, 14507367, 92143758, 98631502, 82094414, 943986504, 606460496, 909974690, 43129556, 941650874, 381544800, 676069742, 185913346, 43013479, 242478574, 757309975, 208365837, 314060863, 511754275, 640030849, 602430435, 208785862, 924951516, 458763916, 331521767, 238358776, 346177092, 949186743, 712878247, 992306786, 985972122, 9368114, 730644454, 470116656, 481614812, 314819896, 271426779, 60951423, 833870446, 365734093, 692666903, 393049157, 885498520, 446863901, 476829633, 121625104, 479603682, 791578510, 89786453, 392797064, 102055897, 97696916, 452257632, 50008708, 939528210, 886907874, 17459481, 52220594, 688850313, 890109149, 246494690, 566822072, 961968709, 962278831, 568899548, 708918014, 46132077, 384656621, 721541487, 406108684, 238031205, 171758116, 36509452, 791567091, 484622231, 753454687, 400967158, 371635211, 238447607, 232954273, 176917320, 493368676, 770786700, 560018227, 662700429, 803574511, 388867946, 489477245, 651307235, 66815742, 927349964, 559647312, 319996234, 341270784, 237183316, 831807857, 697329999, 121122977, 425428787, 327248586, 113250074, 745755502, 974416165, 360579843, 274848914, 613109561, 344807703, 523997877, 996697564, 992055812, 709530246, 241279943, 500296354, 17894447, 545599413, 122648368, 521510558, 871504449, 741289886, 969550422, 388819582, 476062149, 236600652, 568011756, 857038985, 946628561, 962336779, 739012696, 301301004, 244453360, 824403518, 520642044, 483418297, 216323747, 999247942, 566553820, 165479817, 607411792, 226972139, 353016017, 318996086, 221744365, 264639834, 751201387, 871425549, 201169655, 492275167, 883544683, 421815240, 215566087, 535494050, 709708483, 853774203, 424915465, 951682171, 737387466, 456857767, 312823927, 616903216, 478192809, 910124306, 506583832, 858885357, 865880200, 314720719, 419988065, 367292416, 357347191, 848509316, 396280140, 685425246, 471682140, 859758916, 559375569, 171818464, 227736165, 792692429, 678118680, 12730692, 545069599, 825455549, 889490852, 258598733, 642245422, 336192940, 707023066, 682394835, 932936353, 890730348, 12269199, 454775306, 954906102, 699360678, 408306726, 16779926, 307146374, 356781658, 926844515, 705609156, 388231977, 556491325, 24118741, 997868676, 797013374, 746846264, 865864256, 197038421, 600476118, 171468457, 808724104, 112553449, 462542619, 608977688, 911005386, 969746573, 60384916, 443991716, 470216522, 708931550, 880139700, 262876788, 363452764, 650712341, 307020814, 482889094, 792486640, 303528667, 424509170, 599126112, 703259745, 833116494, 690601291, 234209881, 157654572, 374619575, 332918475, 47545032, 656534505, 908363718, 852549418, 950324203, 455647078, 23496319, 327981464, 48508005, 43590968, 980900715, 347468949, 365530979, 746913333, 582262872, 602968096, 443298904, 574821787, 888817756, 591514126, 365529680, 44910659, 474714977, 767904028, 227333539, 492272360, 160240485, 467770572, 845628888, 471248899, 406972170, 511257723, 926491498, 267888792, 497088475, 318225186, 350600412, 632806245, 60573645, 295644632, 767330325, 702883247, 268616543, 613366441, 987147862, 355234647, 299788617, 527309062, 423115395, 655994868, 960986759, 513390146, 237573541, 327644833, 931510332, 517203306, 994599371, 647939085, 104687566, 311691816, 895808905, 973301648, 313165507, 95454768, 13816966, 932477438, 635349587, 245734717, 646526206, 269800450, 118579773, 245399438, 481267014, 884239406, 45215190, 285403499, 429444090, 404871194, 70189537, 146092431, 960719510, 29655602, 57798202, 672885093, 759586328, 442815683, 863780353, 531891709, 742036871, 825691919, 966242363, 246901285, 157392087, 143542861, 405609179, 412392056, 494833533, 472112724, 715069453, 594808768, 596157476, 976328405, 605285521, 926700299, 865343058, 757603318, 934256809, 887651256, 55486397, 821994079, 776031485, 552484422, 779775278, 437069965, 410081837, 761766491, 829186328, 224592992, 930086616, 512753420, 695918343, 432792593, 972546514, 291416580, 550633142, 151155741, 443157088, 344731927, 128034701, 789870179, 802015903, 236460214, 252999206, 930041488, 360438775, 450099611, 142115845, 485782686, 163267891, 883197173, 441981251, 152170003, 990323953, 396733356, 846122099, 745356529, 257262884, 292548922, 747110155, 416782140, 133901962, 33966644, 384062679, 338656430, 871663411, 241362537, 416476458, 565903492, 246193974, 976376582, 737432499, 691847885, 320430492, 621240590, 569592088, 32934038, 249272466, 267136460, 959232498, 386985444, 444911234, 241029823, 45102491, 298518781, 206783354, 126856420, 823505084, 438880913, 953628527, 163498487, 639245528, 826275386, 407750842, 977346347, 751108044, 117795631, 916616440, 761950191, 557091813, 370115120, 202977971, 726694101, 407119800, 568516574, 909448665, 310544529, 586651648, 293153420, 594792604, 591731077, 549898194, 622542971, 612697539, 754602483, 96572198, 114667008, 997199786, 548890215, 161950348, 622006225, 188096916, 190586675, 829003943, 427103001, 929351179, 15114334, 933130080, 104488290, 788561760, 849867586, 130178182, 918718283, 86512751, 930735837, 145331342, 966122957, 9662376, 277234221, 199707825, 763642910, 725609137, 583222533, 217128173, 145429001, 637385070, 79597641, 643408578, 107895731, 475840633, 391906758, 503424054, 512057300, 962036817, 961867099, 375101067, 12622004, 706234374, 254819911, 850676816, 976926290, 725906779, 925057855, 516563702, 984614764, 828814770, 670957114, 805023873, 277853737, 722874366, 800664713, 153750191, 864958114, 859388024, 964654259, 870056419, 536230917, 246605724, 177773224, 310450674, 561077327, 393136233, 808718641, 358662781, 253296869, 419271998, 876528214, 19314857, 498154003, 841551097, 444002258, 337182396, 189809587, 542259739, 869581633, 519983802, 569297307, 643941415, 271325560, 551897404, 803042757, 727302042, 461640780, 57594051, 261535198, 283688460, 429267154, 724518299, 772047345, 434002185, 882013916, 234079997, 395505090, 266826057, 450988777, 764486853, 652504219, 156057714, 640200149, 591849373, 720345823, 665528199, 806573540, 650243529, 98615280, 672174569, 83342765, 525844054, 241602964, 618068498, 388849442, 624124976, 741089997, 408463124, 640498118, 246427263, 239355207, 49022205, 58656732, 316455533, 811982978, 5516960, 364802270, 778009044, 59827089, 686815019, 142410824, 719244332, 732964504, 60989844, 510167911, 66760429, 202153166, 223623969, 317230930, 295317457, 118549362, 570753087, 292111082, 667541117, 931112185, 306286832, 462246520, 997430001, 287178066, 483942290, 853860790, 879295926, 160733711, 999980088, 766347913, 858382281, 279245421, 795376912, 834740273, 356773591, 720384722, 976084615, 714711948, 588562161, 323899703, 694329544, 228918127, 241164460, 639115935, 755298645, 645427166, 232992225, 581445290, 393498857, 915713538, 487440381, 307251832, 653686965, 723480562, 96363874, 793570192, 76443587, 379250841, 411806512, 506315727, 703124164, 660300555, 713828981, 403928896, 178145574, 385730619, 500930159, 833237432, 789796192, 500014160, 547709225, 402598150, 492280599, 436569759, 956782341, 303154601, 254221430, 963913458, 723572217, 402973280, 482465462, 820892053, 806197235, 124253151, 576164603, 7324696, 146547170, 418431386, 503088497, 893156082, 54447699, 732078541, 979631032, 696271349, 790950864, 70928173, 379615666, 766748192, 83034653, 841640558, 219605905, 738995098, 268972922, 581254279, 326543135, 517773586, 148372073, 705380562, 456456383, 718948036, 172248393, 346005020, 582690085, 683324942, 150640772, 546837198, 376482559, 547734278, 924474578, 433580195, 513577798, 444132014, 593850043, 764387603, 849533141, 27756613, 592341437, 946026923, 414410945, 41288764, 726286651, 479723746, 556917525, 522182256, 934859166, 144897492, 459003192, 785100568, 535542558, 74465130, 123005132, 929857874, 30152868, 879907324, 756100178, 665167176, 702189753, 361067631, 634679849, 931355958, 544698531, 683122049, 831244911, 283292506, 261073165, 213964498, 421418827, 517469630, 445691523, 140972956, 983659213, 405340122, 75504630, 87739656, 777741972, 346807007, 230159180, 373220633, 170871982, 764089472, 789216508, 362551353, 347255606, 454028967, 258598345, 359016083, 607451136, 55267279, 943691458, 163806138, 347158767, 94874216, 414862903, 638825254, 335695395, 260711617, 365400983, 354212632, 452096274, 118979261, 100446032, 867367618, 749706497, 162108512, 618739484, 527852324, 424147305, 975619002, 293397959, 586585968, 389535405, 353968454, 144900136, 782433005, 44222350, 959863234, 11728096, 187544824, 483671149, 582608226, 820339404, 180584932, 805278559, 662165564, 943542302, 45675727, 343266961, 656278462, 891592074, 633108580, 490177419, 746960953, 562984859, 507870658, 978760840, 864215134, 703411226, 821398131, 679389525, 999440091, 691731880, 536548199, 454609803, 848393206, 804413462, 719097465, 976904811, 447764420, 933267905, 567243126, 999088700, 345717792, 527052207, 448026288, 631203084, 297967687, 166637586, 359974458, 802653017, 564777573, 589807493, 504372948, 272160531, 795863499, 950374053, 937319607, 916636199, 470347562, 29281579, 573328968, 386831991, 474328244, 837670593, 116773706, 916389078, 414728785, 821147470, 257906636, 364581985, 806949584, 375028852, 891957787, 117279639, 433182968, 32109669, 757639627, 13423051, 548406925, 395731602, 123298838, 853072555, 992865610, 263700137, 400479293, 18903083, 617998247, 988397953, 738671426, 105363877, 887433578, 436298571, 535353135, 323697762, 286296414, 205360347, 520260820, 841482123, 912278629, 380093329, 63376843, 127705436, 841737446, 400015973, 122237108, 555730827, 759936730, 569137427, 749537061, 544203044, 46609973, 445310920, 217995068, 182798124, 672963802, 585734580, 854902483, 400892973, 673662955, 726030371, 631355539, 987211030, 39599765, 937505841, 276683527, 257688682, 784643097, 294683055, 545345256, 96946562, 700346957, 196775118, 616490625, 528347683, 998242923, 985906495, 527379628, 628166020, 372107284, 468502294, 514949377, 913352409, 93839955, 12311153, 995781521, 889917614, 678569936, 28235740, 951790845, 843968442, 266925081, 328930971, 328620628, 714674383, 95134640, 385259619, 165309005, 167368052, 644309826, 123760721, 653723478, 992814109, 611955798, 315823879, 95694953, 775676057, 107940173, 91181920, 44447784, 754506929, 844565251, 702059553, 663915493, 372738275, 360937093, 311736146, 813433469, 557753097, 241268819, 94395183, 835473101, 366608739, 165278571, 802229119, 832593844, 939625651, 246821979, 963068151, 523797948, 826639969, 480435045, 915373797, 242158328, 677728220, 515135032, 999775228, 892790026, 447861247, 970819149, 634415387, 569559873, 394761509, 412922562, 109298577, 86315514, 234061981, 414053491, 290758021, 736948940, 434918669, 687229690, 993356162, 193086072, 907704447, 49881258, 978377006, 534710816, 115798782, 160635497, 283700307, 358077204, 804563869, 104574798, 11134842, 580439954, 545181251, 333176740, 855977474, 519956496, 903584356, 787916003, 159990997, 274078995, 930997326, 746577531, 768314574, 37482105, 221375050, 595141698, 850712411, 925781328, 25047941, 906020468, 29848622, 796528823, 809650009, 787044564, 472568714, 778055093, 245181770, 780866301, 684151796, 812873609, 644723616, 423749993, 208890445, 937904546, 125328582, 400948246, 969810975, 278183491, 987594833, 518887491, 195780204, 372316178, 335166886, 727906165, 486235287, 203083605, 441727609, 995745327, 607768603, 402503519, 26101438, 217994989, 406862647, 5458173, 23944474, 327833275, 601544754, 954555711, 797564873, 531934814, 775141915, 457972602, 121200607, 492606836, 161948004, 255323590, 874308099, 864365636, 420811904, 258679270, 482567826, 173631054, 488003372, 370166147, 650262875, 457285382, 980559133, 790480835, 948713083, 853438406, 377203341, 723176785, 262234635, 129919747, 767228623, 754866082, 569002867, 615827352, 264413254, 627705192, 616778342, 824523129, 94049348, 795021419, 830505699, 808337915, 195086511, 914400613, 440509242, 795983661, 99937151, 210114858, 888820569, 359746368, 971965525, 696425571, 605364953, 591790556, 502405837, 733873032, 944098694, 1434224, 739969224, 332641775, 846738543, 39216682, 388128134, 866915217, 589008994, 760051733, 530749256, 455298474, 968085396, 677190011, 784456571, 540819900, 613589187, 841658415, 841325952, 294957844, 335655990, 501637018, 331122123, 718985521, 894245835, 333977397, 445331790, 642725996, 489042598, 427505061, 151756529, 525967306, 428235055, 802541420, 985276886, 956074961, 548087845, 140263784, 467945001, 506054992, 551065424, 26478013, 754725149, 563673972, 224985493, 410838307, 123918341, 52259466, 731422342, 136264095, 473281077, 333536246, 905671953, 131378921, 272163409, 33725218, 1401299, 425942308, 868871972, 488261340, 510501432, 148813897, 33411844, 481761336, 465838987, 148104749, 1671097, 695835460, 86049739, 700141689, 98921445, 372703651, 321339806, 105363283, 501624113, 205358460, 762032933, 820518255, 743704040, 810784801, 438049582, 412454911, 833112616, 806249302, 331993051, 234092477, 149549816, 163484887, 630599695, 965346955, 697529382, 844633088, 411394034, 659549004, 194970595, 336015759, 497684234, 907103855, 913483877, 233262539, 364621503, 686620566, 995548396, 458007092, 182854674, 189194663, 65286915, 979650714, 284170182, 152292438, 449281065, 585933569, 274979912, 31413214, 850778745, 569262478, 444059119, 922840905, 928115457, 274640204, 989888300, 933349101, 128810219, 615219874, 286312017, 115398104, 431144108, 9160100, 720484933, 136123507, 452787753, 42401205, 199416549, 80253625, 344135614, 604047271, 592038217, 82257365, 433885492, 18561214, 267392100, 106918662, 164943979, 407043873, 369551850, 904662313, 854474684, 165513931, 544013975, 612453760, 24110043, 228402560, 267298848, 220764452, 674843662, 13305931, 897299787, 547924845, 785743971, 899660287, 840453606, 994849107, 361564451, 886130000, 608497218, 659141636, 239641469, 645710591, 675524426, 10814064, 623540809, 82806898, 676835363, 596146879, 958154002, 434352919, 670573360, 640156485, 213434657, 358950488, 48061030, 441370594, 553369066, 510611826, 276370797, 735920753, 935126, 732677044, 53550674, 606441818, 179401823, 993189047, 453819986, 892415986, 800988835, 467267164, 507870456, 394124635, 799116211, 865126582, 945593428, 375243721, 261435732, 475905032, 448437511, 147662181, 832339405, 942414243, 470224028, 773743854, 401014977, 446039401, 756890437, 851553829, 961345647, 551479507, 182429484, 280020979, 231463237, 537124079, 855933518, 576630317, 112048914, 237984525, 947079475, 650164489, 126548757, 881940881, 420413973, 302123778, 239465653, 864987527, 644432776, 635087121, 221374854, 1794239, 700947700, 334500657, 463924768, 613063935, 582030380, 824510586, 20992291, 639216553, 414693562, 268607438, 779413521, 791572200, 345834720, 49402596, 851736860, 662138037, 806933588, 113075767, 798794576, 428946708, 213674458, 999238606, 383295482, 928110778, 248988371, 39094647, 367221970, 429483196, 158649950, 56434938, 857452519, 223547565, 21905510, 19792122, 163471296, 429607650, 466486431, 238183210, 224101010, 462254321, 960233747, 225597569, 477628764, 695262311, 340136017, 386562807, 427767714, 694060911, 783029908, 722247048, 560660011, 145749197, 900556772, 163832905, 588943785, 21900977, 416890677, 202169199, 399235950, 879069475, 973945499, 744305647, 134805026, 796114947, 629756220, 43130600, 498576557, 799754727, 721976399, 556741155, 238178523, 777282658, 715924392, 692883732, 798773514, 230718350, 870488293, 169202874, 735458646, 366447548, 194464909, 653228996, 549532705, 312106229, 279341004, 495177406, 815738894, 240791721, 329144941, 379022801, 474129774, 299364726, 80107916, 127775590, 93329757, 461189117, 411731808, 590591821, 262906196, 208729630, 140438965, 521780889, 222923419, 149144982, 396868145, 59126015, 30319138, 161046665, 655868068, 185348443, 162400842, 833838860, 734640756, 218519523, 160991312, 323903, 21657131, 294056278, 202447997, 849803896, 761219152, 882388152, 715384793, 547150642, 543612858, 822330108, 842815850, 994356983, 855729041, 291343514, 694849646, 438687306, 114271145, 624756438, 255647617, 956820150, 110332002, 841582523, 920400318, 755013172, 143062550, 296156252, 741373784, 14415769, 489157078, 419801181, 539004141, 164285347, 762919237, 425297876, 793795339, 373957872, 769221596, 365792709, 426328047, 251371880, 109886277, 531583438, 410260286, 159969373, 378136399, 343909264, 290702656, 272304909, 774853765, 536369643, 514720752, 328432625, 845268484, 452418540, 600663212, 300970740, 193820407, 325454187, 924181982, 5852963, 834917737, 676122723, 44432659, 257668727, 365311286, 88078963, 437059879, 371439850, 463128111, 486700380, 961919913, 67456362, 359524522, 784648651, 719692530, 186678945, 110892768, 565305514, 678168431, 346011750, 200260131, 416473489, 291722970, 678047973, 942880345, 10473616, 190840994, 700020868, 956922924, 576974497, 578510819, 71460454, 355524481, 187286155, 550796839, 791873452, 650113078, 123414854, 968657402, 444228129, 449561263, 724688629, 292836009, 241858879, 536982348, 954632352, 873640375, 41868317, 951415295, 922084548, 426738561, 101736136, 801699598, 846406486, 659370709, 128447287, 424270144, 156643996, 723438338, 688745281, 235895343, 748722530, 91181443, 435481099, 151888515, 858845496, 8110336, 188090121, 531431329, 483988599, 934457527, 227647009, 777377475, 946493123, 818626537, 894302333, 490617566, 368908889, 225795445, 429019636, 942414117, 405977445, 210655578, 743018013, 958554154, 842703759, 760002906, 894558985, 149894126, 812619509, 438787927, 765148398, 368645560, 470426937, 78828812, 623439372, 884606799, 982509926, 353789665, 348422453, 79837446, 145961399, 58445036, 214807040, 277639896, 785343363, 717363756, 15287672, 112707333, 594665252, 792711048, 452604846, 384252465, 341393602, 896080876, 494689727, 929855806, 745819924, 284005983, 808063934, 199161568, 80796476, 30063371, 803988372, 994440902, 681925148, 235296157, 965165032, 711751245, 147797305, 558377781, 393142351, 913562303, 820116626, 660651554, 98261604, 128048349, 496223457, 437150856, 165867017, 789258325, 632288955, 791048772, 58847045, 420324822, 666239516, 118009197, 209898266, 646796190, 526322759, 158892819, 413387144, 908163594, 877775380, 151941012, 55019689, 842576774, 878799308, 743476099, 163845920, 722965863, 800309026, 946673821, 594895181, 534582470, 585278714, 525258132, 234051682, 596217902, 710359460, 138988756, 533332801, 158810230, 220810077, 49390247, 907380430, 41308581, 332941243, 232542202, 814841954, 879257754, 189877240, 3601623, 356877971, 692841081, 720799767, 109039914, 182869720, 638478997, 799913821, 654811215, 839741573, 716605537, 335721081, 93914112, 620441774, 30649506, 525895271, 515772904, 647274745, 905447005, 537360703, 216901828, 823411277, 348274172, 458892942, 408103035, 725337280, 213506815, 967045518, 515788169, 566583661, 661274653, 222403521, 404503364, 38516358, 290310686, 900785774, 236871567, 619425061, 946658072, 283499625, 582131948, 810303153, 489636001, 465813058, 830144138, 72760278, 967543058, 218768020, 317116151, 463289811, 106819487, 869341881, 89930456, 485099394, 658661031, 923270028, 865119073, 719586031, 919003069, 19521693, 886581642, 824573472, 844157392, 271696741, 250419914, 150583749, 124535160, 177906553, 237780481, 789731297, 461036996, 509413020, 824318329, 270770258, 16592320, 947962589, 459960142, 739854467, 654611658, 147272243, 968503126, 862297049, 694530881, 161268745, 418708790, 939168820, 165605461, 948052992, 588506931, 895886235, 837690694, 980746439, 361354438, 381164142, 42296335, 73175120, 536295656, 307910606, 729662996, 145252699, 994778601, 731335696, 55516679, 611979554, 697515044, 276826202, 540813026, 702190154, 463721567, 218111818, 746092213, 536226150, 388324370, 763003334, 955939128, 615305007, 934348037, 333113631, 6870393, 603875172, 575364613, 544905066, 309110109, 574479252, 552188735, 407186041, 671466890, 96197196, 20172943, 682742454, 264786331, 714493580, 531392724, 355880544, 426332970, 851974006, 203547725, 888083287, 663438467, 420283449, 329631291, 716266045, 522493487, 518103218, 667266799, 328210230, 303264899, 5503853, 283650177, 820515203, 892515804, 826066361, 955378362, 104079872, 649437200, 17873688, 819846887, 782360448, 150669097, 53062297, 143863109, 544501800, 661871811, 739698915, 281202909, 887716825, 980405451, 147793507, 211264811, 898394361, 902799743, 592496241, 420670328, 950052816, 938747985, 974906047, 129581623, 383618164, 146741310, 355115130, 665147922, 507653521, 416179465, 162056958, 280160153, 290573463, 506812890, 989164173, 772360754, 373050421, 701039448, 196360581, 398155638, 873206936, 922179211, 239575867, 535615792, 319950609, 849763402, 236338896, 969737420, 684856948, 117254207, 44703481, 326957240, 732529123, 352670712, 622833330, 356918823, 635616434, 608679009, 424020894, 790221446, 224762215, 639721517, 776035430, 262234193, 88753699, 485511933, 472520717, 577398896, 211604943, 748547004, 94152455, 106872901, 723518372, 94673687, 200845157, 50465946, 867350318, 225089167, 394616037, 753082478, 706557930, 770968209, 435548787, 611011296, 217968221, 212601086, 382088342, 689751289, 736769362, 901593607, 359071861, 787233158, 992279197, 665839032, 838870257, 145588434, 449188964, 106820715, 135286252, 764298449, 961952026, 393655973, 148540360, 186103151, 649207333, 442647835, 700284261, 360965575, 718215016, 805572363, 154224461, 910773703, 681543797, 698599886, 229486538, 193991269, 283055300, 516224870, 223561637, 809824729, 238888013, 644728510, 71635229, 936375870, 158322554, 245653133, 662216007, 419139512, 649797874, 128163697, 548017599, 212542978, 340117698, 255322031, 874433289, 996698406, 522279422, 464712718, 390083055, 430421514, 170253129, 691008506, 453650242, 421358029, 369146484, 953703990, 389198827, 341831893, 886087062, 916174392, 323984302, 47640754, 891713111, 323817259, 481656741, 839407637, 930380844, 639711355, 129040754, 246612210, 697935351, 216656310, 420462343, 202168438, 848067373, 824797964, 733673932, 251398265, 292346740, 280414412, 252089772, 442842020, 776847110, 477332801, 440472930, 511308713, 97825747, 456203960, 567457998, 88889141, 858145795, 811706879, 672816284, 291581789, 20691781, 627653068, 205431341, 101683459, 198632868, 975045810, 793890099, 186353969, 55357375, 700741775, 824817240, 620891277, 698680782, 720662241, 978334111, 603081008, 775600626, 946501221, 914257727, 102535726, 578257116, 811132980, 641082619, 763831183, 553070315, 113236425, 312834437, 871639299, 771768264, 913851288, 972484309, 421905684, 1079498, 348630792, 698898306, 729148120, 295895099, 442999924, 622095955, 95030959, 73362275, 599658002, 735536278, 541098469, 86000147, 454903327, 460544670, 493610739, 627079717, 608385127, 536157394, 802408518, 877822612, 623747813, 373800075, 942284380, 431442712, 854375051, 5280773, 395707641, 221696974, 806773919, 660926249, 46806811, 762309317, 723546504, 254566643, 337271668, 187058135, 896758747, 717586329, 48369679, 778999585, 375320463, 439198007, 334381422, 186925336, 801437024, 472047455, 576398777, 917052175, 706801965, 42142207, 624159915, 477706492, 416237953, 449222416, 598561752, 423042377, 587629362, 713981769, 702152363, 827074648, 80139440, 587737931, 822184967, 534502494, 30073542, 680162097, 876297761, 849354905, 16425417, 93362562, 219605555, 439294023, 337245060, 265378202, 119956397, 709283177, 875087541, 916237298, 412589748, 382369339, 20979036, 835824126, 254005237, 367596543, 213879937, 286807449, 64230645, 205243278, 359405363, 737827678, 579897342, 503769814, 619821280, 419652265, 889335801, 624674646, 741384801, 63311723, 17805628, 726165270, 649243064, 953628978, 548160922, 151026989, 265795903, 60570484, 392615046, 806284867, 77037956, 552033716, 254402776, 298745941, 521750803, 639177345, 991679443, 558397905, 724651763, 386539329, 320436117, 183615891, 438671672, 640670588, 252918204, 203895244, 983771757, 206983673, 120863648, 550869161, 452850785, 70830251, 7996030, 313708211, 181660607, 203605285, 696211640, 787911979, 974702456, 759221670, 339080404, 957610205, 455702478, 695697653, 236637910, 523323304, 924655086, 132976229, 581683664, 470551737, 257314848, 552957373, 251123237, 273369662, 969763973, 294074915, 143088219, 903295448, 51049298, 778098269, 421868367, 467999358, 127629937, 920662518, 524006248, 377720321, 427157706, 949967864, 860991115, 664398713, 387689990, 381326225, 857515708, 81672917, 669507813, 980600296, 280559730, 600493701, 178749865, 217278265, 970449306, 966792098, 513068179, 284741600, 439845450, 270196772, 647274684, 243744417, 743905646, 774941435, 348999077, 629677922, 229724049, 338523793, 783731744, 98676801, 735200138, 865629387, 286266380, 105705597, 17405104, 798511348, 513354905, 126220137, 138639503, 780958092, 699194785, 460634269, 732924939, 971149381, 265911342, 331986186, 554944501, 333342494, 772717242, 563399795, 863310111, 341026970, 5628968, 565109461, 979589579, 867628745, 579141769, 77217886, 581294679, 606170520, 154510538, 942035087, 938756820, 326587178, 670805514, 75790395, 80955329, 65690488, 913286534, 667152869, 866375334, 776991692, 255499150, 554092579, 826090215, 595060719, 316033562, 173895176, 650944431, 58769168, 203200153, 160697180, 257074851, 869368506, 264336697, 314362517, 408618667, 447853892, 383789576, 762897464, 539445336, 258637726, 33384154, 672918624, 529287702, 401038953, 875719204, 499744134, 84571545, 55428656, 782871521, 171851749, 217388996, 343417601, 323783903, 710180222, 914634273, 960116979, 898446222, 681751993, 563141135, 683147929, 99637146, 882612154, 971272588, 25373209, 855589936, 188562225, 47373203, 616093910, 950881695, 220834631, 661118658, 437571081, 439749775, 853487967, 611835921, 265033615, 979388130, 505181851, 810862376, 598685677, 981726750, 178514539, 109629301, 702511275, 491826925, 701868090, 946420672, 30963248, 994107945, 104899738, 458907602, 237546336, 695310423, 362583707, 320074758, 121123160, 498957209, 194368210, 126878995, 512390774, 322864608, 355507753, 438335508, 33344749, 235097617, 694187724, 692977260, 456483749, 671732625, 115487448, 934354659, 923568406, 559028211, 413370432, 257388566, 846219292, 890026043, 786182220, 521034672, 243169226, 25521035, 268456871, 891662615, 851709472, 505647475, 793033383, 419764267, 289494215, 573271824, 283530619, 666025611, 606448203, 758028777, 813013912, 455981970, 963715079, 879904751, 939550476, 367896050, 519530626, 637535574, 490213389, 536852820, 799318305, 530178387, 948938856, 330903649, 715535210, 556302335, 711785362, 253923429, 239606883, 817288168, 382805894, 73058495, 536032294, 699831745, 879512294, 571432223, 561824778, 325143892, 374905925, 823203919, 928230279, 137991677, 171668496, 442590461, 118872178, 193479685, 790948187, 444611003, 907005955, 769703902, 199693094, 800875617, 317785534, 780466716, 774657401, 113873406, 714280676, 552084016, 344057998, 658109352, 620620096, 10336411, 252649962, 396875305, 136084606, 829325152, 337609269, 294824766, 943968368, 944223511, 391179539, 819930169, 71174456, 694392298, 243528357, 733609313, 642632014, 828898762, 766054051, 27965235, 135031290, 882833429, 197680046, 588025569, 716478075, 880604326, 319572749, 227728410, 682235968, 397398826, 406481443, 227581004, 924074411, 290186624, 286604061, 510454238, 13160235, 584858733, 604370490, 266802332, 22207009, 610594078, 589681499, 283035612, 337573484, 113648330, 144372111, 445665256, 679586048, 596991565, 240154760, 341607639, 606300517, 106494603, 991712627, 580745904, 775614754, 180504230, 405690603, 649027967, 321671817, 748763912, 56090199, 738891348, 659629566, 146849446, 93985123, 75322936, 987649423, 298795724, 95762679, 26905923, 670829042, 254726950, 291708509, 370338592, 825000816, 579119015, 343713669, 406207940, 640467450, 609264728, 285388519, 991068183, 608218554, 563231758, 600661442, 508426826, 8607802, 362717493, 98548992, 136597220, 777833922, 681001835, 133196505, 160218236, 703259457, 601785539, 713325374, 780700657, 372515939, 62258308, 771801496, 831713708, 809548468, 653184156, 379273577, 353002683, 662771112, 51187462, 566512704, 221133343, 227665505, 657829540, 888399311, 386143082, 573334527, 573377775, 965074208, 930204327, 367012030, 158459379, 152143911, 959606751, 368080145, 611131077, 304867037, 396245529, 787639788, 310040292, 874794188, 205046926, 315688420, 226718444, 704602509, 187307906, 702647521, 97495384, 343276480, 393617649, 413140623, 402653402, 662334624, 832260817, 504460362, 699297965, 101884077, 120559990, 661537358, 696136770, 719188617, 675723892, 626221489, 309735668, 441151583, 332308574, 874874792, 896630062, 233951075, 158700344, 839184831, 226027534, 520466622, 975023008, 514307341, 272786692, 464687835, 31117395, 390213999, 189191559, 103748634, 223686065, 614772857, 199881488, 177790498, 240164202, 404515583, 88583199, 819817845, 202994052, 694254474, 179276026, 937577520, 612356593, 842462778, 226092705, 32134023, 15035356, 372041348, 75152630, 675498003, 837547545, 455963276, 859227027, 918732099, 672387118, 499525579, 452910198, 745782155, 441641858, 576950557, 815309167, 604484355, 263468954, 431219865, 498009553, 759160576, 800482705, 774312529, 570532271, 323345156, 912700015, 28165361, 305613132, 14023585, 30230291, 970839576, 23443064, 275399716, 988379193, 926123925, 703090797, 146117245, 857125475, 617595105, 252193842, 116793588, 466617224, 606689209, 413407923, 502760513, 218153453, 421920362, 449473944, 462838351, 154478358, 571763566, 609492902, 583248942, 446376914, 688990727, 741657677, 822545751, 581546920, 131271503, 556250695, 500334036, 287611586, 932925681, 277611476, 253168199, 662015392, 668409502, 515556438, 233140346, 190189249, 406436741, 987370889, 62415689, 396434592, 542538304, 457742357, 414462460, 415899464, 130777265, 386662864, 9151059, 5391844, 284246402, 668604593, 81883600, 690618221, 253150283, 363506606, 498837706, 572191486, 744044036, 714389969, 537815226, 924100374, 447440254, 512520021, 506472120, 152651465, 901750327, 96069281, 447804556, 730196864, 244246800, 646109482, 707066881, 441512970, 209362668, 777676138, 313348109, 416037550, 141453723, 782482689, 67516761, 378990756, 429598565, 430861097, 533156578, 905729229, 499822277, 288897114, 749480513, 323468185, 584163247, 82800799, 401341861, 925632012, 143371392, 377964957, 95670530, 223073833, 47645680, 765438097, 266612863, 807949643, 776907247, 748494429, 266550011, 338150848, 884150863, 871328783, 333780607, 514711255, 410648653, 622292967, 996112496, 510190019, 159228759, 336626837, 34093263, 982127290, 297590334, 800684258, 17266928, 582849686, 275486092, 433050081, 706181280, 181697569, 354201360, 324591688, 484139671, 761641602, 331166292, 530726905, 680049009, 273067573, 264091026, 291551725, 584915898, 710915267, 39960411, 670059640, 340301050, 894359041, 197461964, 225283753, 638339035, 521509780, 550668137, 747706671, 538505229, 73782847, 929548297, 44886662, 283094544, 981620035, 762789583, 120629693, 937485660, 71455423, 370583528, 454350576, 250615277, 624801583, 792148820, 657179381, 243444698, 443255006, 344152801, 550240051, 388563506, 11958621, 636177401, 103240191, 484526019, 250986841, 770362880, 521614385, 479642843, 584680678, 788055785, 286837858, 56474995, 224685196, 66459097, 315548485, 467647181, 725268466, 944524747, 573146838, 267094031, 257956172, 902124344, 567796897, 860468234, 89146210, 659720962, 340325792, 52528130, 381171538, 615160524, 195625324, 947475236, 982248112, 112265012, 379285396, 195274226, 342816495, 288085332, 563822216, 363624384, 344091102, 206536799, 356820961, 870952359, 901104279, 630541540, 298812461, 98449879, 308323393, 6125923, 85508942, 146617981, 498692081, 777737818, 947443862, 623367334, 910560166, 305442618, 439228312, 302909711, 740502279, 156719804, 458671749, 322949489, 444659730, 957166783, 483975158, 342354508, 493854383, 108835723, 545479535, 730991766, 198512701, 343418743, 72146481, 58098512, 262976474, 989833357, 621610953, 771949924, 380687028, 857025375, 899804255, 587424612, 987317068, 187052587, 45292921, 707558655, 32965384, 962789733, 861717159, 451341390, 23441802, 731042747, 280627727, 739028353, 446880389, 665223082, 591208452, 669208805, 683241939, 960873897, 651303156, 74792170, 627651826, 45479383, 74990594, 243996792, 807817777, 985483770, 357892978, 349016656, 482008335, 902577723, 632142010, 158274376, 50527782, 798395587, 968462976, 234618269, 398675807, 117611394, 887946069, 699419900, 783195175, 362141020, 290915258, 488241384, 679246967, 798550087, 577984472, 879263788, 817352329, 524012152, 153375887, 679376147, 774224809, 89711141, 822316752, 888416536, 483255058, 686086048, 338720866, 861101960, 312746127, 184058940, 237701069, 620078287, 113434559, 443721537, 240775738, 997601797, 430003490, 758586718, 923414627, 298315171, 697978191, 282158246, 751645143, 108132401, 42438836, 590618293, 661045272, 922507837, 801461861, 376457512, 290984547, 290481580, 649211928, 929909215, 810667201, 409138188, 547823263, 984349400, 537007772, 927423149, 301031994, 965430054, 491385642, 196409122, 298291672, 185535862, 695006691, 396019696, 60539064, 793799747, 42566837, 798563125, 313144383, 546924394, 260118524, 878691439, 564209721, 785165605, 593012092, 894887677, 226237666, 398444876, 542053093, 780379779, 746491329, 674414550, 23434124, 52328897, 571387458, 603540501, 704953300, 862189466, 903393789, 277682774, 442598928, 224985893, 218233410, 489257692, 778816702, 425681097, 183941745, 652360723, 598028933, 849939178, 373069049, 99046646, 757321813, 496224317, 818176535, 938564982, 853229215, 461470604, 273016990, 593365616, 479679251, 183691381, 997192064, 307975666, 567669568, 896597526, 876745551, 273057201, 168869404, 274249327, 724433837, 270683890, 935224959, 406390296, 881269702, 457134732, 119482680, 691198304, 902636004, 945972522, 629575893, 775206386, 873057045, 335035414, 272260545, 618232345, 294134244, 133305530, 753170574, 244669305, 256572638, 486945122, 138357064, 534217663, 961433822, 631705556, 323706780, 401955106, 726042352, 577236727, 418342490, 629777587, 979261588, 991662526, 520777093, 393975515, 3833866, 53734396, 396253019, 101748070, 954713270, 701538025, 723498157, 625575640, 283558838, 683478918, 595681993, 165403163, 898128119, 470565119, 442251720, 651441384, 602086999, 963725256, 500256808, 992758369, 311743106, 853586774, 331714711, 212055046, 921133338, 635825104, 792195374, 711041980, 912246507, 248540080, 841039519, 593605856, 858687414, 180225780, 555633062, 682155868, 21617418, 852573973, 820551457, 780070727, 996574123, 721216907, 10602392, 409579956, 423282062, 274943810, 749014414, 532654238, 821074488, 548164976, 937077353, 192308298, 310267710, 705384904, 151306263, 812134264, 359414926, 605079392, 61811925, 929461191, 249982630, 431891144, 779687762, 608571011, 558632365, 122832811, 51866268, 624599451, 130685225, 723042473, 667489442, 25003975, 763746474, 160000032, 958860852, 984169012, 865164895, 873962204, 394493261, 264880618, 357293449, 176537409, 865753924, 21161624, 177050175, 489806745, 581168411, 914843707, 195262827, 262922994, 422187403, 921455130, 638233418, 232419237, 79620537, 105185082, 181693009, 305913003, 352122600, 834984238, 451345718, 740615544, 870874553, 65015650, 327814470, 225972573, 952498200, 629469835, 866284165, 316934094, 375527326, 955468457, 898648452, 680126489, 651638653, 206894023, 422914643, 284868734, 971904944, 820544168, 970008119, 395928939, 616829953, 381717579, 820203397, 128048377, 549914513, 735388611, 214126038, 438994900, 197690811, 532112128, 274687089, 183146322, 677532287, 733235973, 539413485, 889284018, 988013629, 460396438, 871014050, 538055234, 822243704, 11808820, 970602708, 44429888, 723462544, 112639887, 985541682, 870463480, 67150722, 118070999, 323609692, 120461446, 286383777, 914039766, 660137044, 984003747, 584478472, 598218434, 888870427, 169335578, 394364549, 688787451, 353568446, 787334415, 131724891, 225080907, 727726574, 233189543, 560649316, 363074279, 540516863, 44871867, 217328868, 829748608, 604712081, 415286855, 423764033, 96806338, 236540678, 682133566, 98024555, 4892170, 474648012, 557386014, 845506223, 201270305, 778104215, 360797827, 883697066, 92906288, 123851346, 475174788, 478256731, 223180319, 693895535, 475897529, 335723964, 114582851, 675453317, 511922348, 725778952, 545118274, 101105026, 176317662, 984018308, 676564386, 212826331, 868553929, 441640723, 873194793, 9407715, 530018543, 563186946, 120612295, 365564886, 675887212, 792734504, 132808987, 57731028, 592326154, 331673014, 156330865, 683315840, 649514797, 246248927, 817751581, 990334153, 675313902, 98878890, 185205282, 161732100, 816534312, 445996579, 319266002, 4767249, 844067356, 784221516, 56756811, 126628839, 931542756, 582168530, 548989677, 247330582, 504090880, 147283190, 882402163, 395133357, 656929734, 397298009, 752204294, 285754564, 717464807, 456396553, 897968037, 140729496, 823867838, 793446773, 163723419, 669005895, 783528560, 943298955, 248503564, 728087404, 669608884, 492742530, 788572753, 585072720, 461576760, 787085924, 272511551, 170211789, 10551558, 351775351, 462710518, 803286542, 544117443, 730847556, 520135101, 49967033, 740813074, 810941331, 301853357, 505691637, 550902400, 802240767, 42716940, 155218863, 242460258, 358723733, 150254832, 751354269, 987500290, 494917683, 36875962, 449081841, 970711726, 943657242, 673353435, 429061268, 18469843, 934510338, 570361724, 819099131, 919211961, 477832975, 583202791, 823328847, 155074284, 16514752, 977195048, 38344151, 206546844, 267085647, 252989127, 506653848, 533219118, 703168121, 447036318, 626366273, 234309605, 213235418, 861165990, 200273099, 497805476, 774970200, 537941200, 838593794, 456861166, 557994906, 472752410, 814427148, 462911098, 511722117, 46312980, 778667836, 212942341, 688171012, 609108638, 254453718, 179196339, 349167027, 606675119, 57552586, 182664168, 482014156, 400574313, 578813969, 138118250, 473368584, 73353454, 972426370, 781104440, 374910930, 10915531, 412041794, 801419424, 365196147, 619104780, 824093335, 222437565, 810116695, 923864799, 740604581, 252418489, 182015997, 813819029, 85238282, 307150056, 87905916, 898012572, 768928846, 622169946, 226238719, 571994974, 791291735, 996852407, 952791529, 74252668, 143695981, 749416537, 83783362, 969207445, 767046476, 306145452, 985296125, 619765, 107224832, 433270613, 923616365, 816933876, 105747978, 190628160, 56874788, 569255638, 706895891, 834554357, 416658825, 375142006, 995045353, 625075675, 233753181, 87992519, 961823702, 595299473, 332148240, 347215411, 799275095, 940203602, 575781349, 66665850, 146021056, 320364358, 613839351, 559461990, 366696203, 474115013, 599610060, 177069771, 125813220, 529237333, 913876747, 913677436, 97364259, 114285681, 901093304, 641578845, 36928134, 34758513, 66511495, 324280808, 995783094, 402428879, 169552515, 999051637, 928685553, 83567860, 438618392, 611848635, 330174507, 104110901, 543626201, 510469137, 153885260, 47465273, 293934015, 225976840, 53077536, 779364484, 461717978, 178980892, 79813349, 555879210, 581899533, 862815340, 933843375, 424687741, 841785784, 748702758, 344551170, 965157746, 823487802, 789336397, 913069887, 738728824, 854671765, 576516423, 576729143, 172045594, 718638394, 402176641, 78768140, 365308244, 210000547, 557858746, 91685925, 375878879, 25186993, 798452149, 383062043, 747170954, 979162724, 792825592, 980199307, 298856881, 998399715, 696698077, 77456875, 673061204, 780625634, 339986033, 516231085, 43663835, 527191045, 828265552, 603064553, 599356320, 279172915, 770635230, 362820393, 189455942, 529256824, 989832700, 67337259, 436047655, 989643747, 82641496, 68574632, 242648588, 960358536, 267501730, 356845843, 834352617, 686514652, 676846980, 402117925, 695658255, 743134028, 169779611, 36455198, 995752053, 720772331, 364802724, 352246914, 33426943, 675091892, 529928632, 438802204, 308492503, 919411145, 505572492, 144006544, 948772089, 741559429, 396317224, 847603191, 405212799, 350026618, 367583432, 475275729, 631287381, 759837257, 668211978, 649634606, 445466928, 376447879, 375446911, 229292941, 119783029, 654489360, 237201922, 491347469, 708536851, 243566164, 54742016, 519235480, 589847169, 298014959, 609323728, 567124837, 358549579, 534641584, 720593377, 251205249, 901298484, 421692680, 803025805, 207865533, 785604351, 258140281, 991763226, 278009379, 59879481, 620599710, 341614201, 421785329, 704945543, 584963916, 756658127, 903671605, 503879586, 617152040, 554413843, 530560928, 359045769, 927432482, 121393144, 351526322, 875760874, 885562599, 578481069, 122998252, 89227803, 260399451, 155708455, 96260541, 394125583, 860728568, 633108430, 890552460, 404280217, 364027209, 407268543, 39987694, 419320656, 137514152, 144998388, 841993639, 688530109, 4072220, 107910849, 267742831, 685372994, 788289114, 151610440, 51604980, 988825154, 792411918, 100265983, 766215411, 81395813, 751605550, 755457967, 30728420, 626832479, 247023679, 983589697, 391822903, 325546336, 776783036, 30986778, 657397449, 426854474, 796231884, 228071509, 153422995, 865341993, 237197007, 104197738, 865109775, 929552360, 813434935, 730290252, 511925067, 386123036, 664343376, 610262571, 482428511, 511977752, 42255374, 550462179, 916262891, 47204445, 787990188, 904749762, 453384443, 715630370, 39202292, 788668448, 359926951, 268280084, 196845616, 125675027, 223330603, 182659953, 723652040, 556940590, 845321698, 536140837, 913270025, 471995907, 483230871, 678787322, 86602388, 89260258, 973196382, 177804635, 680415312, 891489156, 489728931, 163401849, 608578470, 13577708, 281855178, 528835024, 114482200, 401123509, 724722791, 149706175, 416383274, 215032358, 57722934, 800259675, 990100303, 698248438, 838423055, 868697481, 759566671, 517810695, 546759825, 991545221, 321470055, 266330298, 805632, 355675345, 508426872, 147931700, 874660221, 836756429, 45523497, 967757363, 702449094, 595015213, 108436726, 415641228, 461453456, 463346322, 148987097, 91987203, 222070211, 975481438, 125425777, 917969439, 369497204, 824422882, 34140508, 261318719, 569096799, 345322217, 280824374, 884901676, 522239094, 344548271, 122013883, 788989245, 932226159, 768267687, 791750694, 717563128, 738487066, 333873496, 301664638, 356620230, 846994005, 469785759, 960909859, 214397561, 693664307, 454248249, 685562658, 959969197, 544446787, 462840102, 674360482, 359750833, 215104616, 969589773, 294585954, 829676876, 191299648, 67497978, 894281326, 396530907, 821612428, 38453586, 838865992, 284462738, 683310921, 900137429, 132380918, 947606708, 799394072, 212247350, 225081122, 662630227, 287950070, 932085607, 937074209, 437661386, 51024556, 185784849, 868242376, 761471207, 112274920, 674073507, 31494507, 515080632, 605671438, 463054053, 615020436, 966109545, 993114249, 134095391, 470531102, 283308172, 406981926, 825894087, 304604178, 776980550, 885860058, 631788050, 151756317, 542260158, 991763556, 706642291, 583099858, 86050980, 734524600, 703140515, 847842664, 439108900, 304995825, 485681489, 823867113, 134860519, 132885091, 175131181, 94574421, 135717582, 50948343, 374021041, 910773554, 898655363, 706211568, 719089810, 714000676, 412000905, 269515404, 933193293, 672131207, 197189927, 574022941, 246798672, 743336546, 826464886, 12186674, 838765752, 599034957, 485655499, 586200638, 72477610, 692867903, 807862365, 482770874, 102216375, 974517113, 950078823, 90975208, 345752681, 141809613, 722254499, 561676881, 498904154, 960019201, 586602343, 604752978, 321163754, 762657226, 215965535, 117364521, 488283035, 390973124, 140569456, 137566412, 692019107, 826370139, 784321806, 683924612, 588663500, 636565641, 675862343, 67757443, 488567942, 777637439, 180815538, 283010912, 172044828, 935676397, 534443137, 523514494, 873561422, 720545433, 558497250, 413841366, 262312092, 268743115, 910399376, 714074237, 990667775, 882184076, 686809503, 669190472, 516620361, 995897980, 61203984, 165887647, 43137605, 72311397, 717897766, 290333983, 449134745, 717508856, 95190688, 527854305, 787593754, 739381614, 370925820, 36184834, 348615487, 693702696, 886258248, 659775035, 60113739, 773698500, 511990891, 851661168, 410001171, 103514296, 87800935, 853751918, 45684433, 976425294, 891549629, 815876466, 70085971, 471539031, 601664832, 361493385, 590846971, 275244358, 925399043, 161451129, 619022898, 1515021, 811287543, 621530252, 59872598, 821023682, 575097706, 216224568, 798050994, 670801241, 308458590, 387680117, 50602698, 149327761, 380917973, 81119719, 898271743, 202703313, 113285119, 500732073, 621934918, 771015788, 239982682, 155133562, 337269033, 661492311, 333416237, 869851496, 473058681, 751648240, 525821409, 306213953, 495266473, 978480715, 679710309, 475839623, 524498558, 418297969, 83011491, 484177649, 899224751, 52847387, 677256, 458539383, 485329032, 677625135, 911140832, 327870561, 916350050, 943087241, 285480521, 325856837, 367101667, 437669414, 986438980, 961154263, 722234694, 835777810, 775762689, 143257715, 252199040, 112222358, 91944169, 552732758, 683068035, 565343841, 437715205, 248883335, 597295167, 806825584, 374880493, 352846945, 175780197, 487337868, 296566099, 757351697, 489182833, 457584865, 278793087, 646823772, 600591442, 667800767, 526581192, 933820306, 18379652, 907033286, 46629495, 198530114, 429963336, 554370472, 296114182, 178221570, 366126533, 352578711, 564130459, 744757028, 874181069, 80845457, 72038443, 509762894, 355739238, 63635284, 491417626, 837383477, 929769075, 470363253, 707735092, 495708998, 357744962, 412746389, 210696582, 538723775, 360805143, 313197326, 762256706, 567728426, 310231289, 984171252, 213712160, 955314817, 922338609, 393491807, 363962649, 272326399, 707182447, 448260849, 105038666, 101487275, 890158424, 152480625, 926204686, 209099260, 492679060, 307786580, 891001922, 64877600, 517959362, 618779012, 390938773, 858656040, 811786931, 278674685, 532766472, 841546763, 10264889, 98156995, 417550120, 759842005, 941160570, 746572198, 15288857, 813664369, 466589744, 800500762, 713809406, 221748324, 521583433, 3254715, 326745884, 180517078, 134876828, 448306862, 768457919, 667879690, 815730641, 513193796, 475334571, 926822764, 215972569, 922826799, 628334854, 518954749, 481785138, 846189307, 623900460, 153482337, 983603283, 577907011, 163670429, 675284844, 428123444, 498028951, 506091493, 471518245, 679214599, 819783537, 648330629, 585052987, 681171611, 894908824, 426054940, 444148732, 471585830, 739719298, 767547026, 727950328, 993534576, 870037888, 801357087, 273845071, 293317983, 43731343, 502165019, 538937930, 405395783, 552581893, 565528395, 287356759, 633522951, 101699488, 692254323, 427429375, 706834845, 875661779, 75788767, 650194844, 601608369, 604379778, 855683785, 357383650, 257164358, 976107086, 498746019, 88269610, 323283678, 172471796, 425458181, 532139425, 263174227, 167673748, 266345999, 983073459, 883636108, 978659961, 507367119, 702619079, 15810092, 738197515, 211493234, 858825595, 212186351, 272479347, 935191845, 4331560, 634355354, 28070938, 934447160, 403760553, 696878741, 300528727, 407884834, 901221308, 134512458, 666529196, 706378552, 831836828, 467368264, 838605413, 812792804, 262183389, 630022457, 902359908, 995003345, 818070253, 89002164, 205600327, 396473682, 223953440, 527141101, 35490886, 638911187, 907960567, 459217656, 866921803, 887734007, 143147811, 262096193, 508278030, 965065122, 44005933, 319855343, 612401940, 248292083, 64527793, 775657938, 152901021, 310334541, 585945128, 380950095, 822873998, 123168259, 33579433, 264458179, 855161314, 605705742, 197819255, 680530585, 255734846, 291099490, 167223453, 708995209, 675385646, 174234614, 941106862, 681040255, 395843152, 480991671, 991312049, 397788373, 624267090, 413573311, 361814921, 911445489, 711114734, 7537397, 871362469, 791781129, 898748019, 176510219, 986456735, 410651520, 360103221, 973512858, 233138930, 823431453, 670295711, 145545859, 730205645, 788245660, 858538051, 552774874, 765549268, 220080096, 939843583, 287541689, 531942690, 927959694, 783601796, 730506503, 63810857, 967041299, 684938117, 691312672, 182758556, 678285624, 665830956, 996447588, 962783743, 390358861, 494182040, 255132659, 356778192, 87795313, 328918608, 600678096, 997113157, 731373121, 550145894, 878146367, 596218846, 176879221, 462254667, 499304504, 392089536, 110605341, 765106287, 41972184, 525300077, 88900762, 782617897, 228583466, 151791756, 598957739, 571173279, 830921817, 67473963, 20465904, 308177925, 100365693, 856036703, 437072449, 384734371, 824117151, 164476252, 836147604, 822105949, 17366361, 53675200, 583686149, 872936005, 223292575, 475749079, 980008773, 432838291, 772776999, 780844103, 311684034, 326652442, 69308423, 590916454, 720506884, 266300598, 364859360, 479885286, 119406376, 392417852, 539225012, 579946259, 945900710, 343528190, 909525405, 647182850, 740265348, 405308821, 375527357, 169965553, 334305373, 143985976, 335526490, 986434193, 795247429, 784934793, 652287050, 964464508, 66377196, 980368563, 830782816, 571563553, 40442955, 404495887, 408560656, 901672339, 175201628, 329741969, 872201937, 686117023, 149058779, 497237050, 878870308, 990445434, 476202519, 179171521, 977959544, 474332862, 77191314, 752763856, 65070578, 733988646, 364042090, 418709487, 975415645, 510713236, 272543697, 984035528, 458914035, 234876666, 172041114, 398788406, 967429151, 488243437, 140537324, 479687602, 479452951, 954019424, 220354169, 684824334, 764341701, 192057451, 45381646, 515961227, 266134714, 482248781, 969221996, 785971478, 335253977, 618972833, 326148060, 377992470, 572444939, 596017889, 933013081, 905240240, 977358299, 494325051, 550706791, 561559144, 122432213, 99823669, 401173235, 938505504, 716613084, 937420524, 598973709, 681997303, 231927388, 958682304, 496069883, 490364980, 28454099, 330529239, 916165774, 241789397, 915949028, 258682510, 371685580, 107395552, 747891987, 313920217, 754704961, 21051656, 561013678, 143598755, 787276862, 332855535, 508083127, 567922303, 177361560, 506942015, 610724049, 624509778, 489142547, 447340145, 111771771, 481377423, 960012228, 326674292, 598993009, 606188902, 618081750, 691178130, 865511844, 580168001, 554815919, 129634001, 719232226, 886458648, 978447281, 884240242, 272277087, 597369004, 135645042, 520677628, 977596211, 798567709, 528886888, 23873561, 17813078, 114860591, 481178695, 445809171, 193276346, 272906361, 31862888, 431616545, 323812668, 923594727, 233245042, 601973120, 937953184, 182844293, 92611574, 749102455, 726922053, 361691657, 819277030, 92309845, 151240075, 767588326, 84330956, 650629479, 675735811, 774543676, 549723308, 581408875, 245463386, 866900468, 721494895, 635268055, 970412079, 173242996, 208768522, 836075901, 783996673, 214590493, 187838289, 60166149, 555358946, 384007669, 394546649, 633514213, 441690468, 714498683, 956205177, 154333248, 394471467, 925433791, 264842976, 661180775, 557377673, 964685524, 362503551, 636499654, 607099331, 317222832, 964867689, 209285889, 980593842, 714561565, 698085123, 604276451, 567880496, 579515902, 818508588, 73281390, 69838681, 520568743, 817703762, 666171627, 744460444, 287127393, 73348195, 237347016, 718714593, 742107783, 127711092, 278686011, 491420714, 986701485, 972186613, 215967603, 253844292, 22315171, 459552766, 350723267, 568437942, 957618152, 721655652, 426410259, 9853362, 646704559, 552643426, 975214020, 696203716, 330495619, 969042086, 201742020, 161206700, 800701799, 390339411, 621659641, 173497394, 714979103, 146503626, 735916348, 196898934, 780175509, 410796374, 202168007, 707754609, 824023911, 98169564, 437450924, 412748033, 891637887, 261352560, 144797164, 335302484, 937751603, 119747398, 48783526, 739299388, 371108012, 866022679, 84801513, 196657231, 435516795, 341139176, 897285669, 837767906, 184406689, 110481898, 56937695, 218419867, 558663995, 380869187, 703521120, 206914208, 859895562, 458565170, 91633556, 582488053, 781055884, 572624145, 567230797, 104153603, 433837803, 595913341, 173008323, 738491643, 409771867, 993413275, 429737725, 242308064, 199078337, 529882557, 906571488, 739980320, 660454959, 277245822, 440002066, 758434482, 525483094, 26186747, 361628320, 109874822, 676502058, 386205791, 474171963, 66658242, 236618571, 490131164, 169471376, 435682502, 6633850, 239589184, 541141753, 745890202, 351659770, 240734921, 490283690, 268633987, 841943094, 271811209, 34695083, 65387118, 591403960, 405988735, 227522125, 602309279, 630754814, 46496456, 94413878, 803443319, 968718210, 108681517, 510341171, 320309637, 706984360, 615040183, 658669456, 436078956, 223905470, 228519315, 744270087, 135781043, 852417957, 961140898, 949858960, 700361567, 675093187, 479709920, 95228049, 222268962, 97805014, 745292341, 239819989, 379323114, 871506946, 778832842, 993701544, 100399646, 258306115, 877233415, 94770312, 334293438, 5703507, 464678994, 788987629, 931947888, 517831000, 496312294, 377616926, 402281893, 888464486, 903248663, 931297138, 315016232, 862153941, 556895825, 739379331, 651156519, 676134351, 933094720, 733079045, 177668833, 719038371, 665696843, 451819713, 452225743, 809580226, 475260722, 809962928, 449042427, 62877869, 163276623, 126222667, 298422428, 74559711, 498546173, 468898201, 16967274, 944459203, 426641476, 847497691, 188104991, 254799014, 759484547, 613206597, 870219948, 60961093, 318398255, 850303801, 61945351, 947060655, 118506347, 649392587, 826051617, 893772361, 69212315, 212541042, 589118092, 114392040, 851914803, 480305431, 380009922, 716844705, 127929162, 747671829, 545125139, 533006355, 799679387, 1644039, 103262338, 648962286, 952939421, 271112004, 838160623, 37552590, 589448140, 559349911, 950192561, 307422991, 84481479, 362299517, 648440575, 27891933, 156098901, 676471973, 878546555, 873686668, 515548826, 810278954, 854642010, 861120371, 375574254, 377338901, 180043892, 660602585, 119686723, 914460631, 410293708, 802537850, 912656910, 820012060, 559891379, 347521742, 317820317, 43163778, 823518689, 181404611, 397073059, 17980858, 601894396, 19324879, 475877422, 692518395, 594970660, 770472579, 73971789, 179384260, 7576586, 458022955, 530315498, 338721292, 718549649, 116325645, 752426069, 11560407, 232191815, 309606206, 377363855, 586162679, 966399754, 659695800, 845408052, 250252759, 414064545, 933245862, 943640369, 701793257, 233215373, 532143542, 104366764, 725840146, 72111705, 446743992, 543612181, 138793862, 418205949, 138980260, 265302436, 260072703, 508266479, 784122498, 524421212, 409468826, 380938443, 646278245, 65290158, 847228449, 898260769, 79122109, 853993216, 750707608, 399240730, 106730576, 315739186, 129351713, 245990316, 166630296, 278517759, 787185378, 282725177, 961169453, 770602429, 203683884, 606739848, 243506347, 112264684, 757469769, 211383497, 993292359, 667030335, 427751132, 933288506, 658951904, 953646784, 947129431, 938998632, 778332425, 319191462, 686336280, 165261997, 680089293, 872480261, 722188232, 45603132, 555590843, 496667774, 102400294, 491487827, 989851084, 66397188, 245680611, 217084706, 693121483, 696146803, 145117991, 273332357, 942328727, 263844020, 829819759, 886400500, 22176664, 694264609, 16444726, 113403623, 154920658, 862861094, 793289122, 503712551, 226769163, 35482727, 824862642, 608728913, 989071495, 187262877, 30220862, 11777422, 928551383, 43509618, 969341478, 965196027, 602801715, 842330789, 825220236, 57111398, 215441418, 401568307, 500450596, 425903166, 894801258, 139774067, 750227708, 878549546, 107568120, 53378229, 132017763, 245819844, 271319020, 387699490, 900572844, 136481632, 861514504, 275296440, 430820285, 599790448, 914517255, 715099852, 806422578, 595159555, 753483174, 308343307, 36858873, 30143574, 916573980, 127997884, 276776502, 169733711, 948795194, 9219195, 198253048, 937574182, 705425834, 231915027, 352585959, 362100534, 267926188, 497777342, 420459260, 812480491, 749059802, 597627295, 434297195, 617916483, 861435990, 767238433, 585217087, 262642764, 307121727, 490737438, 395408648, 991336621, 317270992, 876001960, 216754040, 809858905, 608481763, 37902451, 998956886, 483460729, 764984507, 177948857, 733533200, 100805966, 642296903, 806918250, 673625075, 92247879, 495244114, 851560009, 304739164, 840533725, 256495618, 94128941, 321263486, 327654514, 8370830, 214780409, 154988970, 855266651, 550208046, 966524423, 802864533, 275649970, 416167997, 151260748, 487394844, 175485503, 296016956, 422596475, 410156209, 249838215, 884957745, 703440663, 686328067, 75841068, 23713128, 633668563, 61774790, 621506552, 71355887, 557473884, 661542788, 411730336, 589145946, 783098715, 759240207, 864943971, 700919956, 496440090, 878786454, 483862695, 740246747, 11998468, 669943815, 789722300, 740060398, 908905466, 750273233, 902498923, 230218891, 55400931, 783438817, 421127729, 128407908, 16633657, 491862149, 761444939, 186971307, 479690756, 690576036, 383885914, 294426497, 138456827, 233043899, 755793628, 403864452, 395460026, 962696963, 120516849, 539239854, 183538834, 245012400, 682428477, 633485101, 661490307, 34478148, 845548435, 418472804, 570801517, 297474310, 393869080, 233923120, 491884222, 859554639, 434636615, 401842051, 612845325, 266369176, 820436016, 226125905, 331671120, 918631187, 202822481, 408216322, 242574706, 417079369, 966379941, 579131434, 218104486, 607908643, 852557197, 825469367, 746553280, 921975969, 661642235, 535619050, 431763461, 806331895, 890639030, 314477423, 590438644, 158070030, 277208429, 183132016, 748066803, 183323219, 107097628, 860268261, 447014554, 828311163, 717286918, 323965112, 275315084, 224404751, 843684178, 640396605, 368320591, 495747529, 722438083, 181832673, 754482253, 502381330, 644025878, 708975141, 342479951, 461569048, 882675531, 894182401, 617149456, 159824106, 128407547, 250261707, 123815284, 692386011, 13052379, 702118824, 594768345, 312318282, 507920713, 3946239, 865477055, 673623208, 348126603, 455262423, 838624924, 767074906, 143258785, 939528014, 317632162, 212949001, 344747875, 488704158, 615534967, 650609514, 839221715, 431851249, 916217320, 849690975, 358705624, 738571743, 780991303, 448320860, 906428685, 271549139, 464910408, 728579304, 104628840, 732335687, 256695484, 966925670, 101081802, 941718956, 182358349, 918205841, 28026751, 941143803, 349428727, 702151831, 370201276, 685025546, 385272863, 15272470, 377402135, 813776324, 872390612, 335416692, 592854429, 943389433, 586302250, 759666086, 122070499, 519656566, 818951103, 870972872, 675906474, 483866184, 732011224, 25261410, 197175945, 830747281, 587533830, 661200256, 777060167, 445068936, 129198820, 158956629, 522876845, 988406181, 145007665, 960482698, 462542222, 988417042, 840934877, 31353944, 894818529, 755613526, 907526284, 991466445, 94504471, 481180178, 51850727, 56845535, 680322209, 257343089, 953093267, 502104421, 987081840, 241216786, 109792601, 169448535, 431451197, 587969295, 563827463, 115380482, 949576444, 172303100, 458978420, 783011822, 891122572, 376431854, 881044335, 513673959, 571817892, 305391996, 14778495, 936258838, 822222549, 726817288, 61075341, 90351933, 925181062, 710749583, 77888472, 942138594, 364591248, 984357540, 9611461, 614924395, 84422473, 538225983, 244318101, 774855695, 851244322, 394909119, 977886332, 745489269, 780048639, 256236009, 261619517, 11447864, 651614159, 482127612, 840616361, 116326989, 31659085, 91763577, 64887688, 617963442, 73220627, 746953014, 287256906, 70890480, 320319473, 611352434, 66020711, 992417820, 495279651, 400237107, 84380336, 544376653, 161132704, 609792890, 943858695, 227039375, 667438558, 334680911, 269549890, 609167406, 256206732, 665889609, 307365666, 120974583, 274028793, 338494854, 134526736, 377527683, 537720256, 270385592, 744762546, 700414345, 590122810, 289794070, 819743482, 49976474, 897267920, 322469049, 821163708, 458491302, 441232168, 920129351, 782126946, 901620660, 771628289, 984699155, 560410789, 377354455, 569804162, 847346568, 909963588, 60224982, 39423043, 849831216, 399698384, 224338899, 749785623, 804879254, 620590633, 305289241, 369073298, 391242429, 806834696, 821916457, 367311874, 307730820, 156545976, 159182834, 151558586, 939701744, 283852936, 617404198, 371736057, 117523481, 681162420, 400821120, 743661324, 503203594, 184740194, 343458858, 284726980, 111334327, 87834318, 323454046, 449986335, 838406066, 151782781, 318878283, 575249476, 492229110, 374736463, 370278680, 71274259, 988677034, 401624303, 165343796, 896893196, 153110788, 229474163, 338786651, 781475066, 692953352, 783697043, 19622186, 979166196, 880787484, 546380476, 694721070, 81055586, 829326322, 393128648, 965565, 54588055, 461931798, 818951190, 224666631, 422189647, 95042455, 49968168, 837744004, 69754132, 740724832, 965793210, 51039130, 726459309, 322682526, 653887102, 313898375, 126463568, 473972644, 429703076, 269252061, 453719304, 417235740, 313695010, 823544063, 39098495, 469228727, 774101172, 779141396, 786827970, 78558213, 350756721, 221379255, 721372259, 725908246, 120327304, 68101505, 603053334, 57122788, 839946470, 810633565, 380048342, 526713020, 889712043, 429418107, 883239830, 418795830, 374056041, 16236426, 357382624, 220193767, 344304352, 949725395, 596493042, 357316393, 174515703, 475585585, 527951253, 413660238, 941604857, 661195102, 193127586, 144241425, 499010011, 999500841, 662719259, 37903768, 840833537, 447684596, 405348610, 457711100, 275249643, 238363721, 966730211, 217772657, 657194481, 206628084, 882220919, 190608476, 790441693, 742448102, 375758489, 676384672, 48717934, 537702158, 983071097, 245710285, 158290004, 187582768, 477591809, 985099392, 794745144, 198768673, 289202467, 543745929, 101046942, 941262823, 798870068, 783381931, 440279499, 816801842, 284060347, 359182524, 915088178, 458465843, 540025912, 400272864, 494820333, 275043725, 361484647, 156629262, 342502516, 274448394, 821727757, 165591775, 626762433, 374823413, 619386913, 370010984, 104921633, 188087731, 691019303, 150347514, 830499392, 126848915, 227363603, 130050659, 7647471, 552939033, 803479940, 834608467, 693967667, 295914381, 833777675, 887702286, 889063953, 768073945, 881829843, 158943959, 266390003, 829497006, 47423145, 221484632, 231423270, 862856712, 972400407, 763918514, 750298603, 11339049, 75634452, 488576313, 627046293, 649691226, 673205572, 445330999, 88360829, 592507085, 311375056, 699611676, 600355982, 799531386, 769610915, 579692912, 873373967, 304615960, 776465119, 434862714, 357842356, 346926856, 139801896, 539993275, 421229197, 46673106, 918515590, 534225455, 102279612, 797629918, 578220525, 924358904, 68541285, 717605082, 904682916, 46243756, 708671598, 839557638, 494240129, 732853252, 91497645, 982827274, 506194191, 817869756, 686215949, 991554200, 938469469, 445622220, 285746600, 54491821, 897858777, 636280368, 912031633, 828920042, 264160889, 350716689, 403680633, 700792844, 334073644, 635996754, 782083287, 911420742, 3275135, 109267833, 550223136, 500448338, 490198079, 205679562, 818482742, 853072655, 579108003, 390783490, 684794894, 880572464, 772467307, 59350975, 979453196, 147583668, 2799021, 520148808, 943965578, 580129649, 110013974, 134293422, 313214699, 375988040, 749401871, 703577893, 594529739, 490758402, 651308414, 146382841, 630612305, 502783671, 275432108, 416279153, 813373301, 721942772, 133578982, 538329591, 86655085, 900685365, 84711938, 807067306, 991061773, 206435234, 185795562, 584649194, 805122162, 74738440, 198844821, 436340724, 939878341, 558415435, 561004431, 490673610, 736291374, 765924783, 389096199, 195024650, 612293223, 762370213, 646079088, 21224356, 96364247, 262008730, 389518108, 857216905, 544091482, 815011057, 700302941, 316042752, 44795493, 730440990, 116316400, 207221261, 475910079, 69359992, 926155279, 437728165, 683045013, 454670194, 414616463, 20791037, 4584922, 13063063, 780081048, 353905688, 18977310, 309830601, 351487718, 74597298, 269168801, 849358223, 774073818, 881551854, 616884847, 237314791, 950708676, 926508213, 308312512, 587782297, 618403982, 889174212, 993446864, 130870495, 509879780, 762732373, 912575266, 290884251, 648906252, 140019741, 112931905, 355082844, 153668134, 493059286, 133137048, 123494441, 701775459, 876310199, 757994490, 124663820, 79371687, 412734353, 323251942, 60721499, 734344410, 36496052, 127622108, 331993243, 642970089, 768812540, 264873271, 963296024, 381377623, 466617273, 46833659, 816450635, 617693522, 691773748, 247460315, 553260496, 50733490, 170178635, 267260362, 198903684, 993281857, 499185384, 157934877, 663571591, 781446187, 857582438, 347309049, 658614028, 309406412, 824049255, 804489307, 831295883, 584490011, 976305952, 412792224, 618909365, 701665677, 856425022, 601925379, 315037364, 862733748, 592570686, 471983336, 318062259, 19679068, 653116217, 276714638, 511587512, 689173976, 478011689, 108100257, 200896074, 357629990, 341753125, 956494888, 351942699, 980250894, 48100610, 825595009, 838328063, 764145027, 482409118, 387207587, 713438003, 717010784, 501299420, 652013692, 586776676, 860542760, 592796262, 324673761, 512505414, 145172157, 543706553, 604106304, 627722273, 881516947, 277233778, 341562233, 743829651, 394647825, 431239806, 636071576, 866402032, 402224962, 592526139, 107201671, 46016269, 111802450, 680590715, 309318992, 712863167, 535993913, 593055133, 685895260, 651878562, 262560473, 118267832, 465841290, 855910442, 176261586, 671610029, 297359575, 379606795, 793265420, 584146273, 691827966, 218612584, 9767539, 908216742, 497909848, 928388625, 920841791, 732831482, 552897072, 413751035, 652081908, 310853352, 73264805, 264343512, 975792741, 254569573, 66180942, 646637455, 648643634, 107797943, 199678339, 417834625, 770580014, 126416915, 171943896, 799251759, 106069873, 598605474, 151689982, 106226694, 896041846, 172653743, 438886344, 694233011, 755632579, 768030794, 72186403, 382253565, 530290220, 18398896, 381569514, 117700828, 987610510, 300780539, 817171224, 242864462, 45451933, 264370859, 226004518, 350520471, 64808793, 413916361, 38386643, 457565193, 696249402, 514985766, 665271822, 460417375, 633693263, 473554189, 112038024, 355226355, 95144279, 667861591, 173044764, 287837803, 928079326, 706389852, 627083416, 222242430, 627730489, 421158540, 887523837, 371599325, 140857267, 550915522, 821046819, 684048119, 505286343, 102628758, 972703755, 198995842, 464037897, 743125608, 858296155, 190997295, 297356800, 433499071, 213987920, 283350579, 632278822, 838944320, 732453331, 447261852, 507822806, 991542371, 82401742, 599350390, 96731403, 489349439, 866904284, 835429135, 250018291, 225664806, 560160124, 13174010, 893256262, 189277335, 770421320, 277600324, 512903989, 165986253, 429773747, 871604621, 572091494, 264170386, 202882438, 96095936, 398171041, 260067545, 137967251, 156028419, 74643323, 649820794, 936306278, 19696722, 538895923, 563066862, 240510110, 354009065, 244068855, 265913639, 210609039, 384084470, 767876925, 751108306, 536646919, 61294353, 161702146, 902821455, 652859324, 446036756, 920216677, 755484747, 379162497, 845253638, 566516841, 260670419, 38516526, 249099623, 187583226, 217664452, 741921507, 203416089, 132098034, 479384943, 929147940, 292764128, 590104500, 981598203, 415410595, 620388749, 295380453, 901430571, 417139736, 517499078, 378626822, 648504304, 915774518, 644200106, 471532017, 560230199, 234527451, 286660168, 568039757, 397297932, 399395069, 455496402, 917575049, 937205938, 101594302, 106630427, 192041652, 372660110, 243699738, 487450875, 172505265, 564552511, 238590814, 258026913, 904342273, 434572825, 220094930, 560222175, 796112726, 813977315, 360813279, 734856428, 801527145, 620632545, 248641079, 452604336, 466894839, 453239370, 121640906, 49556302, 790276056, 362245151, 425065151, 754444537, 289814833, 725793254, 904425424, 942664214, 21862785, 541604084, 949231076, 940390144, 597801166, 426149449, 195029753, 292055, 251470607, 389461271, 487567652, 51897983, 415290506, 477262762, 633780297, 889505701, 754579803, 251182112, 72955838, 901820006, 996444970, 112061854, 198775630, 973505072, 277386336, 374881839, 456093534, 959095243, 794185720, 491877538, 15514983, 452730129, 61643053, 926150749, 264714826, 837144852, 477465923, 802669126, 680602266, 982595470, 753176604, 89694151, 516907825, 748906399, 441225893, 572314284, 41956052, 764618595, 136244891, 863610356, 414225758, 30765501, 345960412, 667756950, 30857959, 140885934, 630099533, 835176303, 648912110, 339815910, 175395102, 23903801, 929692868, 52799381, 700826562, 22771533, 194000897, 251937514, 844753779, 487506318, 144912509, 585974306, 54581534, 376991718, 760005126, 357171136, 238769805, 19580699, 425924547, 815385397, 916288625, 876648938, 488202365, 989569584, 230667052, 493865657, 337584461, 523122870, 264300447, 898838526, 125334361, 846471863, 512705808, 213380910, 577026155, 601842961, 100491138, 398532070, 650176755, 35196079, 62462031, 666188543, 880212076, 259998038, 813747566, 883841681, 275864350, 193061884, 329319700, 598098562, 980513580, 273787638, 110203545, 413703799, 115654823, 689887127, 989898878, 387826592, 672131810, 406530839, 904183643, 586633857, 64510009, 681071156, 532198451, 178802784, 164356977, 476179433, 782911848, 938759586, 809523226, 501306340, 647474741, 709564577, 62189560, 655748492, 223954792, 48583339, 487744408, 260621220, 669601342, 330982875, 611193688, 658636621, 453341404, 948529641, 139330958, 451139525, 786795199, 978216902, 642453791, 856723563, 503168388, 589003394, 505676606, 535723691, 405806103, 491545840, 173198079, 787871250, 759881503, 516140513, 124720984, 50338043, 859178985, 920116835, 896092550, 942490700, 901499685, 644039834, 791528349, 64207408, 910801362, 112758546, 457280968, 565129342, 560631741, 299211179, 196488398, 316333872, 447407654, 199992402, 373589609, 211243055, 198204091, 593770656, 518595456, 655675808, 39262696, 588877622, 228408799, 144380476, 2077314, 27892170, 966138518, 302716660, 565069208, 211232706, 579665978, 973873063, 931794823, 732413250, 527889800, 907999836, 540604005, 312298267, 874813970, 46555252, 40486715, 263000585, 11410737, 635227948, 182796810, 761312682, 665546319, 192942580, 708570083, 795465913, 499978724, 5332657, 858622660, 472732039, 609470492, 88365425, 799470382, 902300863, 354562056, 934926692, 175152443, 529828828, 417188443, 109811768, 557955036, 298505775, 715460500, 489930959, 865908223, 895425229, 681621824, 88194766, 694008957, 665854819, 537582346, 286955939, 220867277, 227351508, 609020426, 881620482, 632034226, 903853450, 194820960, 822499573, 385292201, 633177113, 338492887, 687642938, 44704837, 680747726, 648919616, 728161489, 595392312, 288348946, 673531831, 436159440, 168224401, 265576848, 250358911, 696675236, 38181561, 185288917, 105862679, 273322632, 755439387, 177232044, 978860171, 674320733, 921003494, 532070160, 845004773, 388253207, 594436346, 432910345, 259478574, 506747179, 987105179, 755576488, 155621057, 211371223, 83112529, 815584995, 848445686, 28532247, 494660397, 386812403, 41884134, 814172805, 64727581, 927281748, 832222849, 733917621, 789205125, 736751416, 935454185, 401610251, 277857885, 442402843, 865979882, 882671085, 947034513, 660482815, 358219117, 444907313, 256237863, 997280031, 398589603, 75485054, 727206408, 103355978, 402620286, 353909236, 754582897, 439482934, 812539868, 606997118, 786534169, 338539097, 265270400, 911137261, 474880774, 183535756, 162678202, 137389819, 184561693, 177547337, 750086392, 575308086, 788911833, 361197036, 292296619, 147174329, 465166633, 354378341, 520598646, 760200194, 719035673, 650076070, 710634283, 835741177, 934134597, 274317758, 257703347, 430139491, 806096710, 561053446, 493413105, 148978341, 623026641, 828970747, 669132717, 566556154, 712259925, 153789210, 131701240, 16620790, 730886005, 723809706, 613243777, 190703377, 140944795, 628934484, 712284225, 823909722, 523585951, 107345019, 397987725, 799564539, 63063741, 824022925, 42627628, 932510526, 522591848, 837003001, 851304432, 521421452, 451461769, 536572668, 782867680, 224711412, 953141771, 907949807, 443374727, 706698923, 696278639, 798576274, 160318846, 678059576, 225969376, 322553745, 730931971, 482024658, 420625371, 607802039, 389068115, 989613268, 958845539, 802504263, 903864409, 215411677, 735336675, 417512450, 422998069, 858848132, 590917835, 271317898, 171346746, 996073605, 986588234, 62863229, 154063513, 847849444, 588550531, 39777817, 499053933, 132566264, 938756766, 887401403, 643153261, 208784302, 270971630, 440361171, 979599566, 83290514, 788944153, 951222921, 786058195, 452406902, 600593375, 830593159, 119973365, 77440400, 79302206, 105234644, 735213203, 171013340, 850229081, 871497468, 209729684, 799993031, 9198503, 21849629, 433133418, 867217835, 593286164, 573325300, 933166195, 581902040, 797189311, 260943367, 711758997, 731464820, 864889402, 340818894, 760442532, 413377056, 587206381, 19171570, 949925874, 560268087, 73729964, 535442674, 882936219, 408133196, 918182807, 360548390, 713217772, 500953810, 275160135, 824773820, 764258338, 445027068, 159088674, 933550497, 357279468, 771666012, 205059183, 578867913, 264769500, 375978976, 472262667, 965649514, 630515931, 800798070, 356479781, 181002546, 720263995, 243316573, 22011608, 168654920, 542025485, 223903130, 665401281, 435073798, 549197527, 824548147, 108892333, 587986875, 894161211, 313290857, 148820806, 211079470, 174128679, 343896205, 716881015, 70045248, 299318457, 808702977, 267026480, 659287514, 149946229, 949972863, 880332310, 220621114, 469536722, 951980013, 694098101, 263219142, 561101484, 994431471, 230213198, 476051982, 821696772, 493196909, 905576448, 382876442, 791209067, 949036115, 217518480, 62221077, 42521671, 294170374, 628542361, 99734350, 250586145, 712435539, 696593127, 440147051, 774331040, 390628147, 537481553, 996541541, 609845028, 864917078, 768800226, 20577943, 669755106, 714184567, 789296339, 788632177, 664354461, 533469981, 907229056, 332679894, 93336418, 162341542, 543689387, 362752613, 135918538, 976827533, 626485698, 968202846, 927449603, 431337332, 58071788, 273164626, 70386982, 784459119, 884086349, 982407273, 725439576, 428356489, 809901574, 981965378, 940400975, 603819748, 955210949, 298749678, 688655744, 90640371, 776952109, 165403577, 532756286, 85046173, 471733378, 842843893, 53235250, 727721385, 271753196, 988972557, 972548837, 495613807, 723530352, 451585593, 367562379, 689876409, 580628052, 198025119, 552941543, 377209718, 430795222, 195479081, 579527625, 23109234, 450592803, 187715556, 183922142, 254788690, 330172387, 673700604, 824795781, 415270168, 872277361, 822372071, 436886547, 43326825, 876807592, 168904159, 289015869, 737429756, 2816519, 175458626, 502986653, 995404795, 657479332, 852743386, 216025448, 604835310, 265922956, 870062694, 69634142, 644631913, 227371586, 455213656, 499216723, 856536, 531001934, 949370982, 869618335, 363879440, 217613128, 378303477, 214259861, 791159216, 645785400, 238916699, 734816922, 408729744, 873402763, 682537468, 255021633, 200054950, 199595378, 608095952, 590202059, 625040717, 256385135, 651558231, 165945176, 666568268, 686493776, 995963738, 522022672, 878271092, 791730363, 836740762, 851768889, 577162726, 868758045, 256695257, 123376050, 590536443, 655209570, 211693179, 516323053, 747207724, 197893550, 746385132, 337773551, 534068649, 184616578, 152254229, 160359156, 809765179, 18601856, 843231928, 289893854, 691130419, 966473673, 61789148, 768456042, 841286222, 656300540, 376428315, 60642873, 435930088, 805148511, 848631646, 566187298, 832917923, 624900532, 848227933, 10207521, 581715493, 201869244, 305564778, 71229963, 856053134, 431107460, 57364590, 818209700, 300144615, 636790741, 731093655, 965154034, 729285652, 675574314, 940007056, 379135875, 746840126, 806244243, 317486805, 404132523, 558583582, 400184070, 473155355, 688984747, 265187534, 192030925, 889915412, 175148676, 814481376, 38805707, 583994494, 788218417, 863804979, 979882327, 126777113, 515880582, 64046480, 162579274, 64918781, 677374722, 788444466, 822707028, 557563503, 613885176, 591941832, 785822518, 175188436, 113744822, 562992286, 98707985, 352174519, 228198117, 730549956, 107162166, 246982953, 729613255, 228511632, 368377484, 559063018, 131447108, 570356448, 588948210, 996023817, 726545501, 160490477, 317480472, 109468140, 17609779, 870164725, 165580459, 670391079, 603204851, 163274606, 254972777, 206823365, 652525796, 166697243, 358669093, 19504782, 760243599, 278509644, 442354112, 41562744, 429789417, 248715273, 569532963, 976480932, 350003706, 74642102, 450630043, 595724143, 440310916, 99016376, 69777871, 959096216, 905355385, 139889455, 580636060, 95259756, 337811673, 358341079, 551362611, 375708091, 615381005, 295727525, 376287785, 385039563, 457419791, 444060651, 515716665, 526652198, 444111968, 932030047, 670854224, 296551126, 507085822, 848076393, 382560417, 682707484, 827836327, 593548419, 207483679, 260409226, 607736506, 824857507, 327060948, 760370774, 643730650, 300012636, 381475479, 585269229, 197543277, 37014761, 816393708, 428229244, 43808634, 127487065, 720769059, 498477631, 63567047, 870676743, 369925298, 913355132, 251676894, 633574834, 844940090, 871908458, 552706292, 206431197, 789877522, 365320156, 191033174, 115938667, 469269546, 757399708, 800787402, 498415935, 965804875, 7917780, 652682443, 902237460, 967889310, 410872947, 91859322, 335473662, 559305898, 306151252, 843379203, 71560703, 161529531, 302336161, 53649287, 244897674, 853132982, 822694020, 696334242, 187637639, 657500779, 364557026, 684105073, 902387471, 897450011, 845097008, 207182923, 742408349, 762333488, 207140333, 345207788, 430466035, 606602073, 314646204, 663905005, 263177966, 608839747, 941673735, 996119026, 924098307, 157673935, 454289631, 145082128, 762201018, 415699446, 804365058, 170427782, 977595948, 436672161, 13695828, 35813780, 138422923, 729425141, 680357414, 513190488, 156665067, 330171044, 19042455, 618544654, 599637975, 576502519, 237860593, 817008471, 70345404, 249155890, 516010464, 831648324, 20455228, 810020007, 413698005, 164716246, 854225395, 36428319, 542594806, 828845249, 363490950, 424922075, 482544718, 55197705, 499024795, 103353740, 238920329, 958945583, 598570711, 826099875, 519927603, 972195079, 820259464, 812583656, 707782432, 443267683, 841131970, 645097574, 73584378, 358711559, 98757891, 201900700, 340656356, 138604563, 953868689, 864265365, 149166736, 288099661, 817461491, 906205810, 400678695, 708296853, 650164916, 491611223, 74637041, 510245079, 394461930, 175468945, 841944676, 927426098, 636582015, 578335688, 205431291, 198992931, 526431051, 792571928, 649029541, 109427637, 838235453, 67264820, 181380626, 956194479, 343733402, 583662298, 631309329, 12746419, 922345544, 652794733, 673525454, 784633206, 332948989, 858664225, 911004600, 991128058, 503841185, 298001481, 709307886, 11715769, 253932862, 543771600, 333712074, 83942105, 354966838, 288733648, 280331736, 389186645, 354099660, 94474148, 663194908, 697909243, 780640659, 96735145, 610251791, 103681806, 396229756, 996644687, 611542573, 669239182, 257535382, 121704928, 553167420, 458903456, 691263049, 128051666, 445032958, 10211676, 197795416, 50492589, 200507509, 753017095, 195673198, 695580729, 715378492, 459778827, 102934036, 524935641, 209053807, 714993730, 670351279, 278458377, 675356761, 731474268, 32075051, 999154195, 899809689, 978459524, 300487313, 309308871, 502691312, 768098434, 519833799, 255706175, 236689014, 320268605, 485789048, 156438261, 208245903, 408942471, 30174025, 713133966, 616541684, 771495931, 151638177, 822241755, 58775269, 252789606, 869005394, 353189358, 238436483, 942970949, 300009087, 963220930, 669695523, 652741418, 641859820, 477371755, 100888607, 719278415, 450087152, 300593026, 497489584, 477784699, 771657232, 69422195, 92792938, 489866360, 904652276, 727097924, 882871805, 445981070, 482262475, 20538083, 902392860, 453410996, 650914262, 667317004, 956509548, 717143458, 813616012, 30613808, 160812067, 33946636, 565547628, 98131823, 63968729, 374648233, 580072152, 353993211, 123381690, 189943782, 767576223, 368003869, 842600043, 832579638, 103017235, 95261486, 765099816, 492543021, 568758492, 821161414, 146915204, 328955764, 270023319, 120022274, 189984474, 221763691, 55992742, 640640069, 606986037, 441910466, 946771096, 712348230, 217532057, 255807092, 511504980, 320989283, 755984257, 266884073, 748844321, 909998968, 776850245, 990889170, 651552909, 800965820, 149663706, 667568035, 501013983, 691026443, 122677168, 817739668, 239032084, 76320713, 972870722, 876512219, 83325293, 911585721, 608329676, 626317276, 162097837, 332252470, 850778627, 302651417, 493916263, 994962866, 734507053, 986600913, 171198090, 411606222, 234013887, 508152126, 403850503, 487150479, 542495447, 799135254, 662973895, 806621278, 209714576, 27757771, 509313695, 182298047, 411471573, 528622273, 464472315, 483133772, 63394196, 710648195, 415443683, 570626746, 971255973, 514662733, 176515328, 119511007, 44371131, 550554987, 351853248, 572532130, 786303657, 257864361, 93987925, 715329686, 842449972, 328708761, 358661737, 264685541, 412095514, 941634446, 461770409, 72442771, 786904110, 880002053, 324254512, 999404757, 816238334, 346172959, 112298395, 949279121, 429815675, 20066929, 448156115, 473775439, 750171651, 102993418, 3431823, 754777183, 345262265, 151220692, 545518967, 494224308, 410361020, 611208251, 453165322, 29982556, 503013658, 408264203, 287061613, 12792194, 367653469, 260550057, 895115511, 631709875, 666086139, 841407092, 357901239, 528883343, 650953159, 350486165, 812195536, 146021683, 248107729, 954092854, 341499924, 378805406, 938104796, 424040232, 310584733, 527661531, 730049485, 999873941, 129688748, 519547351, 477256057, 579546212, 615077247, 369282888, 39955395, 953272447, 692813268, 336229846, 827145450, 326851720, 548574200, 342395156, 323722284, 205474918, 43442197, 923790920, 214595133, 668447465, 694980596, 193755554, 674182101, 392951999, 953274795, 206447195, 758371887, 875894307, 332225578, 143061307, 531440849, 102011009, 941937679, 398165267, 53123728, 491866906, 224760487, 148061735, 231147204, 667018445, 773725228, 624542435, 432671273, 22606803, 604946051, 627735318, 623382419, 100829448, 23441942, 351789191, 169779800, 578886989, 282079055, 947527682, 344526939, 634436225, 903238457, 12642472, 303329504, 195244900, 548591537, 918477948, 30464334, 966562119, 402849388, 280956539, 886244012, 747309743, 329667171, 379107947, 782430583, 77129728, 912012570, 246592016, 238736842, 95469708, 191194342, 159337732, 276738477, 223023648, 479808587, 249648246, 290668165, 958460195, 361791655, 691417393, 734679834, 826645186, 803244682, 344304720, 365641723, 616161448, 966860150, 814850525, 754280677, 182050124, 475828654, 360088508, 816503535, 235836863, 24798226, 816555739, 882011108, 991070388, 547038468, 357603102, 174153108, 161287663, 694347073, 730588135, 922226621, 346834495, 446123616, 150542728, 238391242, 770599265, 794729134, 741533250, 86984474, 633305094, 585847945, 838891907, 416807891, 846480087, 607443319, 404834621, 766613686, 334360805, 227675165, 731826805, 450008513, 436042342, 796673255, 266565614, 567200834, 449653785, 584799935, 37667389, 36496554, 326891529, 633502691, 872971082, 28797213, 506333958, 138923424, 348806147, 4428225, 457211884, 92586199, 190366170, 714673050, 263723423, 955301375, 158072234, 477110443, 799522813, 475257534, 236515360, 623654672, 552865181, 705975363, 331854443, 534151605, 477998291, 186926311, 475798476, 79227493, 619484665, 227139761, 974330107, 771175620, 149657501, 116587252, 613057865, 206622447, 814697975, 16015926, 606376748, 95483770, 775822971, 255434378, 850444260, 349679342, 351169237, 960202749, 57305047, 366291292, 405570871, 630201225, 500689650, 88485493, 684153433, 508994710, 881491704, 700859437, 205829667, 761995276, 853842719, 425717944, 979029429, 984567787, 873785172, 651367836, 75224954, 182308436, 552307013, 915779211, 482875350, 293686264, 93313462, 55874661, 259133714, 699744573, 853922152, 137830442, 329794640, 88599700, 608913333, 104774965, 140762360, 949487845, 984612292, 647418600, 184999285, 356829198, 726458218, 432287830, 334105853, 216661910, 593172724, 124615880, 821555830, 278067307, 73706412, 168644775, 440863097, 805822624, 570094926, 684529293, 495096428, 682212265, 33537686, 696272690, 303131272, 792455928, 770657395, 868599076, 489122371, 550815919, 111573930, 112620075, 956691476, 750627300, 16292527, 90715073, 573892029, 242025226, 13591616, 446556344, 229893257, 454394280, 422154568, 40062709, 249473516, 549713510, 432715011, 262065522, 73248332, 772675032, 957695608, 789459748, 340025869, 356217285, 239743090, 789571230, 932850564, 401055326, 737836468, 527304660, 322508532, 40766434, 713394842, 293730766, 932268888, 632193397, 147047742, 55988889, 251995181, 479904274, 687797230, 275172862, 291100329, 975187213, 286715093, 936351394, 569639183, 279976997, 200357626, 388899851, 324653146, 139616002, 143834063, 733886741, 439407207, 836937388, 414535735, 817720342, 872643977, 895287870, 361866708, 520944305, 978216515, 417611506, 703785634, 832829094, 565172906, 963516171, 681475911, 542906625, 275687226, 536099520, 564869024, 716122903, 664860996, 182873656, 546526364, 104445386, 770682417, 783569136, 961088215, 824444224, 556427879, 684267239, 500705366, 399741318, 875891911, 88945279, 580616694, 139251894, 991481768, 894972463, 453801399, 506164775, 234104029, 768720849, 220876955, 128449713, 111038780, 944300807, 670570509, 168061775, 272613433, 523382287, 954701407, 455207593, 985246100, 832988236, 773849609, 532221537, 256346889, 414979339, 839243029, 608897508, 229050458, 406435471, 995573677, 160367923, 850898715, 783670683, 929554770, 757831238, 548950029, 501134534, 265733161, 399692186, 679714318, 571771152, 846346626, 491478357, 365864900, 578918391, 412098631, 129598497, 178527037, 767280365, 602539592, 529044697, 982920016, 407698888, 142081875, 639301897, 104338813, 367228076, 121435324, 200716816, 700998743, 707745056, 165880902, 258752991, 518547770, 559935719, 667562964, 317531441, 8758426, 346173889, 73363656, 312913453, 614479667, 919357481, 256306254, 100047913, 320916021, 59086175, 907075363, 461753251, 881579315, 777390109, 651559148, 198783604, 437920934, 14747041, 118174913, 239971055, 80341596, 122576484, 694084832, 91158425, 258568038, 695907856, 552272869, 953551323, 793737751, 65887860, 589184822, 745106064, 360673559, 178317894, 348248111, 396650592, 353940862, 423935265, 765360435, 363602907, 854245044, 819929785, 82817188, 214777397, 423310899, 336801630, 976192326, 960928685, 359718716, 684171877, 66270106, 565827893, 981698586, 698719855, 271654907, 111639338, 344594770, 248951806, 579330620, 709967883, 910980961, 569798936, 250854867, 723655759, 923947289, 341650461, 121931649, 169477336, 875822957, 856199905, 782806968, 158490305, 407783288, 428227660, 313388995, 666456282, 145985687, 363477623, 611093587, 207545778, 869067233, 280826534, 104199097, 102762804, 53754307, 889294862, 22967183, 140039053, 26303819, 473247412, 176192716, 649829249, 797534404, 168531159, 390402398, 930463602, 474710053, 176298219, 996424858, 517931855, 755794578, 59023241, 847941047, 60591172, 389706918, 639655759, 676926560, 162233279, 682456036, 657454911, 527064328, 667312354, 563341476, 305800901, 503095732, 194515149, 417530359, 342134292, 385628844, 155685860, 358036081, 529535740, 501388889, 70073543, 624725256, 368309873, 68525105, 557959353, 650087098, 292507451, 499599354, 464521166, 53697175, 146695027, 868338878, 722323046, 959223812, 444905357, 438604630, 780581449, 735367502, 740126887, 46561752, 729046881, 922830594, 937596199, 420269753, 142644353, 638974424, 26976093, 461886723, 988005804, 720124580, 545330013, 316747930, 664346357, 304897634, 271729062, 934519503, 315502513, 630039111, 265668180, 514905019, 266181479, 721517070, 9750556, 492702117, 796387231, 352047505, 638399745, 63331513, 138136588, 25809218, 807564862, 268197298, 9997187, 818827936, 314481872, 83771110, 372666339, 523086981, 725642427, 803150138, 717930630, 222975676, 491859032, 633602885, 966987636, 946854406, 544598813, 420085450, 883803886, 227699352, 485383367, 410722285, 66487260, 619589778, 610198360, 940025718, 255711118, 555076605, 890613624, 72812511, 872550513, 803415575, 747305603, 338373799, 454553261, 453015167, 357467752, 841787874, 832725426, 490748296, 349029984, 172087429, 361137575, 337583772, 445826229, 511108999, 666353070, 902311329, 931684506, 643506142, 634114865, 543653093, 189602453, 871727889, 128376309, 275266270, 359952147, 482695719, 711065079, 417565507, 487118308, 151641897, 566258714, 221435261, 399291992, 674017818, 347060122, 20128848, 882419045, 323312138, 182816315, 453543806, 61757894, 486769464, 232338097, 559131341, 212265881, 194317166, 492431526, 76044368, 715173258, 129885999, 225314210, 973638181, 274172192, 888798480, 596501801, 684663170, 55740844, 398474497, 662225844, 969892573, 720525237, 646691807, 101026120, 462758163, 408133322, 206272242, 439944953, 228600116, 6333061, 968587679, 243348598, 668335917, 84548728, 935957301, 232018516, 516813070, 916457151, 152458235, 924635259, 550348206, 309492138, 844999795, 711945832, 527283986, 290702358, 766105759, 466301153, 706597038, 510702468, 166569734, 220106372, 721303718, 285121156, 765107725, 589148162, 250873312, 576632696, 578722895, 398018431, 369752931, 571587295, 940393726, 353393816, 322642421, 605852352, 447538060, 935123721, 517884089, 262068921, 493746548, 388411477, 471903289, 28479837, 366478215, 646824684, 300270901, 509370129, 661944281, 990232077, 909940877, 478592695, 668966872, 187911558, 400382332, 1931057, 194038323, 567249459, 390265577, 605532346, 78225247, 767857912, 63460219, 689533589, 559983439, 634103239, 643231538, 286309726, 604374406, 563467304, 117450956, 234118903, 322968379, 334845631, 479731593, 882028130, 505121166, 900330120, 491734599, 628236234, 288810101, 189730271, 667596429, 531605669, 724841063, 506763552, 703858769, 509585385, 717727367, 759773659, 457457214, 812597021, 743099809, 200600906, 893168733, 364294004, 146524807, 68624027, 692039705, 8929847, 770281225, 539325767, 428135191, 915225446, 521415816, 199895303, 930225075, 642562656, 555966989, 688828924, 435969578, 273131730, 403056998, 164273856, 301345670, 903412602, 688372398, 1815902, 674236672, 438371819, 52771588, 673465023, 765208519, 5302158, 214671540, 365780354, 649037384, 438014334, 252431656, 401615979, 381379172, 10575127, 797055137, 141403077, 590036143, 210930387, 155136186, 522807908, 790444354, 306694882, 174447345, 843176084, 881038476, 149186011, 174192678, 503760652, 89116110, 23108969, 936749789, 359655636, 536317124, 689383635, 182394412, 993918530, 794195650, 241969865, 864628736, 834475676, 820947073, 957820763, 47330030, 129624228, 670138518, 358818058, 963724192, 980349181, 416153615, 951810921, 629969434, 887536378, 764733768, 791645234, 67686409, 109864023, 119891885, 650807014, 422683284, 112292189, 373856258, 422201071, 485514209, 879022069, 412148069, 799500682, 634371430, 274648061, 621118256, 903487362, 276841791, 15450163, 397197598, 303770376, 386487195, 984577599, 304989847, 428623776, 165749674, 206416860, 652484357, 763294656, 5097933, 249535089, 477320170, 65415844, 382525582, 892591444, 694537343, 214296802, 41863943, 97164514, 387216896, 624222614, 49862500, 397193947, 221205202, 50288722, 123268472, 356614075, 70862036, 529988596, 522916632, 848429316, 250736092, 93981558, 48862978, 199997387, 163364568, 519773556, 271725604, 202342116, 535800336, 270786260, 778005388, 928064162, 880902048, 372040534, 560137708, 279161890, 981199024, 677343302, 93592601, 16688726, 685330193, 87646389, 552555626, 395939688, 728668698, 993213881, 80821801, 524803409, 212628394, 105139636, 343729516, 24651923, 200288703, 772740012, 416917350, 857969626, 621176899, 937094772, 169580123, 252444778, 796466863, 331082986, 598779026, 184593558, 123570821, 150980805, 958357018, 870873584, 556111728, 644864209, 655973057, 437762081, 640002884, 544849643, 522644922, 718764145, 463775790, 81857171, 328102151, 727134506, 572779456, 914665181, 88956433, 383256585, 740368138, 602894577, 687762689, 239542721, 554673108, 828874699, 178870417, 799750569, 698616454, 878248359, 383806768, 768864372, 492989447, 26898610, 969042566, 675642578, 447547094, 167908040, 356745590, 363324741, 852827512, 756665704, 991728112, 258575679, 40251544, 36778846, 819249410, 821886265, 854701048, 759576969, 910673472, 680970809, 635763772, 772392478, 266205498, 184534417, 879639100, 112914764, 229855909, 721678703, 212051951, 691567450, 721381246, 539481352, 117311659, 503730417, 198875721, 224990570, 153518527, 941503548, 947115800, 479657387, 666537290, 721992640, 675067433, 392660064, 359184134, 209217542, 882539460, 571504609, 60784884, 587922166, 540117978, 740256581, 474147400, 757524340, 301157237, 743554701, 200766084, 601946133, 980302453, 605013516, 592588311, 432570600, 206272025, 817241612, 579428342, 188455240, 344026040, 231478453, 913815083, 466438444, 13302554, 503778462, 29344364, 703783649, 129392580, 613418941, 4719382, 479592088, 810321733, 482105647, 806477687, 829412859, 5388611, 43052694, 45132247, 990992767, 613864595, 979813200, 142107712, 698247523, 917702022, 741571982, 804621196, 1737938, 743856015, 947731330, 725095488, 134638170, 306611030, 625378462, 229780678, 307380830, 793993153, 368350981, 862606379, 574763103, 995072226, 148459431, 52791373, 544271806, 793581874, 332875737, 597452870, 387282142, 676776524, 842113754, 289296064, 691100709, 796777738, 591987044, 175014156, 871873126, 168900254, 515824856, 289119143, 796715052, 353482041, 343303873, 131911422, 563711361, 951924862, 585186326, 5578878, 903663678, 690096747, 551140481, 316857828, 754351111, 930449311, 965895130, 717361230, 800157204, 512214762, 826848508, 770077575, 80758778, 178142704, 504468316, 860976842, 381156301, 954623809, 345751063, 213261381, 860695382, 543782954, 631981701, 558875618, 998117684, 446798728, 115932352, 102009805, 25273067, 153918632, 799630707, 720631071, 548638616, 15045590, 236805436, 862702509, 23209790, 141467181, 914914623, 543227595, 415909107, 543520201, 784268988, 388167184, 680561079, 671418678, 43942848, 67599990, 918198985, 331672938, 930750949, 826695463, 567099285, 376665921, 884317444, 974087206, 557519550, 526584897, 86754066, 860709503, 863098669, 630111681, 589066202, 181039549, 617469014, 140853221, 448647329, 139945894, 33443698, 601371817, 431509769, 754971270, 676526289, 390604896, 28850952, 279271194, 176834174, 700762936, 192412797, 459388034, 731535787, 204129332, 203723797, 512826357, 263589326, 913938983, 217038089, 624250694, 426584813, 151170662, 475177402, 277075101, 751847372, 446476670, 470002090, 191166769, 132884188, 179368811, 928800405, 58638023, 663433461, 350261699, 64199688, 384350085, 198155557, 57663571, 946531120, 250627827, 233296314, 982281335, 858285817, 10126896, 771012293, 656789618, 734106506, 278491730, 864106653, 478325064, 918917831, 258306762, 956378783, 220935871, 17530114, 519978426, 54098854, 684812975, 749706683, 631302343, 332662561, 464465106, 301712962, 590284267, 903918577, 195718426, 304188929, 450614066, 565146465, 446543145, 618787139, 419527985, 370113159, 158965043, 196907385, 845464497, 694398489, 383539846, 837799628, 308956858, 730572378, 550918414, 483352779, 659666037, 466460370, 540007885, 103046546, 404740229, 190480325, 435739245, 939740094, 608427439, 216350439, 136907353, 573766254, 306795567, 891699655, 30575067, 321155408, 880768553, 127881961, 733826604, 891771244, 206392873, 273548905, 89822778, 511444943, 595223605, 369335477, 810903162, 224101003, 677502314, 818985450, 233915031, 201951756, 625888128, 959101308, 431255983, 346379303, 167985034, 127920318, 422827364, 128541097, 14922594, 674883665, 820430595, 62677000, 790485592, 77931094, 745684263, 109980905, 158462095, 724895152, 253847174, 206747132, 207457234, 296364133, 310477416, 457553326, 344583674, 757122708, 67395599, 23847431, 176390224, 190601084, 859998639, 778794356, 955565041, 335689834, 135690721, 547180987, 603797337, 615524449, 983025807, 216051609, 210378450, 643588693, 523144567, 54634916, 901761064, 986353983, 588981279, 840799828, 442300988, 70763389, 899749239, 628993564, 104171930, 175084706, 303617949, 167826279, 291157414, 767574439, 580277162, 226791771, 216218518, 737985399, 463715928, 734230081, 212967038, 431642549, 517616361, 323262287, 618240050, 541612517, 228248411, 486344483, 899895990, 819747245, 406394272, 999313238, 839545222, 480542671, 717325934, 958783654, 343508762, 446373888, 488003173, 295347540, 652564542, 759980657, 884022195, 153015438, 957930726, 913813459, 176972554, 753109206, 439455542, 85376297, 849252905, 38575731, 539855178, 229968201, 538023375, 726220858, 460733464, 662037219, 532658055, 6787840, 873804520, 881315442, 198777276, 254129360, 200431845, 790120631, 593276736, 444324293, 126488710, 291481156, 746672676, 773067449, 873027745, 260410038, 924730134, 339064070, 603789753, 441042923, 898479449, 188549881, 150577718, 141752289, 836344046, 349090845, 495258333, 658485149, 917495251, 426134570, 641040279, 417617287, 284026630, 376321435, 634030702, 412296570, 501005481, 175339056, 548710023, 408761045, 341290468, 877563417, 818750603, 657481491, 758380689, 327018561, 487872844, 686932931, 888282997, 594533780, 381890536, 706143090, 139703148, 654472371, 203974308, 740802530, 374780270, 647994694, 266356971, 658537950, 715844061, 959194342, 190096156, 833939896, 204791334, 705778609, 762370740, 88058201, 670134496, 888851631, 617460776, 940001401, 812054278, 488167997, 775573813, 428037435, 9578826, 493400166, 440462285, 99056372, 261634855, 697355794, 817937210, 109424543, 236567614, 498067454, 987356490, 430936141, 957969868, 445646862, 967477346, 538733262, 245366965, 310007346, 342471126, 661747543, 532641547, 367062179, 115645681, 927922117, 515840279, 844680456, 19637273, 808275495, 258003131, 565254694, 33326669, 975914260, 268022109, 751443691, 609933294, 744456408, 15245339, 632219644, 507940072, 380473785, 235874304, 701948244, 140298109, 7294051, 738168658, 910386844, 881863258, 622781534, 236107590, 581737080, 441233377, 283945284, 76337875, 188383454, 436356099, 558741601, 283886691, 875238261, 283863046, 357529481, 128465133, 977794980, 2490080, 19095741, 937112777, 631968918, 491862224, 203445603, 843767678, 788299172, 924661865, 532639367, 791224344, 124106198, 741868408, 664266370, 699266921, 654477716, 623353026, 815417233, 918480371, 119265668, 795387405, 857011023, 216582343, 666870252, 608630702, 947291057, 787594908, 689297487, 225983645, 877517147, 468960805, 945059873, 991625752, 699596815, 824356494, 575988333, 971776460, 759752740, 306760207, 147899168, 110118916, 338361841, 75248049, 807896586, 448238267, 404569164, 336592109, 811138189, 603549054, 873712711, 977702582, 652057115, 866510382, 722588557, 213552564, 24531206, 323123597, 346315615, 642676545, 132699705, 673028321, 96133333, 23283062, 763713556, 12935780, 742600300, 146939459, 5495718, 13145557, 237824972, 484319573, 572837266, 285989351, 52267671, 498597861, 232617101, 819693343, 828001666, 460514125, 663006921, 10076417, 219942142, 160466958, 627050176, 883184223, 327909492, 583714446, 310672272, 522914925, 37833643, 144231285, 642835699, 369700356, 263715266, 79165307, 39721133, 247044811, 895269621, 19034693, 981851123, 135546856, 858996111, 204332328, 99305354, 159084514, 111665579, 424300568, 33758102, 271446909, 408264026, 339143561, 669884674, 116625570, 810856356, 154593393, 588479949, 18750885, 551777863, 854502444, 179086492, 839185150, 902419196, 722546667, 615783881, 138430337, 322188253, 825902629, 705727438, 823223860, 364554067, 502183969, 185867946, 861760908, 309748060, 463137487, 770121083, 354558773, 919611486, 188356956, 824066886, 552906102, 876516298, 596428894, 318518061, 107692233, 588874377, 833631014, 59226513, 825312825, 993859572, 760402664, 225415306, 106161410, 104721405, 90625096, 581281664, 319437549, 783520286, 747460833, 214800241, 893954310, 399572358, 124481073, 872033611, 933871530, 837156321, 975074460, 289712196, 692380178, 776104406, 192418980, 800334045, 661819984, 614295409, 124045186, 477290753, 861238011, 947560231, 268757695, 76558442, 641322128, 990900962, 29520086, 772133915, 906143186, 267971184, 123936407, 396827283, 839397477, 977497576, 185448024, 441779651, 813862476, 957008977, 3473753, 594557797, 381625062, 647453679, 34183143, 595099704, 422329982, 653999783, 293183795, 529966558, 279599505, 529305633, 131492207, 4573292, 133632382, 864094578, 112464746, 651469351, 121724742, 857002519, 130838700, 935476928, 327782638, 550342365, 195873817, 375549858, 235506021, 290027923, 274723752, 832444697, 953969548, 333564221, 529077691, 893863182, 929779722, 300156634, 341094827, 161267625, 384168184, 810565871, 277684284, 274270561, 522049852, 457979820, 842835099, 525613728, 792867258, 830161472, 650306266, 166446559, 183448395, 876695904, 653490787, 380122456, 946118307, 904687400, 612515723, 734054566, 609296960, 165207000, 244585522, 197872451, 122111549, 766738222, 683408793, 979325133, 406327335, 239601635, 917189930, 77915428, 823592548, 839059827, 95189261, 812322975, 914519974, 441870675, 90828042, 214583820, 914434721, 498835933, 664382504, 618581375, 794773562, 607021490, 366904266, 703283907, 477029010, 534197102, 746295245, 691252710, 300874883, 765452366, 565175188, 3283364, 45022978, 78913224, 271962340, 419557039, 881793413, 847552648, 582861193, 959349833, 727344639, 651130299, 714457520, 66431209, 444450611, 346805984, 321257153, 187127801, 446127063, 78948232, 48134732, 330517602, 230794615, 601763699, 780768480, 199247783, 567580234, 745777825, 157747878, 898792181, 886823691, 371293389, 139843324, 847275181, 304052806, 463075439, 469788278, 468125646, 319484695, 55526785, 197202688, 481011837, 204359319, 524945249, 16042571, 227861350, 615646631, 388672726, 670512794, 489225530, 898071554, 130671993, 156178744, 994479378, 378036144, 401100050, 781248321, 500527765, 415571908, 60302894, 422778893, 844347369, 318932284, 870405078, 758593640, 628095242, 851681111, 816234175, 871974302, 937529350, 840221065, 314564241, 777267751, 150633113, 719296947, 460215574, 913971773, 753880966, 457256102, 696615838, 399377764, 899466462, 369680178, 85991256, 730757912, 856406129, 459068427, 112592888, 377565247, 87170370, 166743511, 817125692, 778249878, 752231559, 751873633, 328963395, 701607665, 604932069, 349572501, 135100338, 691378761, 153898362, 956654396, 483018470, 281174749, 497279245, 304584606, 467841658, 712656868, 463774370, 709693281, 135599541, 680911063, 940912303, 252683507, 850264352, 786910909, 246609618, 65228184, 606253573, 498063045, 477119092, 75620212, 539628839, 35842220, 213059249, 337620276, 822149098, 855164023, 341812677, 538389667, 235464277, 197547420, 280233897, 920647634, 807758904, 162358120, 638561166, 649147366, 554117092, 63189864, 401680050, 367794256, 709142731, 603415028, 349327624, 12430893, 912855439, 519961017, 952401823, 825356791, 839261690, 265105965, 70373040, 816763381, 193844621, 855635468, 37759568, 517153372, 890439133, 873857163, 348220753, 944730435, 326571405, 865898100, 228957953, 943936647, 285260241, 279666854, 203678393, 57622687, 193891758, 563621253, 493563208, 691826329, 154172951, 424598164, 547973380, 725673070, 537005182, 816252028, 207151663, 253373786, 844530212, 520223667, 426470330, 266650911, 222784519, 366615266, 211876390, 138535252, 798966480, 500123356, 887621681, 565382966, 142804635, 619658941, 998805805, 296351488, 542287260, 288598406, 593436270, 694417929, 358534509, 236935446, 43000116, 435744271, 888732826, 292769266, 311400784, 771269859, 807956605, 706602326, 862150810, 118844689, 192594864, 764780333, 48810519, 808409022, 257033548, 536168075, 44199242, 927445039, 126856146, 257572673, 233701551, 140437449, 457600098, 126183170, 484270050, 518053375, 787389771, 112844004, 142497292, 781843622, 837902502, 516666601, 363005690, 239694138, 470981961, 75470872, 321350439, 671234260, 872205530, 301571093, 189196465, 554671999, 227279624, 708496449, 902345415, 932480389, 649931040, 543822703, 560425899, 538660184, 196595288, 806210711, 309866492, 271416229, 374728858, 654831048, 496053486, 507031752, 717390925, 113765189, 481895113, 902615064, 452535754, 331041834, 69494821, 373597519, 884245317, 493308186, 526105233, 270425448, 503568069, 448810455, 738652819, 260155636, 206127562, 941124040, 712751175, 859181597, 942102280, 679120331, 887638082, 708467082, 384381256, 715654720, 905599454, 924735541, 69152153, 377359296, 652773666, 676799737, 508020944, 613550774, 340504470, 672260819, 102951753, 79426957, 209815677, 477752862, 839200691, 600960285, 973165041, 250353837, 943049796, 566869044, 648944838, 355839168, 615526010, 739847786, 711001560, 987867147, 329519268, 668412531, 221709825, 986190964, 301710377, 498931523, 970575383, 628551347, 117517566, 585482554, 666906370, 47565394, 659798416, 569159808, 499296893, 718184881, 954380345, 855190308, 135709231, 465720311, 613732474, 40740321, 143472096, 392721003, 97476519, 568486614, 862365912, 514152170, 866680244, 356884447, 816933108, 520479950, 256102014, 484030885, 588066980, 617589361, 14997204, 519736428, 834574139, 720223634, 85760046, 406841835, 915876672, 776375116, 50869668, 931777762, 124712170, 129968424, 339341690, 942799432, 403851274, 880817366, 314418682, 137021208, 40711229, 922963471, 840798696, 19256048, 641833820, 194634981, 334990438, 517332175, 276943767, 470072606, 952813696, 275111499, 148915899, 669244812, 121044272, 285612048, 803136861, 698562258, 992779857, 96895461, 360006494, 403889125, 233014436, 914203773, 639382792, 501564899, 438086904, 274120450, 704119104, 158556883, 649852031, 85569287, 810175019, 148702054, 690935001, 934040629, 342079361, 352980427, 973215409, 897701501, 193585250, 811602278, 764037962, 95206375, 171410275, 808611102, 212829858, 15964902, 672858697, 126691507, 199045008, 862797672, 189303719, 728672582, 389652572, 449671175, 659424590, 307631051, 24766601, 435935685, 131003900, 353752396, 278673733, 471911340, 635694079, 892404787, 214063655, 605725774, 738115117, 908954325, 910648159, 1163507, 515392754, 260855399, 410870274, 955221989, 474102028, 117818788, 95743404, 706110965, 801413262, 930362766, 127274943, 29889962, 123078970, 107792738, 70705492, 322522164, 789512475, 380867553, 922382719, 130569622, 534568352, 406143646, 548865610, 884428787, 127112542, 700075902, 27877335, 984537331, 115111765, 960143110, 755018235, 814989940, 879491462, 865719689, 946084590, 491740056, 958336989, 354507969, 945267427, 353848432, 957099158, 814198849, 866000921, 206862462, 575238272, 18754871, 36115460, 788496405, 975557567, 271359790, 646830991, 217521686, 377878535, 627329405, 680235131, 899776902, 663981552, 529603810, 258088905, 17501247, 755989964, 918640221, 87545039, 773710225, 306212753, 834149725, 298790813, 702850878, 186468158, 647131374, 818600818, 82878426, 306436623, 325105154, 198187632, 482207763, 894275410, 721992873, 179953525, 383497789, 667874884, 307906358, 115999721, 955705764, 588502297, 772037373, 666506143, 885435957, 897314996, 403890365, 641308880, 615364723, 258727254, 367637484, 447754956, 698628639, 455337806, 515983223, 977670431, 513221383, 821855698, 433320101, 90604187, 355343365, 161435433, 323128692, 986013680, 443814532, 28345278, 612140935, 11239874, 572738813, 374854350, 901961298, 30440940, 281861847, 709632703, 89719882, 503024634, 315310383, 579626697, 993016321, 358862914, 991714245, 344904769, 234758632, 603560139, 335659391, 656482669, 560035777, 92322253, 537382534, 516419738, 745278622, 59761695, 36291542, 510257982, 881089307, 407863264, 413379458, 84247341, 756277214, 850268673, 314454213, 518975784, 115840169, 223409260, 77919078, 294383190, 810836971, 68096348, 823357844, 267719731, 810258953, 554993391, 711971279, 994717142, 759675675, 728063406, 276311275, 256190317, 84460383, 418564189, 132627782, 947659973, 617241959, 261981205, 652511832, 39418872, 703669763, 314995622, 564828023, 993630055, 522281638, 283433824, 357067247, 60680002, 77064896, 535628477, 752099267, 619544454, 875708339, 344549441, 816484785, 855454074, 505818354, 897841811, 771322779, 927080937, 508164617, 449670526, 40180505, 183575888, 477727552, 812160775, 428113745, 80787001, 57441439, 113938770, 861959748, 814254446, 217248793, 496451639, 883672390, 741030247, 353399434, 139183982, 927573384, 948898371, 663294456, 769262260, 175127533, 404508166, 53844173, 640900712, 199575130, 735865819, 304451528, 611690809, 693755040, 947908932, 60778226, 429094687, 314492614, 768777488, 350551193, 743084668, 562546278, 810861252, 980010249, 26064514, 910724450, 486733738, 390879150, 498775706, 961124415, 289334001, 594154305, 413178315, 740268881, 48362262, 538124917, 752078678, 564264046, 439120000, 222952825, 850249973, 299315648, 80228020, 377368816, 37595422, 133401522, 999899382, 864800740, 43750499, 980976959, 632709024, 192011907, 120938095, 720634781, 488600747, 152064382, 567636962, 348153966, 155177727, 496365124, 813492852, 503027625, 753741703, 867500607, 776073117, 529660499, 967748626, 919286616, 319651641, 869485664, 600391486, 438592518, 982538006, 505007092, 114270888, 923417085, 289325235, 770444392, 315132724, 284664162, 740808506, 567496146, 617000074, 77828794, 158386448, 139247219, 681327273, 966843950, 902209656, 522532823, 203135559, 316161868, 451336803, 278729807, 592191941, 58850719, 576363727, 51852448, 963551198, 366355682, 553076777, 610633345, 47322249, 629826526, 57479290, 506508163, 738269328, 544731146, 953952625, 298580084, 710726411, 804093360, 358574086, 819067864, 239312939, 612390979, 649742897, 886385537, 560470457, 403358121, 443743370, 475143775, 156723362, 41630939, 791700625, 881106856, 663834601, 738561082, 811841217, 800166325, 813663905, 557473257, 277110679, 341165971, 148238303, 139337358, 119890887, 854014082, 912574033, 999474680, 387693714, 136106687, 341231746, 438134050, 195135064, 78289889, 54105749, 593126501, 720854714, 189155524, 21362875, 746181712, 257701106, 401538525, 173612000, 38481768, 511890651, 713188839, 727481392, 662026826, 641697007, 857056183, 227435647, 479912202, 773466660, 234573242, 546748023, 21986246, 4955029, 801905354, 755587144, 455698694, 38022771, 501597896, 27550096, 462684040, 89538640, 772757436, 258908163, 949174456, 274747616, 875396861, 64044412, 78160158, 836362526, 531652689, 202293723, 29311670, 804091732, 401701999, 74184019, 81737290, 656331818, 632283538, 77498411, 700014933, 519967328, 213224923, 893114092, 700048853, 775640996, 86467358, 355857148, 414192656, 350042952, 641757645, 926969969, 577615238, 725133960, 698091324, 269923452, 177122839, 728805935, 342238598, 81259628, 137476356, 930700095, 643815219, 136452752, 345729005, 21679865, 417946559, 291098815, 321994997, 377325283, 945320469, 482741786, 271682357, 888909867, 703611769, 12634348, 72584833, 695875938, 815622459, 789616389, 436527698, 268453485, 908137804, 775319473, 127903468, 328056803, 513773012, 143106543, 515230106, 276454506, 298404436, 716826381, 908283624, 558379187, 563321916, 462695988, 541999000, 243112751, 879064160, 270104741, 948221974, 246248365, 163103806, 112249006, 112636864, 390534808, 592830039, 578127810, 241634093, 838532904, 29511230, 112968728, 126100675, 37095181, 500385727, 464009138, 712789129, 441194524, 662538737, 804689503, 796648255, 967656117, 948597422, 186192715, 43126319, 976268014, 961976237, 318000466, 924257144, 371824576, 183388743, 164950523, 194149393, 744014723, 304921908, 365236546, 966983014, 482103135, 636737379, 606069548, 353227499, 547394190, 809877478, 815405875, 693398450, 560302486, 735575771, 198430580, 92188906, 842327029, 455781820, 821328152, 743417122, 211046858, 609482157, 214319401, 554760515, 939838654, 136078813, 151103930, 445919915, 225314398, 939936842, 939805872, 960193822, 514007710, 755538299, 458521956, 970569121, 358546817, 844721061, 68016949, 980973595, 862322338, 735113856, 638973162, 913750604, 522731661, 649458903, 965842663, 586549288, 541605751, 706026628, 506334327, 602213020, 845362490, 358277302, 404522342, 473866612, 233542607, 173561465, 239034027, 733816880, 110734824, 582157790, 217286357, 8890178, 540076969, 434994200, 599335972, 754811333, 665181250, 253791546, 797955550, 477162710, 340584750, 861568115, 716415040, 875249000, 850253919, 197099983, 460182691, 888915674, 705290527, 260077691, 309134279, 840527267, 656424918, 745140683, 241585708, 660519532, 31017195, 866000084, 894162602, 346782430, 397445013, 463627845, 541242595, 279717502, 42879674, 154270520, 168661717, 258933230, 503622407, 783035682, 164306587, 839961110, 92800812, 471093035, 811876465, 333061406, 614845939, 804096120, 915996451, 59937335, 981123859, 519670409, 435659449, 418514543, 386422885, 460612850, 854034485, 801816944, 689813212, 97516853, 632511482, 434023918, 319322589, 719634192, 949591731, 467405392, 226429095, 200806742, 890925881, 9369923, 388127652, 241089895, 872021749, 15837414, 282259152, 604903880, 86179228, 925920414, 592259321, 930193973, 775944278, 198426201, 630014591, 780010342, 295413079, 178327772, 710232004, 571394592, 580527408, 656311449, 759104154, 820460826, 215105366, 396587382, 522051112, 373424005, 569418304, 313796002, 901941423, 679405887, 935552881, 384699114, 478720258, 172666051, 614767865, 206460383, 652172150, 38432778, 492941529, 681624375, 539589197, 511707864, 10006563, 360748915, 255300467, 252308053, 840041385, 133394078, 814277895, 190263037, 918352781, 328327324, 431225142, 717203564, 705138692, 115783441, 20501195, 317433877, 683071083, 320710062, 63339030, 391971556, 847792330, 148737252, 882331150, 994408596, 808520976, 221966635, 244075970, 834069827, 655030673, 120019222, 817321442, 297439379, 287052430, 913513725, 827828866, 571740002, 350078605, 379727749, 885930816, 76944896, 709822238, 153531293, 277251444, 867775358, 586867404, 356888894, 612331494, 777084081, 126947731, 790978147, 187076579, 104619259, 531594801, 456848120, 719265797, 783606598, 686366807, 263579882, 898495324, 888272639, 870441800, 739133084, 641871890, 853431140, 486913693, 822222558, 680029532, 903556017, 463677461, 578948182, 795290447, 489304614, 957122358, 679634954, 844795347, 871660810, 314933203, 158300833, 683462099, 281971147, 994053681, 468836571, 253261954, 879379244, 61029659, 476815771, 368971416, 152524492, 56193680, 125388120, 558052600, 369973574, 770949124, 822320869, 665294570, 686401301, 192480880, 882597343, 18736654, 988364174, 312470961, 741568989, 924536010, 950664119, 610885480, 369712059, 991644535, 243226523, 258494856, 420396202, 169503029, 313993615, 232126812, 919608073, 761459064, 552396942, 985480437, 239714948, 565264035, 662939570, 887362719, 755640725, 417062269, 977602901, 132166064, 902479648, 850169855, 33493712, 46012069, 541294967, 393353826, 27989780, 564444219, 410763312, 556222399, 105399276, 467169389, 177805436, 650775222, 640178504, 37579617, 119598655, 616573300, 227871621, 884466073, 354923840, 498748123, 91823394, 49745778, 296258013, 905572462, 23078190, 824178349, 975958417, 107122087, 139715044, 268562012, 286406055, 783892967, 233810370, 610740943, 277630991, 83001039, 948655752, 129802816, 897863669, 820688223, 767633881, 160191460, 797649838, 268431203, 140200678, 339227108, 201871904, 596427268, 229193536, 414108185, 165170153, 12283887, 190636897, 223300156, 206113622, 215614102, 910553648, 825901882, 929860060, 271169441, 199194662, 237207972, 570235131, 996064380, 84942891, 353586408, 631218556, 577929339, 960992495, 634110583, 368470802, 589185641, 508288220, 427558734, 160425816, 344747892, 840905656, 191919645, 93420117, 913422218, 38105695, 826552285, 138681228, 721940186, 824239910, 132503686, 391628247, 779908295, 569019426, 944974722, 657355114, 189931256, 541257781, 722804833, 98880205, 705037310, 534501643, 205492257, 120546285, 414284187, 993743377, 821993907, 431330502, 909844934, 780917520, 693656928, 617669522, 949245169, 219403041, 365951690, 732093137, 483514587, 469172160, 569024952, 167168500, 149726118, 340582588, 333161821, 470533815, 854984003, 866209458, 334368217, 456513059, 107617531, 14977061, 140342351, 629211801, 45431517, 843458349, 730251754, 834220608, 921284691, 626512144, 64663129, 694647167, 698456483, 818182355, 355645952, 855607511, 557832324, 965187481, 476299674, 548278026, 53071607, 756087332, 133111115, 552658287, 948778417, 497598301, 719005572, 991462856, 451795699, 230546301, 701615656, 921602948, 614268489, 683259460, 76758709, 475492676, 68836204, 691279426, 995441767, 210370442, 750431465, 430051819, 418375703, 734778365, 251778975, 844405047, 47436412, 328077826, 604543037, 350498038, 997458829, 524911906, 744498817, 664362186, 474551897, 407649261, 778824636, 484080862, 714157302, 806622464, 510981625, 687778174, 48236465, 247896868, 360597912, 799867980, 803321837, 532100017, 9063476, 945261873, 708850644, 771708143, 609169209, 558226768, 391699253, 952952018, 475386291, 100825837, 496625486, 952389161, 204233462, 614481041, 647838547, 865200293, 282103556, 542807130, 793458919, 155963110, 901523537, 429899663, 993299134, 504958255, 634146677, 86804534, 114240559, 801206807, 523322130, 264124363, 454350099, 806065057, 346500141, 733595286, 887238120, 253665301, 320704027, 275385947, 386754837, 561473885, 911003812, 721936931, 950502965, 749861745, 877170723, 856093093, 103386382, 464864045, 394364108, 889329210, 372886987, 72605220, 791168910, 250358953, 923263798, 910066952, 436093164, 874905191, 387905278, 920157310, 409548519, 805451519, 980544420, 417402526, 807931802, 673856669, 866871618, 18834392, 495029631, 234171275, 961847600, 282285654, 966557207, 240748867, 920056987, 904019785, 881104948, 736081201, 466073948, 663450195, 462392985, 821392445, 473552160, 150478913, 920492583, 212674080, 233781751, 827989710, 902812318, 897516505, 57351645, 344260635, 678281266, 231059480, 375623663, 590597197, 160829798, 919235890, 659604653, 834274455, 620586907, 876040551, 218016035, 103627658, 436777100, 273305268, 647387426, 644538854, 635176068, 596431298, 200228039, 243979852, 497577431, 660486366, 825329116, 534784481, 321914413, 100166833, 57334218, 996946925, 159283257, 768302823, 235181858, 559512139, 891906127, 983464086, 814558318, 981038097, 23095935, 409756672, 498131298, 192034134, 393811617, 109865681, 951424641, 578020202, 715925908, 669466381, 513616261, 565096034, 681321044, 30411836, 899758778, 727952935, 872975561, 482720803, 314950525, 41147680, 607248020, 965064284, 415163047, 667914638, 573125014, 783281814, 389905257, 143701006, 420587003, 256926747, 916347377, 119727068, 404900794, 407189613, 866564968, 832636018, 18683501, 525926351, 546880266, 742124350, 157230364, 680199475, 159629449, 948015337, 101329728, 479567773, 703858193, 762073907, 484646507, 471310994, 797223603, 684609063, 435156789, 274918840, 339380336, 6696788, 318929979, 300124555, 501812098, 815315290, 31955672, 559557970, 278690758, 171619447, 987904143, 818217420, 679646533, 399511074, 197491165, 827985975, 730354015, 66962787, 447202980, 130160590, 728832629, 800286023, 564805639, 410510028, 847178314, 880488067, 45814778, 258694030, 401368934, 733826312, 602182420, 395749577, 340859656, 27862101, 273907685, 411692552, 642150747, 449673244, 575709819, 52553941, 205272413, 339486709, 914837320, 694511332, 320865417, 196796899, 74228662, 606366163, 100456284, 119385508, 40476047, 68984896, 645303356, 116179943, 56645434, 446337095, 251122470, 546193936, 951847182, 594385645, 908541181, 889641327, 545643465, 752682156, 472717054, 915223708, 346740204, 858973551, 255058829, 382045066, 121707165, 33176347, 950963604, 936508870, 768356512, 589965140, 271678715, 608640037, 643466571, 740293109, 869827977, 759801147, 164879501, 854891438, 544479768, 145280095, 358069325, 237153180, 868177129, 66289524, 910263546, 371922960, 779017584, 126877698, 220352789, 354303976, 607552954, 166288073, 514328537, 624133612, 374713240, 323438293, 866115721, 220761676, 47105080, 569477197, 666688077, 685624042, 272609549, 853028082, 812510560, 718948408, 290168101, 540012571, 339281816, 264919564, 566589343, 586628685, 55282611, 113745364, 242857812, 305571710, 24341021, 260877529, 783620334, 175405541, 535130782, 983054970, 287212072, 681014096, 216816055, 657756834, 487721243, 823531048, 479471089, 77117684, 402072028, 53306603, 97149288, 781838876, 438800353, 202429299, 128171885, 835763904, 711467966, 700720651, 602276456, 478207874, 826324118, 973693717, 779252373, 728485050, 637226325, 124973209, 936133068, 325784344, 428509548, 606849943, 467913561, 986932315, 216603456, 735870611, 601556356, 911097953, 539821860, 131314873, 373029146, 758067858, 653291624, 222742622, 980425225, 876437774, 1010053, 797286054, 892552884, 685053218, 598908745, 286077942, 807523903, 252929949, 352782069, 932011535, 229959497, 566434067, 958731851, 335394488, 349786188, 165865452, 22986202, 402942708, 3773229, 851271510, 232549718, 644461731, 251869185, 883143495, 127558311, 147371336, 712892475, 88009020, 471062131, 781562997, 85676022, 824774758, 305099909, 255552383, 468879592, 802017089, 337898609, 907718807, 15635792, 918854664, 119093256, 725595805, 705989038, 819001717, 256770483, 329812775, 212357087, 308287148, 539800479, 290789536, 973425954, 545939578, 269677214, 557014747, 21794144, 668122443, 122037818, 95252097, 501569747, 258807773, 603944939, 872226483, 254633036, 597206052, 284773952, 418532491, 124582984, 536189327, 328146343, 463656731, 921204092, 610708408, 687982100, 925907450, 615883720, 240278935, 807448670, 922836594, 852308954, 464799651, 938094686, 672838027, 694144482, 810591106, 615292962, 580693113, 875900869, 757783960, 82822616, 927824749, 747839247, 779828590, 254649617, 118185806, 114172870, 593168218, 991993786, 752420131, 986703240, 270489780, 616463907, 534386269, 148148864, 582266018, 637758787, 791860745, 478541139, 879918789, 522647337, 119905528, 420466120, 703681430, 9775828, 466884434, 853581509, 974547928, 987880698, 994869950, 150527195, 551598293, 186587383, 52113928, 129927167, 459669511, 356328168, 694657790, 176432829, 307938966, 599642871, 163508975, 84184090, 56759257, 655633754, 100587083, 829975548, 368795830, 228384597, 810710403, 713858903, 8555520, 997629920, 295507858, 92942344, 426898816, 570363260, 672947365, 50616461, 430273347, 126863640, 625280479, 267535154, 939084934, 640473146, 371711787, 763818369, 215422556, 526380614, 166994074, 475390023, 30277464, 848497720, 594118569, 335035562, 291470296, 10046152, 902661811, 568093164, 860079407, 822398768, 624626712, 355896403, 726378464, 152840218, 268887409, 177316462, 832601100, 41889908, 890842312, 780786931, 958467464, 627883837, 941726537, 912915520, 984188741, 474275684, 138840580, 704456282, 417310261, 306315282, 844512281, 70174299, 364646578, 963675979, 161176518, 492949047, 478062110, 643352591, 501796845, 3094477, 104487149, 990543975, 471627427, 310371345, 988541085, 973271104, 680402412, 579629411, 78180123, 873675743, 796164610, 907834702, 325496530, 617902535, 166863158, 762933739, 274215334, 135473977, 181630098, 964253900, 509122011, 572627068, 234334005, 62773723, 373591015, 583128384, 872833330, 173399383, 736481226, 977222137, 149800033, 665133797, 28393796, 349735688, 42966486, 46091453, 368552479, 759316745, 298614862, 683306356, 401141154, 28220200, 902307866, 983480759, 235135824, 38867829, 178076707, 394243742, 458894132, 492210406, 724317718, 797816801, 967898161, 438853042, 35493606, 225104733, 773539667, 916923381, 368155263, 310401346, 658554028, 393163001, 357479798, 570296647, 23922795, 706140912, 29262665, 282904854, 972865114, 666340311, 596621327, 644148687, 315949807, 248647560, 907027724, 30076831, 741357279, 594090125, 633335347, 717325973, 779537243, 125447286, 30984695, 393002353, 812573460, 949774146, 666615133, 149849187, 473851568, 624163290, 494161198, 400004606, 319073065, 129598637, 61182438, 366580972, 760810107, 981481287, 271566502, 735030815, 568379010, 134801702, 81745906, 923205290, 283996844, 641610962, 996013243, 501828859, 93608872, 514123895, 609551997, 881510045, 288854859, 633482921, 774500479, 921638472, 549002622, 828745381, 446664886, 640048174, 986756976, 120222968, 390406658, 811853376, 571569033, 91567784, 613318040, 146529240, 571302567, 910919638, 390581717, 506788731, 304567638, 229571932, 367244820, 547946224, 698546630, 11530736, 336811132, 968342252, 493082477, 779062201, 280999956, 573862793, 197316606, 169915407, 324529536, 486023479, 381964030, 773423652, 341846614, 459410194, 552980874, 844694689, 584502458, 670473126, 643154062, 903171440, 69574753, 222538550, 585814333, 246580677, 231040626, 196396984, 79328195, 926667979, 452652298, 555438445, 528005759, 755962705, 503624708, 928386030, 297805669, 630107268, 616914285, 529105558, 91813721, 891429007, 65095504, 874811858, 647150717, 842248800, 925210140, 637723797, 591407512, 285775626, 480350473, 11782362, 189867875, 680821858, 29094697, 86934908, 790589915, 955287682, 311596094, 396706239, 704150124, 522562664, 982691501, 446015650, 275162076, 581869103, 685254717, 927418579, 475165182, 332685919, 320238333, 731257174, 284899310, 623465202, 477030626, 874123309, 157113122, 793573550, 79936777, 827971196, 266964270, 531194394, 792790880, 918576027, 293190237, 1098734, 693893292, 584995361, 12629569, 892940849, 317532998, 158541497, 685796258, 124887371, 823067766, 587845669, 282163211, 270117393, 767161578, 347540483, 118758548, 753640217, 101152408, 622613771, 558910280, 234001427, 691698964, 668734251, 960244339, 745013573, 753053521, 651923285, 366017719, 112786513, 561840179, 678822530, 56912830, 798595482, 993533747, 70155532, 706604314, 70755857, 831104331, 676147148, 804349096, 865987658, 904227019, 777983583, 968715490, 639355277, 561920005, 443620583, 60699664, 331031744, 614665553, 207557785, 544633293, 780986712, 327667453, 424246770, 609828807, 140354771, 430434974, 406442226, 310159097, 389752021, 110326421, 965522318, 909010506, 957153628, 207906089, 36036781, 513719552, 397759479, 294861223, 555962220, 202728970, 885573951, 722832972, 207904210, 72392233, 576526550, 616185692, 346496561, 289133527, 316385166, 675342410, 11276378, 542061673, 437177301, 68154365, 293483530, 47410578, 460602157, 760987689, 452099157, 770583516, 639747655, 797382702, 446345923, 296219928, 470638283, 622902286, 317854381, 215582678, 274819794, 403648961, 352851647, 521715876, 656586702, 544598602, 431834621, 156438773, 365542691, 746453039, 340043679, 880696263, 729694275, 147163254, 864072679, 825345871, 542186226, 531042202, 425044711, 640998423, 20404531, 893277103, 970436875, 458140791, 846321222, 509193318, 870449853, 282884270, 998190097, 940773249, 958196980, 496272728, 723197122, 219032406, 613296624, 214456348, 527866471, 336674423, 586649450, 415382459, 534747071, 782913358, 841924087, 861067976, 664314620, 987821657, 424936432, 668161206, 870246689, 574905975, 254824451, 615338619, 240505587, 872894700, 556196485, 812138153, 546091022, 233622661, 838960941, 45508719, 389878868, 814962830, 752601635, 11222337, 923683637, 716936256, 444405018, 274900412, 420525499, 380413531, 189919258, 109252535, 219634995, 248682634, 832532264, 160650758, 48659741, 816637145, 439264394, 973844302, 460445394, 661687345, 846109941, 328566176, 799749392, 74116493, 938078117, 733155001, 274267029, 212540808, 430990655, 772349791, 43588715, 942068985, 714198623, 698048392, 126832578, 614837813, 48181819, 741067785, 875445922, 632126167, 913799278, 835214157, 281072951, 255047420, 411773891, 332306969, 679072692, 318379505, 19401014, 568445584, 921225096, 421748561, 235264196, 331586065, 299987466, 926967363, 766883225, 81279779, 611974328, 719348056, 987284792, 813307536, 891464320, 639949350, 408625073, 306032429, 489063226, 31769546, 354170573, 98900392, 704904459, 778142647, 130023880, 711601473, 606010616, 551471989, 375460706, 4804625, 532254086, 724049130, 916128828, 500130809, 598634976, 3912024, 635076347, 592799203, 40397277, 419092805, 403511644, 539054243, 61998740, 749369285, 904577121, 13975776, 832127778, 781861161, 202217978, 217188235, 348222393, 386743006, 723659475, 991366078, 983426489, 483153311, 214552448, 600175549, 347461324, 794346309, 17362402, 968141810, 540710866, 935536864, 254673837, 173959740, 837235446, 898802462, 644118042, 233583985, 358118269, 582415193, 618837355, 444565934, 934512893, 551183089, 224102457, 364269139, 930525369, 881643993, 734077712, 474187447, 868312764, 399131078, 398070390, 26139612, 89100108, 261031379, 561755682, 409587435, 447808794, 518786953, 655286931, 722782698, 58743318, 39896952, 155012667, 740441120, 710449436, 577802065, 946528455, 930789118, 438771041, 930011883, 715790801, 928647216, 388894565, 611260545, 228026964, 470990369, 716781969, 983940359, 889362134, 500246517, 63927011, 332055676, 138534934, 299746630, 162883377, 903062258, 47197781, 978366450, 794850630, 941847403, 730617202, 299927304, 388189062, 160701583, 757025948, 20071369, 11317674, 457492058, 95813624, 356607230, 114935244, 854744433, 574278021, 561223390, 930997464, 678865823, 318887483, 309294318, 937986150, 136845932, 312877893, 164871362, 583175226, 945104232, 788422264, 90192650, 265929179, 229531201, 17046393, 80251820, 634483404, 452539240, 793926016, 405765602, 534245441, 39723201, 914030276, 131295787, 562810756, 461381107, 194487207, 582630256, 797848745, 547084448, 124729860, 516233705, 720451388, 132959503, 790606617, 3558432, 835758613, 290601443, 944157096, 694351030, 156512558, 509956067, 998287599, 724016283, 115096599, 88865938, 452189164, 697528273, 856091948, 367903290, 505018262, 605662838, 48044952, 884860039, 809684003, 727473067, 78729811, 173984451, 135298975, 521245554, 259105329, 408169237, 553796948, 820125739, 13343762, 693087641, 778552159, 446219851, 432414447, 498947500, 22200379, 759605645, 705206405, 476838197, 127513834, 477675008, 732886327, 261733327, 147315659, 171330109, 879574923, 558004557, 972604551, 280540566, 983426368, 67072179, 153921750, 905438815, 988533936, 515383271, 974337177, 73599801, 635644607, 409048201, 476045299, 367977358, 429741158, 587061332, 562892876, 852903692, 122247438, 486029970, 177170992, 821430989, 126067236, 940184139, 355618100, 214866085, 36487825, 912312761, 993128519, 409715128, 503087187, 537719330, 988735196, 197630454, 498700025, 720222914, 513818727, 100681486, 146330083, 787109597, 981553142, 211918700, 577269701, 633548524, 633231365, 591582975, 971365305, 55323179, 211384033, 193557574, 546551094, 923211606, 417532458, 193895981, 862393036, 708516083, 126297330, 679940990, 742077904, 792893868, 71281580, 101692278, 750065609, 283576300, 497822996, 859382501, 741794412, 423126118, 749288439, 515345608, 575234466, 517460876, 792137479, 457986645, 263181742, 649196289, 254710278, 558686842, 467964913, 734928105, 106889162, 467118077, 352517541, 888987431, 425619506, 547500432, 529417589, 808768410, 456250627, 686080405, 893166494, 10523506, 341648895, 723117774, 336722665, 460522382, 650851947, 100656309, 846542434, 633321697, 798112072, 407197827, 298821440, 523393972, 684535460, 113097033, 341915921, 505894224, 988650384, 200661929, 292870580, 535347219, 956951429, 644916758, 661962562, 826551761, 632729058, 999525536, 971693238, 907621081, 888335828, 233588407, 286769182, 204587878, 611885346, 271769505, 741954510, 185548658, 986036528, 461713699, 745635263, 570804890, 247242183, 119602021, 227865853, 711387977, 690523430, 869617592, 541208735, 254896125, 789741439, 163977759, 474540480, 739763008, 567607573, 709941350, 223157043, 949856938, 474492100, 552358848, 308200152, 116875776, 427748235, 241336856, 421501653, 270592087, 148773414, 850502567, 52611414, 667582710, 469585848, 110692382, 165098898, 224030215, 63845365, 314151302, 878949734, 535095078, 459295527, 87442674, 480637795, 709948612, 739777331, 143779198, 758916438, 918521544, 275045458, 781135592, 382945158, 149976581, 387760994, 88565296, 226246620, 348828934, 28248348, 845116231, 884045849, 872607527, 987780252, 717682046, 474754124, 70686220, 168470584, 210032163, 831875729, 556752376, 348784031, 832852214, 749127686, 125244806, 518180867, 69551291, 85228085, 373790692, 192557193, 973090724, 884146697, 588224391, 948545299, 832700366, 979619547, 41861125, 132550534, 392941835, 307988771, 973104508, 31265734, 502501451, 47621746, 616793015, 478800789, 451265534, 331541659, 776735021, 529422808, 781351874, 99293069, 396052815, 67568266, 774727321, 167855360, 274790366, 618406504, 75405121, 636029445, 213185995, 625939251, 135200737, 940191469, 356446812, 327480107, 868602981, 462406742, 31688166, 825537752, 186344812, 954874491, 106959684, 657151123, 686083171, 206722896, 938958914, 210678219, 710128966, 840735527, 425061892, 436321067, 377502208, 588092765, 422200694, 616141078, 642914147, 465168674, 476073522, 573082358, 163841825, 219436931, 41886534, 808879207, 148842314, 516524250, 928008347, 64022695, 252381531, 966327521, 622209948, 549031635, 563031821, 772747111, 133746901, 303765582, 760809518, 59176564, 972653758, 24115067, 423632722, 568505303, 212935452, 834678397, 351324124, 80029695, 663810790, 261843180, 526579224, 91836947, 175964922, 51525262, 335800543, 422753877, 477608084, 698429531, 210197284, 671304609, 332737390, 804155886, 738093679, 436734438, 551599291, 703951907, 243484766, 676439442, 933028720, 902399855, 108663292, 569064038, 407642353, 610192820, 151300703, 531806018, 345789625, 539454296, 639555634, 34877577, 27208531, 466111619, 899465896, 350527628, 579942674, 833741075, 428070209, 517659244, 100483460, 30720148, 267805284, 616124114, 794400140, 298584313, 794375808, 984328067, 113778688, 475298800, 420070072, 884844946, 134962945, 87843048, 568829708, 202670809, 143461660, 791990047, 394757068, 50121380, 840303541, 55857068, 666135358, 272975158, 843576230, 965114990, 208220446, 861436388, 290145491, 900266046, 362328648, 266113488, 997276867, 140922136, 618131922, 189841113, 446834078, 49828603, 454648755, 589968645, 290065515, 629181140, 702312908, 146724538, 167193627, 106931934, 401308933, 157949683, 451653318, 784948134, 875892100, 340451518, 397822371, 19179729, 468591123, 356368535, 657758840, 6672231, 692724148, 241667486, 243929500, 499626783, 92109101, 633524989, 774122037, 964053368, 844112246, 987454895, 52640054, 274427615, 351554246, 865896831, 299041863, 736333540, 509188208, 91941619, 565214311, 689473676, 211887988, 871779329, 985657244, 299576392, 482656177, 503665186, 545435870, 365096234, 368230241, 973294674, 501527558, 614099637, 799172147, 41839241, 870031612, 230904840, 852836218, 675730016, 374083643, 234259590, 187000841, 127566551, 372295813, 801562947, 954403441, 970418785, 172934332, 708906608, 95176919, 124949257, 910626729, 476839388, 470063935, 280200916, 86757486, 616911630, 10070908, 73291322, 183018681, 399370258, 661423237, 289760895, 197718057, 105152079, 146530056, 791190852, 465583256, 125293920, 898288070, 172675700, 512370401, 873398516, 95628260, 466427150, 797225204, 747481156, 624157750, 553886981, 163402339, 226394882, 940575440, 313658350, 328014748, 675692142, 436275005, 68300730, 583475497, 895520095, 580574097, 904748516, 332419488, 293989664, 552305486, 758460940, 427723072, 694913712, 367689624, 390289426, 701671605, 694354688, 924507062, 261800416, 677813872, 279404236, 137080787, 512152045, 587884240, 139308895, 899990510, 706329401, 328696106, 60315681, 141703179, 106734943, 156077670, 42865410, 127460501, 810876196, 635648130, 768723337, 524813091, 951550317, 183780926, 299617580, 304368990, 129737139, 271161564, 377356724, 387319700, 299118036, 382025166, 426287346, 797475115, 34262578, 67074743, 769876452, 66918541, 362442429, 458177783, 160109155, 771488059, 630067436, 336181035, 761174149, 969314746, 437875393, 606098196, 64132093, 299279811, 431298675, 363349837, 749838669, 221040285, 820467411, 308046016, 197526240, 238864597, 687997186, 513944383, 8861284, 633798686, 908855741, 155865007, 425366171, 477534120, 981291977, 82701707, 313504121, 814274559, 412450566, 547500332, 723517582, 884997744, 202755484, 984532654, 701286726, 588969580, 992719349, 422611958, 407412489, 373013126, 292826412, 664698827, 885416156, 504336796, 580628090, 897433152, 142534994, 289103267, 259436739, 681102020, 46350161, 316714723, 855015923, 215721861, 622782825, 339232289, 906811759, 261409904, 417566930, 194380456, 688241922, 929102624, 121241987, 682616217, 756781390, 333895587, 884973812, 203623832, 363118307, 526720204, 341238277, 456433669, 372116609, 644992593, 275045578, 45034317, 648733507, 692648533, 540692874, 746717550, 333880895, 600361506, 868450372, 404552446, 976629390, 893762369, 522518839, 542270632, 113231009, 510793114, 50339501, 380811031, 738452620, 463215308, 501804292, 930523228, 48649761, 721464372, 763827400, 568135645, 209068720, 101715062, 608355521, 234628247, 648131425, 767190052, 561965397, 940029706, 28261008, 765455392, 612190432, 224758931, 308863483, 347498443, 89667589, 601098520, 481097257, 436554424, 809634320, 806576374, 664336370, 5369061, 489411620, 667219560, 534620803, 492001175, 782492807, 867685298, 928566665, 302729495, 676207138, 42337643, 482963000, 736872039, 892676796, 586492442, 783134119, 99094452, 423045744, 906530532, 829435562, 589767373, 641603468, 287592113, 349211398, 949530553, 110578638, 911439894, 417181853, 428682703, 522709042, 846369843, 244065452, 76830143, 645044068, 586245266, 474360157, 455559474, 783443591, 749739486, 609523136, 676289601, 576477030, 221703283, 28219577, 3788122, 113828003, 12636993, 166256969, 993957743, 450322735, 831109688, 30067040, 326357061, 792491398, 531746690, 613225358, 189107930, 849404576, 905836423, 193335643, 888654246, 454318429, 224860382, 203037416, 436513686, 176146507, 776198713, 937646109, 697251677, 143537120, 235688481, 161851027, 43498177, 477383770, 225236675, 570730725, 279457821, 436067520, 377487894, 499654842, 369066936, 560768956, 285648905, 714758069, 669259674, 808061909, 775285369, 681019483, 457351592, 578972343, 122455601, 720745177, 247011782, 796492346, 178971515, 551051921, 178241077, 368310012, 728639802, 755487261, 603841816, 137593046, 866949441, 587265213, 961306827, 397755838, 462367550, 771277118, 963396750, 247188901, 415962433, 436810657, 931115010, 929680918, 660510171, 878548809, 154194200, 247330112, 146141845, 973332856, 788043556, 322319752, 15658280, 226090881, 17371629, 996217937, 804883881, 174563239, 661538535, 83448337, 222971789, 637833963, 516797284, 257461360, 172369541, 818369538, 351882665, 735994504, 367695134, 190359370, 249357617, 110029703, 65434021, 103641184, 638007401, 561041336, 600274138, 450236574, 453002454, 526394789, 813904853, 932671036, 849365776, 696451543, 287882402, 588152634, 854699107, 592845555, 548895730, 234977911, 371753361, 572591431, 591407343, 735137659, 951457528, 427881666, 859280640, 188923345, 129463843, 964864068, 677386163, 83502598, 259777238, 762790192, 303292469, 669636482, 843886647, 248808591, 620527174, 881867102, 711024717, 414730655, 717230831, 571924024, 948346490, 587690373, 361206653, 185235184, 95781663, 579384372, 145740991, 36875451, 383139954, 224160813, 835130896, 706417284, 876057992, 692967501, 691093504, 16687546, 334960410, 289022965, 874238574, 503569470, 841146970, 568965328, 597081725, 5924799, 872274512, 504375716, 639297060, 639358240, 604201494, 238943649, 820426727, 4528647, 348573826, 25495369, 225429068, 334507190, 716263718, 497257496, 877913711, 879897774, 303817293, 179024702, 162917374, 186805909, 393662118, 800744500, 768528711, 692201257, 213480814, 725475778, 891136079, 780520037, 257625807, 324971920, 279175874, 317643990, 932944396, 605366336, 488217803, 867674481, 813842451, 726749396, 904952382, 751975823, 607970477, 307129773, 818990003, 736096513, 977840374, 770019862, 572171667, 386164460, 558507891, 215588474, 705024683, 54392735, 920340177, 272779352, 705565009, 251346724, 721630960, 53437586, 313176368, 952420108, 328304742, 339342336, 699569883, 958097351, 634722920, 748176470, 382538753, 91312115, 260829816, 319160052, 478418294, 837268150, 569618464, 224282205, 334478485, 391734857, 354287857, 909264714, 777545545, 873893392, 127745789, 42300905, 758162278, 513698653, 714210069, 840114339, 290289384, 52897477, 180510780, 479580950, 307323734, 7167192, 428254238, 840605536, 506611711, 402180312, 9050181, 73981999, 742729891, 876355972, 58542493, 796758780, 797601647, 95775723, 958399266, 191394477, 819628807, 290563972, 947435300, 600307478, 408208585, 686153293, 429246615, 361976579, 500599446, 27958981, 391574921, 900301742, 399552348, 337170585, 148391627, 926587242, 443680945, 647704330, 690469353, 314091582, 520483807, 228410428, 686558077, 632035037, 94310884, 465850037, 492637830, 650856321, 803607028, 893442736, 492118737, 723812794, 110046644, 618590374, 837240084, 376525438, 571093144, 252309811, 582100828, 639744900, 6193063, 961123790, 482137847, 810930961, 744174186, 671882024, 331547188, 961707894, 452423810, 13114437, 130063721, 565501334, 441796199, 52352736, 263426472, 899701376, 18163933, 305903325, 799169973, 85385886, 731279660, 406885981, 641410062, 708752510, 302882152, 76109445, 2319261, 953026720, 293964413, 374074932, 461352525, 986169481, 447145136, 208236997, 178469043, 662853650, 132581861, 636404797, 531349785, 92954885, 978688337, 781359008, 952418322, 888094430, 765712198, 295514277, 129544854, 289388617, 51943003, 760737201, 12047482, 428102990, 350683000, 675344311, 766109267, 949443519, 469303957, 735590156, 568848613, 956246577, 264810363, 951884294, 593690445, 337774800, 893425615, 357697327, 231284140, 372556770, 453541800, 5649213, 213013979, 836580435, 309637197, 607618095, 611054840, 162252556, 307001968, 709186222, 515934223, 21129721, 571357948, 8390141, 526475910, 142321090, 501216397, 39188704, 927857566, 403096672, 235239976, 210858656, 481113946, 732931517, 397102948, 125829285, 212095430, 802944666, 990114695, 165105151, 258730096, 887244477, 494822032, 573627418, 101467110, 766088594, 254561209, 389317523, 277883544, 792382612, 868470755, 953198082, 391800120, 436396869, 473066705, 823740483, 414621445, 627747305, 996082049, 601394253, 502802580, 761568246, 200048336, 259260025, 403049439, 680239907, 788029160, 568168341, 233130420, 415076110, 316093887, 601394906, 743410974, 721401009, 414955196, 890370227, 737794929, 155631222, 394493740, 662561983, 504439316, 69446291, 41714334, 94788809, 368526417, 413919142, 108072281, 915946317, 383405826, 150277859, 526763461, 99100158, 980603036, 229707774, 992143554, 459614268, 718028479, 258278958, 228301412, 844216234, 450901852, 808613636, 95280929, 835762041, 892378209, 761751704, 132453558, 303186016, 341713177, 992399477, 991558366, 625666951, 469616959, 37229891, 226611034, 965174298, 313809821, 361612105, 119427687, 432598751, 171041, 645163999, 426501662, 272687709, 768601986, 167690072, 393549684, 208585358, 769857442, 140454373, 614306702, 240749769, 982586308, 367546817, 278726207, 968092174, 161179739, 889475509, 490745763, 854220885, 263328158, 327061340, 146552066, 854458858, 354389640, 327788061, 977360189, 358237797, 214219544, 816829230, 270778416, 890354779, 628356578, 759982262, 639361833, 909885712, 421253665, 943063266, 615606885, 225328959, 856298633, 977707869, 334887943, 888560494, 977661077, 589348479, 10004639, 348119146, 716174240, 249327264, 932270211, 674841557, 233402643, 821536498, 654492875, 665878046, 309947603, 649854170, 897212907, 336777826, 558117577, 479300099, 902063695, 318822557, 101372520, 659132044, 829029066, 203516629, 488173918, 227822757, 242579940, 830745176, 375083661, 655233469, 319148529, 968419563, 632556121, 473893179, 501833580, 457741441, 495989038, 761878870, 190853222, 42716660, 364846070, 350771681, 429387603, 951042907, 843383084, 387753333, 712345288, 769154140, 877695010, 586558187, 678808215, 993707848, 150085616, 619078727, 245085639, 388019722, 42792559, 562305221, 686994352, 98718513, 832338661, 268184956, 64411288, 545908016, 886573286, 495663706, 832473535, 112919003, 865914135, 687800687, 230317321, 411872860, 990610199, 177489230, 283089504, 784033910, 521777925, 891149826, 294008243, 77279013, 42109068, 338321865, 664073497, 554078081, 245033641, 624374615, 555481800, 841336624, 822471575, 68943393, 308261034, 44998821, 996273508, 572624482, 836649886, 946769039, 812123320, 820693837, 769622492, 30608072, 112428502, 550489686, 247157190, 733093183, 119807329, 737436506, 937488755, 342390163, 29972696, 43644131, 397422842, 347445203, 311570937, 296232124, 76476341, 636919561, 383539282, 577559643, 507058881, 106314659, 119733100, 35720167, 592160837, 807551366, 995539583, 250194472, 721545867, 636036581, 750785553, 78622696, 19240965, 69803557, 800377067, 973297972, 154458481, 413840235, 951808864, 829964093, 449991831, 534848490, 730705180, 815767204, 479183168, 740476626, 892535741, 477794058, 758430467, 674880266, 523965882, 670584233, 542019549, 185071441, 542637774, 248473229, 720979632, 398482434, 296669530, 215908402, 247355174, 891701365, 186149867, 55725822, 343559436, 696231495, 214486386, 335318799, 425431437, 454813861, 100057007, 87676802, 317426868, 588433895, 586899684, 75848150, 823119326, 188861648, 350315866, 988438303, 945482653, 980958576, 995224950, 249499545, 767555153, 7067138, 551116120, 460199825, 104941100, 451889511, 486454749, 251280095, 722868380, 793849597, 161032783, 68109713, 224835517, 372054198, 766223341, 206559308, 614708298, 570577334, 10086036, 538685625, 960905895, 836107015, 381104167, 935193727, 452198864, 259834025, 401572814, 670542070, 530822169, 805011829, 131173000, 26441473, 80891755, 655331488, 38276565, 954146776, 415948259, 821209144, 285808685, 441226952, 632161889, 758227494, 101865491, 989373351, 744338107, 788851290, 693096066, 823362036, 74748726, 819245141, 465987126, 572693943, 77345892, 687840578, 284534469, 311512800, 4592094, 45087442, 724259647, 858458490, 613121098, 25814635, 992241310, 265845605, 498744010, 350955211, 803976464, 955913902, 19195555, 783303833, 38602384, 880070523, 982471729, 163098564, 838852271, 533870151, 406938027, 847657892, 472344792, 95068879, 295938195, 70001508, 867233231, 910321491, 198048771, 856057096, 375753389, 608118124, 38599839, 873310507, 248125878, 513104871, 957100792, 491728605, 364779634, 355654107, 164143298, 13051649, 6646246, 596039864, 580350648, 914821014, 2040164, 549974826, 23303066, 292525130, 433226622, 199166101, 781023929, 46834380, 502005289, 89836812, 980545072, 905812312, 753401598, 757650950, 678121966, 801912969, 863132351, 297244199, 470353970, 2613628, 729230237, 498673218, 137510193, 827775893, 755902623, 884062676, 550268095, 633889408, 773419415, 22591879, 850958770, 308591834, 688906450, 454079695, 702658059, 644185452, 693766702, 86881394, 413438601, 109609446, 983142966, 880103340, 103026240, 424337259, 764540462, 538248641, 707140644, 207841428, 991633570, 136966175, 221420234, 713017642, 305342653, 66633308, 419028373, 598333887, 555261062, 181804207, 354963633, 832484156, 305429404, 202809669, 653000244, 112461822, 72934867, 852081173, 544879967, 883955175, 121706892, 344993138, 786995989, 533300955, 821082598, 718465107, 557939121, 773428251, 671582539, 606259961, 729989392, 847411600, 219792304, 505577846, 152529822, 241962371, 142800456, 897753986, 301360815, 208574742, 623236602, 583675368, 941938482, 820611180, 494962694, 360973093, 982135372, 509171639, 18013802, 48262511, 456755886, 283954472, 655751712, 16720598, 366658564, 320749376, 187956349, 969406556, 137758971, 639362842, 962441608, 928488938, 802397035, 981088675, 961084754, 484671939, 922757268, 834099501, 901830193, 828557695, 429141933, 425645139, 553026856, 458634866, 232484341, 431297647, 617595692, 179120753, 547611102, 847349559, 441816135, 663696919, 774249632, 84435780, 950575110, 598847886, 633559034, 111592416, 309527364, 132066724, 308247828, 734567047, 472431781, 979400418, 529488035, 858388903, 127398401, 967930397, 369219921, 296832022, 565835023, 276661600, 571799028, 137762894, 506908306, 929916630, 993555031, 985724734, 531491998, 973931462, 994407507, 377648371, 923150304, 213499299, 359882824, 177388107, 189746619, 144863524, 600923528, 553163838, 448914665, 501892863, 179790347, 243659521, 603471391, 695737968, 607204180, 805475602, 206255092, 860317315, 433774687, 652155793, 156972062, 512363976, 54586004, 806962027, 17118176, 916625110, 617043259, 881750980, 925695158, 661260465, 225051827, 820827622, 400928915, 160286473, 670975538, 681204229, 705594708, 437715100, 473255537, 896915148, 950886092, 755205804, 850813527, 674281645, 730461250, 462706809, 91041175, 333641690, 372038206, 423007242, 148277965, 211830341, 658281511, 924414881, 895390043, 394970546, 920239966, 622602994, 292565597, 552856294, 703349749, 285560501, 137711875, 472477437, 289049904, 604513754, 520882609, 735314434, 536045447, 686037984, 279844448, 315857327, 575775620, 954103984, 801746754, 236438823, 329616951, 986720147, 815242015, 447104884, 512563544, 664128521, 215535487, 260971422, 419997136, 584734407, 786258802, 981346116, 909958027, 951668957, 638366840, 267195725, 687471563, 396695133, 232160047, 491655693, 393417523, 668513931, 794640476, 52308736, 839366684, 153320758, 127099538, 664017582, 68939806, 454294494, 24587921, 795459506, 945816755, 607357256, 303153395, 796363233, 92371717, 280417153, 823274015, 606458958, 209792025, 816032240, 699395383, 584074893, 78068694, 718655452, 427346218, 249270458, 317146103, 633611667, 773722091, 616507688, 52488678, 145874897, 810183023, 292579974, 838208674, 297544147, 454246532, 843299925, 408919073, 394772657, 985370741, 793056983, 194317703, 538039850, 727871023, 503776557, 4324656, 875239420, 966421143, 321369930, 486133020, 27110879, 883616795, 690846422, 931632686, 148244235, 406193808, 230499962, 625200149, 149689948, 853227275, 205202305, 122916023, 606472493, 100880718, 550450443, 638473729, 555134491, 266271474, 857114032, 623630331, 760231121, 768123195, 735221279, 320339631, 373889716, 864686112, 717466203, 751031914, 478556602, 152317247, 911551278, 104259593, 244005423, 59293489, 18605904, 266408324, 9927781, 66947044, 437891036, 588637245, 470153116, 581591372, 843925813, 240778871, 283903329, 283299283, 307920835, 971704380, 836246357, 24181578, 893017995, 88042409, 647841543, 317757915, 332423236, 855385620, 749089516, 952614926, 499188679, 622907977, 667033710, 946723260, 848810951, 746292775, 467340671, 728624740, 83853886, 712363106, 359841792, 419054809, 838786497, 437103604, 735874456, 93406381, 744895528, 583662610, 21166513, 830355599, 707248699, 590832746, 418650156, 768507996, 277340258, 956619712, 308314852, 830669725, 144694877, 767448222, 241944191, 245067429, 392919416, 9485138, 930739378, 518061858, 979516692, 657613707, 690448540, 52618693, 189260085, 4375978, 738156418, 803193397, 998760298, 681939927, 508773293, 939240135, 822086590, 934598619, 423128419, 278751587, 168948595, 530913092, 935694012, 457484976, 594623912, 331716212, 512077512, 20768290, 981985230, 837672022, 123929948, 676364012, 518142268, 67620611, 352813042, 764434388, 315339393, 50617564, 930458250, 515110569, 251637214, 393036784, 89116332, 205949594, 527404847, 202638223, 331750610, 598004101, 581000524, 749613709, 255259116, 356983607, 667993200, 523735735, 407008900, 425178918, 279440795, 627789711, 932652042, 775489368, 211703684, 696085028, 301877768, 344647483, 136995103, 866901858, 863815814, 587049070, 965975351, 34544471, 303406104, 332681184, 252120492, 935340140, 811613848, 45253678, 99105361, 534951815, 176027907, 765016229, 306469769, 739389018, 837906660, 811187440, 121678645, 308815965, 559082426, 860466875, 846113412, 399299056, 778989301, 131019346, 539554187, 448433214, 37650505, 545700281, 331151119, 270668384, 393102540, 996431585, 760657714, 918655890, 216126167, 568848693, 720643060, 262398288, 248043665, 802836917, 17112812, 744357785, 84596124, 275242267, 362091164, 614236935, 665739650, 18044628, 535974143, 499059391, 367733184, 88211227, 366985025, 563500519, 847718310, 842605065, 926196566, 627558199, 836277166, 354285024, 719531111, 202003041, 928530557, 870687429, 368090919, 303513233, 916201834, 320466512, 110246309, 212319880, 748373222, 827049798, 302759793, 123762649, 493267915, 705406843, 755623162, 501094833, 541605612, 148174505, 73499562, 522665296, 193437178, 308542815, 179415432, 997053488, 756774863, 650730765, 452764692, 528117455, 325492311, 114741932, 587835500, 519851335, 295003138, 700108337, 745426754, 21165748, 138036439, 712028621, 932158439, 564976443, 346556527, 967526341, 916475307, 60994197, 371787510, 537063823, 345731155, 480362116, 670106540, 832373996, 601466663, 312172168, 734867842, 589686498, 462782028, 978169113, 447028445, 989725378, 932175605, 608925614, 132579079, 254982173, 62765641, 660390343, 268500164, 35262155, 995537239, 508459452, 748061449, 791683145, 303518843, 527074935, 914005667, 266102388, 422246509, 516916236, 673589381, 85826304, 133137640, 629338087, 948252420, 261685703, 979216672, 984182706, 94162756, 702915052, 345073907, 915454800, 712548111, 103024805, 421042905, 414312415, 844181076, 574925823, 216953616, 885523209, 707216045, 40573843, 112000659, 88527476, 723121644, 257114187, 23458158, 923205255, 128751202, 874643797, 963309956, 858277582, 713857553, 632104882, 846550674, 421783752, 628921108, 743101387, 600224406, 114529064, 519363668, 885339427, 630051126, 76569756, 368373235, 979439248, 689476857, 176577548, 744154932, 654905185, 796260422, 20950114, 145764397, 680247392, 930872525, 806607026, 505902830, 755593791, 886211528, 631348523, 547785708, 648692352, 653583313, 190980043, 706596919, 903471080, 367927109, 718351757, 270037864, 654218554, 519413560, 469653365, 634064115, 541477767, 130994683, 752716450, 22940815, 445961804, 598536556, 541526332, 696638526, 405597714, 236874088, 28620215, 991004836, 436552452, 622925456, 691778976, 436775076, 76400914, 342188911, 262731134, 933771003, 833473940, 820484787, 758898580, 348585302, 536394857, 601690961, 821095953, 542151011, 822789431, 17013016, 895321508, 400107619, 293808876, 902777612, 344585321, 552837863, 685708936, 10340365, 383750979, 475983228, 268702111, 71619091, 964950709, 697878862, 795210115, 720397536, 613460697, 515902610, 543231265, 138419089, 742983138, 190873674, 292495689, 353896811, 834952929, 560807599, 989843266, 609499764, 652011629, 833433830, 424618398, 125946849, 651078373, 934547395, 312069476, 238513383, 771713114, 136853201, 250257234, 679533557, 386120640, 210066406, 181233659, 98128992, 130675133, 704046214, 521632392, 523029608, 515837461, 884961558, 2051680, 102777579, 332991808, 245882965, 895329938, 473659571, 360405950, 364614330, 940615067, 403396445, 912105800, 299593551, 837269110, 174751519, 576406629, 144295030, 447892424, 196218731, 415504948, 732015698, 720837330, 320011003, 514964124, 633935605, 143114039, 369559741, 751097953, 836497957, 805827556, 829767202, 175582172, 557616019, 985507460, 92179272, 506115334, 94168945, 543532368, 969636638, 636939005, 110768729, 906136660, 615951129, 468322786, 364765251, 356062314, 858469474, 189252331, 871930470, 328380394, 531099380, 896619081, 585693316, 628028039, 817196532, 630728016, 172927248, 263656547, 939252518, 688448876, 71078543, 746898211, 259440209, 342259400, 685212827, 456328366, 675153031, 966337874, 791093130, 592609559, 846843223, 751341953, 127876043, 483615425, 684714994, 441178950, 979595760, 938889428, 559493793, 117476419, 250093731, 570556382, 213375369, 841746564, 900306550, 598726771, 228452473, 87982565, 414327474, 94060905, 78914126, 63120273, 118253920, 422107744, 669009979, 963332296, 319503299, 528606565, 86067334, 273850660, 578821380, 473807218, 544110694, 442811539, 890739991, 855716817, 193741874, 980941366, 899740156, 774168953, 672468680, 574544313, 218912559, 208443338, 976965166, 658390998, 771952199, 894753651, 517474171, 680920701, 986160858, 569746821, 502975139, 777979733, 269949794, 180463947, 18317052, 611062890, 721307458, 744751176, 192434933, 868296451, 796011162, 130219010, 64942067, 991558286, 332849342, 766210876, 420440547, 399288966, 376654154, 541644352, 953309240, 533721737, 608547339, 693660532, 116350712, 916556057, 236953510, 83545929, 190523354, 279631668, 451111726, 359917157, 432562221, 973941752, 24521101, 737262758, 935312381, 369587816, 697588868, 530114584, 186029187, 870654624, 916504654, 124273455, 250291865, 18175913, 352496943, 400040733, 222183854, 569688173, 545080584, 911915010, 915103686, 693766081, 221142747, 806708101, 470357762, 683534792, 558673200, 63572453, 538805663, 793420237, 319234196, 875774806, 849838623, 304324950, 613571907, 362920896, 845198641, 787478288, 777233443, 291083046, 980434963, 467110959, 556189060, 364139112, 930894776, 777065181, 216971905, 14701011, 977809366, 449080287, 590457654, 783461396, 533335799, 598332114, 976341571, 411968935, 938538176, 656318702, 830358415, 504120408, 906041621, 536284969, 844590518, 340965848, 688035043, 548682061, 578927791, 690802991, 76021159, 11832908, 760845627, 661228667, 70996732, 216076027, 735732605, 506201830, 3746383, 899210672, 52632029, 982793307, 155045599, 287497350, 190706987, 77379497, 134070223, 45833074, 476264953, 687473706, 650263092, 429596771, 930474719, 761318548, 832828440, 62434903, 561606562, 805748968, 473026826, 939391788, 688983687, 352892469, 632739296, 146494041, 483121741, 457918169, 513293710, 69393219, 621534671, 924533493, 633392017, 500787814, 949743072, 915416167, 245242109, 349554776, 634191380, 986633157, 96002954, 955074160, 21338562, 334898123, 460967995, 55952906, 448216549, 912996298, 623102823, 84202405, 32519234, 97105211, 900568286, 35223452, 522236945, 826629630, 922279838, 796127788, 325341838, 708828671, 634271614, 350578971, 20498661, 585561136, 596763621, 960699383, 470280133, 161509779, 720103812, 584923853, 200706634, 237074003, 91619995, 736322321, 930363598, 827753479, 798421062, 450913348, 44294569, 21979090, 946353051, 584785626, 837223002, 435242958, 54482626, 146594760, 438609741, 316595530, 779990951, 107492401, 820671612, 739325768, 371970864, 907607801, 214491814, 479736528, 192064401, 817179502, 760431351, 499761352, 716626995, 445854059, 286454593, 501754380, 880926898, 964009397, 183133432, 152543799, 959858407, 720482518, 703109919, 853898985, 729233272, 138905571, 288683219, 253853605, 172466202, 250527754, 747091059, 886376322, 384126919, 904406815, 705087551, 646400482, 809314361, 696880431, 120783879, 271077465, 926709827, 550939831, 710095969, 683662376, 933498506, 951879005, 902894494, 81091461, 560964767, 263635057, 962727668, 531215406, 720924180, 699362793, 445210545, 172275113, 722659837, 743662989, 384311864, 504929530, 77514321, 963673928, 676176760, 69830067, 119127017, 329825122, 600268386, 936904195, 761304071, 476809750, 949738071, 411493657, 408471972, 420505484, 312819931, 480535741, 210107566, 376241813, 151371292, 334019978, 798842570, 480482979, 880039111, 686498667, 125860191, 799054257, 708255577, 324912616, 407889220, 807758416, 866467291, 834876971, 995766861, 153105946, 22306238, 402673812, 975920632, 513235178, 356058335, 141705164, 407895758, 386000371, 165740991, 827973965, 280872132, 976434679, 542374611, 101683589, 161035470, 342277812, 334230075, 759623122, 268920149, 979789285, 837750333, 504636180, 720482285, 808531485, 879299467, 485623376, 313897927, 528724299, 9738585, 295234598, 854417007, 994488214, 733309129, 540676609, 454330431, 601846726, 625973603, 45713900, 204900475, 761238246, 59958915, 265160766, 340511927, 157850062, 212355478, 621879156, 283455503, 465539352, 182450536, 837290550, 14278311, 33510254, 946877523, 693238310, 505528484, 397431461, 749805280, 589346744, 237950533, 327449234, 204915219, 196214007, 726204836, 228271477, 785239936, 889057887, 728377214, 472200753, 446592675, 726859034, 974309059, 313664838, 527161388, 606834912, 417131297, 796629245, 481104214, 655353486, 430099257, 127514986, 472062966, 216210627, 477873656, 472408931, 188884959, 329408747, 877867384, 868581580, 382835018, 555549071, 53373521, 457553512, 751071271, 290635452, 233766511, 84275861, 125814947, 67928438, 957061798, 478387195, 256404601, 735846672, 541847479, 926690776, 415748391, 124187893, 531631159, 554229116, 69461793, 819510512, 957037440, 490567640, 660840599, 350828944, 268010997, 490635585, 246732103, 802293447, 629624876, 92113165, 556475752, 282835298, 864916675, 913989261, 668595660, 259048127, 79318112, 307141151, 864422125, 734751895, 121357690, 810968413, 173594320, 749812863, 481963122, 273645678, 780087105, 615624710, 775690228, 944415403, 500550284, 675715001, 633512056, 629551896, 37134521, 826492738, 806723020, 462197009, 822954700, 465550586, 486388762, 334855097, 664178785, 893448154, 792642533, 191912676, 178612994, 438558658, 385926698, 272265061, 177791235, 520645702, 79235491, 913132293, 82709328, 123677885, 102878111, 533068106, 913791005, 956443921, 663901538, 651386046, 61905260, 284581541, 687382795, 423354475, 720105189, 974465596, 534927695, 879552147, 224047349, 559381686, 502460130, 8218958, 5786842, 894702525, 511149378, 349242964, 820662458, 632197260, 434033120, 419521287, 494625594, 647482887, 18287048, 768091243, 39702283, 454859108, 508744669, 699877586, 163161543, 936157638, 562663329, 134973468, 288300145, 105240902, 409039009, 153177440, 970141357, 543998394, 449864889, 625110681, 607034246, 605325421, 687952128, 598259761, 954113358, 373942864, 844899804, 327800757, 332885267, 762428319, 629743963, 830723265, 964691431, 405142838, 813921089, 935670387, 881293763, 830422176, 787939412, 379967579, 535884781, 919971469, 371695323, 216590465, 172576493, 400055763, 348304150, 910291136, 673756910, 170384168, 461079370, 957831244, 177088786, 951248280, 597534575, 579485777, 892802638, 802750374, 104583650, 23644324, 252541876, 156492565, 377455096, 53783881, 357662714, 213832720, 40919233, 924233449, 256976270, 723648609, 688009495, 765326407, 944558361, 692612090, 34305663, 944289832, 521854683, 224341051, 856900590, 331862950, 448612024, 312727932, 229307705, 777727946, 662088291, 472175904, 984105705, 80970711, 871906079, 433944142, 776533554, 588298477, 275248212, 784514179, 481235040, 453705638, 588406141, 273194100, 444283448, 198812326, 336560780, 493327593, 69084286, 116097652, 398654767, 591520568, 111525698, 631835003, 658233318, 791899313, 543891041, 105254301, 652978585, 804351360, 225714793, 194692780, 853493339, 250965089, 837798326, 37192775, 3046013, 127137214, 481600422, 77849258, 820712538, 910376621, 983147166, 987507110, 361839292, 787422399, 238321150, 987777134, 868465324, 460939233, 83154512, 754014846, 205962202, 441537203, 769432654, 538644735, 458892469, 266800674, 920367778, 7139862, 614990505, 913441270, 19598439, 232660272, 181465846, 136626025, 305155235, 503663006, 501388818, 159546515, 922047702, 594200882, 507201146, 248195628, 83669091, 406389077, 833574392, 3924156, 204482313, 91024345, 91154330, 324787390, 646562990, 519954247, 561024285, 916178576, 757571234, 356048961, 222118452, 897847791, 884436354, 328123492, 366605555, 877638110, 296547794, 239458110, 410694786, 268557637, 925212933, 646782738, 183838970, 430544484, 855027917, 8822523, 195766820, 413929987, 795348022, 444435341, 372506480, 912854955, 210589889, 660679814, 571613206, 368544274, 259366956, 609406310, 133850492, 153397521, 906402375, 547042647, 381660788, 883904281, 961224348, 771726249, 676751479, 60232953, 791482894, 155185134, 21865619, 398503461, 755651937, 441232891, 598752242, 234882632, 96459010, 562709056, 890624433, 203889473, 886186863, 401242192, 14912356, 540625753, 544751968, 647838220, 244413779, 293719352, 472562514, 370041079, 129086013, 113487650, 609637089, 585174282, 526917712, 850599873, 553145933, 735698450, 466275056, 585681385, 69536355, 917666779, 285127146, 940924941, 44923153, 773663352, 742590222, 552151529, 456558655, 412017230, 339971907, 635053893, 980238015, 41648141, 709316524, 388510231, 857508952, 665250041, 854823753, 756943070, 529982427, 202318420, 283119844, 95359202, 459802114, 59175445, 894901338, 21839887, 578745142, 135457614, 584361392, 350998146, 601312398, 590072593, 332328885, 863923127, 238817062, 40156415, 73141681, 900738399, 535686920, 595319470, 583197384, 642745128, 613077770, 581145915, 991828509, 111354815, 919654942, 67990264, 201553951, 807297154, 632344209, 263378587, 277016077, 741921611, 464017193, 58455307, 643729714, 609341836, 49336573, 511198677, 416830130, 305719853, 528152144, 631575129, 860319527, 358887476, 291435724, 442612037, 346246361, 965391816, 986516039, 749482083, 371071583, 805749828, 744588078, 932658572, 645397328, 397831781, 161474277, 340729660, 510827447, 67128319, 339408092, 998780840, 615667014, 316997584, 814316091, 106898268, 248134360, 188993281, 501387756, 681983715, 707112838, 357782778, 203080218, 40099089, 73373089, 753393495, 479616055, 35628745, 86670021, 792527801, 670163911, 834588057, 854269008, 221373718, 115070552, 671621718, 702531887, 232812638, 177760199, 653453001, 435885393, 469577460, 99230883, 428360328, 360416580, 894813494, 673663607, 731877970, 784699785, 269868226, 24053098, 676509313, 186975391, 190927083, 402425515, 847048675, 252592622, 12535501, 108105555, 588323534, 680862398, 571726092, 103369375, 772482982, 27372223, 992232271, 745203853, 693131273, 132309034, 653619438, 330533979, 869374682, 569587065, 783127897, 558507470, 802534458, 469733094, 992745577, 506218059, 267700157, 736891484, 877449317, 980376499, 366885151, 604597507, 24271293, 581276590, 462083454, 391309075, 456920874, 478814001, 1274789, 138454120, 994017212, 598626023, 711861305, 688823720, 540064871, 96159281, 44312290, 64968617, 287487546, 285696445, 713922153, 757093428, 87027568, 876219930, 441432598, 269545280, 699179703, 712401690, 448095529, 368914612, 317298408, 66203637, 368522215, 226533527, 201704992, 594989011, 771416053, 693844834, 328294773, 647744964, 574438226, 176445074, 498673608, 425660655, 256450125, 61531157, 454898876, 608283828, 86838080, 601108126, 159465047, 796561236, 323827809, 452844707, 483424106, 42474353, 752754703, 464583874, 997197184, 616966341, 472542225, 876679788, 119111563, 63670661, 562988048, 772251014, 767276550, 408913554, 870531124, 405314812, 357474114, 669293909, 203216873, 226016105, 947195554, 971146557, 991868288, 486860901, 908077010, 817557529, 163602155, 710428261, 327670281, 794021215, 530995234, 196516933, 991805824, 566539026, 584635158, 737743725, 444324066, 111407610, 536635198, 427523707, 875034420, 555927401, 454463821, 26436687, 905755662, 697084318, 618423932, 14168380, 383988823, 119464491, 509277356, 430194271, 822499172, 733425211, 627989028, 289786164, 112678895, 596468179, 613260843, 703567449, 599699159, 555728501, 375775237, 221574007, 52712275, 443626965, 247465981, 992252564, 678906579, 712075549, 403054383, 612451615, 463025285, 958233401, 7908239, 251200576, 984871748, 989832530, 326761101, 218231096, 606725177, 63965786, 102691614, 277471556, 838127347, 319748511, 162601365, 249170081, 652723712, 216288635, 218366835, 704658951, 817966337, 14214683, 682497516, 969343529, 431270034, 46261301, 645182074, 644597675, 636530200, 91118728, 235923739, 419162453, 864203288, 947704079, 540254150, 849025112, 666001250, 136414486, 629633795, 251823590, 260463149, 342959231, 665473590, 231748850, 529680646, 923832406, 785190860, 63389208, 918771647, 605500593, 683028214, 721627271, 718176687, 912137271, 635366233, 242900437, 66531966, 274685095, 460877736, 480536250, 353151001, 152926943, 184298572, 317486214, 148300218, 708158558, 176495236, 536387362, 528730891, 512271308, 883639578, 201823706, 190389586, 160114115, 477523157, 411350100, 667355271, 7554911, 225807380, 161622595, 620472381, 254068616, 815769481, 457096394, 225587949, 570562842, 304062467, 625074534, 692063303, 274335331, 277199690, 183821500, 646834760, 109202719, 165718349, 707860562, 791805307, 901513755, 901563609, 88045108, 187604236, 968284588, 639502926, 837643719, 122058980, 82346430, 519360198, 421222368, 529344165, 79933307, 611222121, 226266734, 559108529, 572631746, 156050551, 835527336, 119974488, 158095560, 41515968, 521016992, 931327306, 670661728, 763510996, 411861814, 634864230, 815331698, 460049494, 670010300, 557752978, 385520818, 712561137, 961905234, 328760829, 705443257, 904029672, 46861263, 573455914, 811969668, 502523796, 320107369, 653130344, 488924137, 297733926, 670755922, 722058216, 254041342, 142520737, 54751526, 300589510, 548639601, 80186675, 493081949, 923002116, 366712154, 369672176, 630509089, 119720450, 5461060, 925633120, 306929057, 248985298, 743999709, 962399522, 654662160, 244657915, 536062021, 379936532, 407552066, 844191703, 706461541, 443196155, 432456461, 116150589, 552696680, 445336851, 454323619, 569444884, 537134255, 99247906, 7610446, 594404955, 871879778, 231587904, 601272788, 257165713, 249981751, 693314356, 576601830, 447508467, 69077370, 18679927, 209949987, 765519272, 921867996, 194733229, 25339930, 143137706, 614153931, 652778617, 963944397, 196209330, 378400226, 917841310, 82347648, 549467286, 509523455, 776102483, 253196343, 600524649, 993124542, 967002900, 845006256, 169038985, 358568025, 786214632, 364654042, 194456151, 757250627, 18456624, 654487650, 167173611, 678625385, 807480383, 165601513, 638795848, 518066731, 705841105, 838944719, 458435779, 494859278, 646832834, 528973397, 861821160, 884099165, 252958012, 399078379, 856910998, 622129278, 81756003, 836758825, 866700341, 447340708, 906178777, 530657696, 268628101, 313451725, 223571938, 966632178, 583175088, 497416047, 709594864, 594919438, 201123226, 848218758, 452675201, 618567574, 818964468, 39315190, 282632492, 457857715, 212112396, 87810794, 986997782, 234939459, 315662499, 128057642, 301762414, 684944036, 103669870, 510548035, 522024977, 151323458, 246185497, 691380011, 247405496, 491247477, 872481373, 359322447, 800588336, 384200494, 332316577, 795044308, 66868130, 319441870, 150217728, 229457867, 414575373, 277982636, 933872981, 508116001, 881812938, 817826383, 170651394, 578566655, 358119509, 531290663, 455575508, 21826259, 225009494, 744151274, 437920585, 77470166, 64420343, 572743070, 637154999, 88012175, 60730682, 625781901, 696893359, 514636665, 636454027, 930488006, 544728024, 63142546, 469567786, 124918250, 428745376, 172717836, 141733831, 255841338, 611660629, 218479292, 992276614, 62793036, 887166531, 201369981, 647378600, 509083944, 364573867, 383500166, 968662758, 854073412, 962149138, 577338083, 600751143, 465558861, 795843018, 810821658, 231226639, 359411003, 982765083, 973550604, 61242875, 148730991, 635208766, 852460888, 580058408, 736731760, 811832828, 147866163, 153489853, 693246162, 690496987, 354603609, 635012897, 359407413, 907289867, 399001724, 22018551, 292067621, 71729398, 406076992, 242774694, 794399526, 376776376, 898902394, 545899877, 361105235, 865671498, 510235128, 565008861, 617827087, 308296431, 23416454, 369246111, 624098861, 484212646, 835063287, 815304393, 434685850, 907204077, 617335403, 263214779, 712879517, 199876148, 485225982, 68931615, 778359055, 989380242, 422253638, 503593513, 847391360, 49293061, 548374150, 528985892, 428217494, 568224022, 718431702, 43984898, 709250072, 63693897, 963965655, 15748105, 593262397, 470846130, 566683354, 329287025, 640737706, 763585473, 620966020, 60354309, 698983433, 78238193, 292346827, 518865214, 277142724, 153137086, 173595802, 376225142, 726794563, 392723142, 230015672, 432577056, 124651384, 742048581, 254435308, 990537717, 648499912, 434513632, 654513875, 803009990, 508126793, 844806794, 170700306, 841713324, 558391173, 573196640, 454820056, 327538164, 357069234, 699976494, 185152809, 5643812, 643080543, 996144522, 971702640, 592978741, 736601076, 155317007, 961288919, 567412593, 843488705, 157111771, 892003675, 438302927, 654750325, 99562222, 200610713, 789208253, 198556614, 404634639, 259604986, 359314936, 708279214, 294143420, 85862179, 627272322, 560611406, 804409821, 74848740, 523942263, 383286150, 29902243, 961654247, 642406302, 923558678, 695784104, 348225706, 121399156, 738200273, 413472275, 83746231, 319930361, 473834543, 414659890, 366646048, 439835497, 428176810, 227294828, 966496772, 811648740, 353931149, 90274719, 163908779, 337062496, 440988332, 997977668, 222764510, 434928799, 375956217, 554684648, 59674478, 707559182, 838153011, 225120700, 312213291, 715091654, 420655842, 633590876, 143477496, 427829945, 781048047, 910180348, 950837307, 890903520, 797000040, 489582357, 916394161, 673315132, 845618422, 307058695, 196788318, 272254881, 544288848, 741440846, 14232595, 608969897, 677757265, 895269368, 725593652, 140659624, 314670880, 362892606, 998468489, 477945854, 350905135, 120443374, 773664675, 120592004, 755616489, 667143457, 629199415, 952052594, 299869579, 190753567, 911886141, 439345822, 525556879, 294540157, 860518901, 298577694, 511744756, 15774656, 56174735, 7866860, 696304653, 787693358, 154944885, 861453601, 203053852, 533169368, 896360229, 169687523, 262733889, 999340313, 885519950, 748410870, 276106313, 842173865, 43178212, 915700290, 233109034, 313367047, 821002632, 816035341, 385517491, 492884629, 885310826, 786326431, 312148193, 331030690, 789982990, 952435660, 989509864, 7199635, 355703385, 441418352, 660101922, 726807682, 827890184, 909016557, 887814046, 696307752, 534682414, 483921158, 533170493, 407295160, 657893614, 338231503, 434972691, 555707388, 353784684, 683307468, 245091882, 371476933, 963773643, 187019628, 790410060, 306864275, 288129222, 705096199, 734110014, 973463642, 594204316, 203069670, 78534249, 133081386, 568376275, 436690221, 576196153, 608774237, 890377424, 878604129, 729079994, 390051006, 382547265, 117267811, 481292338, 727637765, 607213288, 622380093, 213471522, 577127067, 693361304, 147927793, 715613110, 317491402, 473723544, 152185622, 945926485, 446839637, 396442701, 367711171, 864096094, 705665350, 834979143, 263089437, 166336229, 155759794, 991207790, 902038119, 524430309, 176526892, 972914090, 792822833, 610916451, 2488732, 556033436, 112537369, 724683579, 363890508, 935677853, 781329004, 698126984, 711856953, 591771874, 131579843, 842902068, 134046885, 559219339, 771312530, 142837584, 600565627, 892844829, 921657185, 114466719, 896361805, 87567969, 828847084, 405409736, 859936012, 889553042, 262741174, 824516917, 883903410, 485277323, 244832908, 696759027, 410357851, 506928792, 872233266, 699790601, 368161656, 435576535, 853681672, 486611789, 875043212, 982304727, 984700583, 723994787, 433568476, 716227893, 449213294, 551843852, 751852853, 971484679, 378873194, 889298161, 800611238, 19840320, 508959166, 106357183, 227691506, 511611457, 356857099, 75913193, 527733454, 975825022, 444592062, 76826034, 230914373, 936546577, 412007895, 490651866, 252655775, 277283344, 895466171, 836173245, 125995511, 879077941, 314210687, 526467170, 919831973, 417822312, 752291556, 889081052, 729235019, 79832846, 590108361, 298739636, 4573794, 832666450, 772101782, 312586419, 796166744, 980010845, 937883207, 49011160, 182456958, 143727027, 144091689, 621541501, 841203454, 51071602, 311788725, 519197880, 758988925, 680137824, 659967734, 763130434, 332517516, 943426882, 278016084, 885092572, 129114426, 42550444, 559935798, 586005730, 124241515, 337091901, 726327622, 735050223, 573158772, 535793258, 546533308, 791712420, 361560246, 747897117, 772880744, 846930302, 278917082, 649955250, 451061237, 761433239, 626057651, 353622225, 93314126, 506026275, 664541245, 880872577, 330967414, 110167716, 491640695, 822602536, 274032393, 879938081, 752999093, 541496727, 212235430, 386833490, 942674474, 589417719, 482418879, 376115830, 431141987, 804519998, 371393965, 510202821, 718301282, 595124340, 575616562, 865009549, 615467533, 373065697, 20769753, 392394510, 562446073, 142113219, 425415331, 718528843, 611130046, 759448618, 678876864, 124769912, 128940191, 90500981, 782165982, 726849893, 997679447, 733730588, 933208663, 242197332, 788593914, 671868253, 988831054, 455597098, 262863330, 502178333, 280945664, 745622807, 202616159, 752466342, 617577745, 448035746, 179167980, 20571370, 702426113, 883964684, 430823962, 223563304, 771758334, 956578738, 999702550, 208753772, 576827837, 484005446, 882073641, 487593631, 279681310, 757824772, 274491305, 260159149, 499512491, 776545764, 305885389, 96048118, 799444727, 835417942, 726752053, 733168515, 243877057, 31592320, 155766697, 568798236, 645929102, 664562128, 632344925, 50999281, 313903484, 427065032, 652116364, 913720496, 213600823, 907450548, 510206338, 601968996, 803001545, 424984885, 276542332, 372874782, 423246964, 513948354, 844738976, 310244015, 217579875, 300580065, 100119571, 283332949, 319619876, 26821084, 738239351, 712789665, 278977171, 155470767, 983516579, 269595686, 197623352, 356271281, 471452458, 806944502, 672207908, 450654422, 953810218, 669306180, 346840586, 82444226, 7697100, 550519674, 367111957, 742109031, 207975302, 918579302, 698647248, 27119635, 882439219, 202372190, 129945298, 2029749, 684549854, 848859054, 450495807, 905784207, 831248893, 15539149, 377335913, 812539329, 451545712, 725985909, 869732354, 90380797, 259576003, 479308283, 778495756, 128392007, 275321410, 272130406, 152634566, 148925110, 235164129, 61416783, 723290776, 926479361, 119937826, 168866228, 221671493, 813097281, 522391465, 412196365, 221848940, 254448803, 736890407, 815500503, 995857945, 177717288, 934075295, 320087999, 695902623, 103889484, 49783050, 738840966, 697745138, 254303915, 557596827, 252708500, 266066735, 792653518, 721493060, 381189551, 345525771, 331997287, 446704538, 382019841, 862298658, 506045479, 64187701, 188424207, 465100522, 566790779, 959571996, 993552507, 736307226, 69452205, 495302969, 229572684, 648298186, 197109249, 99519563, 917900666, 37858606, 661429629, 302065661, 371627194, 984547317, 987028980, 243000510, 889497681, 159292173, 192803553, 839190357, 198711440, 927300728, 413488603, 242115795, 980085143, 378496881, 945965212, 840387368, 386644637, 748579404, 719684649, 847676494, 355964476, 355896082, 286820043, 327765397, 976536852, 920171015, 42469607, 502850269, 305208535, 861375957, 868676333, 270760764, 559811591, 499933144, 350171568, 266453907, 771049782, 600672626, 273497659, 770000963, 897777008, 645760041, 689621710, 178459638, 433084859, 146155377, 560533721, 967206589, 545997555, 848517618, 644382349, 106242419, 93746030, 282087377, 717636219, 890178964, 995459802, 50723225, 789360256, 487390847, 935917168, 623582957, 282986959, 52401506, 35475291, 757137987, 889086275, 761487078, 774212049, 320134042, 425283249, 886442308, 820224332, 403557766, 426083052, 276479512, 175200244, 552730221, 255410395, 400027329, 249038334, 462830811, 678734997, 378900819, 42369986, 945274118, 176958827, 163052244, 404807572, 609225743, 398635495, 742446154, 717087521, 5479131, 325337279, 531427557, 734997736, 561377410, 223807474, 393474095, 219600905, 280880215, 70015773, 678350951, 326536362, 29803296, 513237558, 677308006, 758604174, 717349310, 162277436, 11287962, 611788830, 628636913, 615611194, 257607332, 779245692, 88534506, 14077830, 91117441, 672826369, 310245880, 172050250, 232132221, 328554407, 87799582, 152470384, 779568603, 127795046, 926871091, 548168686, 881915108, 448765196, 572961689, 870982549, 567450453, 174478733, 37985702, 565982962, 942170210, 480874009, 572087050, 815582714, 971860408, 648647208, 704480321, 12103748, 353153783, 354806375, 740732845, 970807743, 487664836, 802726173, 316696166, 285589283, 224190644, 133521901, 699737498, 45077002, 572220390, 690698688, 477160903, 90759481, 953656821, 558470999, 695704918, 299106955, 652480086, 639874091, 269696753, 352850949, 333330232, 870189431, 212917995, 252815082, 605610196, 531722916, 531601296, 581541443, 39332200, 244245180, 609690340, 209097258, 766159653, 79050400, 488037846, 987889486, 467610277, 773222026, 230785242, 32708993, 371564284, 17294707, 591031451, 447668007, 584864461, 908277620, 936834717, 65013047, 157889560, 548808056, 336219162, 833851477, 892701853, 456992751, 690684599, 375740302, 625123520, 815332127, 198791708, 996741335, 990924234, 407066848, 588476557, 28495454, 108102538, 704929362, 811123541, 197826809, 960996297, 740603862, 814718275, 653329469, 47030490, 274964696, 235183864, 7097075, 973837950, 858429573, 280082515, 672597963, 899729956, 331580745, 430405656, 963507805, 930855803, 948567989, 311748006, 451501722, 104684701, 277272312, 522638437, 247382706, 170798358, 850290040, 444859557, 501940403, 58650644, 254746304, 954189151, 518311040, 938296064, 371928365, 136076423, 222979625, 143919024, 228215005, 570827845, 739595377, 808690179, 629627776, 717451052, 28928868, 779694038, 692199662, 389539424, 46817369, 376190273, 640185368, 517514672, 54327409, 769536952, 171231430, 67497396, 152731599, 817664761, 7926445, 997161525, 308980685, 44247701, 511102914, 306256470, 940864850, 868583635, 998513942, 480001812, 668561367, 974620184, 649960620, 409622371, 823423502, 812616163, 820386598, 867543215, 746514671, 847185686, 805118420, 865341583, 228176912, 738496657, 581780462, 358235029, 260252807, 367750211, 435043250, 274435351, 423721459, 122446359, 955792221, 754256466, 938875273, 605179273, 568983068, 314391262, 964452617, 724144529, 341473711, 811798726, 290328558, 854775936, 775589024, 198459432, 611596770, 478432177, 172752294, 32911427, 703571385, 222422128, 137948398, 629129471, 849996391, 356595675, 423059553, 72802046, 909348151, 550388719, 677447233, 376318487, 531131248, 63691629, 455467561, 490906742, 709271643, 340196896, 949416849, 905844230, 647730448, 330671188, 33754782, 255334667, 184115514, 991022051, 638454578, 739432588, 880826429, 423881377, 681969418, 238126030, 620807163, 359386253, 152154928, 646336142, 18812597, 113573319, 544175872, 619681864, 508302771, 664370676, 929556069, 569885480, 253347809, 162791077, 537121718, 642413231, 164780703, 843254238, 645446281, 495334833, 872628240, 54773286, 16609138, 130596913, 772886846, 514454215, 803666542, 833167003, 846565103, 129511795, 925726330, 337984912, 706215644, 614484701, 792430834, 216683865, 147671819, 693218939, 811218764, 948675589, 646331100, 800343631, 316829983, 939590991, 426216111, 520302377, 468250690, 868636548, 16617741, 18206660, 715534489, 794720429, 553642684, 776466655, 793696855, 478148131, 107981997, 531345083, 224630852, 719765247, 681588332, 104025890, 649617588, 96243586, 458356392, 342667056, 640860511, 581417007, 751888052, 349699829, 308614955, 430214632, 431034953, 732114486, 304223594, 638141394, 605138082, 407556430, 115218376, 785903626, 9269051, 729790652, 773724874, 181020173, 250019953, 848116478, 113510410, 430193877, 194526203, 468125637, 613500808, 86085081, 795449973, 151264388, 425386448, 673750295, 714945202, 323263770, 190973071, 839162434, 695181085, 517354293, 273748447, 537614920, 428849198, 353693586, 62243374, 403696362, 53084939, 316556712, 394683433, 450103460, 624899753, 307285754, 574135790, 136136323, 329401689, 567797283, 471863277, 644906671, 888472919, 339166597, 193545550, 317240618, 467639132, 531704379, 765323070, 851861264, 209516627, 824139553, 207178294, 498968249, 100290209, 776015845, 18466782, 36870829, 763323248, 566284905, 330303958, 266372029, 951476563, 105951643, 354031801, 922709824, 282647226, 989635273, 784551204, 594983349, 140520823, 664450418, 656071256, 646406193, 931218697, 103369748, 590123620, 449691590, 499739418, 408051668, 726126269, 72382946, 831455436, 473744905, 923248029, 263599279, 832305537, 941005969, 375216324, 655456871, 769251503, 324431456, 987444835, 853260158, 996147587, 518700343, 961527215, 814885741, 305559555, 304652930, 915860036, 460137833, 81364881, 540900882, 287194769, 136412821, 877822544, 230080610, 509263408, 935593907, 531798043, 753389080, 71170165, 495683410, 968785066, 843005380, 421611778, 10086138, 689847591, 922082316, 205801563, 49443250, 532735080, 510109282, 429041764, 124116271, 323675019, 907364638, 582382688, 329740132, 301443284, 311307797, 869979633, 727053434, 776589710, 631860366, 31126237, 98328879, 30628705, 397592378, 27738847, 827865710, 701540947, 835207664, 600267227, 188530733, 739464444, 147192731, 465855006, 190554999, 559979417, 697886831, 221625093, 683301217, 682727653, 993612753, 584736995, 905750555, 886381574, 492631942, 842669232, 462069751, 780230727, 89586214, 693186327, 750306719, 636791303, 83860706, 673374589, 485124523, 361544279, 355245675, 912145362, 312555498, 974837376, 661921469, 760302228, 300168236, 347156791, 742420337, 273048710, 127834418, 882936232, 116907566, 155150045, 847975331, 541006721, 971731835, 843021769, 97039086, 108688128, 777093402, 105710572, 624265924, 801139964, 943463313, 4651957, 485745107, 605317447, 786705319, 675613365, 646005703, 392617789, 843470329, 375512313, 192325473, 75263368, 757729620, 244116728, 874819157, 106025429, 71039503, 748919178, 375960924, 709653636, 111419595, 985619329, 450864895, 258697719, 147584540, 713323509, 550500028, 291860597, 183267828, 981507876, 202259058, 331935531, 47637479, 769982534, 553919965, 342038701, 632025790, 884722301, 130923459, 680766959, 88487771, 297792455, 748606207, 481791004, 730808687, 977392341, 743569616, 483200672, 996552552, 818583241, 380887190, 782300287, 875348639, 49419156, 105935216, 583441383, 566598344, 273339098, 124073901, 635355688, 286122916, 919499171, 364207886, 218312154, 621617249, 449312114, 616240555, 381869840, 791422218, 686858530, 712999327, 829337670, 755326314, 511838779, 534082041, 868020015, 439327889, 624269793, 995784109, 543361632, 415813604, 632130510, 543334549, 801770925, 369597664, 95619902, 632061974, 882258140, 761785784, 286990979, 619199602, 98087573, 687346952, 131256660, 194535241, 652455676, 606545851, 357821347, 221868640, 985846777, 240306103, 379355975, 409639977, 827978151, 614969943, 150714069, 342985055, 558354024, 807497166, 735846802, 178086490, 827941603, 832987955, 612684088, 644828681, 649790495, 239589485, 529047515, 82624241, 211958558, 851070409, 156272052, 906876627, 771700234, 891433683, 41807464, 378462698, 450144846, 638140295, 689547869, 155614385, 233319295, 779043877, 859991134, 495670186, 519935151, 882369900, 22879851, 638737058, 207831766, 495965727, 585497355, 234220379, 284992656, 613141106, 139376703, 31617286, 314255792, 509316531, 557059452, 59406638, 149284157, 478937743, 378211937, 134544035, 219716197, 982349772, 619708817, 166453560, 752954136, 853910099, 666846838, 199369347, 848285056, 45181092, 70925834, 379577215, 5462093, 669847005, 767713769, 23897582, 950763309, 878274156, 676849963, 420214341, 42560355, 253664756, 451372079, 926642111, 658470194, 652324869, 488665836, 237245550, 860202259, 72252229, 658405159, 38940977, 558772264, 538954975, 325768180, 132559583, 392823611, 147321500, 925966003, 806578591, 651147731, 672746313, 352625151, 124039218, 228161030, 762934354, 794794553, 611963462, 911064477, 741734242, 234275538, 35202586, 798519059, 899211830, 713040566, 272449675, 176583904, 554686924, 942872802, 152603246, 273364225, 4911971, 438715275, 245245127, 618746830, 696558498, 327379098, 523031778, 345189004, 590837120, 826696090, 874036097, 409768716, 18817052, 979808193, 867030553, 276217428, 29673583, 30709381, 576682413, 520154934, 449235382, 751261234, 91914008, 669174281, 239231228, 266351707, 206775206, 113505445, 184122504, 553045111, 275343854, 2566400, 97615479, 701856366, 697036039, 326769252, 768532127, 395722145, 59963707, 733536410, 241053906, 617039559, 544590924, 275237432, 651180810, 439867855, 543640177, 404839381, 935379609, 477004247, 811738902, 795681678, 707468821, 534432211, 888997914, 143391136, 117208022, 769721274, 437534220, 950345793, 940506009, 207536906, 897262790, 651837610, 677594710, 510687665, 540781673, 732294298, 85559309, 126136269, 839329054, 639680702, 823806175, 965022932, 551923281, 867958248, 784575131, 815656767, 56954160, 665183125, 954229586, 310227353, 913442824, 78141688, 752309510, 303834700, 422750913, 18438523, 606040354, 673478113, 65008594, 38243492, 945376798, 892230541, 498481770, 650547561, 382977113, 972367104, 947964673, 70658010, 907410788, 19979077, 712406943, 34865864, 107419413, 159430039, 567492204, 41886796, 160601948, 882227946, 829948267, 282041536, 433174351, 264941050, 196268227, 919113182, 455243990, 106417178, 618042949, 776241467, 420049266, 421548138, 406715544, 54986238, 757256470, 224515003, 663237742, 557896810, 725527206, 538557657, 965348714, 25673856, 758993306, 758415837, 911173794, 39849675, 448072669, 231776660, 768058330, 588053024, 311478904, 196844941, 704265039, 1729061, 441836604, 958461184, 229066149, 688692977, 809409075, 640768917, 502641482, 828141398, 429608509, 572956173, 833909924, 512900989, 241240630, 188423164, 19520540, 57417068, 805897371, 169068604, 137307238, 893015664, 818712885, 664107193, 197418990, 50573923, 19013862, 500559729, 610164218, 964739296, 405726832, 718033001, 404079032, 206744670, 588264804, 778036615, 527708439, 646056250, 123995853, 717910837, 528493604, 747120599, 248007145, 808587947, 866194079, 581575001, 523302934, 991723949, 287404932, 564643558, 741412681, 550454413, 908009170, 962314590, 994921396, 355820259, 59216766, 841202371, 758112944, 429215812, 216124232, 500642481, 691247224, 408833648, 920270788, 986833980, 691190134, 598952062, 650512279, 577256715, 78295246, 410941014, 287356697, 805713708, 244215496, 224550366, 503939199, 731916700, 970422959, 105865431, 776049246, 534490045, 461788339, 898473698, 401852345, 644715602, 818058269, 356022950, 186463632, 221750732, 17239698, 931802100, 200332899, 438735783, 412131859, 17982449, 330666930, 151814922, 784470567, 501120053, 883978324, 274191117, 235344935, 611496866, 547046625, 686770183, 718046692, 498791255, 302251959, 181614995, 414108852, 773598389, 772306317, 209066377, 551442973, 724956683, 133327727, 531431277, 294904498, 115701263, 754917926, 557665879, 326891732, 368923867, 151961056, 113884597, 662188001, 326030458, 570397285, 383221862, 168548899, 472061720, 879641046, 142200084, 537027552, 619838471, 775649920, 677030379, 427697182, 332349501, 638916435, 775256055, 808443995, 648723529, 666703020, 957707531, 326270660, 450359194, 441627298, 856446825, 488731955, 693292778, 131483059, 952068939, 415772940, 973120280, 867232910, 405238424, 697890262, 599583031, 436603259, 224715219, 108070168, 501618666, 510946212, 942329168, 60423801, 911169432, 574503394, 501403931, 278258645, 853071962, 421271274, 342887191, 595677280, 115388022, 376519445, 577376225, 112187712, 581622086, 195373352, 624981580, 877986078, 819228900, 642075384, 551852204, 258504672, 393611382, 448967185, 646892207, 277682435, 929871691, 123964146, 451123666, 667233018, 432511738, 843678772, 242363225, 160295708, 478820993, 233182795, 25585297, 551929955, 116196027, 464013001, 188025400, 310509361, 446524430, 281569534, 327266797, 322639157, 484659968, 335682725, 800555312, 909229715, 435077425, 963432311, 694921182, 949112657, 59344994, 607278812, 73136106, 900732690, 636544592, 870575900, 141062822, 66698559, 714112281, 35626486, 381149079, 460830858, 436028991, 691621858, 24517740, 309701413, 150697621, 859890553, 189193890, 508322775, 61956260, 719684631, 570203247, 62750768, 697139063, 462192913, 462979001, 348009903, 777062194, 745713828, 519494036, 524003738, 244143348, 976964330, 541384816, 427690790, 3588623, 47821358, 926183722, 157985475, 637116720, 35008209, 718286603, 510136669, 467698194, 980270177, 152493358, 963530558, 588393769, 28459098, 593857638, 525017439, 371548696, 543390164, 750255622, 217694786, 697433935, 235653377, 605024982, 50930704, 342770342, 497908997, 49438181, 136708095, 248454413, 464713212, 127720646, 187694822, 521681426, 603406144, 179816041, 779567146, 739354810, 993903625, 54582833, 990928119, 291298394, 202593453, 339658480, 551875709, 89412170, 976170183, 70593092, 743029067, 633951485, 475407171, 900652794, 687743388, 133684601, 631431664, 620430853, 508789428, 432901539, 224177461, 43018941, 380107361, 894741883, 698045228, 209337695, 483089542, 671015043, 490968163, 29942576, 474115966, 968936417, 465486698, 253421321, 775997707, 757094427, 223502524, 115387068, 431665836, 511029049, 923549566, 374691969, 112315298, 596696075, 659434237, 15467437, 712958716, 877368504, 372708657, 89407439, 471887127, 997434724, 339199432, 281321307, 405133212, 233208534, 243451205, 48107923, 88534176, 908026337, 86283189, 337977220, 835451596, 822895186, 694994259, 497771214, 836012170, 203269779, 984776874, 583711734, 891370965, 905707574, 774694446, 652333748, 242790530, 167959563, 941929330, 442808494, 528494654, 870686794, 471316573, 238996992, 92593715, 860859801, 856149788, 25872067, 196422617, 285556084, 681313959, 468483443, 535942194, 852343238, 469103820, 807134987, 89021718, 721667640, 280287449, 971043432, 702016402, 729549280, 626532439, 793433724, 720465751, 1251158, 261232722, 458191545, 189770571, 879025747, 168096561, 640402398, 203276537, 622181023, 814610106, 695626401, 456512589, 743111910, 213810995, 147218977, 121512428, 747953746, 486231772, 820424427, 507933613, 738142878, 117062786, 569622079, 577144582, 154007601, 894758007, 272746483, 606470758, 778616375, 317613420, 668132248, 980250087, 106521530, 789365948, 790092671, 599671025, 191028272, 305509005, 785982588, 984857780, 251659444, 74445056, 452571643, 55721969, 509830111, 27504056, 640558900, 434459485, 693336845, 605978606, 206502092, 282163817, 466661054, 561346409, 532821041, 175230237, 567820242, 718440384, 944341032, 734623031, 383509543, 435398631, 202475964, 468121703, 907496591, 775562695, 484603829, 18664093, 635697594, 915847482, 600403628, 237518478, 241111446, 767087029, 204032832, 150960805, 289096117, 308655228, 846226523, 143997929, 259492033, 880352395, 116219762, 800040164, 283082761, 43964201, 417348376, 10960550, 628244377, 154290445, 564233698, 624314290, 791702897, 20989263, 906031187, 140220452, 279581718, 755262987, 858786359, 890616858, 412496998, 354362918, 71925434, 741036775, 53813356, 16978412, 568116143, 29283870, 304301641, 884218981, 667938004, 229960290, 380224628, 270011157, 77911258, 408555380, 274902289, 105643564, 657319248, 97067641, 425236243, 721304730, 600286901, 206430462, 470418897, 95066701, 675642630, 361601281, 498749028, 554080656, 572340075, 103332260, 280542245, 97732307, 881855486, 681702733, 274269734, 424237180, 597796479, 80176557, 989837602, 213574208, 517179339, 400674009, 471033459, 924367029, 470338583, 1465062, 100947688, 899200344, 669069928, 120538356, 752265219, 614937653, 66028867, 556113098, 25876188, 386535517, 536648098, 499008798, 109764649, 739728284, 190264425, 756856771, 584692249, 21650077, 485519820, 918863476, 156560914, 990164795, 717944391, 69289113, 605865463, 973329714, 834741626, 536530754, 91061060, 809950180, 404931925, 756858935, 501793966, 70090062, 53658381, 164367127, 961713972, 938039269, 134713417, 642708373, 243548072, 756227055, 95858562, 208436165, 536348789, 166094691, 90226061, 717820768, 205838276, 137296940, 500983395, 513211879, 331145449, 21257252, 135156862, 629774610, 752849598, 754602424, 642806833, 847969472, 733627432, 691580770, 851347688, 770291221, 453962071, 613487798, 646920340, 436369547, 869087373, 952152484, 469175836, 445247230, 156438921, 259918212, 99166602, 794885677, 49692941, 299057205, 672474545, 898256575, 279810560, 664045179, 20892434, 690877809, 32260509, 297641050, 146089006, 570610862, 70322128, 175070652, 193337998, 69072985, 843693736, 631352688, 261886820, 630038955, 189323775, 150651126, 13605633, 747398824, 496182065, 516570891, 712469180, 268317721, 311144550, 982177023, 939701070, 149716171, 603632344, 185509365, 219863822, 717196044, 811258706, 602524572, 922824651, 243231665, 217276099, 171726769, 53400912, 942425183, 719055474, 216892085, 811960349, 281451339, 790752171, 92253854, 72484531, 614799843, 341650447, 996185778, 894706221, 641060454, 332607345, 21403210, 755102097, 300435884, 699665578, 167047721, 197965638, 76711048, 5255229, 636491482, 126610202, 972187939, 456340237, 389937923, 748938917, 127975794, 492956975, 738975217, 458565726, 939270356, 850506969, 278364182, 738128568, 501407135, 388881898, 761244426, 889047358, 36180454, 530873060, 410607376, 913168801, 417264421, 772802228, 9131890, 744900029, 519785693, 846656643, 631801359, 399926853, 975915898, 395039214, 437730375, 92217891, 80896530, 516884956, 577903902, 328397464, 294322294, 533642122, 886194274, 123552865, 231393283, 828448002, 200756458, 861652622, 83175160, 281364002, 747255864, 335855685, 271845170, 421890837, 954261237, 339629323, 245643398, 757722546, 221325560, 166937300, 880279565, 516364374, 666601412, 732436769, 680942181, 307820288, 981351359, 596725642, 825895645, 745345774, 241314864, 260537695, 233460729, 572507240, 243468814, 783630645, 14029662, 317070568, 456701195, 896289748, 126721950, 724193326, 639780764, 872587867, 764917598, 692473217, 696925601, 291562863, 36723708, 410655050, 237893041, 69787554, 778083111, 660922728, 651695250, 618514877, 184110425, 351179161, 232196742, 394402946, 772608486, 15229633, 621123272, 559194860, 288277316, 8935881, 74989493, 132208102, 42627275, 479247204, 121988251, 823241096, 562112451, 827176783, 915617863, 343080561, 549294711, 865609270, 717034646, 881996216, 287399074, 600865630, 641430718, 775826581, 390613903, 89241306, 478381278, 875631072, 618924776, 408921007, 788971251, 461946108, 14193260, 836190287, 400757080, 146118782, 975693802, 371882249, 521556322, 65429912, 2251007, 575377779, 136468510, 120252306, 674029042, 451041278, 630424112, 200425646, 301555488, 732414751, 857871939, 213800609, 185624245, 689733703, 311392877, 951144072, 444773076, 65339656, 981083986, 263540592, 106848103, 694706974, 335704668, 347620382, 927146380, 967986177, 685973921, 220516863, 128044757, 623705898, 603063716, 903800838, 586325212, 787484110, 386204315, 784209092, 938871932, 752489335, 357188221, 862459157, 974004332, 729476991, 574510212, 358862002, 830929668, 492425741, 368820313, 909916007, 502552341, 645419044, 762573243, 661655654, 837835696, 564957028, 692877572, 693817906, 350336480, 630843872, 942009463, 597396720, 894796671, 611014931, 407950723, 923974846, 101790649, 207098448, 159599549, 732078064, 499836804, 140114168, 673107412, 336534874, 615247807, 985077907, 449882615, 500839317, 338864873, 115107057, 92899102, 759210687, 928943614, 640470375, 852989861, 536788119, 933281046, 435784768, 619941407, 393291801, 19744672, 538688282, 142982344, 792138988, 252404699, 318130287, 912472508, 522542705, 447728101, 213309208, 261418666, 272390182, 107302349, 565077922, 797861999, 756263506, 238436719, 603954435, 91881008, 452687787, 119839168, 479177611, 932499515, 876330279, 660185110, 898253500, 646388139, 11961650, 35170575, 896165668, 398052106, 22887177, 318218465, 989107771, 411806681, 462810033, 595979945, 850539552, 301440394, 417927753, 423527459, 380684815, 308023621, 306420979, 131022556, 422480327, 191690352, 755474933, 765427015, 726406307, 964037505, 765527280, 282234099, 895827456, 20819226, 259876076, 200561987, 346088648, 137083033, 516244356, 759348083, 360770848, 621777469, 482000020, 882964086, 532884071, 773410856, 196091483, 504911891, 644793570, 333680627, 158702473, 82948778, 888813971, 672640956, 578633196, 815767373, 644183721, 687943836, 385999557, 421553762, 78210190, 183395059, 654687290, 325511075, 583543379, 590361729, 200554722, 996331822, 974645485, 164299619, 919076554, 64217877, 376570998, 955818761, 882781022, 141724649, 595783641, 109365282, 430635474, 647290731, 226371531, 736983361, 383346152, 861958403, 228155829, 432660245, 873719762, 606560955, 798589892, 415490314, 252598163, 762618031, 392501087, 518685645, 617074715, 12623337, 39296542, 108903101, 202125663, 892627910, 793887020, 141498851, 234457318, 658778466, 733211558, 779428209, 160304437, 239775896, 600224376, 621476519, 231308379, 94025851, 154686205, 76327008, 414610216, 748102797, 172718703, 463493197, 901216449, 365101832, 345338076, 274206900, 389790171, 912019022, 80704828, 245871693, 213720393, 33046472, 968439484, 304113120, 891420190, 449494765, 112314107, 17122319, 775578165, 534331442, 543295763, 279066758, 864191132, 860942172, 326309481, 881806850, 369710279, 357030669, 602397619, 654480517, 898177004, 202021693, 152593434, 967898861, 749511144, 988708980, 620973379, 16295828, 468171550, 411185803, 808424985, 425849116, 352725424, 628668145, 162868585, 694836331, 815185199, 433028656, 148342863, 296164824, 568902924, 386920325, 355041930, 148525866, 178487654, 977723881, 770726474, 435806972, 487287746, 373243703, 832782289, 349468057, 564585027, 593910096, 975963767, 115642833, 338305753, 490317082, 448014017, 694862227, 194051893, 384999610, 891486592, 345358886, 315188904, 7514867, 332971104, 295638365, 634081179, 636616910, 464695900, 726155216, 320338599, 45810026, 929943388, 610072673, 91268188, 229691586, 991956232, 606388637, 489699568, 950319119, 933030914, 40558195, 496157863, 560731742, 844275312, 704089097, 272135005, 183667432, 246454930, 925158336, 110671751, 782280892, 205351563, 692942205, 734389120, 222598958, 539992309, 978958016, 607176295, 68487515, 649889104, 509180964, 617177688, 792178853, 308829526, 447911579, 612033970, 402669446, 877995560, 572991823, 720961461, 580394118, 1538051, 138715384, 46157416, 62584580, 522264194, 136578103, 1731631, 10030798, 883341809, 340757426, 330992547, 262086333, 24412918, 744847321, 476888010, 455635785, 326670115, 674812961, 260817119, 324305369, 26232354, 297733668, 839328360, 697846901, 943938858, 174821435, 778655961, 736107012, 200561855, 470656886, 597346088, 95017524, 148498319, 694549131, 936068686, 807079657, 880149783, 469052044, 665736401, 190790598, 943591617, 384313615, 192138854, 844441247, 956693796, 521627633, 190059616, 18592385, 836167739, 948671177, 606314169, 996179131, 310661907, 602566725, 234185481, 818467079, 299885768, 278823807, 816498315, 717550547, 371471359, 838321176, 876205215, 191087463, 15143137, 503737266, 219719535, 666530098, 493141616, 953118964, 49245416, 747938854, 360255506, 320805383, 631974883, 530733502, 602958552, 784249024, 496964948, 311423080, 276053113, 343921053, 322674971, 59025306, 879976705, 264035192, 686134932, 198502465, 821106073, 734406366, 490528929, 729819598, 228971583, 40705680, 42184321, 925395474, 150956761, 372102413, 878889855, 807758505, 104208207, 832050676, 895328476, 15657816, 150608955, 535244251, 756175823, 52037259, 170952956, 569182198, 184791413, 645601752, 951254431, 65772019, 974894799, 798081432, 60981806, 444053250, 585926602, 754118287, 541449871, 193752980, 38112224, 840737308, 543343560, 286617660, 64322454, 906936073, 11269027, 310446376, 297563692, 51735093, 696836118, 608302127, 16481553, 210726683, 405013070, 790693999, 650481972, 716106414, 154004661, 929416629, 693872591, 839414340, 3195470, 473548006, 517039460, 598239970, 130744830, 116755908, 820397256, 436635487, 70615269, 332767944, 740396309, 986719232, 962301331, 883144337, 239752455, 517992515, 492993418, 118904498, 224327180, 18263394, 762391103, 36293419, 486198444, 947049103, 241218622, 878904002, 30383389, 244226529, 821601527, 32172579, 286484866, 702778820, 564752679, 866961276, 890285433, 444650394, 22220417, 585415501, 24549168, 995421888, 52580003, 800400585, 287194674, 511667054, 15185185, 867171641, 141036317, 766093647, 307524028, 441551489, 314061137, 298490665, 783873365, 346757168, 494331575, 617747111, 837716593, 125210769, 417899973, 788369636, 953295008, 898442809, 857515269, 921420540, 319875715, 927914234, 263622534, 306705519, 564050069, 405272323, 406777248, 637544209, 236467234, 317370960, 397650324, 346133813, 555767102, 384337439, 1893234, 924947075, 451007605, 243406095, 171932917, 412507391, 200636570, 868996621, 548163110, 450292403, 841799715, 367587222, 641425036, 217080973, 933250026, 322976558, 535059493, 607624535, 704558748, 388255992, 337316892, 844737072, 194441616, 686396822, 229702734, 821621322, 999914326, 242667896, 57415011, 323158675, 491184579, 945276098, 612105118, 734944140, 403011975, 196331584, 742016199, 747380157, 655820042, 399257207, 621349283, 169476216, 34850104, 308083642, 5542215, 774505959, 475948589, 835427038, 22525801, 531593825, 913214672, 544870919, 789891255, 681056792, 698127528, 370594345, 407613333, 542723643, 719310884, 306888298, 573998320, 144027075, 201831110, 716424723, 70212951, 695478847, 279146124, 666710847, 467236312, 776507526, 581255794, 766566421, 827609219, 878203078, 709294736, 705156294, 969494362, 306336697, 737160468, 47726132, 506197190, 972608162, 90998115, 310105317, 42980950, 345790244, 186723709, 882380195, 834010206, 973931552, 132817643, 556602033, 837823349, 270865382, 568152307, 485839034, 526903736, 941737983, 353928507, 830505231, 77139873, 405819024, 471625167, 23589760, 206875051, 943459250, 809527246, 319921273, 358818144, 551860892, 870911037, 598891254, 651995428, 344628843, 907903856, 572780051, 428688874, 507339194, 457061930, 17147056, 595602122, 65516422, 97983937, 433665942, 19223090, 538962096, 975565682, 694600635, 12178739, 46088992, 25163935, 963841361, 941675885, 833153854, 715981943, 539155, 325974720, 836188187, 904248133, 188895975, 232039316, 968828411, 337476573, 586575524, 400282279, 558396002, 317155956, 86024342, 544934387, 271305939, 165636760, 592969406, 82527519, 191636346, 489802076, 300890781, 633049825, 520538669, 715726800, 378935140, 331360327, 984842525, 713422607, 158397705, 825329854, 222267752, 798723252, 273692245, 314589936, 540416711, 920209718, 25563712, 211460486, 325294357, 5434372, 897841141, 13895417, 25181683, 133000644, 604025991, 662640458, 135379421, 7433962, 791622500, 898498009, 30867818, 5409047, 638428788, 638319255, 985681357, 698314774, 173770062, 607095073, 28317120, 415843900, 2163503, 459329136, 461006789, 190876761, 144722020, 105473591, 148968445, 114921966, 892769463, 847132142, 710585908, 358755725, 694598252, 565453871, 542664574, 691330187, 664567725, 293677846, 993730428, 568518781, 107402551, 273893800, 685954330, 404123976, 62826088, 14065390, 566859000, 999700648, 407775177, 133938790, 528559527, 788072572, 271385785, 551102849, 625172713, 538748681, 154045894, 23234964, 62485725, 894438357, 399321272, 472834621, 967061717, 488688996, 22172700, 510746522, 67339558, 172658212, 380089840, 427937420, 362392528, 29836608, 601103596, 562086736, 736116700, 876289158, 647445493, 211891101, 715569574, 71143357, 282357971, 960982598, 651345992, 22081167, 789275275, 168945824, 985852487, 609011587, 275771148, 832562822, 508276258, 789488990, 874910740, 740100672, 196247919, 13123306, 212389282, 772622744, 548898781, 557311723, 855962336, 416963379, 138281406, 735090771, 202709106, 940190690, 682964515, 69706823, 227164949, 491210956, 312815608, 638110549, 974430754, 409453517, 636948837, 624775891, 848818770, 231052821, 851007442, 665338264, 359083944, 980930985, 639316803, 576016408, 595191216, 707175522, 191621263, 900035951, 29200823, 558372579, 883777878, 541531500, 857656313, 53562555, 534697873, 114011077, 267648987, 169494928, 921011144, 232172939, 481378769, 433014422, 363110524, 934103384, 284866644, 273855490, 205231224, 87824987, 514065013, 592147186, 371965929, 280012840, 257062686, 618830459, 795856508, 483241855, 876063032, 994172868, 503105259, 138074342, 849867097, 402717910, 692384856, 499855499, 682686835, 678570264, 10848913, 267071322, 840190879, 654935057, 350589721, 637705459, 703056820, 895065463, 313658091, 952904510, 989705371, 34835674, 630657277, 501847346, 514964939, 771530347, 806227231, 169022178, 164659359, 892187943, 871029546, 786888161, 763266857, 26830584, 280749102, 696623347, 479065819, 252493506, 643523125, 752041727, 529087681, 765327117, 876657831, 41489170, 427538511, 359408061, 609198232, 205023357, 245080635, 8172277, 303831405, 775201867, 104996286, 895439557, 556741263, 528190486, 784157994, 336711451, 514745397, 607150872, 347569569, 393302441, 952531800, 660442610, 154519066, 963787965, 659307449, 198059993, 422953731, 920513765, 689895981, 601031904, 675472647, 286921941, 152647377, 420325475, 717577450, 630232759, 977219965, 135750408, 813692601, 541067833, 853361221, 521849416, 693182646, 814101740, 430233763, 222713160, 200535078, 877351035, 928823133, 978558376, 976209384, 932132469, 966415565, 523441025, 972874208, 71171218, 735036658, 510039047, 603186678, 270521876, 924529940, 243516660, 330612537, 61511559, 481966176, 459536085, 466819854, 66702511, 38407280, 4584392, 952699727, 226584275, 883181925, 635363312, 712657973, 626343724, 413897297, 440566236, 274402221, 690712684, 534894182, 764626536, 859580494, 359575167, 817330131, 725700027, 827811533, 732083391, 532656019, 387724508, 684177761, 546652142, 264925210, 792927217, 337926292, 220659387, 638874336, 374386014, 218818468, 887422311, 618777629, 676547927, 509603112, 475082087, 275522337, 646481457, 762807097, 797610308, 877342371, 284547337, 759162363, 607943996, 128260993, 777628104, 280593631, 198050540, 922011971, 244463534, 249807607, 518934801, 468740401, 825299958, 281372968, 992002732, 3454561, 785859345, 664958834, 110713852, 299504606, 275702428, 965243970, 453327719, 317962258, 274511586, 344088195, 588789651, 920829617, 100788282, 815925795, 739442638, 962198570, 76151773, 948988814, 809432527, 785296858, 691061725, 271828280, 841216035, 485468011, 171328556, 854224384, 88008946, 41261318, 405148339, 551414682, 947518730, 820652192, 272444218, 699534209, 671949632, 395377574, 722701284, 840497541, 308489344, 999781107, 128170362, 424595687, 460061998, 107707889, 637421670, 859198251, 749195654, 174584130, 699572685, 679907518, 970807303, 478705117, 14592267, 904223536, 276473484, 512041258, 316496375, 66012824, 419765435, 898322311, 140787664, 833768401, 74911510, 758598843, 205821206, 708028012, 381314920, 694624382, 130029828, 838528151, 855985394, 320228870, 770906025, 640698869, 327965358, 369117077, 595700398, 274323981, 60105256, 100999320, 408819709, 995704638, 539352626, 322552501, 79029201, 524615768, 386286890, 766886583, 110839741, 736740754, 26264418, 263302184, 643256038, 540419757, 549262068, 697837791, 146634895, 596753151, 157731403, 630686825, 702321551, 135514055, 699793614, 306949331, 924479279, 494639703, 245394444, 806957480, 117273086, 51878086, 506538333, 478397513, 180638253, 954983745, 794605798, 938176453, 762896304, 384831367, 754265838, 50096079, 585949136, 340329373, 711461773, 408166433, 3108610, 487103674, 742352920, 919264245, 896392235, 4008165, 846193270, 63258968, 548713282, 350502627, 368556128, 898399840, 75489968, 270126891, 378028709, 187771538, 712697019, 701121450, 135821832, 478044636, 148402178, 335966697, 645866196, 969061513, 456269626, 297041199, 215839452, 461749312, 781224571, 852725448, 773775286, 981882465, 680803895, 960019070, 983730122, 239275948, 197248281, 274177234, 654866892, 33197563, 822998756, 136541881, 722189633, 803031250, 687041531, 538755083, 177602457, 844191250, 393658578, 148813885, 37208154, 784573924, 119358171, 926366866, 766502479, 607754055, 664696463, 310341900, 894241992, 568059858, 516442032, 873565062, 36974746, 108508298, 921334422, 283414731, 277237563, 95570063, 730678611, 308819684, 106909499, 1680263, 932266698, 840380140, 229353584, 395523064, 658164835, 849607143, 894888494, 883694879, 483568611, 30269276, 466574586, 457781478, 737257760, 725584810, 337616385, 720341101, 893141943, 400891038, 297826180, 419337572, 523297664, 984731649, 637875250, 155386130, 246654203, 301842670, 729240573, 436837873, 585844332, 652799706, 294259931, 583040718, 277465629, 700666046, 728492822, 747264320, 464392544, 541523251, 200687170, 573857602, 561397451, 803219730, 380478134, 442523232, 846580148, 407544660, 231754084, 715318638, 782724185, 786996994, 652534801, 947196195, 561526345, 688801032, 186596587, 339873094, 988264214, 534837003, 723707501, 943449212, 635472762, 381819142, 725382192, 447381583, 511435204, 642046447, 330737596, 692131819, 400570374, 441761370, 716040648, 727727721, 248010201, 992544727, 222841375, 866121190, 359878763, 783945740, 347815423, 149897189, 914703139, 148030614, 827503349, 214898231, 327344109, 398338680, 39862976, 445942774, 877955076, 811542353, 449754915, 206355677, 414859796, 459375954, 419653896, 39689789, 748316478, 642440176, 812819484, 991965623, 696108792, 22552041, 158941369, 293791147, 811570624, 721741251, 193555303, 959590022, 740375100, 646778651, 141796144, 983119284, 303271765, 141353124, 415889227, 644618606, 255666427, 667477616, 554761268, 40180893, 915499927, 864213667, 649587944, 899524485, 329366390, 109473304, 279246975, 290292804, 165392357, 496813608, 213424785, 492688022, 221513307, 548831862, 629697557, 886768148, 78346064, 651834407, 104917268, 858634864, 268410788, 704446205, 64580854, 494022817, 655178103, 206719748, 355769429, 886737457, 35533892, 246434759, 305493575, 590664907, 681011077, 869086476, 151185760, 274303598, 933437116, 702367741, 645546035, 823890365, 638614749, 627766631, 910998064, 165269551, 604221559, 762748929, 904342345, 974964057, 350108497, 159384489, 591088676, 246504635, 276183585, 701971020, 643364705, 394323162, 367228005, 103465573, 724312507, 387990332, 667545893, 762119252, 854857471, 836167506, 354321673, 117180002, 46940205, 391867419, 256021271, 211128892, 853367635, 407306122, 305328535, 626318149, 241843726, 172803871, 683816728, 300979248, 967934599, 557764491, 820726014, 100578739, 336226348, 580255943, 842450170, 579655198, 56577455, 143242041, 138083132, 829544633, 56282154, 668485532, 531782485, 99541696, 393707493, 403217592, 891827863, 553447087, 161829138, 865580030, 229337892, 943778227, 618999382, 129922024, 844810898, 831213021, 345605195, 878547033, 199815801, 621896236, 427316143, 300645763, 711491379, 7736303, 213576725, 2598364, 693469575, 68564832, 8117699, 170069583, 812084096, 412396023, 839930459, 700904768, 6327382, 367849806, 3490967, 145526511, 616463806, 25267168, 908803873, 494511956, 611098663, 347349707, 432761298, 657606740, 50436697, 480396398, 264435100, 230581635, 117861380, 814893195, 290741204, 753909194, 643969955, 270673751, 983038659, 978696129, 960269849, 132212285, 873697953, 441527422, 147639769, 430219823, 34826884, 403022099, 434814409, 618476103, 655295220, 647014502, 192027478, 21003963, 971578219, 276160055, 686088984, 466750841, 235452727, 734159069, 290911153, 184857099, 933958942, 79898406, 699887181, 344398206, 535051089, 566976437, 766991007, 202575324, 882742573, 574073700, 855994205, 418649479, 127715573, 897781372, 485338270, 559192945, 41042443, 1963968, 143188005, 85000795, 983183788, 18083879, 968357803, 301458497, 750242544, 227114587, 666382592, 999242560, 359253360, 946504152, 570149928, 110582972, 459797340, 164637806, 111957975, 396775625, 724309549, 723991291, 541020699, 890969006, 520713771, 877837987, 385912900, 634489869, 528325156, 890868670, 433225008, 769460061, 859229083, 21768061, 541864309, 726971558, 237167629, 404837874, 237211660, 362525318, 810439042, 674691389, 615769436, 523537557, 953042513, 61927141, 529766720, 742157013, 739324781, 252109479, 232281672, 926147795, 381213121, 42842956, 407332643, 472564938, 692493573, 556383805, 744526559, 997525945, 389450971, 51117604, 610063418, 285390641, 306978261, 737290779, 787220232, 711296153, 217238440, 628031804, 481855245, 346173161, 753630543, 543671072, 10952068, 299881288, 427990541, 177450998, 343023123, 40789619, 96416206, 107864423, 807070766, 322376312, 421366770, 84736607, 733445214, 760968725, 476167833, 323713150, 928334614, 117431177, 360567672, 940523735, 40826653, 122956030, 623704921, 15970543, 256687235, 106678607, 195657381, 506735430, 812098613, 812345195, 880613637, 43045744, 803426462, 254865972, 825575150, 674576510, 79867622, 474694525, 29470405, 757095028, 765360886, 360703816, 544727940, 242778367, 378394721, 267097264, 575123259, 766254722, 679297774, 240170322, 810288579, 27823298, 402873108, 730868903, 867194977, 637359727, 925466467, 272943394, 431114307, 894976662, 892267722, 724811721, 477824864, 558030685, 629145489, 557729453, 452558733, 278861410, 825882831, 43445291, 987194229, 35597321, 74570261, 801314747, 332829867, 551639398, 32255637, 107227477, 871877904, 285794790, 848376, 171731908, 723385235, 479306832, 39826240, 609839093, 671753077, 57985233, 841838650, 301591261, 550812427, 131034162, 915472876, 257416242, 633147165, 806208914, 820324524, 551720764, 578903503, 672724944, 254159663, 18468400, 788062684, 880937085, 230398102, 533875730, 95588596, 56615856, 165807281, 953833427, 488236048, 77248015, 547945096, 722927353, 282486834, 28756593, 211602833, 332332119, 695976194, 444435461, 901791993, 690992068, 117890785, 693370248, 899294448, 178266338, 404492883, 511731986, 375870275, 726765953, 916441175, 894958068, 56189375, 915434675, 202047551, 978706851, 840048824, 234000760, 9290662, 525155754, 329109290, 176261279, 581434684, 567056189, 304083599, 514227783, 492745124, 506647425, 20940027, 188124823, 664615090, 72198266, 924484712, 377565974, 632066083, 188266750, 763960924, 299821430, 958014681, 218028473, 57166001, 379096629, 699864880, 280725864, 901028964, 898875729, 201774053, 219155806, 740897261, 315214599, 946459244, 430577875, 393762941, 472200864, 373434171, 273063527, 767207931, 875364339, 487846508, 458269178, 544740356, 868569754, 598509340, 939021839, 62590149, 249348835, 511759558, 44048392, 653248326, 706592510, 947470329, 173141198, 587204708, 410923850, 724573029, 741679711, 207753646, 321937713, 351662456, 485978746, 770760903, 166138792, 595519440, 609457139, 106399132, 868971823, 34927262, 677479811, 144797701, 100062324, 245804607, 205477150, 821788433, 851093006, 719955965, 658341631, 520540794, 87257294, 846309672, 831357377, 38423826, 721837275, 560270529, 565858572, 808143655, 467391180, 239840742, 803628155, 366339198, 863398075, 186706977, 814301825, 603661947, 875885144, 768396098, 364569931, 779708796, 619445088, 496915031, 805671144, 927531735, 614471698, 251029341, 905057678, 479537649, 900183526, 924877785, 718449076, 571212663, 205168621, 641590648, 865590572, 950873300, 207078392, 17804184, 505501780, 557691310, 270405778, 402427383, 459225416, 443453493, 742111074, 591138101, 761192493, 550011153, 480998551, 1983085, 161393124, 152694842, 299987904, 16172852, 123316731, 579012529, 196711804, 913753306, 167855451, 860503294, 298585701, 546211233, 34359325, 288963693, 263230074, 892908435, 828535921, 800011684, 829708225, 560087762, 828001848, 476592871, 35363789, 223848778, 375959694, 794067796, 175844400, 140339010, 31832767, 39540526, 879590573, 281678459, 422928018, 557407954, 97858262, 537889206, 305195820, 68445588, 776602837, 156279827, 669685931, 7722283, 136738509, 760265602, 968604241, 41511808, 350372824, 954272091, 76056856, 103372549, 385331642, 111880332, 571945413, 781697584, 22179514, 911990957, 366782345, 783745348, 644869433, 699474418, 188227291, 149550568, 840904412, 177451340, 117126553, 478102789, 687012976, 614266985, 175583144, 601856767, 23478339, 444137492, 534404455, 275906008, 885999450, 590807611, 843256057, 481904143, 351145303, 160497351, 707451485, 731129253, 561292356, 523760135, 384908341, 755939076, 270453125, 870443016, 925760232, 321287956, 202254239, 445886359, 878485344, 692284244, 471730143, 65099870, 108442278, 551064982, 603717332, 459566869, 92351111, 516060097, 568004492, 940317240, 790039537, 254934120, 530785760, 679570426, 634856188, 589612877, 705585531, 711040554, 979888871, 112135626, 482552320, 644598683, 66455908, 742579874, 115746080, 357928707, 90127355, 692425778, 304579075, 623727780, 929573007, 944992965, 893254249, 204716537, 686000277, 716908544, 986823776, 736896999, 582122364, 992291718, 39113498, 473680071, 932891993, 206410727, 96889681, 491657966, 661207966, 581105584, 150263869, 78654087, 437622560, 782688192, 644715566, 308253762, 715744813, 363030663, 762633170, 403682738, 945980068, 301295240, 462556974, 154499108, 993052645, 937134074, 11497710, 6612705, 590535183, 227620264, 985182726, 515209466, 530625520, 334065835, 379430128, 616019236, 557684926, 924771734, 960485896, 694533292, 129116718, 884061535, 87385069, 870961363, 535941023, 570032642, 973624679, 217754539, 82166689, 172092137, 845809556, 1436351, 178228854, 385503031, 971914591, 967015459, 478225667, 234517452, 820802238, 717499693, 493188508, 724259393, 536588080, 314871490, 145860411, 781069691, 605976259, 270228312, 899519531, 584931032, 255778423, 894660913, 394787592, 620191069, 574981116, 331133567, 187791065, 25062858, 585480649, 636884701, 454177773, 195880406, 756929322, 694954532, 491911767, 925592267, 600890205, 987049118, 948774785, 763991527, 782102841, 976630952, 34001822, 828432258, 394376976, 411982414, 39243045, 243897664, 853195698, 439889578, 121747918, 698225470, 357485575, 606042506, 611443036, 982309397, 616890367, 591213883, 114282557, 973863887, 103430061, 799155191, 642756644, 41789196, 706217453, 510773622, 707126289, 806621464, 743239703, 122666942, 453339814, 42511932, 971847185, 427167385, 150107447, 68895636, 424464600, 620009668, 922758391, 176803077, 867229896, 189539385, 721324076, 77751507, 273363999, 385013521, 997657347, 661311965, 215600026, 562960926, 768375720, 545446634, 777902841, 211839105, 79235617, 453497439, 406938197, 195393094, 647094501, 177891130, 909215907, 483778348, 994277527, 161885424, 755005084, 193561844, 805671731, 89673186, 121406233, 163794772, 374542424, 991622776, 594915941, 585991599, 790984299, 530227716, 75551740, 672298501, 707988479, 51460439, 17622483, 565964819, 556487086, 784352880, 363979888, 460514311, 974566655, 525888445, 681957050, 134692327, 869854141, 677431531, 103684297, 764193713, 264687827, 541197673, 310522097, 385706037, 889171693, 61245876, 556833819, 843103114, 30501347, 553408452, 734202965, 166629768, 745827240, 163622396, 231434278, 628727198, 472758104, 927445570, 567290631, 405920005, 952882755, 400984096, 324799009, 317794607, 490908773, 744607036, 317551118, 497249427, 552202846, 64750085, 645333556, 103138154, 330806188, 526460427, 1257568, 666077150, 84604946, 895464799, 661816341, 102021166, 625413658, 267726023, 437271903, 294285901, 647528678, 589300400, 971058473, 206386745, 287030079, 630063434, 846474109, 729183349, 152119427, 574437569, 369717690, 390572324, 481261433, 126164278, 17388586, 359276023, 624590074, 728511360, 690508011, 880047110, 829903046, 90064097, 842722976, 149746106, 806029898, 404342951, 951043440, 145978240, 994767536, 819746484, 413110398, 649181270, 493661540, 892862114, 846767041, 288224156, 307437807, 288286036, 395023166, 640257327, 67524342, 431520100, 318435640, 616934938, 855775132, 824517539, 734698710, 362484218, 804255087, 995358043, 45874380, 666696886, 303595585, 757341347, 460828752, 498270652, 441101869, 369238673, 472192588, 121651869, 633378217, 627868195, 105202755, 866607597, 272072515, 295524068, 137003299, 14291177, 619444197, 358210707, 371118226, 543747789, 999354013, 212306149, 184434193, 738078753, 752483986, 611918926, 679673150, 717986812, 114689898, 764537213, 576241856, 301434221, 328632059, 862368415, 209678169, 652371206, 624740218, 902490885, 631768958, 839888315, 660068069, 104908312, 158179617, 860023080, 208482623, 953988666, 96163979, 376038978, 761360261, 935057942, 635639009, 2162346, 225681102, 383212745, 437682555, 294480661, 143728628, 658272446, 812635664, 302267912, 997339407, 630235850, 697948100, 886003018, 854203458, 183968909, 879731623, 9702531, 646492414, 769561213, 861956652, 401417839, 285463135, 817184984, 319209301, 132231663, 6533503, 700450437, 451878594, 426944868, 505312045, 363723650, 925571264, 868285927, 984997848, 499082589, 290056528, 92748621, 759979031, 131165146, 730909651, 260582396, 766591792, 337524182, 64896852, 433147773, 824905081, 691762054, 541760201, 558206633, 612431813, 144523338, 403175275, 611723415, 45405456, 214583171, 694215702, 474540191, 17202549, 275951758, 212848193, 656413856, 348220857, 472748803, 914977562, 915317557, 472119245, 631533982, 975486450, 194903758, 771374210, 399399361, 950051841, 838193223, 808981755, 482385589, 140257684, 555620883, 204130070, 238362801, 646067819, 160110863, 8275988, 860096005, 118186223, 272927796, 203195766, 439666860, 918289912, 315089838, 831690689, 802755023, 325930337, 129684425, 316580535, 950622415, 879099964, 689909925, 264505070, 407402333, 215539297, 649299205, 338471231, 14667583, 196007748, 336112915, 12587692, 546183798, 3023270, 322387692, 844658117, 666797472, 338279126, 716265538, 316798275, 197507827, 433455116, 247939001, 416876011, 955212490, 786576882, 531024402, 606105159, 631802461, 624017787, 608407127, 259032194, 784556995, 621023922, 383560174, 473730560, 896085105, 78349315, 457752485, 774819089, 228589264, 694069241, 411214872, 116293957, 462204229, 646627540, 80386289, 549624671, 793530533, 20625441, 737277235, 712659277, 441757377, 535858379, 47448869, 857070027, 980374581, 715833311, 750199236, 277217581, 134251645, 111643591, 905875947, 656543363, 751106829, 393397217, 533008439, 679624903, 206189682, 95802502, 143988094, 983740325, 600230734, 900911653, 963262310, 476979672, 385749562, 449674425, 277897633, 127156913, 884122244, 888104494, 132550983, 993065525, 188194917, 88031069, 148810659, 618677901, 664501364, 271653950, 47825158, 879096378, 740575244, 33394736, 994037166, 860017818, 932153893, 328320906, 480714040, 724289748, 475861049, 274477960, 51756737, 488157468, 165965065, 755827403, 368553752, 199120598, 328418123, 359116487, 757788943, 343097439, 579205920, 192898367, 276165172, 529120373, 166062930, 797148837, 326950790, 335326532, 78390667, 215925069, 548960206, 721819122, 364861520, 912735897, 31950301, 41781653, 966733477, 96004025, 55054167, 772727209, 582657815, 832226974, 976454628, 780295008, 748717372, 860564300, 964400340, 830856901, 64863039, 198140000, 835972738, 571866615, 743111180, 537275323, 223016078, 557997220, 242003690, 416204377, 268644029, 270043908, 746591764, 784509798, 538064959, 541877674, 635358662, 149474272, 356769637, 750959667, 284369516, 553741848, 184532009, 835978667, 773543854, 616480578, 582870675, 476982401, 996879229, 434647407, 347214971, 93803035, 953501340, 598318350, 88351071, 334526735, 302357234, 413694106, 586796668, 935811257, 868128269, 4216865, 917826693, 611990611, 645872610, 434010611, 112122219, 474486331, 505417103, 31676300, 753197122, 10482225, 568736367, 911414148, 117353173, 601682390, 935934682, 662277888, 55712958, 784708217, 804602408, 119273939, 151946253, 954274418, 465009302, 93647046, 929115467, 592252611, 523794377, 641060497, 711396210, 409051427, 380569596, 852380547, 246550301, 147753179, 602548768, 693958276, 798272706, 740907961, 571061139, 77180395, 751466931, 83118927, 698986180, 173300951, 520663813, 626892094, 491395627, 172487545, 855868882, 579502651, 400259680, 495335489, 309359953, 799213215, 344278814, 147562786, 631139904, 489375024, 702425683, 986662056, 894197674, 407523640, 349722606, 32091787, 362953884, 163378990, 851527035, 487420838, 113553483, 424414641, 897550850, 825829200, 236700558, 174489972, 95833863, 126737383, 873384353, 39181681, 236311348, 973931267, 964059643, 848785388, 944652490, 716391365, 754529583, 598033743, 655959903, 613092679, 849852077, 21130302, 934062901, 515818122, 899862981, 413240992, 713612117, 14988645, 863879106, 294603323, 613013758, 631542676, 133810198, 81296677, 988397273, 827549902, 898652499, 812202157, 742791241, 889001887, 250085371, 656393127, 355343358, 667850798, 532522640, 662834887, 646859325, 687152100, 375757828, 759699311, 357203070, 568828622, 77390867, 102221967, 529252916, 255338945, 5418443, 628902398, 461619764, 271700256, 828489269, 59032710, 725678887, 119541462, 881248400, 442040493, 655405578, 458416505, 51671226, 712572363, 604731846, 574199400, 489334419, 315827814, 242818427, 225979214, 779629263, 813281436, 853032845, 596061384, 6320217, 748551591, 337917255, 491000526, 338302955, 631900478, 902852055, 342564234, 531811412, 999958302, 134714111, 243992538, 119637085, 867176120, 835353375, 941189477, 525187012, 8383627, 332505300, 336275739, 601910915, 625385802, 56977972, 565637339, 217847492, 435633847, 45971050, 186975401, 583618262, 570037726, 750774914, 436348690, 510957068, 922478606, 371148642, 316825992, 770746137, 765058792, 41593048, 353563386, 807952051, 106650755, 755917745, 595472122, 669377215, 770697944, 45452056, 55442612, 697656550, 804223808, 160047628, 161709018, 347186538, 339455917, 451492883, 786784732, 845642260, 785893584, 506339048, 760230271, 226671560, 968502931, 314512305, 337884253, 838046852, 564598705, 589033262, 519000508, 569614410, 797086728, 286404367, 868150359, 501802110, 862182106, 977973941, 215924993, 735408016, 952839439, 813764854, 367880270, 285871799, 574861822, 63255645, 327025708, 627370474, 156318187, 421936531, 202493755, 278267882, 714635066, 801683830, 958477929, 125749361, 69420186, 52404616, 961783953, 119718482, 408030710, 747725186, 996081011, 273369845, 84811917, 983303831, 653450063, 753789031, 781912301, 900005822, 82373356, 267188403, 242489642, 627070657, 396407254, 657990065, 534387586, 748450396, 497431345, 346613256, 760797749, 356497643, 933380008, 4819065, 749298601, 433000942, 954593524, 50083268, 739376409, 932827310, 704351156, 535176690, 717927695, 822444595, 885151468, 617542074, 466659399, 470737628, 135115333, 570247409, 129970082, 307384789, 649325909, 454740223, 508480750, 463864262, 681741005, 650617386, 645083437, 816773097, 193205304, 75451042, 541454983, 322564981, 76885936, 617680771, 608600376, 517152586, 906447958, 698084321, 523197941, 805098823, 290878839, 799408057, 602050128, 733382666, 727675246, 877692844, 778485039, 953448696, 861600025, 512448268, 470854689, 498757763, 856645659, 216131857, 579543766, 237470014, 735326617, 436769100, 387320113, 411819435, 952090684, 382278882, 515435824, 670496986, 414719349, 80654961, 844352048, 834880166, 825288543, 913690073, 211020937, 323828818, 16175448, 418043863, 413822171, 795662925, 633675283, 394535108, 973788689, 325641395, 454397744, 358690738, 516461112, 74864563, 263351266, 786459048, 849292248, 415380218, 639256758, 789427087, 902861604, 872987671, 627182688, 607179473, 27712050, 912522679, 395358745, 133135919, 439211981, 687388804, 262074249, 599054544, 405632793, 289222946, 198503462, 271615580, 711975636, 29692605, 278507173, 762588287, 959264740, 245631739, 942589034, 281447006, 976798870, 744765054, 505074465, 41049047, 315029291, 795935184, 236442478, 285809831, 281660740, 538162593, 777723493, 945119193, 835769610, 596110613, 517478618, 643571793, 910143939, 593920975, 976062220, 659638772, 945092181, 836712343, 835952708, 657765817, 493506321, 965571198, 17361819, 453599275, 264281062, 506632912, 567676825, 182924351, 485065635, 460716436, 572758557, 119650031, 370065331, 575922072, 994816080, 352955271, 432071613, 69726903, 1807750, 192559564, 990326065, 391929229, 172468642, 918177657, 373010477, 350488198, 969765498, 748955013, 519212413, 94970664, 382487113, 775391968, 806754699, 337466873, 143863867, 885778635, 764167230, 150791401, 554791485, 494542298, 202630314, 377822783, 679974028, 75935901, 52732285, 574226032, 323115054, 252513619, 750578907, 665121988, 466670944, 763391092, 620947306, 51568871, 840090550, 463729534, 70350164, 981820843, 627146962, 633565134, 837097846, 906895555, 855049023, 952073599, 649900702, 706853833, 114113528, 943154262, 796353742, 977996136, 996636002, 463122844, 625149478, 446358775, 802797050, 845882953, 690533334, 354889812, 436747289, 940096778, 450223073, 63597937, 988203022, 505463708, 21312911, 410367726, 427782090, 245015900, 186153360, 679845385, 474254627, 26360090, 810997907, 664938117, 54018066, 445771968, 80295017, 447628829, 758244104, 678565397, 965144084, 60859280, 99878186, 827264330, 842019797, 987931357, 323057755, 134430028, 537526111, 315410176, 621694550, 8653807, 989090727, 920449634, 398177142, 317185245, 280402356, 652671214, 997116437, 709668003, 261162591, 249751694, 24475647, 963630476, 121370487, 739479437, 459557395, 671224527, 743106162, 306995024, 736061986, 704881542, 245793245, 306361486, 19497959, 75409688, 385468160, 339477516, 68340200, 350062918, 496585914, 433587772, 302249001, 581137472, 427952993, 712817648, 715327702, 817487352, 631804114, 743129164, 24857130, 922286046, 809588847, 884478627, 775269959, 905739568, 914814576, 408398850, 110185773, 913953199, 615369622, 275256065, 60356721, 933428303, 110712775, 262735758, 263157706, 984944027, 74348936, 139917414, 622630373, 398545454, 12839812, 495200738, 305542233, 327020788, 628026672, 213192010, 282500037, 99616080, 471362702, 71241494, 46363476, 668291881, 674920429, 328769394, 492926871, 336304974, 637188767, 877885713, 665785631, 556796654, 584293073, 864222511, 245450259, 160581288, 968566692, 583577467, 213994728, 797434768, 965685819, 934379592, 323092381, 44406439, 84305690, 39806947, 257096551, 207117198, 953912770, 227536414, 155589508, 876526664, 606613048, 369438588, 998078976, 339896635, 784425244, 940340200, 846026807, 335486560, 242498446, 32754417, 737738294, 81148899, 264241924, 318346693, 177828567, 943278545, 243229580, 760525001, 575853339, 923962298, 633612633, 273745645, 574626613, 756251881, 369559423, 544396940, 958893423, 507879207, 306592699, 389444, 269713454, 748388203, 570143819, 765286277, 443136761, 194578426, 605645840, 751056157, 197744752, 434859383, 959592409, 837893365, 57148005, 744937303, 655104446, 971083513, 18256768, 690286532, 59749877, 167884824, 952428292, 361434810, 138046503, 453590138, 35783422, 734696839, 737978537, 234588835, 713687863, 877161432, 844645527, 771896211, 236425880, 365718240, 373171220, 257700690, 576692432, 587103117, 88361998, 727586729, 213191517, 907326826, 411611574, 36361588, 46105267, 300708920, 58971971, 120899604, 324239431, 643539957, 458138647, 992805887, 775008682, 370946144, 731902890, 975004770, 977498278, 659804738, 356197672, 853245817, 747553970, 768983921, 852147088, 213082584, 686246079, 786333397, 185100413, 874430515, 486159438, 239658622, 939210441, 935658250, 35239841, 180771850, 299820300, 933065844, 230384990, 403544415, 357605125, 254800912, 186711210, 16264569, 551510296, 515164598, 71510949, 536508200, 437872839, 389179615, 454445658, 951147412, 209390855, 176996907, 518183399, 340163187, 413958679, 582137002, 202171847, 61446221, 122692499, 363053573, 50002933, 832615038, 711106473, 147514967, 144646679, 937949150, 657201342, 255184561, 486005249, 305024717, 170499701, 241542631, 507022710, 299438052, 636873862, 306372305, 788209796, 751356103, 498336265, 818173155, 548131852, 588127602, 778482506, 979301240, 681649281, 862087806, 650693864, 512649177, 359606958, 717125279, 361431323, 566806405, 487219111, 838853946, 337577131, 128516569, 770416719, 713581899, 264317428, 391402818, 342087723, 610008324, 426837118, 604811923, 181387355, 947238623, 822224319, 105275785, 305543075, 305978460, 914179365, 615620173, 805835793, 331564815, 482550901, 343423281, 12457861, 732942963, 291093100, 158709330, 64274419, 886582677, 233256255, 121572423, 813217453, 116442978, 550176722, 941027810, 1467570, 948103325, 918849379, 552209959, 465632393, 558132634, 35553627, 304166059, 49014562, 932175051, 174996038, 211775192, 843446330, 868226495, 206137936, 161267806, 926179789, 597314740, 625128535, 251061438, 927251751, 928400304, 124427839, 598450368, 320003648, 14533175, 779461906, 130414338, 21944978, 647152265, 255610868, 535412403, 173733051, 622706655, 954472771, 11071410, 150472064, 451064451, 506433676, 825038075, 526121272, 659744258, 92007238, 930118217, 697434222, 674378244, 63976918, 526445009, 428828494, 575469901, 325366297, 440234478, 352926476, 400310412, 168972633, 522813530, 568690816, 11393145, 491030756, 759596515, 954701378, 44967105, 412696591, 962846976, 297326323, 229833265, 528670104, 771904272, 890234781, 330860964, 348548827, 964246742, 791753502, 103716818, 297559799, 578873656, 193786654, 286716493, 677257281, 147659354, 521215132, 87654533, 721381074, 631499644, 845625677, 309066132, 845007299, 545702406, 395174374, 149006129, 519316824, 596588600, 330482724, 224253612, 683079787, 897572480, 746018827, 609382828, 243249463, 345439305, 339792463, 316972451, 672198735, 501394236, 277854501, 152023457, 38346488, 37860003, 64950690, 818834418, 854265422, 18395000, 879566336, 506467976, 333410518, 764808768, 178168037, 624023009, 94576204, 175210979, 771533368, 208275921, 647825821, 139640759, 892610440, 48195530, 606092312, 544140866, 685802474, 440469137, 962331104, 335940925, 874068950, 550710108, 254714740, 367667150, 250085389, 605757769, 232849148, 256428355, 668304305, 758833826, 240702768, 58251385, 148597304, 560319818, 271681361, 760993544, 850421946, 867196798, 801999986, 789419960, 944616993, 410126241, 191435854, 643934676, 721620866, 540466700, 229358390, 841005360, 538075798, 797812137, 603963027, 744699904, 760367031, 934933920, 406327344, 648806810, 765563058, 638198897, 932666726, 528579515, 962033841, 727511352, 928679408, 507766908, 142220655, 254146624, 249972143, 152815496, 32271567, 449571325, 963195650, 870415473, 587215983, 606928889, 57940373, 216701957, 740845806, 367954006, 339851307, 747989773, 213293578, 462154181, 466719530, 585337946, 730615635, 42363664, 992371122, 379062080, 222755876, 275350245, 440326763, 654446559, 264727677, 629542902, 418800794, 426947367, 962649332, 836752338, 26935082, 326557041, 705676327, 641490366, 378773928, 813679546, 247326560, 323098177, 753681908, 469959314, 891385459, 543667275, 388737095, 392325780, 160544507, 891996128, 755076019, 823425114, 599117360, 335560355, 883125077, 728839086, 166393731, 675533398, 174510294, 371829581, 197917891, 851718816, 740478236, 779519518, 180828844, 743797264, 438566521, 227853240, 282453928, 69523390, 403417298, 591855280, 5367543, 127983717, 938288493, 671281952, 924875759, 458247120, 905958508, 249890809, 86093272, 152844452, 828004914, 9601489, 271582657, 943748759, 295636027, 334844045, 411940093, 112510605, 607545245, 357178686, 926451371, 452955418, 490164620, 353010209, 128605775, 970834388, 353390980, 548903863, 264182734, 72982197, 504284913, 891035023, 219798995, 89215779, 583215081, 867357496, 195601027, 158557003, 980497617, 731693033, 219912146, 581195375, 290979391, 739927530, 248910520, 703585663, 361055410, 639374988, 883495933, 995265389, 780745577, 574273362, 605182185, 596453889, 435591544, 840326581, 495065315, 50092571, 50641198, 212822940, 431649007, 990543785, 337812246, 751569523, 322022960, 444858176, 762321796, 284667109, 802704908, 88081082, 185561216, 608308033, 282239147, 858676622, 888604860, 939622062, 80443916, 766723174, 31380000, 764130673, 424764098, 292777145, 403409409, 378612588, 914393859, 290979998, 622646297, 446789469, 918868102, 4022487, 814151539, 221083742, 26423777, 798930227, 678637283, 572536673, 407608574, 202640616, 750259026, 140131419, 166028371, 259819287, 985200628, 706108241, 377882293, 771823209, 493458512, 72717887, 54662498, 383987678, 386494524, 520962402, 234371659, 584197635, 138061664, 317089824, 717396016, 69952546, 355760792, 116772319, 498104192, 91735342, 835406575, 128267351, 374256554, 876518645, 236236492, 97557071, 786668758, 353793878, 217894723, 535973782, 481704388, 747305888, 510702598, 755183085, 434005523, 384887148, 390500711, 508679730, 592972483, 819241419, 398920759, 184758391, 920925888, 809805436, 707774430, 847653654, 297433027, 602405074, 861424855, 799181650, 993663938, 25148505, 568454837, 962495700, 732483514, 12973882, 746094598, 449336730, 100677093, 290879358, 259141638, 522923815, 772891220, 420397244, 92832934, 84854555, 750849486, 809152951, 558970096, 287798598, 994329897, 34979134, 31167554, 240695483, 770507934, 134752608, 671847734, 731306951, 593223743, 596835894, 960281983, 188651946, 640947225, 511527266, 950577221, 450989581, 281946340, 455741817, 662468491, 23789777, 80431133, 727724066, 597833398, 996829729, 758253750, 166006266, 634691258, 812800453, 21987966, 909697552, 831047711, 349912777, 624869852, 26087708, 682673935, 303723590, 8246759, 590719049, 511623177, 933062532, 978857533, 546434035, 632046070, 502837661, 33515222, 453446896, 198312040, 921576750, 891841708, 810533390, 587870061, 748269303, 884333028, 954281693, 168962625, 861821783, 71799357, 428471685, 140381779, 832776791, 619723015, 851997421, 802049505, 445194035, 773456731, 647450416, 70427278, 981383431, 322622922, 42726445, 836387439, 620052000, 721086454, 557248695, 466510177, 15550548, 378555590, 686800009, 837067426, 291903972, 385314365, 740691290, 423069209, 694123399, 674206981, 307716854, 30858067, 92134321, 461638389, 325569398, 890696671, 58838211, 343399773, 175832566, 321395412, 151394900, 1993095, 178278406, 225346349, 42208690, 847675937, 284103473, 857545125, 625059221, 360848123, 933904454, 868113865, 701962196, 544633413, 872089089, 283466679, 551270587, 705567967, 916417483, 457671505, 878331070, 917497381, 449644314, 443780360, 750314946, 624638802, 12605799, 962668311, 58166656, 723569187, 682611747, 948134622, 308919436, 997365249, 73183048, 515070742, 632651741, 418907567, 963855965, 359381399, 785514024, 708861968, 67351139, 938015887, 676212874, 946674498, 298590811, 923366077, 931385845, 417430324, 610477973, 967435849, 537245781, 228803339, 164506759, 781931950, 673297995, 683655676, 108883728, 821915533, 676859007, 721399902, 441603953, 611070752, 556694189, 649888774, 739145541, 577238753, 47798021, 515891068, 635621363, 723763029, 854007787, 666214460, 286612666, 690481205, 878012963, 252108656, 974576196, 122227742, 919329894, 309507671, 508602460, 16576172, 701798520, 688310100, 730582920, 398155645, 761186458, 33732775, 490915747, 922535378, 937155424, 507280399, 128762762, 769896292, 187239946, 779547127, 386020705, 216659848, 373799138, 415316145, 133530733, 871990339, 180470139, 775479799, 616119671, 92572261, 58261195, 767135969, 504069550, 26064845, 765793968, 982915756, 438801218, 911622002, 285294569, 178398260, 442815988, 686630903, 41408195, 943817185, 867603823, 801222729, 797207777, 904583889, 466333083, 242086974, 953389044, 980592361, 358907651, 762014693, 522867366, 85388037, 26530367, 386389786, 165147874, 363953973, 752255258, 939724329, 503104541, 923970980, 647454490, 776265493, 387554901, 948486442, 878326388, 481191195, 774260713, 702048254, 776234252, 826696506, 123046792, 777617946, 798754729, 338204795, 462106566, 253047927, 750677323, 702986349, 770704734, 864912407, 658392962, 910836087, 305654972, 683289395, 294972191, 252343173, 996225235, 90797746, 304795930, 94244289, 111708016, 499951476, 927434023, 8486518, 959966982, 949593383, 413521417, 196537433, 551497547, 665515018, 66553157, 528685302, 12908118, 829463687, 792199241, 424339086, 26054947, 597794385, 236287873, 423213243, 808348129, 987199675, 295612627, 809214599, 479806969, 931397863, 797368232, 210523733, 855609224, 456303096, 524675185, 876239079, 424556586, 868155494, 448112285, 798608779, 649034685, 900270837, 579809291, 45219821, 545837804, 54983083, 57261182, 503602164, 732881514, 292479543, 71674776, 959945347, 677791711, 265288561, 432562903, 111436209, 104386881, 552982043, 759098045, 721954526, 497150490, 476607565, 974616238, 863074610, 731176444, 242828872, 316490201, 102660906, 720947665, 557302666, 635184192, 176588622, 508725914, 375460622, 705983476, 211317378, 389660335, 753057994, 899295025, 684223040, 971639720, 642767994, 557598669, 665479087, 220527024, 671022909, 431260026, 168736686, 907369903, 74818028, 10425292, 729133300, 234818262, 621053671, 728201820, 295253167, 601036914, 927833647, 399290808, 216314875, 322820573, 93987286, 26490723, 376908964, 15469255, 463222298, 542094045, 421907342, 248831567, 373360771, 637026883, 864100150, 513885753, 128206787, 520976989, 453274372, 196898482, 336584421, 269700910, 944762664, 334346448, 519279451, 271189650, 956525703, 111657052, 631452305, 729331314, 392701003, 141120774, 865764989, 651239663, 548721541, 38713013, 215654409, 348679933, 158587892, 969894025, 85441230, 766774512, 276019473, 597460437, 873447878, 548922741, 509989585, 355181766, 379616632, 863325167, 849702868, 222329294, 603625146, 766220338, 141891117, 830138761, 688526915, 673694989, 103164269, 463140505, 119376646, 13686815, 16409396, 62085610, 729454832, 493594834, 837674255, 293053526, 400207165, 140107506, 162048919, 939944702, 639586301, 12110746, 159044493, 507161858, 566969261, 967949792, 833863462, 521550149, 433329083, 753041960, 970606163, 962062801, 292136743, 328375259, 129626827, 949756336, 686819189, 138887246, 197855567, 611478570, 161985504, 832883127, 500837749, 246799775, 281469763, 893002416, 113705760, 359310214, 74310908, 680897095, 594356887, 594553677, 845555156, 864332855, 236863479, 19781893, 578147073, 912421793, 362890662, 299704237, 153851562, 312116137, 440026440, 276441643, 134081831, 922213385, 418861457, 41085348, 321691438, 462678410, 532228474, 697477273, 236981979, 158354571, 352337715, 142136646, 225570922, 225124295, 595769086, 461523512, 427431298, 967694154, 325965368, 273965956, 820243371, 514292755, 497786660, 740232584, 210086, 412074371, 337085849, 806365610, 894337062, 556660409, 187462062, 897147360, 109170973, 518207339, 821500439, 825684515, 439560557, 505893891, 289142082, 342880532, 858717105, 285971751, 81050983, 62477117, 87227214, 697014940, 31620328, 54082930, 873070067, 180876877, 448439558, 567323253, 428844593, 378159146, 923488313, 752937016, 930369877, 462439327, 634613620, 794396876, 388877505, 140084790, 80651325, 501910844, 161666616, 817480665, 151307187, 223358166, 673350780, 454561804, 877461915, 840709525, 376247493, 124108420, 467002316, 880863917, 773930412, 128860304, 810086388, 74526055, 604252412, 988584982, 279135447, 625180660, 949900939, 114128772, 358772823, 468426586, 800606337, 200993106, 257503398, 338895549, 900401760, 420233522, 686550354, 331795305, 204067573, 580228564, 392938851, 884004886, 671201467, 429811289, 198878717, 349436674, 933157234, 882709414, 872547623, 465376961, 462836351, 848326249, 335140676, 727915118, 52966086, 362637962, 395327441, 229114177, 810501338, 328050764, 985882791, 982536859, 89218422, 105619330, 101915160, 220244433, 480298478, 348634873, 903210602, 224709140, 616635517, 310568171, 258883266, 564941888, 162344528, 887542373, 951078653, 484310827, 386351422, 690496880, 525673836, 968986849, 687804825, 63154626, 444764190, 835108308, 398322910, 606556858, 856142904, 525095595, 745488612, 950312538, 274837257, 860424617, 156072552, 274362410, 212292860, 797240829, 426968950, 648937996, 467063726, 151096046, 261662072, 256897330, 426773448, 527168145, 872609338, 613026102, 747286996, 763446433, 262096511, 285135845, 546764805, 635676627, 861215590, 353910164, 495019365, 65760461, 240009194, 433674496, 15260718, 641712154, 507705101, 989829485, 100235961, 175656781, 79522944, 389194505, 118420427, 468368782, 139538254, 913466529, 18420804, 751135531, 525896820, 789421328, 11527301, 94573544, 22525203, 988844770, 841623247, 887312921, 913295080, 727367531, 560843713, 364490324, 297880812, 415429183, 554191963, 467716073, 65045479, 168692434, 893301860, 381566358, 650770181, 670384574, 650276906, 395691495, 293771999, 899427574, 165778168, 239556838, 240267968, 189053180, 679311595, 557532470, 704484395, 741451351, 298590533, 999868959, 648312526, 806383007, 904465519, 826614876, 51020411, 732897807, 862934971, 542739679, 692286425, 898515309, 616145024, 316994333, 282407474, 982264948, 638119350, 716969778, 514037573, 527917966, 375125403, 187894533, 160267887, 606609063, 531175570, 989190066, 795094395, 480908450, 199171104, 152779124, 794128379, 142752603, 383129978, 308448132, 696724539, 653631451, 498280375, 834683166, 383167545, 858710379, 736473842, 846381141, 383810439, 562985660, 772227603, 113466707, 92064908, 445795867, 158112496, 768722409, 798866532, 744459265, 326086279, 513181842, 976228197, 876657803, 73792288, 744503489, 96346534, 981302228, 639222528, 330423443, 335237667, 328690018, 999943375, 497202412, 979183976, 340611201, 389285982, 615754730, 460152501, 136678697, 260710340, 889012926, 916971939, 794690939, 360281666, 108326022, 551609632, 137424953, 54957121, 458555923, 902509221, 816977902, 388422464, 840278243, 109560460, 385770217, 112620686, 935053808, 317421722, 421138264, 173591166, 501930916, 255014747, 391789822, 51195914, 688993981, 724738213, 847249319, 847751218, 903447234, 369958550, 629235225, 533956425, 153218240, 287107208, 123569144, 127868680, 70901237, 909264637, 172139394, 605897961, 940442263, 966966853, 971788637, 343716380, 652749733, 516416425, 570018475, 615038357, 710457980, 853537471, 585235559, 842783736, 137120028, 103507546, 320040738, 309643659, 791848674, 306246293, 845944839, 761507272, 225888019, 504248263, 745015233, 926818325, 420553178, 265721225, 10370798, 716450801, 761043797, 92488582, 836309775, 809336250, 854280440, 246894723, 314056727, 992089078, 273114112, 608885487, 748355301, 711640200, 234676702, 152426232, 497529577, 289359235, 608391636, 416219386, 393191522, 12943721, 730053416, 285140118, 605976456, 779831912, 218330185, 949075476, 934094619, 432240692, 911016577, 966970801, 327698177, 604384828, 49661693, 455642245, 881238349, 937850341, 38237786, 514316450, 88352394, 92074458, 34924931, 736799226, 87653199, 115373582, 584341887, 414076945, 874062642, 652256255, 875415730, 611565277, 229287049, 761487494, 841389832, 532477156, 842524497, 593610722, 963938212, 526248944, 369846479, 118924033, 216803087, 109179641, 919368082, 964141954, 199600230, 848228220, 675446536, 411987411, 489694455, 840688438, 937675349, 429819172, 116109333, 135411423, 222545495, 390431555, 898290336, 162329081, 593932956, 728816035, 44246428, 241049325, 926111230, 450629261, 539232647, 277211531, 891321031, 346701897, 494432289, 35709209, 302187486, 404276635, 574916787, 54240898, 523974127, 575590492, 300204215, 115289336, 412559720, 656919044, 497647599, 139042669, 794991492, 406095194, 256107948, 405339747, 928712613, 991573918, 560644519, 212369354, 799301894, 746207533, 772226111, 651905956, 302986015, 269585881, 339720713, 364236376, 987041180, 336088472, 56680895, 986697646, 990849291, 187150753, 168141656, 712804862, 555970117, 639255861, 40933199, 29870089, 101705579, 401878205, 549224128, 625268544, 348009724, 785534971, 817194239, 868357804, 311342158, 864407668, 138516288, 361066757, 150867322, 733386499, 800364195, 424204821, 797866873, 934704504, 294457956, 384376711, 81876472, 986803965, 326507726, 867531615, 913755912, 74120275, 397275772, 333584323, 103544869, 407998285, 94753184, 704804216, 730303690, 997454839, 328054864, 797435319, 302985797, 812881390, 442204912, 655613083, 927763843, 473342633, 730851805, 959286711, 480735617, 332918100, 544202349, 441505610, 875307576, 139488764, 741722739, 401850304, 992532779, 759039348, 777654737, 71016813, 471315729, 313121696, 163734579, 485714382, 473823549, 368755013, 533319549, 222901492, 520268913, 961417844, 999490355, 242980958, 950987895, 153648698, 764335086, 292278555, 437625025, 870718497, 3259434, 128182821, 845445343, 379187674, 360611677, 660851840, 557578480, 289871336, 125625625, 583496474, 289791698, 477438282, 326002015, 444650012, 23015622, 473408455, 383313005, 312515150, 583804223, 552092221, 59517326, 876403847, 381432100, 940486730, 580926245, 384226650, 859634917, 279732979, 830915996, 295044392, 341729567, 457017676, 224840704, 980812174, 28832037, 976420633, 291173221, 415232957, 378586671, 951928825, 295673901, 200537038, 427171496, 905452637, 316601728, 834189428, 199062858, 253351187, 897754612, 202473982, 379003184, 88153785, 286798427, 901177158, 910017449, 6216646, 423210666, 800414263, 558508711, 319959126, 581469094, 874102689, 781126045, 747223390, 923232629, 354864045, 592600682, 919583654, 46835090, 278722870, 689949190, 617268529, 667746693, 239962593, 224075730, 618520901, 212341570, 629634000, 292008114, 994395629, 128094614, 463961813, 647720005, 620617589, 764220760, 760186803, 377929427, 933887046, 697607701, 303349060, 54973991, 899911277, 903969056, 793970534, 209414033, 246554123, 574444843, 45983400, 174504897, 11338491, 678054294, 781599727, 173648172, 507612831, 315531290, 738410874, 57041492, 274774714, 54171620, 957972813, 563385743, 237880900, 635205926, 783404210, 30979326, 661073951, 353204729, 210881415, 457500056, 361420431, 502819193, 842047724, 232241343, 915013654, 995348198, 485411014, 28146796, 471094438, 195154993, 452892439, 593170119, 552281090, 733387774, 779974356, 429345903, 746001686, 917632451, 78738591, 695291496, 377069319, 736262119, 827147161, 790374623, 423804160, 930250136, 395617129, 953144969, 453750417, 746554916, 564188284, 263903553, 439785380, 364663163, 999475712, 472169730, 383040491, 592413684, 286956409, 230571896, 201725490, 800430548, 417948801, 324531642, 526173054, 34717277, 226312300, 299909039, 778198339, 609074900, 523671469, 204485471, 74078706, 481473121, 532168121, 914766432, 369374430, 417242365, 32813469, 21433993, 873392172, 804230713, 182753072, 167176519, 730573975, 395970308, 667518432, 824321917, 428567059, 432489505, 690132579, 970439679, 932996704, 308359831, 898586989, 197700254, 318757807, 648740341, 519735336, 467593739, 629528962, 49404688, 677057338, 615711861, 293733705, 254598570, 332351252, 464330196, 528207902, 848579401, 585297447, 707974372, 927084344, 661828626, 609551384, 460648778, 485564256, 680984951, 789113302, 420507962, 333136063, 194983136, 378114471, 931579951, 74145386, 300433908, 609401128, 221839394, 777208373, 402366698, 530370197, 215039141, 854406375, 773889783, 307474322, 295159013, 420747278, 439234303, 432747296, 31961365, 550070636, 821431273, 926182575, 638479046, 871113226, 726625177, 551115233, 171648900, 606552210, 483808246, 41767211, 411071204, 666181434, 886149442, 471204238, 86229038, 129872729, 343630247, 612153128, 164605005, 186425606, 515393372, 194303439, 210734517, 501623737, 760339657, 4160594, 749878581, 120239102, 994295140, 667059168, 909263582, 209947115, 168813507, 963848106, 478226856, 748010903, 597164117, 859854492, 556996711, 882537437, 206917612, 505351148, 790050136, 833571741, 295318167, 991105187, 204258116, 258069398, 197721821, 481317183, 53701470, 420566934, 880603326, 940451185, 266351622, 365594311, 405837043, 458035763, 665514057, 668327865, 172549933, 43242762, 602811868, 737948902, 289679044, 569684629, 68223977, 512115318, 335272021, 742123898, 543301751, 612477085, 11374755, 922945786, 443242207, 511865839, 628445841, 532496967, 129969414, 577727642, 503139444, 964160858, 932728305, 477019593, 224278625, 105888561, 130736903, 946609927, 956739485, 90503593, 114576154, 466832506, 607091987, 404857296, 511952019, 82150944, 258949615, 513885708, 117687965, 301102412, 125980902, 88954728, 291784410, 155313074, 140966605, 584627707, 610763357, 57871667, 498511115, 108994565, 495478108, 170940962, 408192516, 562518197, 824163843, 198967832, 358194888, 953942050, 1491102, 429763772, 29966943, 122084092, 421322344, 182657736, 360866423, 998787743, 61111953, 305373058, 152591863, 956079008, 989759861, 329125690, 153692294, 456425097, 839203354, 907194318, 614332101, 869002761, 992717128, 918956080, 371417461, 308231537, 415417212, 619543700, 268028212, 165301049, 865039079, 30996783, 110661194, 991195673, 392747427, 35864103, 576149568, 951938620, 848898262, 156181829, 217391854, 590105679, 270313370, 496206364, 886205523, 740226644, 892227493, 746857820, 445321614, 556782757, 974272045, 464707949, 203335395, 657374811, 420582959, 827135939, 248138362, 179725179, 475338582, 199189091, 293398372, 269854889, 277651417, 883979109, 64770917, 84234966, 295011452, 264202847, 288592056, 82247030, 451449103, 435885331, 89633066, 298696510, 536323929, 25853371, 369842066, 449552183, 31998488, 777086060, 848876901, 181232336, 53280292, 541473119, 748654866, 313409943, 16006988, 285881754, 378799720, 912467821, 542148478, 988992526, 750401771, 952635831, 24505905, 898434704, 817930686, 488653133, 608191932, 302616212, 710661797, 574071479, 76700414, 282191168, 461162374, 162451855, 866513026, 616811857, 977657553, 561341608, 42376391, 437255754, 437900988, 444008531, 265461611, 723977637, 209860382, 640778012, 945003312, 162410220, 504638749, 881300798, 330386577, 640256699, 645018816, 190870037, 326421788, 188336133, 943049602, 834026454, 551096154, 634557115, 338322333, 261535206, 441821441, 332226776, 757896261, 941843375, 538235644, 729519604, 206301147, 921867113, 662816591, 820548538, 791847452, 951452855, 736217033, 605679210, 45522697, 232835604, 442581192, 731231449, 102400501, 412433108, 170198016, 779472009, 114274488, 567698012, 894376542, 421631547, 583308620, 167726242, 89458276, 186352456, 689750967, 702167933, 834826106, 971326861, 461628141, 881255291, 293978791, 455758287, 841641096, 459136598, 463441010, 88789963, 152200281, 176498061, 743172619, 542042896, 641059697, 561468868, 344995102, 578982060, 291714725, 513808061, 899042852, 84652200, 595479429, 300061588, 453204131, 994205051, 305405944, 131577440, 802386993, 246195449, 70514864, 843670300, 652399820, 797155336, 179861078, 614834933, 915436764, 115285478, 543094727, 73565981, 119406586, 617733696, 636897672, 909354885, 682996617, 2728647, 209254619, 416623163, 270942113, 603521553, 179836606, 949051503, 259018705, 967422970, 192297535, 375518598, 352965436, 701920239, 267321960, 20381662, 59959802, 138584048, 680054967, 415989209, 968723729, 683901771, 669958637, 223053049, 974827298, 31172905, 397324377, 276343201, 634829130, 24058639, 308389158, 975508066, 8311306, 570297283, 987616189, 83635865, 302920912, 254608659, 431111728, 302451458, 519546573, 713089665, 558643710, 664767995, 411215703, 287056592, 949825785, 91717538, 551645012, 193229582, 723031410, 897024845, 608701816, 767907632, 38616952, 900322459, 252573518, 8276294, 988876192, 160692761, 356646073, 732266780, 940730209, 44709391, 450108070, 286951124, 423933162, 601813041, 577826650, 884205790, 179650220, 352261388, 478554452, 12769514, 306309209, 977033924, 153784711, 707070901, 639006519, 825208228, 105986004, 372894088, 166740363, 363226959, 331032563, 245099964, 904124569, 581618780, 596277038, 609425585, 576458326, 247892906, 689568614, 696908513, 714804731, 161185862, 758954141, 896920591, 119120208, 107343208, 122662161, 35824721, 23361305, 233399664, 557850492, 52694706, 678912780, 821520181, 997230700, 528199185, 466117551, 571789941, 20403099, 459305170, 589986259, 965683409, 360925459, 175585954, 581001045, 555377897, 793183486, 927059307, 308690799, 701637603, 336889134, 180546741, 638591328, 442235381, 565477363, 287672941, 320585075, 866129279, 771857846, 149553656, 549034149, 380578695, 793869683, 153183643, 936785084, 656360688, 313594471, 24457510, 927307099, 735540048, 829341467, 370568452, 288586021, 951738862, 656988917, 538576323, 596682727, 304296693, 664465918, 912559129, 913102795, 747044409, 9970470, 654444981, 984538668, 436543281, 560516966, 498257849, 860875475, 521369545, 514257578, 308185026, 788480010, 963583913, 375269279, 623060182, 568576923, 756728825, 3242321, 100507113, 866145706, 829306243, 556629569, 235112498, 357596257, 991896814, 864056551, 740085981, 10654176, 578994952, 668690120, 334759470, 216778647, 480067010, 905811227, 824568110, 325389904, 495152319, 564648993, 482621247, 903275690, 257143886, 836613117, 49109135, 39269353, 23090440, 713162264, 820447263, 325748054, 120697401, 932374040, 850443293, 943245619, 708092721, 213167683, 526346457, 581057066, 676629824, 313457913, 462079276, 139254839, 421451140, 655294262, 523466317, 844937099, 768642872, 696896608, 875775439, 139591630, 971430206, 586337633, 436710080, 434044704, 188321422, 3829838, 394618613, 396795703, 194418114, 226768907, 177772273, 701303143, 268023252, 264514798, 378286396, 325559604, 514849011, 848065872, 710962847, 768674933, 988080772, 349031643, 376471402, 64772263, 839417221, 296138701, 951707491, 133991239, 134052973, 888498499, 65867680, 355419865, 877683494, 107879377, 660320064, 481146566, 430275067, 437919084, 331711789, 413644342, 298273912, 287341612, 931544601, 774976310, 615356361, 160954180, 230283618, 128064682, 234175317, 691492327, 581202947, 323671765, 129457064, 884599410, 284194883, 29103746, 923249377, 691241375, 875108648, 680964258, 166290431, 18078187, 792233678, 545050608, 868477026, 202285083, 839442490, 233745196, 369245999, 467453772, 539204283, 779863809, 961646387, 492439521, 925085170, 168445495, 821502394, 91904153, 490348305, 781220760, 551859355, 70923444, 352401689, 655175091, 307405270, 220056694, 831072310, 81712242, 769964884, 650261574, 589259958, 374734586, 257858521, 663021758, 749164022, 783320273, 655141664, 791173218, 4870083, 397825337, 476876833, 167824780, 1079989, 135626860, 137271837, 64636493, 203668545, 652350498, 778614424, 649251475, 875228442, 250718155, 689809269, 117346332, 141178070, 409257650, 563748392, 186632567, 876643709, 169263983, 623097715, 395823386, 830587218, 735157073, 493084325, 944760911, 791553707, 954181186, 898927562, 687602774, 929217917, 928914886, 218174233, 566336812, 267567627, 609251823, 276482942, 790950398, 628931696, 624379872, 119822113, 861230026, 143790308, 987516595, 390839761, 566176517, 649200027, 105826660, 254734001, 917812732, 731884656, 782977452, 111594943, 244880448, 889232465, 414073363, 933361894, 629264640, 829370989, 809292311, 295791683, 98339642, 295766577, 853075587, 284319901, 650310500, 277256757, 31167103, 764546167, 134675177, 179366070, 773273003, 160073307, 667969342, 507793522, 684115303, 534346655, 452065055, 497372479, 668103503, 114480445, 342293089, 990201589, 793527249, 663024747, 903079419, 190709863, 921119101, 456394434, 603759326, 46476955, 453851618, 61156994, 505428612, 253301565, 726017468, 102422578, 283603156, 738523361, 795303849, 679347760, 79205235, 612922420, 446097405, 607527457, 794849954, 860109891, 803135012, 430794800, 641961619, 782884510, 772047718, 679657782, 741375992, 386654653, 628685360, 62496214, 784361226, 340764081, 738974386, 571124444, 677530561, 985202434, 480192786, 633662384, 613694090, 574436521, 53638663, 77940618, 157982435, 932061699, 21148218, 990605909, 248457833, 35031010, 798563761, 350901522, 939070591, 537382437, 204313080, 233287079, 36987881, 27102429, 221816377, 809839496, 332504800, 147326755, 427904647, 933382059, 358858783, 920884651, 511260402, 185687805, 517782962, 875738544, 473574325, 581640981, 609314924, 66212485, 288905329, 377184610, 315685652, 487391819, 153483840, 186924014, 990716595, 517225880, 707243198, 215945094, 562997464, 232232938, 334154012, 17074228, 235685858, 126868520, 663874994, 351969975, 890931262, 168557748, 266921451, 72005948, 721850381, 866490743, 861417965, 552517452, 204742302, 884832125, 363526874, 98484819, 899863574, 847276842, 359486896, 641874834, 864285435, 492288561, 683789134, 732165041, 184595229, 885522110, 610115038, 818021461, 405158764, 989873114, 283794138, 138499891, 392684047, 578757554, 34649921, 867941512, 690249589, 825572136, 633165311, 796997031, 985136054, 133637310, 545913099, 419809457, 760523199, 94371397, 321388045, 701787360, 812980899, 489381251, 809277235, 435538789, 823480049, 96245692, 397221328, 772452114, 146895169, 63163538, 206106826, 64272618, 45702010, 47498210, 367280370, 196785187, 543360202, 971023895, 620851411, 744908480, 968874397, 962959282, 726487643, 27168578, 416438251, 340356384, 204414388, 132351353, 251449404, 785228621, 467691418, 454082150, 947248043, 318123167, 219094024, 614199867, 513344716, 160399855, 267526127, 127656168, 960757251, 527160028, 341684759, 177083139, 728742708, 1430073, 992222288, 338392205, 92983878, 770514061, 415574014, 5604592, 912395145, 112441453, 701330391, 348770478, 337846729, 642275133, 309142280, 618153618, 282102039, 942603607, 40840202, 184654255, 104384347, 784182772, 368490858, 641565841, 465228375, 592220574, 343391067, 186032755, 225661634, 267056122, 347742107, 122624086, 117718724, 271545404, 860892763, 391406578, 575432497, 487260517, 230140626, 587529926, 287007606, 697544126, 427941024, 124865331, 719431034, 449114730, 137401430, 150160785, 152395712, 330248603, 26700443, 654479718, 538001338, 831436389, 223918227, 225251017, 676935957, 268359102, 22659758, 572276536, 290270516, 339181274, 434115476, 135273765, 748698401, 652213750, 355517027, 946227062, 337257963, 973051254, 824687378, 183408066, 546010535, 993442418, 840796628, 627764896, 35170465, 617555074, 762146078, 181639842, 128866495, 592863145, 435473870, 555313697, 906142762, 730558753, 622967616, 447322984, 267618087, 635452254, 755522738, 849995972, 591285279, 528805010, 179178827, 968925979, 836785676, 423732943, 73878396, 645701558, 889376998, 601805977, 991389771, 476648020, 438889515, 140230454, 987217957, 6504214, 70383124, 365344533, 979757826, 440905548, 954489529, 119338558, 198435487, 30597176, 363233078, 927386475, 251351297, 850780941, 527387231, 363030111, 718304188, 645642749, 200840253, 696127845, 543608733, 590675086, 983967340, 574361611, 585083425, 263394609, 369231237, 810716995, 554744089, 9121187, 480829403, 262064686, 423207712, 666550800, 85826766, 561791832, 545348213, 813424814, 93419296, 660926451, 457722681, 486699545, 117760559, 54383645, 697367649, 575744051, 179914989, 188009338, 553152993, 176060285, 963511432, 121952047, 58954342, 158139323, 24881325, 335565750, 381049671, 874951698, 807284359, 513754477, 737307728, 795455427, 532099411, 937192668, 172922310, 104276316, 841137210, 588605877, 586498379, 853540799, 754377780, 920523791, 652507547, 129483319, 426257439, 891955213, 652949944, 999907610, 755982570, 16929331, 362422384, 775254324, 557335616, 785346925, 688669272, 563325205, 736831903, 400553626, 928976318, 924669014, 851857888, 192018772, 565931449, 252858981, 802844730, 753802331, 330498258, 730728586, 957290975, 731834869, 337758527, 943000896, 417952265, 236186740, 721657008, 326905314, 582192508, 1217580, 932544168, 724322778, 878015188, 575692975, 733000007, 71351827, 412243408, 986962966, 763565501, 289146652, 835279230, 719532687, 884989791, 254057701, 849557300, 951880172, 329942195, 79937600, 752424068, 665620564, 876340754, 693773674, 516188436, 78820186, 366136667, 996261770, 693331188, 728418108, 884856619, 258332218, 328791164, 591360057, 231899627, 851425797, 645028894, 191916674, 672017640, 832474416, 949598746, 35491417, 299471526, 773605967, 750750466, 439559049, 588727134, 419660611, 911110139, 242357997, 513634066, 402533678, 395674223, 998376798, 953749622, 428899701, 967590008, 528932147, 518097797, 863743774, 316307721, 835980369, 103893125, 588358912, 396829532, 163315100, 424844932, 468022445, 445879598, 387751879, 268005734, 371929904, 187815105, 452179516, 211225246, 302176480, 703251628, 384086860, 353506893, 664098713, 598301520, 462540627, 456722966, 623175167, 515180868, 883402907, 88001488, 229847030, 808374491, 826567562, 340311237, 454184707, 636491446, 995125820, 900139702, 442497471, 570387320, 933267445, 541586925, 186457247, 892403670, 716485831, 715834544, 408309340, 938150950, 362398982, 764267714, 854089341, 780479666, 390768122, 212348790, 524446080, 510440742, 926064260, 607580628, 722204965, 116081465, 923834098, 184960014, 532269050, 658672243, 707961838, 439714324, 659978392, 803722999, 279268657, 45877314, 649760377, 502447363, 57617285, 145857808, 738074371, 918682048, 157956048, 57216137, 152782750, 153983930, 576979065, 89370839, 488959969, 351251038, 76304428, 154515909, 30097496, 208598123, 507902404, 134970020, 639720633, 216896991, 116261082, 115151012, 646491882, 711559333, 777343657, 362443247, 887746942, 677046472, 837850205, 334594326, 67114871, 397913641, 737435257, 145130562, 820869008, 436280860, 670567251, 911863971, 51198469, 964034407, 411510540, 247792542, 425606492, 695194109, 603593362, 818452362, 552327392, 282379417, 621763741, 696803401, 961076730, 70851235, 293843276, 895321418, 649891836, 662892453, 778317987, 438203676, 274745298, 371460783, 91213474, 399894564, 185896652, 823710224, 621140199, 591198035, 412852304, 423470998, 467706115, 155625542, 56239448, 953216105, 852790956, 10571876, 851996960, 399667269, 544722161, 953919157, 274360300, 278811256, 577513778, 928745021, 166417444, 383335986, 959011564, 834926988, 540471650, 250884786, 443961240, 80652253, 338603147, 479024735, 244304559, 485450446, 493322720, 459092828, 177517792, 210978053, 34903294, 251175773, 350228804, 13509259, 815501142, 515111387, 24111879, 136352688, 769654918, 162047337, 36512179, 24924596, 342179601, 763739321, 901458921, 440235616, 403624680, 789834608, 12006248, 854578289, 285301502, 302347515, 998985587, 973636545, 386045462, 966653975, 198560047, 479113456, 254193472, 222544032, 100000958, 237019452, 628990781, 658353213, 967398186, 430797689, 327733005, 237919331, 801121364, 296302540, 12047789, 449433834, 231965228, 218618675, 233299326, 576554995, 599484846, 189975788, 734043060, 397819196, 761831420, 389353654, 146447749, 238529247, 563384477, 233379977, 577728710, 793596264, 407890930, 492745479, 25957603, 58417644, 503519234, 629027795, 626695597, 321720379, 186039245, 993768221, 775271931, 609053233, 454567200, 316519431, 594267388, 270747774, 217240991, 99142692, 464874691, 390965201, 746970667, 559813551, 850945725, 798096713, 585206185, 545814864, 249826041, 723215182, 344984890, 338394428, 454276743, 485453973, 827402682, 111898715, 410480859, 488577423, 10743087, 325189200, 137538404, 106534489, 542149400, 632399922, 440368650, 923325840, 588884712, 90791137, 404919972, 866071169, 261343772, 748726383, 137469546, 844519940, 442944959, 621086394, 847842613, 827814544, 287126305, 257271686, 287419729, 822862239, 816339349, 518852491, 452718956, 440475491, 575458888, 392954284, 107995177, 776084874, 332264707, 691996862, 253824690, 511727610, 858469986, 94001556, 881198248, 513873675, 804417809, 42882660, 915011738, 470465418, 553729981, 489122259, 62872106, 754480939, 702786601, 498057979, 52612084, 383386554, 773112239, 812766628, 897132926, 986109973, 582283642, 605898922, 854781869, 948824311, 120096991, 891987918, 955593044, 518690304, 381118487, 974084291, 87635118, 954313313, 620777716, 74446370, 116234385, 782681370, 490436455, 637334602, 766508447, 901089887, 113238133, 516634043, 484293171, 745326131, 604670426, 820591155, 5014382, 987211574, 299183389, 691419822, 680577244, 298750927, 901461621, 865552747, 748865971, 440808531, 496067718, 894984648, 702386056, 425288568, 863791920, 838986846, 560939321, 934359081, 847081268, 446224910, 694129074, 102224124, 379800935, 113351955, 533791997, 408673654, 996923557, 947877421, 276580478, 818518766, 136232716, 447350071, 325761118, 449417881, 308981540, 807678573, 455332070, 147465183, 998325473, 596033200, 394518243, 794913595, 840510793, 51633151, 754930669, 529181377, 391390039, 175728647, 429405797, 884293359, 137126201, 464338644, 661111723, 536723409, 692836530, 172535477, 369846563, 924219167, 162176566, 680126448, 899215342, 528346839, 29298277, 249454137, 476704473, 933963866, 378639185, 166452838, 623626148, 294090401, 926502283, 100222966, 223249535, 362862524, 599174590, 686619795, 502498802, 42287220, 2401611, 167097016, 351073083, 133702189, 267673593, 114800808, 505241614, 532988688, 423018521, 55748831, 38882918, 777339615, 24979255, 90050303, 29530838, 985056621, 218070148, 536429744, 994774488, 388621129, 944803050, 308053095, 272691694, 286571599, 58758396, 881259721, 418451134, 494034126, 980730074, 361628210, 232930456, 728143002, 720895572, 769378046, 120548017, 882795062, 57903883, 445458599, 225427763, 254662674, 366656015, 982278800, 506912310, 387650392, 963905648, 532944017, 736761469, 651980899, 145251092, 421527952, 796757875, 934843830, 561271814, 769215825, 889693738, 457289403, 236222322, 646406145, 64728044, 380243989, 161890374, 317551623, 604134256, 764675813, 989202561, 485246002, 577834536, 839381258, 137112170, 595436133, 665010003, 704955091, 232989557, 351582230, 631940684, 403449247, 904875190, 499147072, 58245192, 75488159, 630984039, 506949593, 589390535, 464456490, 823593834, 593325702, 987146441, 571649967, 600962770, 778854342, 666595123, 838049553, 127728083, 593791725, 589071704, 753882229, 51036896, 370770270, 667843980, 543895061, 294839447, 256617217, 890361261, 778063631, 50039077, 889325637, 216612242, 700606810, 416010194, 930868685, 17949697, 576484979, 321334266, 117766733, 735481482, 516247094, 251422871, 518081488, 368636604, 308836186, 157529332, 65168647, 958874866, 966218270, 475086711, 70291936, 114252973, 295880904, 615862118, 243774971, 933358273, 521305691, 2268855, 744080229, 383585883, 356114069, 66450897, 322452121, 746306167, 702408719, 971810045, 111878983, 287999457, 559574337, 219896227, 597601, 325304152, 872970105, 588594667, 336431528, 630391364, 805634428, 604615618, 940126820, 902977797, 865301101, 634989337, 363168076, 442696238, 207249083, 70778567, 735321356, 428210473, 538217902, 393222385, 770398274, 100679832, 863329705, 698923819, 963050244, 192951080, 250210494, 973010901, 419669341, 790541805, 439044888, 36128024, 407991384, 94608433, 268459770, 930568918, 603281132, 212876110, 603933735, 427623812, 574336128, 313056654, 700755772, 48397226, 906563781, 234163813, 44099610, 288580135, 680827857, 40440663, 652178517, 303092910, 561895793, 996790416, 956017052, 592710711, 354243466, 845568302, 260097541, 437773710, 988736160, 500445352, 731962400, 806157052, 909338716, 243548765, 616697465, 285863772, 53907462, 487196384, 697324305, 782825278, 29321300, 633190157, 49711244, 967851957, 331995951, 404656865, 255396939, 770682754, 972852722, 337931476, 475473000, 94020393, 692089370, 772022902, 245520318, 839153854, 858998071, 362802213, 313971663, 764621523, 137504783, 144272033, 378395074, 141075450, 567311991, 843510994, 824067495, 613671214, 475170513, 777723451, 904201532, 307074978, 471654204, 885141800, 63099417, 770891321, 720676337, 405932554, 29973515, 174907625, 708873059, 415978676, 239241318, 602112582, 495945559, 222509404, 249286209, 667964494, 933585573, 546285336, 46390959, 904667562, 43254449, 253697651, 759037118, 642122741, 605390508, 467192112, 441041292, 520946096, 352953260, 389240687, 561465228, 132818035, 956122100, 974557436, 590201631, 732957159, 960712442, 245504942, 97810377, 599141912, 418084290, 339750575, 36350656, 17749594, 149130329, 979128187, 718824328, 537111764, 946458118, 80338469, 669922586, 952454723, 759917144, 279379244, 708632118, 759874725, 265831126, 369534632, 820012839, 541529397, 139276202, 947724388, 35192001, 645500530, 57276267, 471728985, 337266491, 168224850, 344497967, 568123045, 598457975, 57920436, 493665774, 32982003, 471479185, 777172307, 209204639, 907417638, 948200614, 819868451, 979851380, 103409727, 13461018, 198172244, 911885969, 999914478, 882225028, 231358570, 972427482, 593261149, 176679952, 372661195, 96794201, 407424770, 890283054, 432084084, 431998437, 406295319, 632914524, 785670215, 152881843, 574858264, 97282469, 416485972, 848201475, 444891983, 530650794, 588663226, 171582676, 861760645, 789446514, 753193166, 309823173, 898517944, 419203385, 829031671, 132969079, 685000003, 142467536, 486933154, 599315671, 679272527, 575335950, 340703696, 867945011, 395836107, 597994158, 166972224, 518259285, 258560443, 800701884, 957626095, 173768212, 315848984, 423745770, 5765868, 609508274, 547190276, 44737795, 531516431, 392628808, 890929086, 570633995, 247560750, 629405560, 362862272, 418086233, 34605332, 451553017, 793634843, 113914081, 372104443, 332524249, 537989951, 426171941, 806084974, 502100670, 40952864, 808007977, 463063597, 57611645, 304656698, 76149352, 242615466, 619833839, 638998844, 336788916, 874749592, 69390809, 524729126, 716463124, 81367875, 315454838, 631241883, 450016619, 909909127, 772569219, 663152071, 608183512, 796532406, 16873757, 967239046, 113894706, 902772399, 96702672, 970579053, 566546247, 664550000, 575808850, 791203556, 868955741, 241116179, 943021834, 343710571, 921081749, 980199436, 209606218, 251971406, 135005888, 346718712, 61820771, 226060513, 770645554, 780158365, 834951322, 301639061, 283820446, 496302286, 976204145, 240654592, 754386589, 692134415, 591419566, 502175019, 898786542, 572373968, 573636728, 58722731, 350394434, 44575906, 187445604, 359592307, 837840756, 289165278, 927146025, 524146984, 929516586, 441510994, 888737752, 838205321, 759165647, 334615081, 295913464, 381125676, 814388961, 859439989, 936956990, 987738655, 89588990, 420987910, 694434172, 133572323, 834653533, 97865638, 965762865, 551101565, 78821731, 694538796, 432156833, 125967885, 924068008, 930661747, 82765075, 184414344, 606727135, 794210549, 235211557, 363092263, 735005288, 843533581, 723134619, 88005729, 610691475, 837367172, 170055678, 302077645, 234005353, 165636024, 828004142, 756239862, 551385837, 178229631, 748178602, 455511134, 150152644, 341625022, 922226052, 994495368, 429513583, 560720872, 380901603, 469489368, 554701015, 108153319, 471707662, 719408986, 731956290, 962248097, 251267386, 148220109, 457991654, 499447405, 924248480, 287824158, 228708172, 372558076, 610805501, 584496012, 748169475, 511729047, 432033327, 162973019, 701174891, 501715467, 135982659, 359144430, 271643017, 89643040, 660541131, 144096094, 91531198, 18440662, 168732231, 970547063, 493099836, 597381669, 710645089, 149453955, 829489525, 327341990, 903887763, 155340968, 448331766, 789858320, 658738531, 120748337, 470077782, 698839466, 480766271, 142626525, 272668345, 900544425, 765418927, 853624769, 380528776, 53799099, 649700923, 746925065, 230806895, 128626904, 777006138, 487106900, 740810366, 178166881, 366835413, 36691834, 348190426, 910707659, 607362605, 319160024, 799073923, 593987217, 153781599, 682242084, 920300592, 427878868, 136453478, 841523483, 812856573, 768004385, 12905540, 540017230, 898877973, 384713588, 9492446, 465619707, 288111970, 809651691, 596943534, 54564988, 80778157, 182751651, 373600090, 156156990, 221365448, 13405316, 563421428, 491713894, 814770990, 857287988, 900835320, 603931158, 46616165, 21051253, 530579987, 704207946, 494896855, 718122629, 68289105, 666127057, 987064933, 480396564, 520893976, 860363986, 814425394, 500931335, 698717585, 750634890, 661203723, 549813963, 770307515, 440734361, 892375744, 75712992, 309653593, 419393189, 200781720, 286990156, 502699595, 505405439, 365700975, 340181798, 296262197, 422438322, 488616630, 37092158, 618831156, 19807276, 609123775, 374931760, 708614611, 354265658, 302072151, 12989215, 985756097, 880576927, 129647197, 779842730, 520398933, 507216373, 33761100, 140308391, 82629830, 570846747, 12115285, 251200214, 616804305, 227016984, 3957371, 780596593, 760652761, 685532564, 60543061, 55553846, 97026074, 510872786, 104658797, 462843432, 939111548, 763048083, 190787476, 633773837, 520241118, 399526334, 848192244, 990434349, 392330871, 958097658, 281921579, 286795046, 367474998, 901238354, 209904778, 789656596, 518308226, 881758484, 712789841, 320869364, 399614248, 635823098, 67569455, 449645033, 744015178, 209933313, 713150696, 103310667, 183012151, 163868205, 55136501, 860609813, 825602818, 15040725, 753515593, 915486846, 798701818, 245756104, 869199008, 611653094, 433903898, 531819950, 287612117, 685366418, 380147966, 87521875, 986203537, 710240240, 648363002, 205493700, 893170931, 609845698, 127625332, 405468891, 230291630, 710310862, 855583429, 550423450, 749087255, 154198198, 135393025, 935899430, 370556585, 221403532, 504041019, 139145461, 328691875, 764306075, 122624757, 615684424, 885418416, 397923526, 207717822, 834307619, 797062600, 460101624, 850336337, 523433726, 802579339, 147153565, 107276865, 683798186, 874033652, 947127245, 354787482, 265352821, 660641125, 913045374, 842300282, 539614547, 729274105, 401025656, 780557650, 86787595, 733864694, 457602101, 514595754, 679966524, 420737318, 308816983, 851384040, 728226162, 23597826, 468946688, 635170732, 45010152, 842337837, 739292568, 994532343, 109602963, 999300871, 218242850, 740052096, 647918610, 218821449, 591831522, 609974979, 896285524, 223433688, 211601788, 60807670, 389092446, 787957696, 319598516, 995019242, 900162789, 417240048, 591966255, 843628483, 852395690, 684385732, 131335971, 191679273, 58679441, 398270936, 421295101, 87842997, 664691744, 105668349, 736905791, 431215677, 405454756, 122441472, 371959911, 714075031, 176212546, 240232217, 850669456, 149513347, 719273052, 697013000, 106521388, 376724385, 522636217, 561669547, 585422856, 112702377, 46232968, 706727702, 691929567, 589083030, 246853034, 34877796, 980533915, 849499812, 753538740, 763011462, 741017188, 373886330, 850715004, 57882474, 935347610, 461194973, 586928031, 410470183, 609629498, 203201388, 964150136, 136085407, 989150714, 436938279, 949959719, 657885482, 723523671, 662422238, 918048738, 476734464, 492900602, 350987339, 828639287, 295296873, 569121508, 622353344, 970673187, 172845325, 672447180, 221802655, 267095066, 573501062, 437273989, 478939392, 969710372, 729570926, 25243339, 159303798, 448496404, 12510141, 43235249, 334320784, 978793357, 425880254, 44932043, 818718919, 555499561, 156958864, 593966784, 434779269, 869712926, 852159963, 685668057, 182680402, 77522574, 810761839, 42635318, 698423022, 361482379, 713117979, 267975648, 122414160, 612691119, 688475976, 452107094, 45087570, 293302936, 82302054, 359958455, 769774753, 10908300, 762227670, 335125610, 55013256, 56843623, 452017493, 780597238, 448266369, 455815866, 711331678, 608383809, 171747611, 312285260, 144277269, 327173171, 628594543, 968404290, 130566361, 764323099, 896001818, 243619557, 551105211, 645983815, 458926079, 173424304, 930598149, 746174708, 456292491, 454250062, 888444835, 458118515, 470763642, 369783614, 272907050, 970392626, 647903960, 375129082, 977147910, 546443960, 653400739, 146550311, 842369683, 143231751, 43401929, 876996574, 946592732, 184004800, 330952329, 995569080, 575875356, 368573450, 603718483, 267654162, 876844488, 804169736, 859140842, 144296238, 580032502, 944529056, 50845486, 219202564, 124018677, 232159232, 97923318, 24097239, 792866090, 39548039, 3115184, 637042221, 407019024, 553775288, 104916281, 383213109, 474077086, 885805533, 811518510, 487167573, 520046074, 865064794, 919302284, 219709593, 948263816, 686886330, 351285469, 56784403, 187262368, 64395510, 633454144, 976986083, 671977902, 427265414, 67641861, 789591796, 349307078, 65781007, 854685931, 600379789, 490957063, 611613073, 110802667, 829580353, 688803425, 84644021, 384516369, 449877769, 711546418, 247977235, 365667005, 191695832, 815309697, 507277522, 451055343, 339873307, 808407422, 509379157, 446597213, 669793172, 629346886, 82446581, 947502096, 594416115, 992354006, 812339539, 357408271, 796438224, 401036656, 527665909, 639845397, 829708061, 919254107, 192136528, 223083016, 823960871, 231529518, 964631541, 836538652, 89064752, 715307002, 95674643, 23389658, 265498200, 437412474, 447150514, 439845934, 631639705, 771028356, 511386510, 92348866, 52560587, 224542469, 742485781, 401373754, 478327111, 771248913, 428754723, 708567175, 103877704, 589806140, 292793374, 848409835, 476826263, 808850503, 687070093, 703625974, 837435238, 789516289, 216516051, 867773295, 882107921, 832119528, 972346504, 671851323, 93958475, 298918691, 872985659, 450512368, 116077692, 136131505, 46442148, 479099392, 452198525, 627488166, 967837156, 170028339, 253907661, 471109707, 207930204, 218767727, 204326296, 710629777, 159411656, 684067989, 436976708, 655001940, 994064856, 518188066, 791883358, 945967025, 883070537, 45000099, 754091081, 281779401, 158861031, 626266761, 394902976, 686963886, 581707619, 877513351, 27436227, 30814829, 565226372, 279805937, 729821319, 123998899, 415475085, 241410129, 868912977, 354629113, 903730388, 873738577, 206830444, 44877372, 259949053, 74830765, 953209863, 81611172, 451768115, 302041210, 34681814, 898375070, 37500812, 464784930, 142379005, 286415059, 80602142, 453231786, 648272400, 661540322, 872860950, 413326331, 761385781, 439868525, 209263424, 516408723, 799676881, 887280151, 18102778, 881060101, 455024182, 860529122, 262822321, 110998687, 805935981, 130571533, 915916673, 40856277, 94805006, 628725930, 996211733, 555875869, 375000088, 205395585, 135852344, 611764752, 565317061, 259709823, 422634501, 522349377, 448757949, 366088857, 418195009, 850016320, 20111066, 531745838, 338531997, 871787355, 13826996, 411815318, 827376990, 314795086, 237239887, 78967580, 854105510, 140573981, 56841733, 419210414, 52579865, 804666736, 460700257, 750167478, 254786931, 488335471, 94539727, 196822423, 259705931, 145498424, 626320439, 967202905, 488533097, 877702477, 707442901, 545155501, 143374350, 234909249, 931280141, 688275631, 457336187, 815557418, 918471919, 562099370, 174606733, 755316872, 132473249, 286764570, 513316977, 459982389, 486647683, 957616738, 326473976, 876181560, 539811838, 771927607, 510383374, 586282766, 689669830, 516997241, 681236470, 409921761, 180420974, 258296959, 386720764, 970749701, 690528237, 757815572, 842907850, 604458306, 796275609, 281600615, 152333109, 705031271, 399571962, 779633211, 912310967, 981114703, 33499194, 112771136, 820960676, 922089966, 776164515, 777833107, 632832553, 937106978, 920884941, 885792226, 598890393, 469617839, 799767648, 993487840, 594372671, 190081280, 187493878, 369718231, 900206842, 225753411, 684995147, 559374007, 139476486, 584341417, 213035609, 101449310, 681278646, 662796480, 944118944, 683845888, 630897081, 702272509, 627622823, 42576550, 508407613, 972910311, 649353283, 25815680, 160269584, 130529725, 878366757, 848353110, 714795965, 781540526, 620743347, 380625790, 99073185, 812381548, 10267512, 156898872, 20899305, 127423024, 631207236, 69702335, 293360952, 12193700, 856485092, 792237782, 252754712, 898317884, 408311680, 985853504, 896365145, 499727199, 61725018, 37602252, 375743433, 335299238, 389539862, 781593327, 660283196, 268768096, 1077365, 64403814, 720320057, 985522922, 407831244, 125268109, 687803615, 781107988, 274634190, 561950489, 559764916, 248511204, 131366331, 357167915, 700088856, 581183912, 888235335, 949257893, 517946417, 125109108, 296588851, 652335868, 598600567, 743471584, 706423211, 618690304, 233356683, 86316286, 968816557, 595607018, 660672673, 46573670, 985688767, 227754637, 787875102, 143913136, 10092432, 651064768, 316765643, 571334525, 105225733, 149422788, 422153657, 918738144, 956335230, 592730984, 945543657, 845209200, 229718641, 273043662, 297895289, 132948820, 275430296, 174117520, 804834961, 762799096, 318384768, 649519493, 889324672, 649787707, 547339956, 817861149, 773240834, 121823484, 161425414, 236536232, 652940910, 61663494, 380601093, 917166266, 339435666, 758710677, 692704282, 582270404, 781106857, 780900422, 538141573, 990335000, 972541008, 571289694, 268557021, 844995569, 296625641, 516075883, 49921199, 522356250, 995933372, 754774461, 264772197, 897003411, 378214166, 95745594, 921102959, 396094917, 748519356, 808949013, 245753645, 551273550, 224112829, 773805180, 78969926, 286814456, 580179187, 161982871, 112377749, 318794780, 652267461, 242181990, 497162405, 25387337, 223951508, 714709386, 675209591, 279407918, 462776316, 95649759, 939090315, 814676671, 220448459, 460648229, 581198224, 135512013, 581429959, 557190279, 927298040, 7353371, 84620968, 8360690, 433232176, 165816137, 643344887, 251160693, 826289643, 149142102, 173587668, 473588533, 720461811, 246905584, 648685287, 315115319, 190022721, 667707548, 773883110, 37084330, 185311556, 2609947, 432436098, 965743122, 175943557, 40778404, 43861331, 504927857, 669469378, 731403453, 88319651, 705933366, 248250529, 636242958, 77910177, 410006307, 399682980, 561076110, 514997726, 57308060, 922433311, 139409762, 236601936, 26026904, 485924185, 409433693, 914671770, 668349883, 473682661, 551508902, 453395661, 505474222, 694820253, 826417516, 383315182, 200552232, 644184645, 733576036, 248269155, 934315531, 22133518, 766185760, 787171898, 96685990, 261387592, 940348798, 290030772, 706859504, 863379331, 29874669, 949852770, 163698270, 968938570, 349166034, 678787734, 390401782, 278196109, 306402190, 8363824, 925864632, 518158595, 554101406, 556317206, 967401318, 706984374, 533962655, 33283566, 261373672, 801500852, 190924878, 933861850, 274359967, 396231594, 503558528, 48412296, 132169782, 382570100, 685145842, 763217396, 892346211, 633246287, 90858642, 945768926, 479502948, 751451880, 519588446, 128816582, 554892520, 428490001, 610291609, 582681965, 440436878, 161883847, 336832078, 241539412, 217129084, 157632777, 141468261, 607337871, 455954464, 576918639, 885689932, 125553428, 796859575, 540850512, 243004358, 570665759, 400878190, 297283885, 755293258, 111234476, 244794796, 145807923, 89735307, 91891163, 286355849, 737760528, 103317358, 474024045, 132723061, 182098689, 251929424, 745274277, 269967631, 389425850, 428921354, 302591661, 713248674, 702268935, 895596747, 891612961, 323138801, 564833726, 270663873, 981530245, 612999224, 502001083, 418505648, 279846851, 843235323, 525218590, 748987152, 881374984, 157822266, 395738268, 883208262, 983735444, 16320823, 825270214, 224948437, 832792304, 837640989, 330852608, 377548089, 54096014, 269043442, 192464299, 697255492, 680115684, 809888045, 846981528, 653040781, 862337611, 891349385, 429682371, 375108573, 479838554, 730214134, 182030952, 388921174, 95515958, 604342749, 620586603, 214634269, 312434968, 279212133, 910497195, 366326798, 508894615, 604907685, 877945836, 316842664, 269473793, 913388965, 605879237, 712436944, 458771574, 591912625, 601333975, 326704322, 166349361, 87211958, 777635330, 667392984, 604518524, 931598242, 307552094, 860868378, 93520228, 334644106, 437012194, 89094496, 652245753, 880684956, 738925976, 574256741, 734858604, 286110906, 475843263, 239531953, 190401263, 644425313, 229604597, 44321091, 216494792, 740876383, 161916121, 800137622, 883490492, 677918997, 675662077, 501642725, 583395098, 41047438, 237616533, 917279999, 824151162, 212349654, 140433621, 852203245, 568448210, 499712699, 609224353, 582226131, 176419687, 923579011, 354588533, 351962487, 50057488, 462242358, 878848488, 791190907, 994442781, 907500947, 914791080, 316523324, 128399514, 188273460, 114811657, 544204944, 745747722, 455108619, 797957009, 735994630, 173065945, 664749186, 91124987, 65918419, 103467091, 403171532, 663360792, 37061129, 966060067, 748757350, 99159285, 490869772, 507038327, 585776160, 443492732, 114367496, 337764776, 725701189, 695115668, 331219814, 83319329, 552357448, 553800704, 452758037, 652548391, 96257500, 184177654, 249233541, 473994804, 433617604, 851606476, 367917267, 170148073, 958333799, 557484483, 193278188, 893172986, 988273955, 67503746, 403165932, 370877995, 53872292, 661971467, 215247544, 121428136, 247894403, 490303903, 729339910, 692778102, 235108462, 620691896, 396046684, 143150931, 739979931, 379830031, 49475931, 595062159, 714084136, 946872862, 797912271, 105673532, 136518277, 218645675, 258747050, 504870894, 406649167, 310512706, 412538010, 154562711, 459115417, 426708664, 498517225, 909339099, 46036946, 493764045, 28652391, 124951459, 624698030, 959446359, 123689845, 500482623, 27369004, 124104281, 121723734, 766655282, 743672237, 93691560, 436350166, 535489749, 831447895, 331782359, 185532926, 765191518, 159141569, 586560023, 170007956, 395218540, 480301485, 488246795, 666747731, 448396229, 566916229, 932624073, 273772911, 822198133, 273919298, 693102999, 368114387, 330383867, 36281802, 76922956, 395497882, 698971756, 852922376, 693482480, 611174100, 67126902, 761432201, 339033541, 962751444, 121855244, 776480654, 708782135, 688889980, 557932875, 745487031, 9940206, 955595460, 288252483, 16972010, 707339720, 406223950, 376195133, 269590154, 151883507, 268747163, 361793923, 806005478, 626971114, 620716573, 195437575, 449421927, 243838298, 190972865, 502590409, 278704310, 906800790, 195932357, 840495428, 882097626, 777993416, 735196625, 156886134, 653996612, 902531574, 389189870, 160494190, 978279796, 470958479, 813017417, 196220353, 308094519, 68405707, 187641678, 449098842, 231306151, 476129855, 647066025, 248754975, 362410051, 712166410, 333870342, 450713966, 995193239, 585612330, 943208493, 585772058, 178219636, 870142336, 412706962, 971989882, 414133296, 788198596, 308905067, 439294966, 653238844, 230281455, 328863463, 695034809, 330436876, 113145591, 548424820, 865222527, 882729442, 419666232, 163163043, 7386658, 651126144, 634017939, 183506531, 394782813, 364826520, 946878214, 330048843, 509033434, 37910279, 352262968, 367656785, 507739987, 117454655, 730165011, 662185735, 503320324, 584743316, 593692477, 432756239, 552832523, 284836710, 737669292, 332760878, 614724452, 981008965, 870620646, 232294995, 802182732, 780974082, 144876538, 925064616, 567164665, 898227968, 725809679, 547131436, 505667990, 819073822, 517977397, 985206724, 954377240, 904953323, 502402283, 850277945, 597288803, 583985861, 819012070, 676155439, 165403185, 571215127, 169694042, 863174483, 867202288, 410006858, 298924918, 626045767, 920445516, 113695044, 325114779, 940976265, 874670599, 929253879, 214102040, 957800219, 49658952, 824495616, 204420380, 867841717, 34607942, 731110367, 381048911, 606861365, 675446672, 234067892, 796812772, 562069760, 521720520, 612354484, 777202110, 167305136, 574447678, 727660302, 292389752, 771815401, 5598701, 3815119, 602565408, 923817682, 80559752, 45535654, 74844638, 884000303, 916360591, 748567991, 345294417, 583711682, 371938801, 821187649, 990766995, 201974712, 935039857, 570578782, 679328029, 538735557, 702994841, 685322713, 34281757, 622061080, 971800915, 610011471, 623323612, 864972410, 604643278, 597376366, 76312768, 947220933, 323397279, 585965273, 642245286, 110038040, 250003078, 684192734, 376754780, 748328812, 518922558, 839351197, 694337991, 992890722, 913869749, 563821058, 434412034, 517542858, 250804118, 585211824, 468253574, 299905687, 949189999, 138684973, 644120713, 835536207, 399068436, 281260004, 192623951, 937564647, 485532690, 670447521, 548911075, 115581043, 854850966, 381165406, 879971877, 759572816, 581341785, 102752624, 537917943, 746176054, 61088778, 367967151, 220998294, 308678719, 417976940, 156142871, 677889481, 894516221, 622601647, 848284053, 789974072, 554492180, 13372698, 325877893, 721926645, 761055389, 775286552, 226351303, 591131940, 725781071, 328379344, 113052514, 457390523, 69060963, 788910393, 972576589, 362411809, 281717506, 543686957, 294475121, 676063879, 69243991, 469770369, 551301078, 541303913, 304340380, 712941430, 943504824, 72894594, 796141266, 444553215, 857912437, 51795227, 978054998, 533559535, 41141071, 392417305, 884105187, 923040196, 449153271, 741669985, 509795680, 850719895, 285472940, 521777020, 117537796, 586623973, 620666424, 707915174, 665537582, 375652335, 161934849, 620766862, 159207077, 404278285, 218347118, 391992418, 472966792, 190155728, 809424475, 328820914, 336518434, 789224690, 946042537, 958930533, 803556367, 242481565, 382428796, 533880273, 91493171, 74071612, 865110369, 757075488, 297200113, 912752860, 522805302, 215155870, 805500265, 769104370, 18980729, 584213329, 883200506, 372333237, 762951791, 448700273, 433507768, 234954031, 537343002, 701469647, 885464036, 798860631, 5699085, 480852799, 63130022, 482466755, 243278487, 290675847, 995957524, 896267780, 694176054, 841625005, 882997859, 949237546, 510485879, 647165606, 859066423, 808914479, 533149831, 213553430, 605340318, 37111270, 842490878, 209726692, 654625947, 580393749, 952430234, 642775019, 303472178, 272778734, 417483491, 722161674, 969217200, 429261075, 218778315, 227498252, 923311850, 21659199, 815409750, 654925085, 729211505, 255806918, 613187988, 953315666, 37336265, 150550328, 15463462, 253853253, 850777799, 337173562, 677263496, 792669175, 901835088, 785550212, 403100092, 818930670, 792324431, 486941072, 652778550, 502500607, 25344881, 743218802, 392739098, 613438884, 465380870, 846043349, 26386037, 503569793, 89965536, 197455443, 12062558, 630791575, 391017363, 405434982, 474082988, 371732742, 302935140, 219268060, 8959687, 42152360, 407412108, 309179824, 573106972, 541086571, 180075726, 563279249, 180450313, 599223471, 913872463, 88230680, 959235095, 754186138, 669438896, 165450675, 769669045, 10775012, 839488492, 184662024, 167453594, 862257402, 839319972, 532131756, 309720905, 275732791, 784170235, 681356396, 546592148, 1324234, 337048000, 934724213, 986508398, 465275817, 184704079, 182218351, 42809260, 866711810, 881627278, 487902968, 208602304, 333013955, 363370993, 97044101, 487934071, 155796494, 468361084, 395883376, 263690592, 537326758, 65010048, 611443911, 336491854, 880306163, 523812200, 443572227, 878677221, 742609441, 880303420, 496363041, 555713719, 798847084, 14312733, 348310349, 965547643, 290579562, 483145600, 181456300, 404084799, 14651686, 633751534, 488813506, 953182599, 732595288, 205648795, 678899973, 379463109, 977560109, 73928456, 788718230, 154094821, 531240279, 767888214, 867281905, 789316431, 23260123, 954480093, 76585978, 29993703, 869175843, 100693160, 436667904, 612287326, 380147512, 383474099, 702735014, 626915039, 490507071, 766705903, 115791825, 144988311, 720563802, 34758417, 321959935, 985407331, 178854937, 798103811, 907145394, 717348247, 884208574, 307002185, 739404549, 92522046, 425176808, 794451474, 685422028, 260455031, 79442836, 173993139, 261794281, 592460526, 22443731, 188576004, 952818273, 76777211, 317096638, 862924649, 485182986, 197223452, 396750886, 294355629, 376225488, 797563280, 102689951, 540686820, 189515061, 506821105, 29461706, 688507159, 991468377, 885189489, 44071827, 337484163, 716115856, 94874291, 87181988, 555922146, 424358158, 591929188, 859177023, 139864836, 759629367, 546498039, 618114021, 417781728, 900011884, 581716719, 347575312, 182165066, 437227963, 324918324, 990187622, 949080801, 398106629, 10360675, 977347156, 478705421, 363215950, 280242955, 838279899, 47463355, 792101049, 625037394, 228817683, 789161389, 503862894, 244340349, 45601256, 810116578, 158710614, 95198724, 179135561, 641274081, 209380233, 420224901, 793985761, 116745483, 906763824, 819610501, 877146860, 300300505, 737662431, 818701270, 183932316, 423301411, 8413603, 885867662, 530385530, 281551908, 613440081, 400227122, 263707617, 568782231, 355808216, 621999720, 428017068, 385934093, 83974823, 961094366, 780637571, 736604429, 108492760, 580580823, 434083803, 436944890, 430584610, 595418478, 708703726, 503198669, 471962820, 241135740, 689661586, 915832915, 922261917, 937996409, 889044280, 745616616, 55193272, 139942833, 683926162, 968142271, 656690276, 216698257, 873018017, 469688026, 574964037, 187142282, 115058965, 687758097, 243257286, 648949264, 466462946, 782492008, 967322803, 935724000, 263121445, 445938197, 500943195, 600204602, 732121358, 846289468, 197714330, 4818788, 898479772, 519369166, 902203939, 833750476, 740330195, 746756160, 132843668, 821584128, 127314845, 894500838, 569376093, 791748801, 124707224, 612662403, 713121326, 180593207, 863654349, 714473697, 113084646, 572464266, 103470168, 801174253, 659923579, 145445204, 222299223, 318724720, 867283334, 483648165, 851795162, 965671605, 679385324, 935052229, 976786470, 306352796, 592617135, 652975733, 518553047, 954543015, 486075188, 59717141, 256434969, 959369503, 396516049, 721606091, 375315773, 731159281, 517492020, 489078, 871014905, 209938922, 108237434, 920182809, 436736709, 974041775, 826784303, 445202778, 217292113, 619514174, 569443521, 751332550, 285762054, 128230684, 350012163, 510742077, 622455089, 155442280, 195142692, 330798839, 706264838, 33922022, 678349323, 454029913, 377422043, 660439326, 693445297, 691847242, 603406699, 364011313, 904216251, 555652825, 773646724, 893027595, 603164208, 606078741, 438750057, 489218055, 28900244, 907553611, 597335680, 391316649, 110204882, 871882993, 193685902, 903281364, 437331821, 849111666, 266015219, 152680466, 85918753, 848112771, 282598599, 314603706, 67912843, 621984214, 603431795, 2880804, 83915602, 599264519, 52704157, 666644653, 296523737, 628116758, 588453524, 173789508, 19601500, 568033942, 74328695, 574738124, 583781656, 655980485, 155048719, 252167955, 452609241, 505746044, 963272378, 788937899, 602698907, 763690017, 915143463, 597565259, 134008531, 377610362, 470253207, 840378986, 955072211, 192554460, 513598327, 182872292, 101036470, 893366151, 478156512, 635149932, 247357458, 430459859, 826708694, 294651188, 587530043, 586221285, 639124667, 721585139, 838593236, 661841118, 914748499, 399148100, 17129297, 961615790, 30641077, 215950696, 678840313, 312610690, 314757349, 144771860, 42939902, 322061155, 701637372, 408812016, 967704043, 816427282, 466835968, 306232541, 334009077, 974126601, 215195654, 236547866, 461623143, 444494645, 248599880, 503869364, 345902932, 804664078, 662229117, 337880529, 935898944, 589473676, 615279096, 507750710, 475603282, 818819090, 823259646, 678188910, 464108369, 340222373, 908176145, 333971871, 739077695, 147728716, 820097875, 26593771, 978651927, 39336834, 146334494, 612815409, 728862724, 336671076, 437195296, 580507312, 479335481, 209911438, 740847732, 392553490, 918218695, 87579987, 951077047, 914243968, 328041229, 63823644, 551187482, 559532538, 335312475, 538272782, 155936725, 143590433, 561455883, 880931373, 424088620, 421477396, 821601448, 948464198, 407461688, 8843595, 119092827, 142294096, 927075991, 501012874, 168261501, 214463940, 321263982, 402579499, 709862012, 85834271, 941408122, 645783945, 621111826, 124297791, 353960415, 571891971, 331047225, 141554741, 774853441, 66456864, 487767971, 236686933, 462257827, 254072222, 859962743, 642286101, 9970355, 583535703, 313950724, 984055186, 513932066, 481656046, 224320490, 94975233, 765377256, 792374176, 478668290, 497341025, 218242523, 504081262, 43625338, 461321664, 649026585, 482182435, 324617329, 931282710, 649252032, 731439353, 165156438, 848327753, 683279442, 913886931, 773400320, 580297096, 722648657, 555077707, 855216789, 422659727, 347206186, 115446881, 300635352, 338872097, 978205463, 300609228, 131208086, 899351738, 906934558, 576914699, 356010790, 423909659, 90518748, 358071492, 635755001, 863281431, 390119843, 35531537, 7881667, 154796423, 290560314, 849744628, 857856486, 176628151, 71385071, 399762691, 903487170, 157514174, 76552150, 518337832, 813901271, 503028412, 680904608, 147122463, 145996639, 617554545, 26433580, 289529412, 173999362, 534835485, 594129609, 500101351, 277263152, 374321249, 539032231, 624210409, 688394830, 713877364, 995584557, 649952994, 527611834, 575635100, 478202023, 919073477, 294285073, 7197649, 254740797, 661496841, 147294029, 156309431, 804888250, 635166623, 916064620, 796065848, 676739301, 978719542, 163536069, 667861670, 455352994, 851782944, 972900523, 979860900, 189455587, 703812863, 992137511, 981989421, 99234982, 199441338, 446354267, 988370644, 699115639, 337131413, 889540838, 263907908, 989511002, 391301611, 947570714, 466502085, 921619803, 584149488, 197724273, 594453263, 760295558, 204659298, 871328296, 730509323, 330705727, 131390719, 550848142, 844992295, 856683735, 953155790, 781421360, 721281966, 396297951, 236910503, 940200167, 162815464, 851176395, 725184482, 511025165, 189651147, 52385590, 977265175, 750541016, 755417352, 33951544, 694673038, 464625444, 672997316, 510163724, 108719534, 859996555, 529635517, 217674635, 594214850, 247640760, 318009393, 198678099, 727393180, 613224091, 639238701, 130382502, 851434218, 979398258, 210956094, 147349101, 112503030, 249892037, 835987728, 589727214, 718468017, 848569414, 875117066, 827561253, 233699659, 910464591, 783702535, 774154088, 818581167, 926282574, 469540093, 551163174, 170444449, 393242625, 214381761, 309765028, 98669875, 131299569, 4191923, 419962615, 815293701, 496556557, 253287150, 703825840, 174180947, 515359552, 351515809, 343791489, 735789440, 221143549, 189604729, 60808040, 293576721, 194264942, 767562574, 904290403, 765126513, 940126609, 602120490, 562381694, 717933513, 254461651, 692744555, 294251151, 685003400, 445271667, 870578312, 740638793, 853975911, 774011549, 98128718, 480025152, 95856192, 193683355, 161392180, 451078839, 533807714, 864949885, 944232510, 19656665, 958165987, 604575786, 675149411, 982120591, 794499933, 611568708, 974930574, 703715908, 727626178, 129648511, 169680203, 868357257, 217510074, 352068322, 393400825, 744300395, 491087149, 116959086, 150761426, 134688963, 9558343, 730995072, 590637338, 462302702, 631964839, 980537338, 681262171, 349199751, 392654580, 12085496, 760611248, 333735897, 966727503, 96828871, 183164567, 773765008, 262422775, 151858475, 951372416, 95990952, 285422897, 233025117, 939025292, 745282372, 944413180, 388922529, 263359167, 299260376, 325112764, 337403675, 947078761, 178393938, 445752900, 157926408, 168521473, 221453363, 150802968, 816988625, 449844035, 952615073, 418334621, 305692336, 284384657, 190842412, 661877069, 424300346, 725371372, 500979087, 542242510, 334264166, 351038593, 892578339, 441852425, 841643991, 355784352, 467647951, 357399046, 433498037, 985461383, 394752804, 778915291, 538093357, 33656447, 727457836, 626941792, 264847341, 202001453, 139525127, 732330913, 497240005, 435804142, 328649424, 572574040, 623205396, 212868238, 71748201, 404280945, 890454, 223051218, 118273536, 585124966, 159358059, 575058792, 409677174, 164303638, 38185406, 981009746, 926231910, 928659662, 394026304, 801328878, 372329941, 564224808, 874214591, 556460048, 344350421, 592280441, 620048803, 243421072, 205424458, 618835829, 294425470, 149984556, 225920547, 436240104, 135196064, 850062548, 91058482, 147750201, 142059849, 293119504, 616647171, 711844457, 952792589, 754033309, 886163781, 527206561, 191287504, 533278991, 863161554, 216250172, 169136279, 674937578, 895109632, 182554070, 104855243, 154901927, 367393628, 414834060, 664641496, 859029997, 229656985, 513898650, 812792724, 524155298, 90105622, 155447968, 862116952, 285151230, 524556235, 979861194, 771248165, 841969388, 346372456, 702443327, 160372682, 6902612, 496406963, 936969607, 956899830, 67119438, 633598635, 767291536, 517271279, 450654024, 271374393, 34112381, 486148722, 217193467, 567642105, 89152981, 519695640, 694558067, 727172226, 215223797, 853560373, 268015344, 723584304, 777782442, 943616394, 928135057, 560481480, 179935417, 227370099, 953336591, 589352588, 501963508, 228408812, 856930637, 977782600, 820353219, 44540595, 905229350, 750043902, 606659574, 115840156, 225885404, 980642397, 823717060, 287206865, 249479989, 627160303, 971774400, 897067653, 956027364, 214581057, 27699334, 782831510, 279289940, 393448425, 819531134, 853327620, 814101077, 654996422, 786204537, 608384265, 741237026, 405460579, 232870971, 997552366, 208416405, 395834557, 771332844, 908677093, 105177129, 56463339, 886456039, 169909563, 465762993, 783252482, 250931312, 86074059, 264882274, 364590409, 799010132, 516337741, 955537310, 222144996, 859234536, 446399583, 862001709, 719576092, 690336023, 970332316, 357570624, 121962181, 532105520, 206412930, 809246033, 234118659, 858034495, 13252413, 733598193, 514516789, 931896467, 168971563, 93506559, 258868394, 960897758, 570500696, 388590614, 584184330, 688273589, 511156066, 449009676, 848579963, 402529072, 522806601, 687572188, 594346745, 263491755, 203006835, 175170117, 291663354, 397746601, 425368244, 665253306, 248025061, 831740318, 725318965, 906971486, 784936870, 168668410, 802067834, 926457376, 94514767, 421579738, 177121295, 649947555, 722568890, 303200217, 931114161, 272615950, 211808051, 222441095, 516545004, 874037113, 264191345, 280991578, 663362215, 87330701, 422899801, 271762760, 326233015, 736465293, 889326243, 318005620, 499670341, 554114277, 394427034, 528469257, 584594824, 802565548, 661344547, 680938416, 821205735, 153759899, 131572304, 383919998, 455981125, 158116264, 538219856, 984388186, 876486886, 608503928, 717593236, 341030274, 366372502, 887918802, 304995131, 495470623, 264743876, 450738744, 892755376, 871476764, 282712101, 353524479, 751187619, 811381470, 754011457, 581184824, 364116037, 312510232, 842687162, 968873180, 555814689, 558542824, 799761721, 628518633, 333072225, 540034162, 574044701, 21577342, 14020017, 294657283, 291528133, 585243662, 349184016, 823137075, 726743286, 621840427, 779860370, 48811635, 406148859, 362000702, 642452866, 311877464, 166088507, 578690539, 21657919, 204128354, 562228447, 463494122, 601184407, 994722593, 165017756, 769230033, 528579287, 569448462, 693691001, 248680176, 960351431, 245372951, 834554193, 56716625, 138768213, 964539341, 721374965, 673213329, 819731206, 937729124, 851722082, 337691521, 572769774, 854337412, 247099343, 747547744, 2529228, 252325657, 662664762, 961859784, 837427857, 432023390, 929913332, 790519389, 903872257, 261778708, 310065153, 222400879, 653186569, 239296397, 933431240, 857402092, 165294045, 150154077, 499391897, 323314183, 668483985, 484614572, 843254954, 163741107, 591406389, 618287596, 715075538, 160763337, 692438307, 227912935, 693777817, 588670395, 30386237, 805882419, 483821652, 332799743, 5038636, 565526088, 890466193, 870509471, 646741676, 13385765, 725287429, 489535211, 426981689, 752028421, 304590739, 620458532, 193080991, 176510570, 201280938, 327752564, 604851576, 271192158, 695155080, 318798610, 577587954, 296974573, 635414895, 354506649, 249101333, 367503414, 468587415, 550472664, 319416363, 49492255, 126855846, 23097630, 716904868, 324152817, 779188137, 290090638, 767184640, 12349576, 266430143, 585719669, 599530821, 201003911, 414287677, 613510964, 802844666, 214488848, 812097688, 368713015, 161108083, 427157493, 619637314, 806418997, 625646515, 895679271, 284183978, 259259339, 577035182, 542807826, 268629284, 826141877, 821587621, 674578554, 710311393, 906303408, 873471552, 837109594, 545221918, 929085748, 491951749, 868492120, 858847505, 122468285, 870552543, 384284751, 675296018, 652671403, 197362248, 927271252, 484525470, 141994382, 620506186, 266181140, 665662540, 367858101, 310866118, 330654988, 659722332, 518117779, 577827200, 363086258, 897538798, 145776091, 658792354, 743689425, 129593766, 125500240, 713923927, 334641710, 576987972, 628880145, 874600672, 842972163, 370409419, 220126640, 840920093, 319765620, 257897985, 712489798, 494461361, 644556531, 65644500, 326088155, 460211843, 814454871, 291776263, 907715544, 25598406, 353310379, 963522195, 79433021, 657198661, 727171256, 757988596, 599727054, 773361052, 987343340, 945414032, 526125879, 517272238, 826029088, 614106450, 829319580, 960493748, 597126661, 827033012, 86597545, 982476392, 685372115, 21813514, 865914623, 578363804, 530240837, 120517936, 313577929, 237279367, 117834393, 762962262, 754402031, 989192040, 326377721, 993853509, 766946991, 639819013, 988405049, 260296979, 544490929, 783220327, 20598928, 663332289, 389683538, 689784978, 698030200, 300581204, 126430330, 135736126, 213688103, 391092282, 117996061, 188871703, 282885419, 775248165, 852666009, 539082964, 57191285, 395615413, 104580202, 70787227, 615451493, 726653920, 397292562, 453072091, 777588669, 902706007, 945197557, 935216761, 783389998, 837349673, 133667001, 115633628, 989071453, 612766054, 150755005, 401959652, 947446441, 5071569, 161742157, 205527730, 423594678, 247575257, 834132527, 834441775, 470472583, 981135798, 300381991, 878006147, 67716567, 376567808, 130628723, 457294622, 475795349, 840035861, 36169794, 455908838, 956965787, 412483570, 971761546, 182818240, 161403222, 783721143, 770917840, 724075571, 516318101, 171808983, 513636540, 291243625, 378595255, 714639984, 295851756, 589311355, 964932248, 619185451, 303825141, 291454570, 680206947, 977537659, 277115377, 886504792, 286221345, 818906558, 186330870, 728201341, 944887222, 393592086, 876654939, 438664017, 734347958, 190410918, 96928671, 344122942, 358888439, 272449161, 351702740, 788992947, 875336325, 896770610, 881528403, 70401553, 399776255, 815896956, 70037217, 321489620, 696854932, 392680838, 127730285, 686834532, 431455028, 435750322, 402507700, 318976943, 302076909, 407107823, 564729482, 543371393, 325747292, 586398709, 149529436, 859747006, 388674236, 637401388, 621187370, 482515226, 125029833, 360161449, 953276235, 689339380, 971375557, 517282674, 378509752, 199728174, 772185922, 829050730, 858495636, 579977227, 685214777, 86081481, 808490469, 737416782, 676142675, 242614653, 467211195, 70040649, 282093040, 600108017, 290452564, 520675889, 148846491, 607707979, 748758052, 578139426, 862458263, 408981854, 917024877, 879081779, 372890001, 566288797, 411392558, 77903602, 116777803, 427189836, 200267808, 324859480, 875248692, 11466098, 81750628, 753084372, 60820628, 204188595, 6147163, 552540239, 16525831, 777465885, 567451300, 791935698, 207275928, 773204291, 645427737, 756141317, 611573670, 250244313, 968473356, 447010917, 805482795, 256894371, 254551463, 204683324, 321927653, 779999437, 771657249, 486872650, 435818706, 166457482, 253540705, 942092905, 642050732, 735028086, 329887839, 41261966, 236222219, 137849118, 789876161, 228384955, 527831503, 983793376, 969972193, 302620205, 413067061, 660175852, 327166059, 251624631, 357844687, 824306152, 654210176, 438460370, 295196162, 188651609, 974388370, 707255487, 387151451, 94150651, 129379093, 76599962, 529725444, 206832550, 862879080, 1996957, 543656762, 356097400, 305053211, 404918961, 955294563, 360642060, 356749998, 888806999, 870016146, 256325175, 740159148, 489521303, 687191739, 669966424, 271950465, 47350233, 325008544, 180062897, 922699136, 60858269, 129228819, 632475447, 25335936, 634726401, 71025430, 87443411, 566600673, 187029098, 288619415, 980550361, 415139263, 776874039, 19394628, 577975158, 909743762, 75137549, 361956075, 98482105, 836433375, 488548274, 223306265, 790818767, 157214371, 214368863, 271100528, 133093934, 140597648, 462424384, 536596404, 622655831, 74175744, 164534693, 146687936, 640457313, 509856804, 772422744, 332726580, 747934290, 763804804, 722837798, 649913423, 878990350, 423589741, 276485758, 921374451, 851049203, 546131395, 77580496, 129755693, 617827242, 858373549, 540916436, 330197093, 435068007, 786832639, 574750769, 230575058, 195702963, 215835652, 714552526, 969871800, 174791066, 83983892, 661488963, 130292397, 362069585, 984848379, 388083431, 477896741, 12382771, 572145612, 449819591, 911628935, 272124900, 248207480, 902977666, 881262228, 447761078, 787266362, 44852728, 908685621, 355727518, 390668286, 863689529, 950739423, 846441555, 8456425, 175198762, 181794939, 319926550, 25699301, 592936657, 50103509, 408295900, 381553022, 748447628, 227615645, 706899477, 409333651, 668951721, 777113405, 754881660, 258652723, 29420041, 63129962, 81667060, 624121676, 242041690, 550466038, 432909461, 491657906, 971562370, 740801902, 410569651, 111488360, 398037267, 314363828, 498385807, 686735604, 248438081, 792121803, 604987185, 853312682, 450038106, 877495486, 47452640, 856525993, 924134644, 34293368, 127386715, 318325350, 661530707, 862849106, 515621129, 229161823, 304946944, 76068245, 384136345, 35728969, 676112623, 301727405, 32804118, 524082840, 667332344, 166297359, 211949799, 864730848, 728661193, 336274656, 509715770, 953572447, 4817508, 568009707, 6367728, 421646262, 977727142, 942000329, 766155631, 873802521, 636156233, 993766952, 506750084, 932571667, 302326828, 736329145, 462121717, 736782552, 867414170, 658874745, 776869309, 761699620, 385879329, 353922463, 579110982, 47586915, 174276132, 599151625, 19458984, 769597406, 433433229, 2133980, 36428562, 556526939, 303330403, 416244357, 132209719, 148633883, 909418410, 216285336, 877118724, 816450160, 958364909, 373920682, 603792200, 470479803, 109401958, 486967707, 538020766, 459350573, 645290902, 731440215, 323724776, 612717496, 262976060, 230298105, 645989309, 719576136, 194096444, 521513031, 428536234, 581403306, 976123070, 565426302, 913583926, 248379266, 460795793, 599712379, 210440712, 295660188, 389937081, 8322448, 20831612, 690908646, 755022878, 134676083, 812602024, 694616004, 877391338, 400956684, 374053741, 237915503, 380733998, 644475788, 365440619, 321464342, 873142743, 554757056, 196563296, 260659426, 641702977, 818914532, 225780572, 633944588, 366212129, 586048131, 193268062, 554666159, 648286909, 432547041, 360153624, 489937482, 246102938, 467090532, 16174390, 951646217, 685530944, 854872883, 430845316, 442905989, 195136576, 893031937, 48989585, 484350467, 200922267, 25570629, 612265115, 688185525, 543032516, 366420408, 209235747, 305901884, 294614433, 511632184, 839294375, 395044701, 86292740, 223477513, 900111551, 933306259, 247019896, 522038119, 884752287, 623065967, 281620198, 327648756, 923740205, 966650643, 145252207, 12514161, 694612131, 790518607, 410652578, 753526263, 472295876, 349033324, 230622526, 614686673, 640888230, 440532072, 370300525, 540346732, 283975249, 613815085, 605338414, 286928090, 548446621, 637763711, 12671558, 752732349, 326254801, 749074082, 216859911, 170046867, 862906379, 112158656, 691977072, 571792541, 495845943, 631442576, 997883306, 273169106, 626554214, 190863641, 271786685, 303227055, 783832913, 63783471, 131298966, 961020857, 593231647, 672234285, 466146779, 465579426, 990739963, 192606540, 345067319, 159617684, 888450271, 285482794, 1267240, 993756794, 640027469, 38766096, 605631699, 541775953, 864569178, 410860375, 329922634, 543314474, 264589268, 109200375, 873855224, 904850107, 672644046, 287095206, 626741764, 151046799, 560814599, 960493831, 895437772, 693260499, 923387475, 245638993, 985939203, 367589020, 787867855, 697235680, 427587852, 766794125, 949018280, 747550340, 916481236, 231598483, 919190176, 850359741, 197648641, 712861189, 979431891, 551584363, 182868834, 129940855, 170438516, 183500143, 328388470, 161658234, 662408336, 7203018, 606595781, 93141899, 519820542, 392877856, 78993630, 685285362, 550096859, 392820260, 164824315, 325203484, 622286468, 706457556, 757242545, 972718823, 942529559, 831812451, 936825402, 563474647, 610550449, 398257237, 759274068, 103721036, 574747137, 24291833, 400525617, 119838134, 560420783, 750174199, 196406650, 468002563, 757448331, 792575790, 298844829, 810745833, 7767068, 405066986, 251792760, 605391512, 466179642, 812938716, 23960517, 916101696, 555563497, 261907688, 251602969, 933140262, 607652753, 170485711, 814863726, 339724718, 483678970, 242584829, 104253090, 419283764, 800749065, 593214040, 693908193, 685297999, 822410851, 853927453, 812772398, 853321617, 331155524, 146653169, 657383182, 392579235, 249767903, 394027952, 90216329, 18671833, 489911740, 48355887, 695470709, 982922098, 133049871, 537065686, 491684580, 442264613, 436522745, 232707124, 983381112, 351076196, 28925407, 638428050, 168200015, 435945974, 837440404, 166362927, 42923377, 308754532, 254057375, 177058319, 252248628, 925397296, 562813248, 340939830, 286191968, 710654765, 672027668, 259857837, 725983643, 672269159, 311818823, 24543651, 285273167, 828978683, 848184382, 995179184, 65327867, 67805221, 225364107, 332600669, 281263913, 843206763, 872790042, 90993458, 527911413, 502259081, 97928, 602842019, 343600731, 909814239, 815560096, 275705635, 756986359, 539545745, 581173645, 53630347, 672933760, 227782430, 502092869, 282116091, 979103328, 223285099, 429628173, 52992565, 200548844, 126169612, 609696923, 15874869, 606575371, 501646058, 239687301, 335554433, 826512850, 699728159, 590592340, 309489741, 608876208, 406570560, 402654484, 71567441, 781608148, 369359945, 477252773, 591562295, 730621029, 644917840, 796072858, 544628710, 879647166, 808460893, 88919725, 57371796, 241586408, 383724635, 178248420, 12442453, 150557499, 107580255, 506135953, 269330013, 655821807, 102350516, 552884421, 516755951, 835920795, 431419591, 192341736, 985989261, 278385452, 48648201, 350120068, 811122797, 989707551, 818909484, 782944179, 888227741, 830365980, 854741780, 361693358, 249737548, 972931797, 34327492, 538089616, 374576354, 172546687, 414888162, 872310965, 618671652, 202731048, 679766620, 453770412, 833479684, 506861937, 669758067, 201538066, 669614548, 14809227, 894649724, 379583763, 201493663, 709089962, 354163504, 15486904, 50499038, 298005806, 722703613, 912703740, 477941903, 651342666, 439423652, 286947790, 906492917, 981237175, 437329032, 37050448, 508213367, 601839881, 584694190, 627648311, 129024374, 701456451, 789012426, 254124479, 696367031, 679126329, 943129496, 913573088, 135679953, 12142446, 386813942, 900372665, 274024849, 840273932, 94272216, 487655081, 530217117, 410945244, 661633340, 470226853, 896666234, 608396053, 590006526, 449455332, 582341788, 408910312, 171657303, 826609993, 287377172, 770223253, 872903780, 419401971, 567066616, 663198703, 784035740, 144590235, 998884084, 73827457, 614853400, 396259561, 242683290, 935451057, 36570140, 998148068, 3733057, 452057146, 113011974, 569660891, 338527891, 7432852, 437551125, 719302577, 668621922, 152234725, 119899903, 332599267, 62795694, 397808318, 942688227, 678690279, 940612505, 908389501, 440768484, 782951509, 852717758, 717800545, 260578574, 209133578, 515105532, 74457777, 4174240, 944955187, 60480937, 816530379, 972272032, 994574361, 933051938, 648450750, 29590312, 338685672, 615763423, 550800349, 174483993, 64171796, 419005465, 170359151, 666145391, 851458965, 653372779, 359494667, 16398463, 23121494, 12169530, 573163680, 250442369, 521596803, 551648558, 919965238, 334180483, 419712874, 816655097, 367782882, 915454022, 997939291, 470063664, 391639366, 802127162, 274529411, 403712798, 940767305, 184303323, 21038675, 670477948, 137134534, 624045182, 143600818, 244373928, 475135384, 81666203, 423955338, 468543742, 945002709, 483445468, 967080212, 410763480, 381828774, 635539567, 643416223, 993223417, 898445024, 282222311, 91681355, 179236520, 677283321, 569945832, 544244148, 816756171, 524015303, 103510332, 14257310, 30647413, 4478358, 657016417, 938863017, 668123444, 202110001, 425732245, 457638477, 190394023, 707599147, 436342657, 527380642, 211083528, 109667558, 423570868, 395515589, 505333448, 195458413, 623370018, 54749843, 428616580, 17291195, 690690944, 478453022, 24165880, 503910225, 137096778, 201917771, 721753741, 86298075, 130266029, 603444551, 190260124, 694896335, 517849152, 379916261, 511910897, 526624013, 595797491, 313707110, 576170435, 443891677, 545298760, 856577266, 512756564, 211079647, 728875091, 755513522, 70037228, 128929918, 285981736, 599875382, 536815616, 940294478, 88843958, 730644514, 494202293, 725409776, 712709438, 204296916, 26509269, 878438061, 964122257, 957990676, 46004190, 494870953, 448467118, 39408696, 541777155, 546051120, 540084336, 949355568, 85136084, 310376262, 418806788, 714494555, 514180124, 810482571, 212588447, 491412291, 747192024, 861367680, 804491149, 630342162, 188314285, 108159883, 871297068, 725703903, 422052515, 799727223, 73816002, 341009059, 318331558, 179175190, 953211841, 893605750, 181000040, 734983743, 486245833, 762575257, 564594957, 992275804, 615508440, 69168985, 120577067, 765862654, 71086923, 405080496, 697014638, 476896508, 48541057, 249449657, 109059130, 234068325, 777918536, 318250281, 668515867, 324489075, 203377855, 690478788, 48414896, 896798624, 934205294, 527083180, 19967240, 583171883, 918369363, 819672483, 358493291, 453854988, 117972180, 465492932, 312525738, 811488791, 632358119, 86322620, 870941245, 858271908, 512069254, 88719838, 461890045, 678873799, 518054745, 566476482, 488877316, 898829680, 359757875, 686565199, 531023809, 346255240, 325387709, 198185928, 690043611, 143157012, 749315124, 308656420, 996630146, 751775982, 222484626, 701324390, 893533478, 316882420, 841085329, 792348600, 31630570, 567376107, 992900666, 447869998, 945414325, 54389361, 430734781, 98328184, 844206469, 117492922, 894922857, 653349827, 688289586, 486483284, 251262266, 741284960, 314677488, 408682623, 581406297, 788146615, 48945002, 765766716, 23828317, 986203394, 682727684, 545775829, 252319066, 219490471, 431711924, 755953620, 453219050, 154417415, 428246411, 218352316, 125436045, 980771326, 505632672, 767626306, 229184574, 144857985, 630715132, 511520827, 870113844, 540324044, 678206237, 837809092, 955734705, 359408462, 559122099, 114685320, 340589708, 282268696, 508787725, 629716213, 671232831, 49243774, 967039315, 215637326, 609475235, 10243392, 940748240, 894426772, 304457076, 328830672, 492931423, 901368445, 151571795, 487192272, 949489840, 797466733, 714710343, 897994903, 287135958, 182480836, 923571816, 301667295, 832476579, 397954622, 328014811, 214038145, 698048217, 469661597, 545625780, 663655338, 858681566, 259339804, 188672166, 821037807, 25872947, 402790885, 158197111, 384948467, 298396262, 477222523, 293945604, 665086750, 851460726, 56636755, 667380456, 57188820, 210732531, 486550778, 419915323, 240303926, 23630512, 299422738, 800097807, 478241078, 963993601, 273602908, 641591590, 349471360, 964282311, 74358400, 386170037, 824125364, 773662415, 537478369, 378280544, 63291752, 922520868, 561357961, 138093185, 184265406, 802391674, 809124250, 879081738, 647734877, 84449789, 875366471, 849775255, 382689894, 204373232, 387617615, 815425141, 611631736, 451615907, 793083510, 451434525, 738293984, 616472990, 447558286, 852566587, 136077869, 379093094, 905342363, 738277024, 698799019, 527316376, 5868629, 238911954, 997131559, 511249423, 897470790, 268776693, 632161764, 531886372, 616724378, 518931582, 619287835, 414464777, 687092653, 331677163, 107030779, 221372163, 436262151, 648357956, 734396555, 786174413, 164193904, 83432832, 393251704, 291570440, 29341594, 349759615, 158787991, 681462516, 17777279, 713636711, 640333409, 72599365, 858582337, 92447554, 242988573, 839906184, 246050315, 50651929, 333823441, 162443065, 717733015, 913440927, 422446959, 209898877, 121642692, 50006143, 525276255, 94577289, 692126741, 141507618, 118494081, 321661375, 573222190, 130321584, 308431563, 695805552, 116207867, 295262696, 285782111, 321852958, 851707292, 57421353, 844915575, 251641939, 820878845, 980577190, 281217880, 334543801, 479206803, 116026319, 635307962, 888493697, 89134676, 350333889, 787549303, 489754643, 635175331, 726554305, 783109485, 112272368, 558787716, 632927853, 406333612, 616352908, 51809632, 875259879, 567670528, 289049204, 945546262, 446232889, 366031234, 215160861, 436697956, 796180636, 372796863, 210417841, 984337743, 124520686, 832646214, 359769052, 377317107, 78108820, 258599679, 836000106, 351792508, 178248976, 542900882, 826632908, 214865985, 951682117, 140237374, 454521503, 88078955, 339956843, 644070252, 226657256, 726476916, 468045640, 445370885, 264161397, 148430834, 938789752, 41222708, 747215452, 365214165, 33116692, 348530957, 969051902, 584939523, 446648670, 896659231, 796775601, 732394999, 475270125, 539487481, 630616118, 575010796, 670413475, 35002603, 873673472, 469442782, 883822417, 977170693, 480729563, 692148571, 390662082, 710022569, 597118639, 914370641, 130391150, 792544525, 548121259, 561035102, 881310800, 453431325, 721931108, 106744140, 982819957, 725950652, 438943355, 748822162, 518879312, 109720993, 179005529, 150556388, 610719774, 877801769, 477398369, 61833173, 154490860, 847453453, 250132762, 953129893, 745283703, 866175637, 874677019, 58394737, 410997816, 670937893, 539892352, 849739237, 974062674, 243669966, 947196378, 136467250, 725988747, 630582129, 486687064, 146989127, 388011755, 357755018, 174107328, 641112244, 833007077, 466183865, 99264668, 670349335, 353178789, 861021457, 453316276, 829970977, 821757544, 171187561, 859699318, 141825957, 106304551, 927508182, 881869604, 277433610, 549236670, 67579061, 9237389, 409461538, 39785553, 966297657, 194012775, 790034277, 951968674, 908773677, 875566871, 260660169, 769747642, 419062320, 205934741, 780367527, 548117470, 64381728, 939421979, 880166339, 543205608, 537552440, 704736438, 861610115, 70055874, 657018423, 968630031, 264205735, 703292038, 804234175, 502221767, 230004899, 883929189, 14269650, 490325416, 71643182, 671290381, 464888556, 809922007, 712804437, 134767271, 130969749, 976982717, 711386204, 647678774, 936065166, 328979996, 768434817, 290102761, 279880155, 344804986, 352131813, 47090373, 426072292, 723946062, 337370317, 336875297, 517315838, 745134340, 451208745, 14623203, 924286100, 528693478, 307040209, 208266460, 894663969, 882841154, 185000, 649164608, 68395906, 498904449, 328551729, 436642469, 83058822, 900073364, 875582142, 608772040, 33977429, 715282614, 693803172, 458795007, 980124967, 390872989, 646580152, 399799227, 926617810, 394687877, 71978103, 339206413, 965461138, 827910615, 83790989, 435860442, 764261368, 692318236, 980899608, 698224574, 202213961, 279286679, 153912774, 457188709, 461327282, 850798792, 490810956, 486699425, 400260186, 918677838, 484358228, 506875114, 410581814, 427603041, 136505370, 413103429, 521641562, 394073512, 899590667, 201725372, 260839265, 116296676, 560481190, 430582161, 82282548, 291854425, 488565664, 658889107, 541211253, 758016614, 787167629, 298099483, 392676407, 698445430, 939481535, 655969636, 830527097, 824333054, 676973490, 225952389, 236162608, 610950301, 258289221, 454972749, 43994440, 308003207, 81034996, 403410699, 190565915, 140439398, 743742019, 789961729, 571437264, 394067429, 562890673, 867357559, 411430138, 36422795, 388507599, 75494182, 364933279, 792567993, 414637250, 489673336, 55221350, 335595444, 695995542, 93799501, 245697565, 564729842, 207845377, 174582393, 390853133, 506189950, 200157017, 854683989, 770758548, 661140915, 141302566, 873159184, 938195143, 867253797, 995458376, 206322544, 271805449, 911573739, 462646088, 439018558, 154921026, 396089545, 997541622, 887311338, 616569491, 878314431, 803023424, 817361848, 433852651, 554981245, 207675896, 846267735, 687865918, 261321613, 2368798, 686176700, 126635608, 298869237, 202322866, 641259484, 577544678, 80355882, 113325686, 669796089, 708280381, 724192152, 544033130, 551908870, 708244939, 762340612, 711449427, 368156244, 697774627, 439927818, 917309475, 871902410, 695136039, 521719784, 444839818, 158751498, 959632931, 166501384, 253243174, 787578371, 101948274, 883662886, 713199306, 634700981, 739918004, 809191894, 877218671, 969321511, 858172095, 96716182, 376873691, 120013387, 125285645, 122771944, 515154773, 583695873, 528698342, 520648734, 428099043, 976811589, 57858585, 594899677, 275811389, 522811670, 139006942, 703471621, 984789107, 31335349, 302908377, 136197938, 468423344, 489549258, 515167902, 56129107, 179448952, 418432259, 626664459, 746645409, 870113473, 955019109, 867431079, 61037253, 666097, 497193421, 862173843, 958659612, 266550821, 44029458, 666316265, 683426848, 34149347, 849735748, 100927156, 654882845, 501297065, 281759887, 748103237, 526683774, 9848113, 741929527, 294586682, 336438984, 788095492, 518017419, 313460728, 564231359, 905574406, 5852042, 244004409, 350262929, 78824467, 899975870, 759655919, 134049, 630119685, 8160909, 612455000, 989118642, 170976548, 276012731, 588944799, 197980588, 250716006, 644444077, 837863951, 698999420, 327762042, 910203537, 892514955, 651400185, 499294836, 969724543, 788067056, 17160687, 673437936, 384269872, 113164905, 82764017, 241560376, 554807941, 857348886, 212954356, 834960150, 698759032, 119892666, 187794802, 780992823, 435109227, 705670398, 646620350, 48196721, 591015070, 588295232, 411042420, 516805173, 77709273, 382340624, 383470750, 831986513, 567500038, 782206695, 742036061, 794324297, 908211104, 551460893, 503352783, 151254717, 908780216, 120171542, 416310993, 563933836, 46729600, 614585035, 767799943, 752202444, 265613548, 140024276, 58845724, 988711534, 297255506, 152270219, 871461878, 972643192, 92668224, 191540415, 512002789, 796717885, 406003085, 755707395, 342071204, 370710817, 993116315, 868716925, 448779995, 620512803, 64228258, 71630556, 943449768, 329547078, 457503258, 935969935, 253665803, 613519402, 840110889, 113468385, 659112110, 533546573, 61563036, 961471464, 289904288, 606010646, 310161986, 14301645, 732621963, 365023818, 550212203, 62930503, 665142933, 442517212, 607959346, 613919865, 865478403, 119287969, 978884858, 984125118, 670911283, 924037537, 290461766, 931252613, 774153612, 164651033, 312457557, 7493322, 518638513, 336576822, 298973176, 464685346, 330922761, 813116510, 341886193, 880016268, 225742451, 288438745, 806351469, 312574536, 292497438, 481055502, 585077658, 867683979, 556796078, 564092927, 912198094, 787793801, 374775117, 590016273, 313289688, 148220487, 366887498, 991223575, 204265874, 105054964, 131056174, 564795594, 654714521, 689061856, 523802137, 60263805, 871319324, 215589209, 918494471, 152161661, 325701228, 730832333, 651247711, 682890800, 735500640, 245387261, 414828977, 81831791, 588051996, 279811467, 227205407, 770326136, 956707683, 427375853, 70524717, 991763086, 817212273, 74164850, 108528359, 574748212, 525366376, 462523767, 853804914, 929664811, 736007585, 775105889, 798916056, 85918183, 222315584, 299842391, 280748122, 287224147, 990374677, 867055420, 120000187, 355608742, 432713360, 151950667, 477931850, 127403389, 542381941, 585240774, 16650019, 654756268, 681542107, 34811089, 214782242, 234058893, 234356319, 64517765, 944462474, 302143150, 462114370, 479542001, 188819913, 184127203, 887291003, 718378315, 643536124, 259734317, 827561494, 872538978, 353183949, 161623691, 102756128, 753515534, 329461311, 823120095, 135934229, 201375864, 383021525, 194040277, 216614649, 946099241, 264797100, 190960707, 223418844, 228182335, 30138704, 223610366, 138886821, 75310432, 715252806, 622260859, 23042896, 770154538, 648221224, 637634772, 51925893, 511628041, 81957314, 404744558, 513003883, 27471648, 176038264, 558817276, 333948035, 319444145, 586874352, 117197325, 188967222, 362024858, 942773294, 484065607, 88500005, 756728682, 375031706, 235698849, 185825092, 199049959, 196286632, 796692347, 562345240, 600683449, 594337541, 787258797, 319520273, 751645675, 80254051, 753229592, 854489774, 345104338, 696434438, 266966329, 621924764, 119527405, 156543811, 936041503, 310163574, 73877937, 898892833, 804361278, 267244316, 614586421, 922316934, 538860009, 690159364, 432341414, 664133854, 639074139, 87208987, 147752944, 557781281, 128561881, 791106726, 416833920, 442209625, 981920280, 438440944, 824075630, 905544315, 229980028, 43733191, 80119558, 818860353, 226245768, 445398162, 212434291, 81935308, 545531889, 558505829, 976419137, 485205315, 994033595, 585948920, 255229329, 793770164, 769496953, 560305911, 286500165, 383296943, 431561335, 926890544, 396360269, 491278399, 425454755, 507599148, 979669722, 720290021, 571598612, 698931394, 28777094, 525716915, 322089724, 66041399, 312412249, 892747252, 567646180, 515517664, 627571675, 502194913, 803104722, 97575557, 604569307, 418386470, 768105116, 226383652, 170470854, 340834738, 657726565, 737845051, 523663461, 555009966, 981523814, 977927693, 556540453, 997527524, 399875247, 893245373, 241802741, 63977082, 927267806, 133694162, 444561624, 141580589, 200140873, 196790218, 860701813, 539439004, 618087044, 487636656, 652288073, 295389584, 203343866, 222884152, 379167721, 847556408, 445651708, 289180830, 314182806, 855223017, 347291488, 241975711, 130836759, 864434026, 634889302, 631657921, 351684752, 278168026, 551680021, 611258437, 201465289, 5061884, 888525616, 863577101, 465017985, 622158224, 834860677, 742033437, 656003880, 506678740, 659416061, 536744113, 858777829, 993406364, 30894515, 915572836, 195105573, 115673023, 706075718, 990008447, 190922885, 403827450, 979457506, 183858071, 546954857, 522462697, 142698214, 905853950, 448449333, 941072662, 645491414, 406746532, 552570151, 897237714, 844537121, 815660114, 835923265, 131215691, 835200823, 610178765, 440180545, 408432415, 3123545, 395159964, 334811550, 284494629, 784632692, 451828602, 245413140, 80606073, 514754508, 795836874, 318295323, 570081736, 719258900, 531638613, 212981285, 41585219, 202125496, 425718317, 247294723, 991208406, 372040176, 796171620, 629262462, 102551491, 143380212, 422111748, 182624283, 725191257, 649562112, 894653663, 133503367, 798522633, 87933564, 550836695, 973881892, 668121784, 879321272, 214908517, 727109895, 311275136, 496357566, 441878259, 204165776, 942216660, 420837813, 160421053, 480152821, 590659852, 464255119, 288415634, 579462114, 128712712, 296312789, 873891420, 250801517, 996135421, 840927325, 500887517, 555826380, 421929316, 38796324, 103266068, 173100598, 309207620, 893200443, 881804487, 148743091, 673408222, 248286473, 464999585, 807901618, 744565992, 300898244, 118447985, 207837264, 305587835, 194730434, 166136475, 234421928, 311029981, 990239407, 922046914, 420530764, 310232013, 509728992, 166407324, 726471391, 747742456, 887991168, 159356301, 980126216, 502169908, 915018658, 859943693, 565214907, 57082173, 39461286, 921392771, 787414391, 376300030, 603477517, 228696061, 427531997, 603459092, 108682151, 718153140, 556543412, 975078902, 274306937, 921751518, 478351759, 356596175, 135775623, 922948359, 130127537, 573909829, 232365453, 505568543, 442376509, 443740150, 353616801, 462019032, 385104242, 455843006, 67959049, 573358771, 697090904, 376074599, 120197769, 558002231, 739839377, 190298538, 905007303, 474456386, 383855983, 430933050, 748746897, 486119984, 852663373, 959006774, 235108847, 376788095, 725573785, 874706880, 575421342, 781440594, 410909915, 833352773, 527705472, 966516987, 22476808, 828226136, 116301802, 316145525, 708309758, 473966033, 449985717, 788267013, 720344897, 343610455, 828022308, 488834778, 993052241, 215601618, 811436198, 211926867, 778097566, 460452183, 989454209, 209113451, 601607303, 360422605, 223286571, 494507582, 148412047, 728674780, 528369404, 347978212, 684698949, 724508258, 369459186, 165071225, 178329823, 249469793, 904432388, 344331923, 620468538, 990444619, 551907382, 621909250, 746735792, 195319049, 73987852, 103451434, 560600093, 203638306, 381772652, 848384339, 771458654, 523640403, 157083366, 91087553, 370478429, 222944228, 997355562, 869150802, 131694478, 912903348, 816685185, 525175263, 396770730, 434342715, 939569049, 311995941, 607630478, 35894689, 562825193, 33702850, 407551042, 939617935, 591663722, 518138826, 514443915, 791563576, 94362244, 693799741, 490189584, 643559724, 150059756, 633034642, 785582208, 812744427, 218063440, 686600436, 246124816, 983833952, 770752429, 602123667, 672399540, 924092390, 796326064, 535579117, 723104089, 909692145, 337277671, 724969140, 774156573, 862598375, 632922300, 423925502, 901748976, 860652277, 949321906, 976308754, 583731353, 577839210, 30044069, 824827878, 36554607, 60444606, 463552043, 965794429, 752008770, 668651304, 160465421, 110626745, 672230283, 811048703, 255466575, 269979851, 459698680, 342383865, 467607684, 250270471, 463009319, 641089221, 285695292, 586153155, 342877112, 966383921, 760180104, 327381542, 222265380, 374134167, 100931348, 389846853, 342209364, 394053516, 822420121, 808305787, 48611176, 573424516, 656358206, 975771360, 113493525, 394617940, 298897863, 193655083, 802030347, 86953560, 765616952, 170035526, 216199752, 366767394, 735162484, 498764369, 692741582, 333799477, 155128159, 361213079, 514434335, 740036478, 453824414, 817912568, 14116159, 905164571, 97305792, 191916904, 96205568, 332744325, 873891378, 509859485, 347279198, 503356900, 482980639, 421161186, 209858076, 23836983, 745529538, 753562379, 577054614, 14001392, 838923620, 78943443, 923142415, 28454503, 933303207, 64340461, 260294216, 499498862, 182133839, 604834696, 145606963, 119319308, 12840513, 326217060, 838097677, 472627399, 968601950, 213332143, 1031338, 909973706, 324345980, 100185563, 263466292, 421910923, 975424190, 531697825, 910027385, 791294096, 350232308, 84073173, 23688882, 454890865, 880495245, 468576597, 964679829, 713846385, 142678009, 757661798, 440536610, 112305044, 168904505, 546563796, 58697306, 916987580, 953537679, 634539001, 428803569, 376650722, 220787901, 803453670, 176020151, 184007010, 905088496, 655641135, 732069654, 445084845, 545522783, 66141946, 595067682, 701511037, 949110952, 576546579, 721269125, 393610081, 718865298, 393941482, 822210514, 766912390, 562999426, 495030551, 561101647, 482163590, 267790590, 802943767, 92301212, 5553781, 605141630, 281531396, 744345578, 598880358, 248850979, 987060421, 724385640, 167637880, 825117243, 534594537, 41573046, 72997995, 599555827, 528524264, 937707769, 259076091, 310115660, 434743349, 980459912, 908767094, 525097747, 694400266, 864517764, 205056364, 53763884, 961522810, 408868334, 469810017, 326782552, 530136150, 871940779, 420326193, 385313470, 985462956, 56178572, 677372424, 106895277, 741534248, 933745277, 276769117, 697550168, 8705251, 36256069, 430853057, 293895936, 850973569, 786721882, 752552786, 322389464, 665411182, 98676330, 87931337, 774327086, 395157827, 663777575, 353963061, 698416219, 987661333, 643077529, 11051871, 810441145, 641822087, 756081999, 183601294, 924066549, 635129994, 567140240, 356543288, 907048761, 45507914, 910529182, 46871280, 657323535, 589850454, 819673036, 585922154, 73056658, 223634974, 590865099, 759566851, 16855794, 806167489, 868896055, 304499151, 706057902, 825093668, 580264583, 244998738, 179290452, 704809304, 553262699, 500064317, 80086986, 260498288, 556511943, 618527511, 41476427, 428413437, 359722304, 462945989, 20204764, 504858334, 990430260, 717190806, 783094279, 42962432, 114190534, 560145583, 168136961, 887306072, 501885621, 258543354, 430716101, 737399669, 224473585, 18675952, 351404724, 621627237, 557465953, 581597886, 345400580, 373828081, 766616635, 163291809, 100269842, 606350377, 742119450, 277895340, 82955010, 928275035, 817139723, 769300984, 13237186, 693196394, 609625651, 685730197, 540906268, 30571632, 715132869, 847385914, 353064245, 733360931, 577393920, 576858242, 876418258, 747930248, 624804357, 470868818, 19550358, 714610524, 241764443, 913696270, 313537794, 130484049, 2461707, 388105589, 166811131, 894941419, 832486266, 480341464, 267869933, 741127585, 383731642, 79955759, 796489872, 574817151, 958007271, 23471924, 994333833, 712723705, 591431383, 857933701, 973676107, 355349259, 576570837, 165346149, 798078323, 788360891, 46696095, 373947517, 657398632, 786317630, 592062683, 131700362, 292103212, 743912329, 411734739, 19207201, 621407989, 44116030, 396585622, 603388568, 853123208, 901743622, 706085741, 911333189, 316827302, 323366998, 469643388, 887248695, 784382323, 384663829, 521807597, 836979392, 117093622, 748824813, 544145601, 815535295, 68127212, 421268632, 279879272, 141633012, 957076464, 841246653, 249119114, 275867219, 944500270, 451130246, 556425779, 13761772, 995531386, 230115969, 862260793, 605334968, 594074526, 193199714, 97674397, 73584900, 550469740, 831441516, 803645407, 662942140, 685625419, 75495465, 103125308, 743583053, 589484153, 274061765, 40914801, 403132274, 743544810, 832688790, 534784867, 546593890, 170254689, 712459911, 679216993, 530614817, 537458880, 64888747, 144087707, 156636909, 549930109, 115895527, 597974286, 437277850, 925282841, 618665134, 976797239, 175849272, 127362360, 449471811, 596324607, 629484928, 769044079, 656691913, 186531666, 553204825, 724794620, 224249720, 615840103, 422627959, 899934484, 895970742, 123468623, 168609613, 93322040, 645033791, 954142882, 501047160, 289069746, 502561241, 633777628, 43957037, 644216270, 857768128, 339644100, 108731716, 529242913, 219722171, 35623086, 281604522, 14195158, 821043966, 22626471, 620803145, 318832456, 995612674, 735263292, 936459722, 32647989, 326123794, 495601260, 37201226, 916153487, 588730560, 438780034, 294324195, 334128438, 658896087, 577713922, 79658179, 28963890, 351298708, 729359208, 795696738, 956001577, 166208348, 316590368, 184203030, 723957102, 945788551, 324117786, 82534727, 871196758, 887251574, 65595789, 30087081, 915516030, 415221412, 840905030, 374228350, 524699251, 122863922, 144706718, 810208642, 881218632, 373971307, 246231126, 685144939, 696278147, 758870545, 127589372, 441681080, 504119125, 824098241, 153894831, 955413424, 243693367, 214043292, 170468193, 431455351, 83839152, 143529267, 505038102, 319863139, 93588900, 418713170, 420689280, 470806336, 834202089, 614434733, 436579816, 514856697, 60595735, 761086450, 222878150, 707239958, 501657058, 858584652, 715468986, 630663112, 578090410, 522503933, 882652326, 654728655, 171596811, 410314168, 90621233, 829398471, 707334006, 733750767, 776178113, 954070042, 483049852, 606442695, 517297592, 479191539, 423569402, 602965694, 255067162, 453867808, 398753127, 708225863, 18298066, 785586804, 573285719, 144809480, 989478298, 932633534, 584408126, 308940619, 488855507, 178921962, 318219432, 379968826, 562743040, 798895176, 71038953, 547850168, 917371787, 709116901, 709965886, 691012579, 267545339, 33147696, 620762441, 503374922, 516804651, 847549505, 820268989, 865886788, 390039174, 58862761, 225385255, 663771707, 894056831, 435912790, 715442868, 104814490, 512929795, 856595274, 849518849, 53473436, 428482224, 563444968, 305045301, 40853170, 518349783, 831778874, 32343480, 902157167, 780418526, 716566648, 548691763, 38149122, 692745099, 537012534, 714622255, 575777921, 484285379, 162625201, 175820444, 715034832, 941355210, 780634075, 291570049, 604297789, 799972966, 596572304, 596643028, 774688640, 966964661, 227783463, 734590472, 679856115, 923787314, 954729920, 436973715, 32440427, 616980063, 988311649, 997186968, 961339736, 834027909, 970995116, 882154983, 679237532, 431767819, 867598802, 907655244, 869279418, 17684607, 964554873, 482850949, 550510173, 791768728, 331723339, 383208571, 510834895, 677196938, 186903649, 598595288, 127643717, 66686794, 706904974, 309699391, 627812018, 822994726, 475866634, 366194956, 662806203, 932061218, 789205444, 258752437, 422091703, 443053581, 938249671, 305260544, 781020582, 39584543, 970248436, 674328633, 696582571, 354788143, 132009027, 452411899, 480510711, 875515461, 18755791, 11961363, 943381430, 145135871, 731170107, 582322312, 18679917, 525851987, 944054187, 456965290, 866509219, 193822925, 554584184, 640447947, 863080234, 686452534, 592227542, 386440491, 785330396, 744688032, 133498459, 286416202, 505995388, 696573091, 997942145, 804677913, 362933227, 82180423, 825502166, 952340648, 444928607, 265677346, 749413198, 275636506, 697090928, 367880395, 642680746, 715996316, 812330354, 776452449, 182113033, 224471470, 74832410, 841895336, 33462630, 762956047, 419695294, 869532494, 341017055, 845663661, 459420846, 582813197, 541125753, 983279426, 808899774, 146928896, 669814011, 314380287, 608348135, 10237870, 888875235, 542813507, 971184370, 421045350, 934617971, 231759297, 591684243, 952636234, 441700498, 271806324, 311722924, 828521094, 397699849, 574808113, 841888142, 505776422, 92273246, 576839059, 524810495, 443075468, 254176841, 200416593, 875919749, 708643668, 455443988, 486184937, 895158014, 63402914, 313797569, 794470542, 291532503, 497606235, 48355066, 253443991, 419990327, 128482532, 859067600, 843487565, 692454268, 241040336, 319306966, 286324017, 212675458, 692290631, 989417107, 590992280, 28957403, 269831872, 190696492, 815743348, 944421689, 835227500, 549576327, 259469658, 396945859, 363982904, 21921238, 256072278, 177189775, 141590882, 84348354, 811978729, 537589198, 755864719, 132164921, 427107814, 408883208, 896266309, 916027467, 864097735, 696826014, 60900674, 565327549, 159054580, 797820193, 820920622, 586744251, 717079119, 65950104, 938612875, 896745135, 649850493, 563864516, 473672218, 634451754, 596939797, 32201226, 133477271, 67211861, 995950611, 793219763, 247221945, 653756839, 523463421, 758308743, 672578967, 245165614, 881555555, 909526053, 625711230, 239767744, 385358175, 220486380, 953867754, 103033331, 468781557, 539015205, 31299743, 46968776, 182979872, 880566641, 8670329, 763179740, 761017700, 900356969, 633046750, 774220345, 439707016, 2606001, 857283439, 633650976, 455989116, 891861959, 897572711, 91660134, 398789764, 532120950, 482896198, 292459848, 959755591, 635083451, 660968332, 732068317, 611067801, 315389860, 786300142, 37624061, 121875502, 75038156, 933292784, 794245042, 797109451, 249398574, 865136251, 960702635, 978509845, 923247172, 338079765, 686029797, 123798724, 786672784, 851876157, 73378865, 837310889, 157553313, 362332229, 105631390, 313500692, 95198419, 278404185, 524227195, 73148658, 223523789, 393019304, 662925727, 891530593, 6271687, 52416602, 164651235, 208702522, 997072644, 617368910, 912942607, 227080012, 542456292, 861084802, 697723621, 919574479, 207611077, 102525334, 527178301, 132170805, 931141777, 513159321, 92037341, 357125035, 262733308, 329761737, 585043001, 510266079, 403638808, 740672915, 825468753, 285192631, 348732237, 802973709, 61687018, 296666524, 307148974, 745433569, 826816159, 242727078, 739837159, 273280395, 963711221, 824612362, 529359533, 340964967, 514938958, 11525440, 46692389, 228819148, 851873033, 937657613, 143978910, 506842868, 777505579, 995103027, 669939585, 891716765, 55346854, 505476011, 179691166, 858909551, 281294474, 466792227, 832123797, 714726715, 455237362, 819303567, 697039898, 701987141, 403150077, 886092731, 630121151, 280163631, 846509578, 666576679, 90687164, 171373778, 596332488, 511710820, 70394407, 47223887, 422723860, 298972537, 17516502, 559134259, 17051906, 481712868, 798552478, 386650427, 126579217, 165777266, 165283399, 950743875, 688596062, 619122530, 930709989, 463723321, 393661202, 506329356, 634855795, 842927790, 597857334, 84623507, 504009910, 263460359, 552054820, 508384079, 42298726, 130642724, 971629800, 129875032, 94845143, 739544305, 815547444, 132679593, 6545091, 819452375, 148188563, 277410539, 201865146, 617895305, 977238116, 913462161, 727121396, 302997830, 10342127, 638323358, 999564984, 575863822, 180667057, 927429113, 177266651, 903652011, 617517398, 149720318, 454394113, 185916093, 436213556, 432812764, 378465180, 346855016, 466063160, 724105231, 856243422, 624887751, 250847689, 296087543, 452854039, 567596221, 92180627, 722401391, 891323517, 801128723, 562930330, 508760141, 996107601, 433558301, 913966850, 527099038, 286869537, 475509486, 593212950, 963604264, 668067319, 659187974, 919290723, 618692512, 738523806, 952015492, 786424594, 959664470, 177429765, 471038080, 191276622, 498121112, 936713019, 249263706, 384235162, 928013136, 711060703, 574455939, 401413062, 553885929, 206375507, 230646713, 142107202, 46558421, 70330498, 847643224, 640263681, 58505404, 978516334, 540215205, 453943328, 326691905, 684621505, 758197436, 20760254, 60668035, 337819554, 611321541, 598494500, 143070248, 220089497, 848955203, 851145743, 653808381, 191514210, 252235543, 301627583, 465885744, 176998772, 753382691, 863214929, 961044513, 565587163, 460980485, 862044715, 231127354, 820284454, 972578003, 524911721, 517139010, 28003965, 313168607, 698887819, 242471261, 449511518, 433590325, 388397225, 210823581, 721215910, 823941752, 242674435, 177952867, 167260843, 525842138, 46462419, 219898214, 843613698, 284858061, 659283017, 742560722, 560834877, 328542526, 680518026, 505762508, 422607245, 237722487, 926773816, 438654285, 490373407, 446114022, 350724871, 240542708, 481869719, 148543694, 354337245, 339263911, 25181623, 270887321, 741696948, 979309487, 535485940, 811272934, 411103473, 763667233, 662473138, 479560604, 916105154, 146230766, 138623105, 836917208, 266039941, 235413334, 689557929, 879026792, 532881507, 632652386, 227796735, 958491407, 478864730, 255360237, 111807955, 926989165, 257058989, 344561954, 872013702, 271064211, 482220150, 877275946, 741509238, 439931209, 567456313, 239649979, 880519186, 350986401, 267698943, 338211764, 28123817, 785591708, 173328480, 585576186, 144055230, 738997529, 777213034, 175154512, 753399722, 793122523, 228185214, 803363159, 305134644, 694905073, 360406564, 712060615, 623704621, 94010043, 128040314, 851800585, 443887001, 380328962, 882846827, 140632337, 865584720, 220099994, 868525367, 314280131, 68782084, 272785375, 329179233, 33527119, 962417008, 391121700, 738476463, 673941135, 929470566, 158041553, 326608049, 92883920, 638329313, 845555412, 2281092, 963572684, 62445101, 596705963, 670233830, 714103969, 175122830, 348272024, 407412557, 297688938, 786289918, 848554597, 538520339, 638957590, 218571268, 989476359, 680767528, 497917129, 9476402, 63514188, 118764486, 964464994, 182497204, 602965468, 572018795, 947505666, 60222758, 937873316, 732225920, 20850828, 453043515, 342493546, 290056290, 501504382, 836546573, 914993818, 167062284, 457262075, 874557897, 745773189, 863047340, 959202182, 642815699, 656422959, 157591115, 844881584, 368810572, 276469731, 647635308, 927267919, 284931744, 633102944, 990995978, 849154848, 434017103, 297038771, 327672846, 212873360, 487895695, 145570194, 963480621, 276328891, 804561500, 450063565, 63775092, 16924472, 988827359, 998929640, 34414420, 798775052, 665084251, 944086443, 517122448, 60965326, 757994380, 632740318, 191154307, 896347588, 398125920, 615564607, 403425390, 250081188, 96679840, 611319720, 710726878, 465209347, 188255656, 778229292, 188333974, 749107859, 385423920, 111358579, 185353767, 890724369, 810637690, 518273282, 867620643, 989670146, 601026752, 811144179, 655130693, 381895555, 357339759, 571579636, 657244976, 286901741, 435634115, 860075854, 595088398, 229965948, 301962378, 413309019, 576462598, 318206998, 513674460, 833512692, 664078910, 622585442, 491585871, 168600186, 730667359, 978162616, 843118556, 23384078, 724959737, 715035103, 955705741, 831707763, 965919208, 186158468, 9816410, 397016115, 836797719, 974849810, 59961420, 576850490, 944187279, 447446653, 627248378, 960919126, 650315795, 260791912, 532683515, 250938939, 84792923, 909319180, 568206382, 422490397, 216765251, 530021093, 152977311, 333658907, 429338919, 558217898, 478185730, 121662870, 176660003, 61781447, 792801324, 155414489, 745455745, 937632678, 396082034, 528308821, 180416977, 957060835, 438793069, 129818474, 950095031, 50899182, 402166238, 867000431, 906387687, 391101017, 324772414, 735865813, 195571806, 329323320, 51502144, 689600607, 233865211, 43937685, 447283388, 855818272, 553425049, 86245357, 762735997, 454037400, 764907106, 457785678, 217068863, 385920553, 359276581, 381741765, 210224630, 559994260, 988725581, 999772236, 744832347, 210719232, 419294917, 408766542, 161714693, 727790356, 522344652, 612764234, 208540141, 993172518, 876987802, 641191375, 683674814, 76774674, 843107917, 777156497, 720727311, 46254728, 774831828, 620736516, 957496346, 868021230, 6993867, 111096123, 574976955, 747671267, 334586002, 690797108, 821872809, 375118745, 182114406, 295182796, 573542250, 586622478, 3428465, 687357087, 715031463, 865464969, 614559878, 959442094, 607513334, 578501378, 593465620, 207698476, 986424439, 274707737, 192059777, 211396662, 60040866, 572724488, 548632673, 778799918, 601750069, 544070880, 794803337, 824982967, 16079929, 236366646, 684349359, 844358099, 673069415, 565902709, 26582, 615616214, 458608204, 681650073, 360465904, 22226796, 37859853, 548143664, 173424794, 198975148, 929010525, 554990953, 720635670, 868142197, 284709568, 647893028, 158006488, 848149672, 189359470, 759944935, 129099863, 819182966, 450507859, 763989283, 235160654, 339835891, 358494965, 723881525, 936623802, 908912282, 57352204, 51107708, 311240699, 622104104, 286400916, 945839705, 586968463, 733745211, 592498446, 952488422, 950060735, 754528437, 776444951, 824976236, 505637947, 236409411, 829265041, 937680759, 684758410, 923380803, 644160902, 349344434, 681365493, 82141728, 636014958, 82178390, 969797476, 332087198, 874183371, 114705507, 735406922, 522941251, 240045190, 997946497, 140068481, 331916200, 392240168, 415411695, 982186394, 896927237, 651078468, 148046136, 203543286, 585767409, 524163249, 677142270, 324511298, 348203185, 118598354, 946441139, 398542799, 989374463, 965564599, 866419770, 206052059, 627647678, 243870403, 652210871, 28574570, 522048140, 274035280, 881447427, 168942174, 725482392, 988023873, 562941580, 184291914, 943641456, 687740152, 575153619, 665615961, 947359418, 48153152, 716340878, 339108019, 612116646, 198156160, 112055436, 809402870, 49747018, 743284009, 796795079, 304422185, 751583151, 722448006, 256687937, 749913661, 768998366, 596646916, 84792344, 467327401, 100823274, 324132947, 971889735, 62196295, 765319293, 854013996, 664303873, 415421899, 175953674, 161775839, 97646127, 442867831, 204381438, 985625256, 621948436, 568918297, 546890959, 648912055, 523196421, 823718117, 646227411, 623112518, 822702068, 454834844, 239444950, 571966347, 133613103, 606320346, 299254026, 124292629, 550692081, 270491996, 349520282, 608516112, 391716889, 455124260, 191332973, 611711747, 274242854, 747853115, 979026315, 173707053, 726376032, 188940730, 578402518, 678767442, 757133650, 902038732, 564754837, 67633940, 309421199, 373273249, 108957932, 240714704, 744787812, 162499169, 671150923, 918089071, 740447953, 186451932, 199074124, 766170912, 280269459, 987438817, 651126619, 969446348, 119614097, 11168683, 794620994, 564407740, 779398988, 181967696, 872972741, 961699088, 545004117, 59615336, 274936118, 173588990, 954285611, 187306316, 260624672, 807126523, 237366064, 13573915, 426995897, 944494532, 550165688, 456379266, 330180134, 110892512, 557254473, 963033395, 630481719, 228135253, 540567870, 174744713, 513704020, 984325007, 966726940, 619345581, 68850183, 898247130, 944807156, 344204754, 227768825, 588088402, 710148754, 978668570, 857843291, 900599812, 293976014, 312926946, 719998890, 15608992, 133929029, 155428994, 14529892, 301390776, 344426066, 703699056, 926873240, 136320282, 686149592, 315283980, 978415721, 473093322, 180908671, 216153789, 240476135, 747031880, 587172235, 813985834, 431649146, 746970566, 967291123, 813071860, 288203073, 914400414, 328556367, 404224546, 458230056, 704708500, 227648838, 46278601, 379222968, 379476356, 740998338, 661977372, 210986581, 542482485, 725654715, 529532750, 800671018, 80940831, 644498458, 68095270, 885802413, 398817446, 663616723, 376475429, 262817057, 504408917, 97005695, 485985257, 39441178, 854896494, 388202204, 996636922, 687839519, 854527124, 886335339, 179815982, 536562049, 55523674, 827048568, 606073758, 833585433, 511361889, 276866070, 942248350, 895365128, 102859861, 151782370, 475487783, 724027069, 771036359, 849457215, 834879951, 815173512, 359819716, 735046168, 195700015, 569176600, 873974159, 731420067, 701801077, 890027110, 842694096, 533605573, 939472023, 647312158, 564820428, 967661975, 858341701, 564108623, 331041120, 79225851, 354880720, 638592004, 897724039, 837687018, 364845858, 14136924, 543306618, 949832120, 165903397, 144065102, 874044112, 57182165, 173275293, 406933251, 145578632, 798612284, 208397089, 733804507, 147176870, 655599778, 54059742, 245188901, 752599471, 65598468, 686524832, 670135923, 276836532, 845784355, 534212038, 422216559, 84394572, 119964324, 981734593, 939112214, 642434510, 380770438, 470325214, 426222074, 421340629, 241724775, 404048650, 765659317, 938323566, 992752637, 270519757, 381247194, 560015718, 139203506, 959632610, 258887797, 438573189, 55730354, 670726647, 875271930, 699453334, 781353704, 403849105, 32496401, 276209058, 970569308, 211824363, 286392740, 325397065, 792508365, 63985444, 697632223, 974416705, 818094587, 633499021, 851334160, 672477657, 195258077, 862675759, 153823522, 87720618, 701423727, 904542902, 714879234, 853477807, 975667709, 565726160, 593854339, 796885989, 732536507, 921439345, 688158983, 987170080, 926327029, 67263255, 514783527, 490543829, 799618011, 881681404, 172869083, 876855067, 108074278, 218418084, 757927106, 20982113, 100897977, 879012091, 414805740, 755442346, 860449469, 762004263, 975624365, 288783210, 6541634, 53246734, 556658958, 164104754, 891969125, 800466303, 108669927, 259165673, 433552059, 192746305, 830096959, 654671955, 982918771, 964341797, 88671508, 217712305, 982691263, 457414543, 992292076, 102123417, 385212552, 721185342, 279300723, 500278685, 347319352, 783668988, 884142892, 208963681, 884532197, 209775970, 993778230, 548311886, 394557810, 510750393, 225688732, 855741768, 552846058, 814611355, 276236011, 474410493, 19759535, 603372591, 356212549, 441904575, 777038641, 342349871, 237937678, 597165265, 450514041, 585858959, 860855810, 724538823, 149968071, 509454947, 264484720, 604220557, 468286601, 777394297, 14861352, 828878921, 923897967, 193438964, 934032064, 355748606, 129188273, 981375131, 373887937, 186517966, 198662702, 523137767, 967331169, 687190853, 415546633, 666991781, 778861054, 982571556, 672859910, 924963660, 85583558, 257510428, 937931421, 294716809, 25487649, 947852195, 162539634, 188152704, 368736613, 294917338, 231625746, 61224604, 443278780, 517222597, 365085079, 946311894, 966915363, 579963489, 355588397, 698528158, 442267659, 23846990, 191548549, 932509565, 661806544, 718241078, 812623304, 542140603, 24994889, 539272990, 795270445, 463027442, 258795336, 946962949, 229665385, 609387587, 971758601, 457462446, 150404743, 856238463, 500132257, 384654148, 199747555, 50903735, 751796101, 985647384, 913765935, 72308861, 514075103, 719165692, 174259989, 674565724, 452660273, 533326026, 235623110, 133678296, 36125651, 26531210, 85943680, 865776574, 422209550, 243129618, 567812606, 294526276, 748404575, 156531349, 656812880, 872620709, 448138391, 472345697, 490717173, 110743805, 222782246, 793173417, 566588900, 920513639, 895056722, 648445012, 424072407, 889786778, 54659183, 256561581, 546613438, 276586405, 250605320, 230483876, 119406877, 490737124, 558814291, 927604974, 421445113, 315182902, 642472607, 431314240, 23699896, 334236846, 968611853, 697205059, 300977497, 623159360, 775088099, 309954363, 404970950, 968207551, 991475346, 772611853, 310003117, 489025443, 276736407, 686094914, 28643406, 885482701, 419487382, 536775946, 706763067, 730039214, 544538224, 445129643, 414717782, 3897523, 442550300, 701760491, 715131798, 816495476, 877723461, 676225472, 603707585, 585516994, 484132349, 791580025, 526455311, 7696013, 267919109, 195346971, 678189970, 591653300, 473219177, 473973209, 977854743, 917014092, 668079891, 687502349, 382344551, 435940291, 791300740, 935342673, 748417173, 616625818, 97879209, 30056653, 166642106, 99385462, 367027905, 239735407, 759879879, 718380231, 789154121, 655678332, 811653534, 242056784, 569603770, 36918793, 884642608, 158954178, 978315907, 526900649, 277204733, 256120710, 516556446, 797670428, 297367402, 536910377, 237855593, 355009217, 531709646, 460540858, 497816533, 129262983, 421459814, 489540984, 685561911, 739115765, 299371177, 789756326, 704386960, 249195032, 368229424, 467801864, 192381158, 565060254, 883913879, 883672427, 934024346, 398304812, 766232067, 556008749, 306822808, 179861679, 957408236, 733081961, 872576726, 226358926, 421359525, 379414339, 611480648, 627397577, 457362588, 656947033, 752923488, 923760601, 3896254, 598199559, 974660828, 25296759, 199199239, 398072544, 473960740, 927575267, 933266900, 521377907, 353788049, 643096742, 930149560, 871782633, 912982219, 135208381, 326548362, 63223845, 373338261, 347920382, 931918950, 692070268, 449899215, 664014346, 875981688, 869024829, 966041928, 836752849, 255460305, 472446698, 714329598, 639762775, 71934124, 674169149, 222124037, 530916734, 690353949, 100670593, 462430585, 535405913, 443369457, 440083612, 662800193, 882388111, 506153935, 354634355, 94848241, 231563961, 469292366, 847933802, 495019953, 309413794, 130234741, 34993419, 845567389, 536456552, 927219129, 598295891, 214593129, 338774903, 307954534, 306953366, 36740759, 774067511, 325842053, 292998719, 701794251, 334889132, 121978749, 976277828, 167539902, 438096632, 949575800, 764098192, 999579139, 247245436, 843288293, 250682224, 750565925, 110147128, 878194658, 757216726, 732846893, 504613215, 410383444, 252683051, 87588394, 508292426, 87307362, 66201768, 492695027, 367181409, 144042361, 298146325, 173455948, 330916572, 806333575, 274736030, 804018132, 753528717, 391758559, 488657855, 216704697, 381275458, 786488946, 20880087, 526194776, 81964118, 684704016, 769384800, 548293391, 960589040, 710929830, 257311972, 72292942, 965122040, 439756258, 505645264, 481482317, 540519601, 492341821, 203871534, 916431383, 73324990, 173520095, 691391288, 351400554, 378074606, 912611973, 953229924, 633675124, 883022739, 277294728, 334475036, 854469261, 467848297, 302567271, 707004421, 51066868, 425207681, 416840022, 878472344, 2777398, 860045717, 913831700, 143553382, 785930162, 203565963, 111379789, 2758463, 612947140, 655351628, 764119256, 149200508, 112969149, 210161781, 543194772, 661862461, 989948082, 385185853, 39171185, 190637546, 777807657, 658990867, 708955062, 238575975, 838715050, 61858007, 535223662, 169989225, 20845465, 451038284, 337862270, 492234482, 127766396, 344182152, 356685876, 205091577, 186638114, 611925846, 344885560, 992912101, 952382596, 718424014, 47500549, 696726124, 728237859, 108645250, 368973628, 29401928, 474214223, 878236467, 192210432, 372340686, 13166589, 990816561, 22743821, 716601912, 791075654, 643018448, 557169727, 906265262, 826082725, 492836323, 637492056, 467052106, 964781898, 418810359, 18763540, 311058951, 919532835, 992342559, 146783932, 915084197, 611057076, 746148848, 954496157, 564811042, 974888502, 524309323, 623270384, 430972267, 728827194, 766464947, 744440213, 119205447, 539185986, 829692135, 473208361, 466674087, 560111867, 595774999, 760084765, 301150563, 888186725, 307720130, 668091492, 309251028, 801500044, 542245037, 211625422, 439361449, 991411616, 202621573, 807487135, 876263661, 615379648, 453577840, 391529287, 867070064, 177059441, 814920645, 17342137, 664071384, 913418450, 852059545, 341152574, 414320956, 786292087, 411356517, 781740675, 138342248, 120071687, 912245606, 296278965, 400231629, 867820476, 743526100, 836089410, 680106387, 298698479, 848912238, 870052227, 398940233, 70401806, 610416633, 99924088, 594212029, 434746907, 895914248, 604839635, 679547258, 403103413, 298707294, 802221191, 620412997, 506742755, 774461894, 946775407, 258052605, 159605046, 676150016, 667028438, 902424050, 923826230, 99217010, 515870949, 123608603, 549852062, 195231221, 944398143, 999660113, 862256128, 820856828, 180161854, 770607775, 182607046, 594007606, 904987100, 581085105, 886604466, 324545157, 727775081, 306805336, 462161447, 228646221, 986279530, 32607224, 232090711, 525010839, 556196979, 312994534, 959294204, 699335976, 582162844, 996464764, 781239624, 807039353, 101800459, 365990466, 890348460, 500712794, 113698158, 770967178, 591255250, 267958587, 851269702, 841221733, 452852340, 823748909, 298624432, 781442171, 384063936, 440376512, 428923327, 140078901, 683025668, 72510366, 631515444, 305315733, 428350773, 151852541, 527639190, 262860023, 707021910, 717835367, 745251953, 109526920, 617531118, 580168834, 898679581, 256288989, 737149797, 191433821, 997061525, 387407746, 621121784, 571208402, 364131003, 255018243, 1327277, 310124765, 393570669, 371736809, 279263573, 544114971, 617486555, 248122038, 50705111, 437509893, 785120476, 766460233, 227999389, 823673219, 255149217, 696965731, 244720398, 97281059, 720215638, 593722332, 170683221, 189698101, 617175753, 420107315, 923417986, 644924227, 938354740, 156531768, 688815689, 285872994, 406805221, 998011254, 124879335, 116918041, 973420591, 836253971, 75614719, 591126658, 803423920, 786718098, 478795103, 55494141, 150940614, 131568387, 731833008, 194352396, 29189050, 901717700, 681423283, 355308397, 432929680, 510740651, 176032062, 848657364, 634593208, 358964074, 78501095, 640028021, 852692769, 565693768, 330252733, 980354411, 941799805, 17443174, 967821523, 835311829, 487815589, 730411552, 335090553, 584893295, 66924109, 75790067, 856994877, 840443445, 247629246, 378209947, 426891915, 870011665, 618644511, 168732837, 212501353, 238022265, 123061818, 578994711, 201056604, 417774355, 678504396, 642044247, 657385201, 753002015, 739909536, 367123451, 910301998, 252785002, 495461264, 161486101, 177661071, 539807820, 119839904, 126263955, 457400389, 374780372, 845684402, 108796520, 474396887, 581868482, 441015683, 923610150, 196909330, 881340392, 227225994, 478866618, 305408959, 363846421, 112355539, 798138344, 429816981, 950631533, 236695352, 700064984, 987295023, 692294530, 58366952, 610785944, 861397721, 363177358, 675364306, 550612156, 906344938, 386427819, 865379846, 383687260, 96216382, 768931277, 947764048, 443607320, 335370461, 422242855, 911826900, 325219798, 528482082, 856404057, 849127006, 972702133, 124639537, 3843768, 271326264, 530212171, 338610757, 609213422, 84209422, 225947972, 355104829, 192801161, 692792807, 846555078, 123694477, 453313493, 640189119, 818897383, 150453524, 272799866, 173729450, 697660939, 857266731, 413500642, 71031822, 129171662, 728581312, 253442302, 70229350, 529159278, 139675251, 616048962, 900734099, 429140719, 195312753, 99992078, 889198184, 218158445, 59866270, 371458473, 622264042, 144590642, 285597927, 683305143, 42110174, 889323383, 616825262, 886016871, 489174626, 804382191, 32820608, 749738655, 337041329, 232770356, 763662678, 22269526, 572057695, 414770610, 861588565, 107893512, 302626523, 893525063, 586593190, 562400104, 873464368, 995109713, 600450577, 324028705, 91202859, 370238860, 576180047, 312998952, 439336688, 314220545, 599016289, 6999693, 721727050, 607005024, 417102938, 633280095, 348518060, 913209609, 541838078, 383060158, 283242813, 937102655, 411210820, 213371700, 97295786, 602062723, 307252215, 8398319, 336111141, 237926819, 87110450, 427994912, 167793010, 351333104, 619212221, 577677913, 606836195, 645237113, 625147256, 376743480, 813646798, 667330376, 851289799, 758943832, 219361295, 819407350, 732779618, 81363252, 576772258, 329993913, 180848198, 91553888, 63625963, 214172969, 264195989, 881497452, 984168759, 550589641, 233201499, 32055648, 915593670, 604168232, 286896590, 773042415, 457492558, 569242148, 3248225, 422662673, 757821368, 39891644, 105425580, 425412580, 262605412, 738196844, 488470827, 35250982, 465041182, 73281404, 904000978, 510559330, 93790128, 886258845, 884289225, 706409403, 510297674, 331811207, 122642820, 619911245, 868885000, 67984188, 821948387, 715445970, 290797984, 880842994, 176498593, 438270636, 384336377, 178913124, 828723296, 349674308, 906459107, 156002701, 668583126, 555431399, 112844792, 781097042, 723440860, 197052987, 133039640, 97380952, 995553018, 294392990, 563728481, 990365273, 60008404, 700225965, 585854140, 729074988, 591259114, 549474792, 327644358, 754616035, 115266185, 315596941, 372517201, 182611489, 257490252, 316847214, 481533369, 636410870, 803689194, 810267748, 940865546, 978364694, 151250590, 27696853, 382417001, 305304219, 696955326, 575471791, 31481504, 434661164, 82512771, 451924806, 902618366, 614781116, 455617931, 794901697, 64327882, 674152198, 324574038, 20496015, 280119895, 211545242, 330298795, 592387349, 744654454, 990837085, 204102490, 148219578, 631489842, 578920760, 255889397, 321112672, 327041416, 630449030, 49101583, 261529545, 40100248, 983204245, 325735488, 212700754, 207705349, 800284037, 743178553, 611225806, 746823300, 963847405, 504353207, 985690752, 980335618, 210460611, 305360922, 258416884, 163211834, 690617776, 769618774, 293178684, 923503988, 594263833, 888466729, 259589371, 975120130, 792137257, 538293439, 775671538, 130819520, 741378310, 330320977, 667632995, 896652757, 717861610, 585850522, 878539029, 9698775, 564845449, 769087275, 663547445, 390364552, 613328815, 308444190, 957379477, 671924553, 979954504, 812919440, 279700687, 173482142, 877616361, 535094230, 826052319, 326068954, 860162628, 146194277, 756067638, 703324443, 924674724, 413448494, 889239899, 24322205, 451572795, 489259204, 981104299, 409272068, 5469368, 763137935, 23379576, 836243530, 444667610, 333453379, 912278933, 248430143, 301945018, 427844289, 913367295, 548624912, 649200087, 329856014, 44278099, 225560854, 844533654, 972216184, 622287432, 756652547, 839728781, 904384618, 317450464, 388394301, 606880841, 716698320, 97913303, 310971887, 273659494, 849229309, 878038856, 45438757, 34989637, 793564373, 975297406, 565994158, 144088897, 688627282, 182112402, 112068851, 393837157, 83731224, 178679848, 483727731, 142151965, 110465389, 633100821, 957887853, 85334267, 181424341, 467000324, 174427785, 396518750, 126220205, 987897865, 597449882, 98807653, 623699379, 766811785, 394431712, 316321399, 305201439, 721784121, 534801462, 93148354, 229482274, 798579415, 954273936, 490334782, 207763032, 526293831, 310149933, 402609555, 390423539, 459530334, 464174193, 547084687, 729863990, 784412550, 880084942, 793089188, 581117848, 824427787, 325429055, 294695607, 959721169, 808453312, 404606535, 7265470, 886244928, 849927997, 245733345, 987923682, 205871758, 87766132, 307697702, 411961006, 463328081, 847469986, 720459220, 643286281, 34991765, 337091820, 938125396, 936846527, 651891759, 549968490, 928975719, 423370864, 843838092, 881425088, 646964053, 733028774, 970344615, 398537047, 429373010, 141579888, 928517658, 866541842, 669508668, 690727414, 665087730, 2536203, 188696289, 801954027, 677182897, 828364415, 448066097, 53171218, 34714548, 870299358, 220635737, 902732345, 807490740, 78507676, 93276777, 691646507, 56690512, 746706378, 582231818, 536036812, 602812939, 945670429, 924688836, 852373185, 505845776, 500764062, 816067098, 652866734, 982146963, 232492904, 134738984, 504806626, 252355316, 234327606, 109692319, 567543499, 887104411, 117962097, 204925416, 730274404, 987205291, 471510890, 109294472, 427349950, 48888058, 724244849, 566446121, 551555816, 806651740, 940243836, 599982214, 78565337, 654408766, 8865419, 948611951, 998104460, 690193885, 370791078, 754135119, 439219201, 918110827, 160503030, 2434335, 906748419, 893051478, 188006808, 441771043, 881689394, 132160888, 640918967, 432157524, 444798847, 759130237, 849548160, 521707343, 437597424, 131906074, 734440221, 590864327, 619896647, 611890544, 35639347, 857725122, 143302115, 752984234, 216364602, 875314397, 321396305, 259828970, 763589384, 249621789, 42225341, 733411407, 277803467, 291922254, 305790896, 992673165, 763493133, 751053310, 841107956, 658923826, 400821118, 747387476, 835284979, 467249942, 876369873, 276428369, 64382009, 488235491, 621009235, 10684792, 665294555, 766429175, 805592908, 319485843, 248076160, 124226024, 443922640, 491785047, 566337067, 828566790, 928015985, 934500634, 930351989, 909304399, 582289696, 813625927, 740062177, 915163742, 37903811, 480044412, 623487485, 791835433, 822134874, 90173890, 352225807, 497829798, 550217806, 6525888, 996925117, 106814982, 36817992, 733794929, 372642310, 622649107, 217378424, 504338438, 395706409, 521493755, 491888611, 162534305, 948887765, 337389288, 46758538, 849135060, 189293576, 281882466, 293127052, 314846906, 580050099, 191249232, 330418792, 809871921, 384314526, 725700739, 232076019, 149176200, 638125262, 660669125, 110495100, 687268726, 877939850, 210945095, 787481877, 93088319, 529510394, 188382965, 851253369, 524808944, 629460467, 772867500, 928941366, 196051360, 880729302, 15821875, 244451468, 565630405, 836320087, 508161737, 477569310, 908083951, 344935890, 832250150, 785311244, 296942051, 843013905, 134585124, 186055033, 654397895, 344957334, 639068387, 79582867, 782387990, 358042478, 101824208, 111912419, 236445751, 165199435, 155457065, 894239463, 26175244, 387806975, 497312807, 785206165, 210288457, 849691572, 568567802, 899096227, 762943387, 227345841, 998610808, 583563626, 265475103, 621468937, 751894428, 652818876, 104743101, 863972722, 196775931, 70224571, 694857452, 751642364, 501583895, 280121441, 789871348, 122038526, 535988105, 862761345, 706989481, 392233006, 605684899, 683617088, 988888797, 565875548, 218658570, 112207335, 606698136, 693044524, 368053808, 574622550, 549039243, 613252261, 450366801, 438139554, 178259435, 546506116, 647992725, 695149219, 82341830, 976149216, 926964982, 467989701, 901369496, 348798247, 573896609, 570649439, 833805585, 453470467, 745483119, 931218992, 226689802, 636241883, 555476148, 579701276, 678500755, 608449123, 309658242, 926461674, 512469690, 795031726, 932579634, 864200109, 243613487, 12548746, 651620374, 812846132, 515951474, 407972739, 225585531, 946854375, 368396715, 721432833, 761936616, 130832260, 340635616, 679606663, 495820148, 24997094, 316754956, 76372192, 834961913, 724537996, 299464743, 811532969, 721980384, 469244669, 197085555, 612888727, 556374674, 28951665, 714149575, 285066283, 368372041, 318772461, 134537650, 70527738, 921571132, 296161105, 812624917, 340802547, 769296548, 789177631, 488301703, 938949696, 633515648, 886938196, 290774943, 360727778, 797817544, 728682814, 672365205, 215871068, 744097863, 893355001, 995293230, 452979616, 987265270, 205065631, 555341421, 868683068, 11206983, 520812863, 129759233, 938458123, 800546378, 757014414, 449531419, 928215524, 212861939, 444645852, 200843368, 475001479, 323413635, 570809955, 738768295, 145193142, 712544555, 186014309, 805562653, 344484600, 476009314, 854182426, 902940376, 391825252, 725129477, 967734810, 858408932, 446827586, 581216200, 340888352, 109334539, 772178999, 97760355, 951511878, 770872102, 855374022, 942249252, 744847004, 285076179, 430289606, 141682389, 864636068, 423322044, 655182400, 830525236, 40861116, 172629427, 520444404, 440854126, 298603646, 68367260, 544940547, 788498340, 266999781, 285463348, 836338479, 239813793, 729147649, 537051304, 230808263, 863288166, 410692725, 55696351, 849068271, 592933323, 662370468, 899285251, 300697330, 57423374, 418348955, 739628058, 472940826, 342497329, 115063259, 449078222, 478895221, 739922768, 801030530, 525820313, 23977567, 92337815, 309812370, 502228877, 537763682, 544834531, 116042824, 970428234, 292814924, 210305821, 702038371, 836850412, 466270266, 316621962, 103377792, 205587427, 849573722, 244693228, 868958111, 962591796, 354138888, 686039029, 919219896, 118865500, 938036967, 321019181, 273921586, 239830907, 136863534, 564634314, 151324157, 590183942, 999183366, 740752976, 197332700, 706885983, 509555577, 915966669, 565655398, 150136428, 764399914, 607477321, 11391343, 128249430, 456999822, 241645380, 167482523, 365462989, 247194155, 551492045, 904873277, 617728156, 197762891, 217380594, 561452993, 137473364, 169086279, 337476996, 693061501, 360180309, 119838409, 481366698, 707015512, 120631739, 331554291, 406273804, 666111508, 557277921, 129633109, 736574661, 328909956, 597332740, 716809500, 561303588, 129958940, 105377347, 331737782, 745666418, 634545944, 301251189, 874162051, 626812568, 749060557, 958016962, 47531357, 688287560, 291383880, 340692367, 695785768, 791600686, 626102265, 871806652, 133892991, 121831443, 282285268, 228454818, 456812813, 764235551, 849345545, 194132675, 522970050, 362182921, 743610506, 511415210, 917302490, 718520156, 523982330, 9286665, 569087788, 416679242, 243057606, 5463906, 7816209, 186090259, 378463596, 231564929, 989529423, 59673044, 404161280, 600215449, 17668976, 150658134, 969522114, 14289574, 959854558, 264981647, 240234869, 536756689, 777842209, 892103668, 471701752, 92805982, 97156171, 248342596, 166638807, 260445854, 824555510, 571866689, 149800167, 944097016, 760401204, 419264079, 631836265, 607774087, 486598028, 841022896, 764337956, 133621717, 578647251, 163152682, 428459915, 302817304, 545279697, 716926391, 771858774, 433623282, 178216747, 635354555, 427977655, 699079488, 890039880, 826363922, 370391667, 217784805, 332997260, 679041388, 326534515, 918343912, 526824978, 59833899, 335219101, 887020708, 548767222, 285162524, 869622833, 585898575, 533768629, 575923584, 144517774, 106267107, 369664480, 57193424, 158970393, 134728345, 307360152, 143244642, 693663478, 792837897, 411196864, 892047958, 34498258, 72539237, 649175222, 223674110, 751934370, 836164831, 585430384, 271313692, 398579241, 640634216, 482688781, 463367919, 329567929, 524185061, 360751298, 818613168, 823117424, 402727611, 9616541, 833059609, 416724046, 671960272, 326148873, 372305419, 562193619, 100232318, 955731846, 23251621, 810354017, 776635376, 919845186, 560377052, 666747582, 442289933, 228356035, 108544536, 254888449, 914205818, 860803878, 481817515, 744470607, 238845749, 842853099, 868669822, 338033971, 876170440, 474122170, 373658001, 474713304, 854207836, 699860522, 453888528, 914907446, 822449499, 974399169, 425385381, 189684741, 676765173, 942922293, 371328615, 550285804, 127995943, 874077529, 152747015, 804437193, 187398020, 267726823, 877897185, 348508891, 888543956, 898396417, 317047335, 506846179, 122946239, 576107652, 295975606, 434105908, 929558752, 787778125, 362499803, 481601041, 705806442, 875547287, 95934582, 796268958, 826721099, 170130593, 105828704, 477387772, 453433754, 295674389, 347563044, 109499268, 681195106, 278301172, 515627200, 271913801, 499501287, 359664636, 154752808, 35901698, 825326432, 669161819, 523090654, 468454536, 846560508, 525929604, 810291536, 15356596, 44874367, 231869878, 295563073, 426621837, 628914824, 149128313, 315872541, 108224634, 181075295, 736124548, 532533364, 99520448, 238714504, 254090250, 907714442, 882064436, 241255160, 861491271, 549560025, 28985563, 190947573, 814305765, 168581908, 437845311, 533449377, 498778342, 173844311, 357525805, 276878622, 24219052, 330334174, 385982971, 175378027, 129517533, 441152520, 736192003, 919201296, 808816175, 778051484, 586260477, 707725508, 817645740, 534003192, 524479190, 594390996, 531317080, 338721956, 826172213, 527252118, 180458424, 933975292, 942074829, 752907127, 244873994, 875624665, 345766106, 834307066, 998832713, 131763635, 180339308, 216034807, 316755891, 780902533, 330656858, 744961506, 13594351, 437227793, 197135940, 175172158, 681234441, 173786902, 940872430, 110016310, 100425675, 628030458, 732186125, 509158361, 315849937, 866740849, 261267988, 442939777, 876840016, 781994919, 290348450, 459747599, 521258366, 825328585, 253119963, 926926339, 548513258, 776754157, 736412474, 521985962, 213400186, 393310823, 868981430, 998762276, 448073569, 675694220, 523503709, 104048456, 828674092, 593159442, 198682615, 932144403, 26090022, 48014834, 816294972, 656119907, 713103214, 46993324, 292013029, 441371140, 416938239, 436537302, 922210032, 319802574, 970701666, 553053868, 550543826, 51841183, 317316897, 690948028, 677050523, 969679718, 528953832, 957240909, 108518153, 779714873, 616649514, 224044498, 689702368, 826771584, 276838975, 398239924, 626606565, 282910007, 91101446, 118669673, 184256399, 830735869, 249668133, 894379191, 115839789, 902033098, 838320711, 850209756, 642506843, 810134670, 504760471, 890623904, 40732944, 506303722, 806824649, 784277921, 532111228, 756903152, 894899870, 607026916, 591030041, 485490807, 448750424, 932691508, 583853441, 431852667, 160778071, 264164982, 156225170, 775081417, 591023366, 915635514, 437639101, 394855750, 689512558, 729876786, 657377398, 364269476, 604154521, 273323826, 360380303, 599009978, 864929153, 113760223, 418233398, 311343749, 491223434, 209366780, 606559185, 661770402, 622075066, 326984747, 491303137, 609898509, 117099933, 121425984, 331951799, 749435127, 116936425, 13010354, 22764648, 490018007, 451299686, 320887242, 227683016, 106888227, 605033079, 174393085, 635149070, 580141904, 109253090, 53853893, 635796960, 101983317, 249964419, 656376217, 394203672, 427724063, 924374179, 466186448, 191777293, 702122079, 949879161, 490220961, 487496915, 404533294, 461902024, 794625666, 622281823, 444005150, 299315809, 768535107, 509306364, 122091595, 899830541, 440174078, 796256337, 376011038, 740003598, 401757, 125692579, 9091216, 350690555, 111431325, 510933886, 353588457, 141625769, 885731531, 775957215, 734399709, 31295015, 306290400, 148256677, 986965727, 633455356, 196377989, 954638672, 627003479, 697327449, 203510212, 868981892, 154686947, 983118304, 481452145, 669702657, 355240871, 362543484, 413408339, 585333369, 678157498, 216347195, 292335012, 159397, 821024635, 828682118, 59227182, 109933768, 300233949, 769084785, 54419438, 57129623, 652005912, 468644229, 424306916, 157339268, 727714182, 216600285, 371421728, 56197423, 900302364, 743578475, 354552570, 689601803, 882986438, 80339024, 295614021, 950603359, 828236659, 209099116, 684894991, 304843318, 92286862, 635275669, 380948308, 322071839, 219256757, 301276542, 816697283, 556407216, 248020146, 791911676, 834503034, 192581460, 334702475, 494959605, 930951682, 326162155, 35778554, 848056934, 297218149, 125851917, 101788338, 858561868, 193943482, 216695753, 114280852, 649863643, 182580912, 632447402, 154599406, 683353006, 519787717, 154381159, 925773652, 899522254, 87168026, 255357619, 398846806, 702267144, 206409037, 433598363, 113554422, 640292804, 400108010, 289332456, 788941792, 830559135, 315865923, 658100002, 182760300, 69209811, 661434671, 366849002, 668395575, 385635351, 950646166, 534360920, 87079674, 570341162, 227764928, 189929879, 25085047, 650947803, 709637668, 955402223, 537256683, 706242441, 173382549, 526822264, 50849140, 276452088, 49461201, 136052018, 925959928, 977272407, 352457080, 983403647, 450498001, 700550038, 720939405, 132434589, 426257251, 169620779, 8538355, 265388741, 182688045, 736745629, 320264358, 214490808, 485289715, 263578890, 665537384, 239293910, 799226671, 471379169, 406980094, 351690495, 895402382, 960152900, 243086518, 264612713, 597560282, 906397305, 449941072, 499576352, 819573933, 397885298, 287627785, 523395596, 447977541, 32878235, 156505666, 777808300, 810737786, 472699751, 278171490, 216276201, 380925755, 708252570, 902582372, 692069904, 564937506, 737528857, 70959240, 485894296, 522864651, 323508981, 124861416, 237654858, 565187480, 922815770, 413435632, 578825290, 610957311, 339155763, 60065713, 767057570, 564196607, 948999304, 82188165, 917967919, 959418983, 945983052, 337062011, 86752448, 789784907, 333466167, 726859059, 470718436, 5892047, 676875954, 98619324, 17289373, 745734800, 470391854, 527891486, 272434261, 286944486, 317544827, 6216022, 228168082, 58440415, 949078790, 250050972, 812508065, 863146517, 598667855, 862228752, 117485130, 300224292, 405986507, 624311321, 216013536, 749984155, 700049985, 549258425, 811604313, 265226145, 180834251, 517797242, 767992576, 18497602, 696629365, 510388857, 304898057, 22017853, 527169273, 893151219, 822033560, 656858123, 767939340, 573857745, 7042130, 532635836, 346454445, 728704441, 13383752, 42560929, 955552121, 372178057, 880913724, 34580478, 661939722, 288557096, 495666526, 339576406, 691543551, 767755023, 492398326, 304416337, 383841584, 76756450, 518186757, 472372015, 97628067, 517211222, 31212521, 436328772, 727755201, 657925937, 197881015, 625864502, 338298974, 725431661, 999095205, 679055149, 24641244, 812858271, 226723358, 837303550, 975521600, 700449086, 67159314, 762148255, 937833361, 968847144, 298026334, 466575820, 808833420, 609810719, 683620195, 934958239, 508584692, 683363789, 880570971, 160570906, 740227675, 357549507, 808163618, 53906963, 462550265, 472804823, 19042794, 116989557, 803640580, 161512921, 895665116, 569422999, 945291632, 146224936, 251864921, 61900874, 135409513, 624211010, 423555999, 101318531, 679852237, 383868523, 844105415, 425814862, 813113149, 873750890, 654085513, 88447103, 8801446, 629755841, 886300701, 552070947, 939139953, 438284318, 127189316, 803507063, 904052641, 498047425, 768073123, 427937737, 148865433, 103909491, 240363364, 164320474, 689175688, 507548090, 74872375, 5221461, 835802084, 269644974, 750930404, 194629307, 213769745, 630929042, 914577772, 450933536, 43989324, 487618869, 477433670, 334265867, 417619743, 940087558, 672815854, 936719097, 375853051, 242349988, 501301431, 25304599, 12538042, 601877457, 850460431, 46834822, 596183620, 496161425, 631959311, 346484007, 234859414, 105609490, 155798187, 451794960, 276153048, 121339104, 293054376, 294219468, 57438160, 124910217, 87355570, 291928780, 7275332, 565392402, 359094533, 753243758, 277391620, 544143640, 218751150, 951272925, 214242976, 280622365, 655119905, 852067289, 951349974, 527497882, 330428245, 427283376, 764419235, 421477252, 79923447, 636466520, 93801619, 767770887, 784556490, 48256540, 658261356, 634936571, 272876522, 852206341, 108041641, 28482840, 319436397, 790635506, 929059061, 325041275, 203043453, 819080419, 306501758, 539341779, 221345507, 668164756, 527126827, 870376769, 651642594, 516145420, 478270839, 125078887, 348593014, 46604495, 195989431, 67381783, 326770097, 717569730, 52280908, 49544634, 694972549, 649782546, 555054165, 494777822, 3971454, 664520633, 391213533, 292179426, 967470468, 231567772, 92145817, 646736743, 356613306, 253267581, 820391826, 146483845, 555251749, 771693802, 930281537, 259510230, 531485391, 494087300, 145269925, 50105834, 332230646, 137131897, 919269040, 254276132, 322411174, 66469485, 118800091, 368149204, 890352071, 559430895, 23296293, 857548259, 183577975, 707006487, 756213277, 719183546, 339378996, 916820270, 522455162, 599299153, 756157415, 450176370, 255053171, 920826901, 83544306, 880128958, 776205421, 807036862, 78530769, 777199253, 80128184, 685351617, 719640737, 391280503, 59420162, 682396525, 304640042, 930794010, 537124486, 553908009, 636767398, 322554685, 962683204, 753538919, 708031691, 785137836, 46705784, 797069789, 91431441, 90432367, 228462803, 131867800, 55759404, 619430392, 501552089, 659154478, 600393449, 88832280, 479682217, 259222009, 24634, 81280003, 394498648, 99625843, 119181784, 623103870, 439069737, 70111462, 386718302, 287724937, 284396041, 85014429, 275981774, 243409349, 519141679, 807537831, 933143569, 602374873, 477381978, 365335180, 833123048, 545364179, 732328124, 936191828, 917168714, 354761569, 327514867, 798233841, 753999097, 262177283, 184362542, 712506285, 709454855, 698743046, 907430658, 204810598, 119660210, 3608189, 928552755, 871676680, 90740231, 416716729, 860152038, 25730699, 419440470, 619892826, 551805597, 172476183, 861538251, 553335496, 436756251, 723548337, 566464419, 681298115, 722398970, 57844380, 594040048, 959568723, 655058763, 342627314, 866235211, 270035667, 183752630, 832919527, 787284355, 625476914, 357094207, 425479328, 800698759, 967709291, 897215075, 197437066, 824982326, 801919336, 159304192, 121843163, 89161481, 858005976, 652555302, 627861289, 983678486, 882924439, 610799557, 448741752, 366496275, 298595441, 161497683, 432290712, 633226142, 614616110, 122108515, 566455415, 496689912, 47532825, 823359008, 807844015, 606876970, 72861257, 2717209, 112844720, 707375620, 146759076, 689230092, 943314194, 365167346, 9821324, 271867200, 441389224, 692195000, 103474381, 290159076, 883672044, 238085402, 436002919, 822503440, 359221074, 426504089, 536662727, 176690806, 866329213, 910510968, 646852355, 298850706, 137397448, 970099635, 506531589, 107583343, 884815627, 972110173, 74343374, 703704169, 447964539, 894618879, 456782841, 556220394, 138450169, 530925397, 710945397, 160896703, 480508995, 208173305, 242541275, 235337151, 124785537, 64969893, 795519421, 319362357, 142675418, 773169995, 37036252, 205493799, 981833492, 940983847, 437072075, 763425629, 50367139, 753364556, 99137035, 9434731, 724373077, 981285643, 933904497, 777113623, 600036182, 607206147, 743799228, 407584194, 8907119, 405685593, 250959251, 887351350, 589755573, 755180471, 723702923, 193058359, 927960231, 632099572, 595008684, 305086172, 378777376, 134767123, 536627811, 913066254, 178220169, 205002072, 279954593, 265766745, 447444468, 989795294, 940198182, 374288211, 703329105, 683195796, 343484684, 262631704, 503082149, 865788154, 473747523, 852646345, 766096283, 176718551, 249330229, 47164100, 104703858, 542376988, 487311702, 957866330, 706986414, 791139691, 75818803, 738949284, 145427806, 943540471, 552338481, 513231573, 761503335, 70492351, 49248325, 282735317, 293366962, 768855109, 51827638, 272222616, 679203224, 894198908, 99018414, 676896807, 892543769, 380571185, 302279790, 683531419, 72039753, 491955589, 479156166, 93668163, 207488883, 4774575, 240484111, 932915333, 910931081, 696490184, 47649366, 4303509, 526152199, 657832153, 471612068, 944916598, 386803920, 859330354, 742347392, 367033195, 930108167, 170750433, 445652159, 253068802, 251386648, 172110275, 394748148, 374274199, 623329113, 708879503, 281725948, 799486742, 707002613, 108127058, 371673647, 977367483, 325758454, 27889763, 263414168, 983574543, 27321067, 857552258, 15932743, 216359180, 856893148, 677334821, 118565851, 19684573, 458705092, 522166655, 661048837, 893597698, 633849145, 69496293, 844687319, 33658012, 372014931, 765240011, 968132903, 983849174, 869127471, 212608259, 599117198, 265374529, 972411758, 25884579, 945768803, 35242383, 933646909, 636775123, 194725464, 93575122, 450500432, 430776209, 214797174, 577068981, 439717232, 786095951, 454949330, 572776031, 871561664, 636985498, 347212844, 422631553, 927094093, 61545486, 195467466, 42951162, 157241522, 414818596, 125562288, 205079249, 123336839, 158219091, 593800943, 527322536, 336318585, 9635699, 848000819, 643940269, 857344402, 835159087, 981052223, 557806198, 809865500, 517597917, 766093220, 22268458, 883627164, 116452759, 326303099, 107061179, 438489067, 962087995, 803814963, 318802541, 741423494, 985994954, 561107294, 896360577, 7161913, 817299179, 964121727, 735330136, 446365438, 382938904, 986822694, 338270973, 507718708, 190723550, 62087208, 470580791, 166618728, 235898419, 433291729, 572175568, 125065844, 942078927, 11739953, 870905730, 714145520, 82680955, 609114340, 246471200, 838930296, 130817815, 973290492, 472950660, 414279786, 804672170, 343699446, 14998279, 632879020, 62857754, 648879555, 872998227, 442253411, 249791488, 615264349, 35155298, 606563373, 164398518, 205824324, 383507128, 11056635, 683417376, 855186039, 295682463, 127269947, 742584248, 642607924, 788847408, 83338379, 448790495, 849619690, 100592256, 366124681, 935426666, 794330861, 510819322, 512701858, 757027472, 439298982, 176558709, 155714657, 714658500, 283837281, 722118400, 226654217, 791731208, 326852065, 494501031, 421451712, 763709444, 616955816, 555394231, 177584861, 22464413, 591624189, 764124568, 219413492, 175401777, 637225927, 617321805, 602064307, 892777663, 1448009, 290439663, 948851577, 655023303, 711549719, 608973926, 454322849, 515759131, 329174479, 661785019, 732189016, 423325761, 633381110, 645237533, 68684912, 461654931, 752877152, 235261471, 677286252, 466346884, 417860682, 28682403, 628377366, 344973047, 39075020, 885534419, 766681278, 423721167, 533230177, 262134917, 520305785, 348701281, 138219692, 514433607, 718187886, 416433558, 921290969, 476801022, 979103354, 257446239, 559409124, 901267344, 396982622, 533914191, 128059458, 615358827, 383930867, 771162258, 400541907, 223745405, 242670846, 230510703, 568246238, 200620334, 311468136, 504025714, 988178529, 426801566, 494414121, 639523958, 589944529, 210415908, 494761540, 857609618, 501140891, 812893981, 136670967, 80770077, 277118254, 964967737, 852698993, 153289218, 40576802, 481127200, 251976418, 811995203, 222277396, 761535785, 342315263, 170426366, 906601367, 708956842, 884232046, 400863533, 62862804, 534561929, 757639545, 865468732, 12938654, 290934869, 36905625, 245156152, 522646748, 928199044, 25468805, 601276011, 676109035, 742341117, 988558954, 242695204, 988284308, 663345520, 190384630, 55369209, 23070669, 986376208, 537140370, 798109989, 97900122, 133692222, 26142662, 132747840, 549885943, 926434596, 705739669, 456729504, 551704259, 921556891, 443596206, 637491921, 966311150, 179291079, 383342240, 654466782, 909715723, 245650436, 964762183, 348039521, 551635359, 292817057, 294205123, 747655522, 121689240, 834441254, 246913245, 981948730, 986641684, 914004648, 766062899, 561699685, 20140030, 915579584, 329945503, 339693186, 706733493, 67835421, 308026885, 499489964, 888074271, 198224447, 624755653, 435312859, 574886130, 194456100, 405265959, 661675493, 43624149, 89370428, 344970271, 100902559, 917168105, 393417610, 435439924, 370111991, 166098511, 575778959, 362506520, 464451811, 93863542, 97196852, 980258097, 3031152, 906101396, 150660388, 703025449, 209007449, 217468299, 160427599, 478461995, 838120906, 897956162, 156802735, 869840850, 687352079, 138786235, 119360814, 745214149, 550851180, 404727106, 972202215, 650830886, 688688170, 825884307, 256837496, 541692150, 737769741, 865829608, 837893981, 671184346, 362621751, 550295336, 486127653, 1505992, 879620542, 159404101, 253872176, 248716475, 457899036, 532249787, 156822981, 485102116, 305362550, 569776643, 481176376, 520740205, 588479615, 13903997, 52011695, 833185082, 243669830, 664999554, 799345219, 815751756, 755262117, 883337988, 49965817, 159356638, 838798173, 279925401, 455424375, 285350414, 252628326, 685743889, 690140012, 802709835, 545544126, 665418644, 231349121, 280118283, 303622897, 15419735, 496300799, 561041576, 123801383, 536027746, 14841847, 959854488, 685746841, 107855038, 787153373, 806503981, 813524769, 431731122, 792274840, 862163065, 870641296, 119611099, 999585239, 365728291, 377612225, 82566359, 302800818, 172748891, 379649557, 111938978, 924933499, 590083084, 78798417, 610531914, 119686463, 199770065, 789382933, 610627862, 74773968, 727043920, 704899481, 806213208, 822882815, 950555505, 987509261, 387418025, 680177247, 666790576, 503630557, 747304188, 912803966, 438594551, 388659934, 80895762, 692398450, 661570008, 231070457, 26074115, 444051166, 686962123, 69959765, 768844708, 201361963, 461470261, 205050850, 923220903, 401632040, 949682586, 21177593, 743839664, 80409367, 514812101, 705396829, 300151215, 823432017, 167165979, 692939038, 321951942, 914336958, 74452220, 245294868, 349733997, 684077870, 183976587, 716701223, 31827893, 873203257, 457188371, 728612375, 756993553, 930346434, 713010952, 512262055, 863478713, 396505532, 988621442, 476277957, 257145391, 381362084, 284745248, 70177613, 345731277, 90999565, 485712102, 497096059, 312144444, 633869972, 789471202, 915540001, 561646285, 558463522, 67773026, 989302217, 647485321, 507732571, 8594136, 830911976, 13921419, 893427801, 769711253, 199856136, 535025736, 317260648, 257844915, 882039639, 104698543, 426508779, 564602061, 633014441, 898794675, 113534009, 642714016, 28095726, 334890904, 61738794, 61851234, 542549543, 288395901, 170976977, 223502578, 674932765, 728321002, 186803006, 906935803, 60363397, 396897591, 49355505, 68174614, 273257832, 930338962, 703493037, 614062560, 723959168, 581456975, 577409936, 151849437, 690186020, 452659321, 466299374, 10850555, 344685037, 688525073, 360962625, 323563474, 788615391, 93763822, 362979565, 717411852, 204864817, 963166269, 475662760, 211617385, 638393760, 144941750, 827739734, 512413522, 912819655, 841772135, 579441462, 668950465, 321948512, 981387600, 872097254, 527107762, 736655074, 726767457, 338001022, 729151913, 763705730, 181914258, 983176518, 705174703, 473435004, 633633046, 351236050, 328869037, 119697773, 122784933, 106859143, 878590681, 628348677, 575658718, 206446631, 965321282, 61407582, 850469339, 281680542, 662269115, 769415983, 540578896, 682376404, 868555340, 614265943, 185625672, 787535431, 242894546, 1137436, 965059299, 866188528, 964148383, 133005032, 66537289, 685523228, 317811809, 689103662, 186101895, 998353444, 721680465, 485143153, 816416386, 69909903, 58475369, 776313701, 61187959, 80995704, 176015580, 935155712, 561710904, 41643793, 159025107, 834323507, 154438175, 800250452, 738229906, 273466636, 727430010, 461008216, 298293525, 492221196, 743433328, 544521315, 679101478, 257800168, 336310066, 524442874, 1931829, 425943124, 700390122, 249757413, 681810605, 551908418, 820935195, 413847855, 514362617, 157844395, 776223349, 606592203, 873007317, 440245111, 746390686, 410043753, 560649491, 681407536, 675867317, 20084794, 798665564, 705222699, 214022489, 21181081, 62927743, 228412562, 752147825, 140386772, 729642928, 79853681, 179807881, 135703988, 759024962, 266210520, 361118130, 407181826, 822230581, 615897178, 105402084, 820942628, 120018407, 929964370, 642573929, 842438561, 683229236, 369777601, 787507933, 250080515, 231970489, 396160957, 888185555, 833408727, 700740262, 168928946, 815697006, 846879752, 806035048, 886221530, 702670372, 718376806, 332523011, 226792291, 362653598, 578024919, 787422635, 133522008, 159395938, 331400847, 774869242, 587460540, 224246119, 156640452, 135290140, 122182952, 217261788, 642339922, 285298556, 770464425, 167559736, 954517036, 344401724, 820021630, 201432012, 737148786, 823886920, 744128284, 335530851, 908088649, 540918853, 349597150, 431839381, 702484031, 875734229, 68582111, 180599413, 796330961, 412731261, 825652001, 945928617, 305150382, 369411858, 129437306, 554270994, 898773189, 959846391, 797097615, 640003762, 543755616, 131242316, 125634684, 443520904, 730435785, 523077029, 229839598, 43138622, 760408033, 151301492, 112157321, 395907913, 183689032, 480681458, 342723855, 881409219, 953208430, 71889101, 190590355, 148023219, 609639005, 201682909, 150720585, 667845332, 809299169, 865450220, 755120379, 615715044, 86942426, 975432960, 810964136, 613667880, 421071059, 337456863, 950232740, 822236381, 649436626, 316325672, 264501909, 911211673, 584831181, 303328705, 248431710, 19009810, 658567787, 298610406, 669804773, 501530958, 164097249, 863774558, 480777349, 60887139, 32971223, 721005527, 655715036, 735413689, 647823168, 479832925, 296125257, 596930344, 904876105, 418269852, 826301262, 738776226, 881730226, 902772893, 960380333, 760353049, 749853553, 39474921, 291425966, 682190285, 367351495, 88299095, 929085489, 819046292, 202015164, 968957981, 605795274, 331922284, 907297262, 866500717, 63410870, 797079697, 635298247, 117451191, 829261570, 641098549, 265062604, 825972759, 209486103, 195033262, 997966100, 392404282, 533839291, 906011495, 592953540, 684548850, 381194140, 204612763, 371736798, 465163803, 885814699, 599251670, 242680611, 505161010, 99147233, 905560414, 151582879, 308480203, 316707495, 48712895, 291790170, 276268522, 333150607, 506022473, 616003423, 720135524, 313106567, 643149017, 507838812, 588220406, 110318366, 766735565, 71522784, 489018407, 466061178, 119454019, 6296784, 909311429, 645368069, 953222888, 957582113, 767674871, 28045386, 885990999, 212240516, 915508356, 461275691, 970281946, 797073140, 309578110, 678119489, 577474154, 710331338, 292303938, 78561149, 885924256, 494099956, 513005900, 24199669, 436496834, 131175997, 725865201, 517416600, 273441523, 437479481, 659302726, 617822661, 253874373, 149621400, 84518507, 451806847, 300119965, 854474463, 856820841, 233883547, 788010476, 89990349, 574825843, 975315600, 776974637, 976311012, 279856408, 436731283, 698990809, 63218484, 403364535, 710914411, 507656922, 807211661, 195515915, 49154246, 234541846, 794083783, 255818918, 411942902, 916219018, 378645113, 910732602, 318733882, 975080951, 20920228, 16445305, 714634081, 609235385, 801553350, 358948760, 311017792, 363634725, 764078960, 771130482, 426585283, 612925814, 563908913, 169957932, 434314718, 953263524, 76827176, 220560681, 859402829, 851568994, 15037304, 698870888, 532279274, 40099465, 392814826, 222033893, 999561552, 226430401, 380247327, 454906202, 897242288, 992753166, 365758191, 299777625, 522154094, 803232846, 684922319, 762504882, 269454435, 772678025, 491103734, 936749397, 905324782, 486752769, 417003393, 348631719, 711802283, 251949205, 53026684, 790751518, 227508186, 806773222, 791466701, 907320394, 698154675, 694038572, 499909709, 486221537, 973457602, 450510636, 392811418, 656320593, 314505484, 560827518, 896079863, 501545409, 827209112, 679322110, 480687652, 910435829, 878052425, 606003577, 405994578, 543692968, 363271818, 965872136, 155009144, 537040562, 741471915, 636091086, 225905920, 440774332, 758838132, 817384857, 685014868, 847134972, 272121821, 422535939, 229471873, 770913282, 384233331, 480436167, 842180471, 834634663, 416498864, 910823489, 187150298, 90681342, 189285534, 297196297, 325803294, 358067165, 899089510, 94440366, 227580644, 575333058, 128260379, 540641973, 255759257, 273249698, 866921341, 705579956, 233323026, 541199897, 786527214, 698604671, 810760933, 415449094, 124442330, 76013899, 579036959, 451504090, 372002565, 722295591, 435357722, 571744559, 106275023, 710358896, 828737815, 501198408, 623930727, 362161153, 362174796, 701916874, 933552812, 684348417, 173526619, 429201640, 996004454, 706506767, 183686595, 397848829, 38596719, 541704505, 997351241, 384570291, 65244924, 182700511, 895668098, 397102447, 692301812, 751690761, 780938782, 941030005, 992202819, 345568821, 740534287, 496862082, 101443043, 366235679, 7840623, 279674694, 280504838, 495396366, 808391252, 208825236, 848219080, 609407093, 170353574, 994279450, 926886852, 453624965, 178748483, 969473285, 976577200, 868919532, 488939324, 543697679, 776115195, 783977394, 730058458, 392048150, 558535756, 25985568, 515142164, 842386085, 379056557, 835222949, 805566024, 263122817, 274271132, 606167098, 923350014, 170931726, 748776419, 477167422, 20827135, 374035128, 260429104, 670370741, 689598125, 508207521, 392055801, 357708447, 632087849, 829027029, 448064555, 366894436, 889883223, 352650048, 16577546, 210548878, 606195127, 107061757, 648466119, 971355825, 471729265, 945568347, 929452259, 325048602, 924630227, 359381976, 323952891, 197382643, 943863558, 223846863, 407760625, 624656014, 666418988, 224975874, 216070871, 696942561, 215462624, 483783799, 859798842, 798876755, 43068612, 615179936, 824126213, 79736444, 68446716, 753076309, 441088026, 388931459, 584468296, 565280362, 104345418, 893988468, 398586185, 427330572, 947987186, 131742710, 340950201, 927920834, 521111266, 407072403, 270466878, 602699525, 536974664, 552612592, 705845988, 594496862, 471358294, 814350300, 871742295, 639675947, 474621002, 878308983, 65362202, 101116628, 747162650, 547381820, 714635525, 164002430, 898403728, 116692891, 831605462, 82434452, 915574045, 492873876, 370461148, 700441831, 21270856, 610110016, 704996878, 787182037, 699844461, 532156569, 690448265, 344267286, 60369641, 675982363, 580069226, 628104152, 596417112, 780085240, 406353034, 883930598, 563655283, 298754429, 744626668, 909824176, 572129594, 785475853, 182969030, 971473772, 921065292, 843260259, 44626389, 957651401, 196721596, 677542999, 867794255, 433465357, 573913666, 586446099, 551676136, 250158196, 938349491, 489440878, 320045239, 646418742, 588217260, 99143341, 612842023, 857123491, 625326185, 563959939, 881270601, 265020629, 18225280, 135457955, 93303413, 200033328, 671947680, 5494242, 294122228, 493720161, 749440914, 127769681, 543767627, 737450005, 248958703, 942120705, 346579715, 253082495, 370332419, 170861423, 133395453, 210383347, 953924720, 952617964, 109907972, 551340741, 330053555, 766652451, 306892380, 144688429, 793534804, 905871506, 249687443, 474820139, 177352414, 549331949, 917089711, 219651405, 923509865, 634969514, 26484686, 622050114, 474778210, 471726829, 523254777, 48439088, 886290601, 196457665, 493297511, 653392643, 743557410, 237709464, 359364521, 592544897, 738952994, 807946126, 113300775, 40123600, 107920203, 28495025, 84708315, 361063247, 613441217, 389365638, 695784465, 827844392, 19517322, 704057437, 297295276, 126152909, 579287982, 503628598, 37137225, 572531092, 385831635, 83078543, 29749811, 221722741, 699200717, 5756873, 602594967, 86894424, 422564472, 264915822, 74108344, 74181386, 919129515, 764990866, 182406882, 475225419, 597478528, 504060357, 151072625, 585946354, 84878182, 45237569, 170556658, 882221599, 355197045, 12789834, 435486912, 159028638, 181752114, 992373629, 687878617, 861380865, 931271378, 879184891, 479418185, 201764978, 983984808, 308450618, 283670345, 456161950, 460107164, 947927264, 593752377, 273892554, 293224005, 8736932, 415538447, 350407886, 216189858, 285625446, 710194704, 591502388, 98133917 ], 25060 ], "output": 11148692135374 }, { "input": [ [ 649814187, 107388379, 152572669, 810025063, 142382233, 602477956, 134285162, 893767925, 238565291, 416083492, 419117179, 956793270, 987971265, 489142538, 320767858, 535968837, 61589814, 933981044, 808648119, 517265539, 47926153, 723477634, 582240917, 819896689, 667983432, 579341036, 760583534, 884349495, 185264044, 159452584, 665549917, 152890989, 930489409, 268364044, 346877115, 467714399, 794061307, 5246180, 801568173, 999180757, 122058621, 22894266, 357820622, 446017904, 481418253, 876315666, 246644863, 442272988, 181770738, 447061493, 442200118, 721906707, 612781988, 821746653, 519470860, 46901209, 891471478, 792733350, 405746523, 12266161, 280246687, 572211039, 554277697, 680222474, 220430155, 451264091, 493400840, 852830857, 546357346, 404602781, 116327595, 265695895, 465799696, 312629390, 537769436, 304397146, 90530095, 965086726, 272644872, 38730713, 182554475, 191569814, 327477687, 346098185, 57674832, 618724700, 761989234, 19300351, 620165688, 336124875, 98740005, 928370522, 733903334, 50270829, 103263888, 934950070, 744206176, 717756032, 513511752, 443331419, 617997746, 951444648, 678683577, 243011846, 84784731, 593151567, 628133388, 781415783, 800783016, 707227748, 408211017, 33652542, 2522402, 940607977, 987877073, 333479288, 527022146, 601537272, 196475700, 996797289, 117893368, 803935827, 597319758, 306136505, 197482072, 332115060, 914823807, 893882638, 369101889, 299362598, 143308265, 705372668, 536288427, 467251061, 693576778, 370556740, 230973665, 498847625, 188310277, 198250897, 734181687, 664139697, 83107173, 478800202, 606674330, 19471955, 400288514, 25375901, 32879200, 343698873, 58203098, 660386484, 884517475, 720525844, 685627382, 344983185, 586955819, 359013729, 938503212, 820625369, 400456082, 121137102, 379526282, 44672608, 82358678, 602692680, 226516934, 47094759, 937390262, 60680453, 426080444, 833093285, 322768279, 794591098, 67103109, 579074131, 407368026, 87534156, 753199041, 140770974, 434504787, 674688072, 932507093, 489200076, 210443729, 231022521, 798053185, 745323865, 64820571, 428479222, 253174410, 980367751, 436362894, 265606635, 385227954, 922005005, 105342529, 244003, 279880539, 929062687, 805552661, 988687990, 354772523, 113996597, 952284969, 844346512, 610876851, 780457092, 409700284, 689471043, 223848036, 800347631, 230877841, 208871627, 510531447, 299713470, 676930780, 847563612, 753888046, 355889903, 977968131, 66203750, 869523653, 989037339, 760404139, 697520911, 984933509, 382096764, 608972502, 917583914, 403019031, 167324502, 33139295, 720264022, 850966757, 1386213, 290907203, 926394706, 183463623, 305062407, 188279842, 545265154, 36420144, 382251478, 719143268, 535230593, 830567405, 401611391, 473890195, 992598961, 307991729, 165147388, 630433186, 494910649, 965791195, 418661677, 32137020, 360997170, 818492603, 780857368, 827795893, 678504473, 92059919, 760332816, 337040608, 604762577, 697904147, 570615745, 278833972, 642794497, 268929585, 239745697, 572456613, 888304418, 454919810, 393876769, 503124069, 504435565, 359881107, 433069694, 349659575, 207941338, 56427867, 225814528, 135408651, 659618499, 810417411, 863018653, 538574261, 250706848, 860463614, 223745889, 207416697, 625282774, 81029737, 860829345, 634383453, 582558509, 871488190, 823427629, 728431610, 118634465, 257950718, 811362394, 479484417, 357351263, 729062465, 317530275, 523645282, 745779119, 922144655, 325556148, 444460099, 91111401, 85386484, 365308877, 670154858, 291526517, 479114492, 390140232, 415177569, 169152507, 433794973, 135862138, 340942561, 427729122, 301809564, 865719162, 981819943, 771053129, 715574106, 178339871, 473075032, 392190193, 347248700, 229172, 858778462, 53408380, 445012992, 937378179, 868839303, 480011303, 537763663, 344487609, 155540997, 24263579, 177876055, 564378558, 303648948, 641717388, 49105462, 77748386, 186820063, 814122652, 143235850, 617383992, 85873633, 719096712, 268962368, 84905207, 752465715, 173359372, 547455463, 274108777, 333517712, 44655596, 996695118, 352403779, 522794125, 134681226, 992760409, 857078343, 372898024, 967374093, 993898192, 646755392, 881765081, 974443267, 730267742, 865961275, 824731450, 846093381, 622626987, 848800838, 357466173, 929161929, 755670489, 161038980, 67921002, 288914462, 677411777, 813365603, 351671552, 716554300, 443521983, 55098938, 580454230, 763346396, 650645723, 903331204, 982685743, 460506163, 591785461, 464018748, 312959210, 972707342, 134742076, 855041114, 223385296, 272607302, 684652106, 890994696, 127334560, 561752735, 452436855, 777433655, 729407677, 78406980, 655073669, 994526544, 624508003, 264258537, 238028034, 300655052, 639158084, 64389393, 346268694, 264338773, 299232428, 673764519, 984747888, 726466675, 314408079, 890466195, 380977311, 947780837, 132645822, 929898130, 610886903, 785926013, 979199245, 255307172, 480144746, 561851651, 235373385, 544511311, 864139234, 599130214, 844920975, 41641305, 614228892, 90644482, 927776056, 924789561, 984349724, 238621714, 140754852, 758354589, 692670377, 559958653, 519486461, 64024727, 395530399, 310741318, 197546919, 90175612, 346822327, 697076104, 347526351, 773627840, 889863266, 690064801, 182244284, 368528670, 846287917, 950308263, 951441891, 46965369, 582960148, 14916010, 668134818, 962426915, 734696339, 471610593, 342103934, 130027924, 723328092, 274876198, 897993632, 604864392, 505449131, 629027367, 904015741, 412589834, 947304404, 901757582, 442121187, 189139982, 685024623, 82717707, 313214221, 413081093, 737490738, 452162721, 938589175, 914596557, 825601142, 244741521, 493458703, 131924780, 266442358, 145449565, 305218182, 958632506, 835300557, 39146434, 272291800, 628048539, 370424998, 265945783, 531955529, 425171364, 373027524, 916067308, 800844116, 877515852, 988360737, 160842965, 46121225, 589641056, 846631406, 126481703, 175762043, 335481888, 98236928, 67032485, 288483606, 77565221, 427835335, 562987890, 597419157, 763753631, 352076271, 24434386, 984487368, 475736541, 861359616, 428946599, 179495871, 963679263, 348792369, 1633930, 280774813, 81282479, 209981422, 529093275, 292379764, 614171722, 449172728, 974036436, 566196796, 369856623, 488527252, 490984754, 36308668, 587482198, 507156285, 155651601, 230561240, 161289763, 968831597, 652980735, 924170901, 494482700, 939212483, 862372976, 17602663, 964415605, 444821522, 90551737, 431403039, 635377438, 721221541, 771799179, 579288863, 489060479, 485357371, 38315437, 813733616, 332915437, 992849237, 892393052, 354963443, 721672527, 887476039, 768942223, 665126048, 776865180, 474292040, 500048544, 176017416, 878827725, 243214639, 263336974, 109367610, 233673134, 952091184, 991681090, 811077341, 503698181, 104138768, 13893409, 630523513, 46880528, 71604322, 29649673, 348878532, 820009839, 561860990, 409882274, 431718509, 869224592, 884984083, 441201519, 219369114, 420333828, 877601544, 385739222, 914738312, 728838711, 662352743, 36581397, 452353193, 52696771, 365954427, 91384053, 607810365, 52024992, 503506264, 573261221, 468844816, 362973566, 271779876, 269005425, 645306746, 899469713, 525480869, 947319209, 581084132, 411052057, 929959913, 241867155, 98766180, 624299708, 726152893, 794121270, 898100165, 586452456, 56339158, 20850527, 205639901, 286936588, 711849323, 355551099, 750951061, 573746379, 454870620, 606798343, 311595662, 883772983, 715473084, 670014155, 517874931, 101796420, 490344254, 57267086, 206709044, 1562887, 264021990, 159315841, 987733953, 892130825, 78288675, 30181164, 527718845, 266904357, 120371224, 26634853, 471108295, 77658535, 69550562, 317298609, 514432007, 910399868, 449334340, 25867431, 572994569, 717973362, 313522232, 537027141, 385806589, 617038248, 862206893, 556069418, 108288603, 425115260, 290535114, 87489925, 496571884, 263331855, 52636281, 433503695, 543936404, 368408653, 278681593, 207185426, 807641830, 658747381, 915746443, 345593991, 459705760, 880489920, 262805941, 144353851, 217035878, 425267204, 917651915, 88698822, 694199635, 574028160, 518766870, 926118336, 590266864, 716022942, 524143943, 412714527, 23532598, 325952524, 680289156, 495646430, 333916625, 382349615, 967942916, 849731423, 522946718, 336072436, 837665320, 300283145, 156589691, 206394808, 387436149, 586882005, 577651321, 661609110, 604962234, 786876938, 75662616, 682796912, 152588593, 508736038, 321044135, 900030884, 138166568, 56685418, 473270497, 105595280, 716775683, 182177601, 897755754, 455322120, 562450017, 147424831, 975821782, 523982121, 84722047, 65856484, 372376487, 157696573, 163861838, 358593304, 73216539, 119538931, 235653532, 554528445, 782141432, 553527044, 448617772, 170496177, 403508348, 990464173, 905908385, 546134868, 533253188, 827990319, 787622205, 979260125, 880255777, 893810350, 995468787, 945252269, 170253409, 436789253, 836822927, 805274688, 685805451, 134876, 613396895, 491541796, 721098008, 809915483, 819066673, 170905988, 392761773, 786849771, 120221886, 741368298, 781071379, 206632846, 235006829, 906672067, 68900703, 968982129, 812253013, 915057524, 782854187, 956422308, 943653370, 57878103, 897035661, 451961561, 643497305, 670059061, 846121627, 667440535, 909503845, 157558193, 804793279, 913096082, 576986671, 626838791, 68331446, 999045440, 980585045, 799830434, 672622242, 527012849, 416645997, 452465767, 981304449, 459072841, 320707934, 967956932, 100847644, 966024545, 231148281, 972302368, 615348543, 676940737, 433417398, 357789968, 245163858, 339862759, 99163667, 282008268, 103965210, 143720967, 568374002, 6556555, 604033716, 312455241, 580306023, 993954058, 102192013, 824676499, 606950843, 465571228, 539568893, 148518035, 912227601, 248159878, 640213565, 633162761, 479158817, 620525889, 530344105, 905972354, 594763666, 539473712, 198517176, 886264886, 666235622, 506590440, 697986263, 859026933, 600508297, 614847740, 36235737, 722484057, 744187603, 18825564, 105747102, 393428942, 681632599, 857482381, 311480630, 930704249, 265805370, 714913043, 627997362, 172525645, 444411389, 374269641, 808259164, 232415779, 348674060, 221224921, 52892631, 608548019, 163124288, 22049256, 164911059, 485961211, 446211810, 192109543, 461543359, 613799479, 305843654, 309083970, 465792790, 70573062, 542821046, 422433821, 267535574, 359970872, 478278804, 904195795, 590652333, 780111629, 675272057, 706927692, 943682452, 693784222, 489501097, 276039764, 330474402, 19506110, 509897878, 656306611, 727957759, 93176567, 952162474, 15304311, 808917153, 520749488, 234669295, 645680001, 837138664, 670825569, 669992330, 157377573, 199331326, 771916931, 828438008, 842284824, 343235822, 29020935, 685521177, 636391975, 999238738, 923693529, 429204775, 303793592, 939588027, 292481710, 498693793, 36819935, 290369258, 620344403, 877563498, 87444517, 547017309, 898166712, 464951731, 47813592, 888718409, 899407156, 206406693, 930065306, 494428663, 291567711, 572425215, 511382679, 837052891, 831765276, 38693348, 498099338, 34657399, 745932978, 48157090, 433094685, 996836750, 55646437, 118281153, 631431385, 60312238, 365504032, 912135907, 419063478, 535297404, 852231373, 495664860, 818869495, 908618942, 715577248, 379617006, 93856858, 435452684, 668338222, 170470816, 774226407, 918165810, 996554052, 521658534, 769984956, 606587441, 711596946, 590250843, 304957792, 507848456, 476056758, 562874039, 815378802, 752759481, 621171262, 71710310, 646569440, 589368186, 49389441, 833956156, 138246075, 264494827, 531403834, 441398468, 829975079, 176032110, 134093224, 31096428, 196559164, 391842285, 10963877, 803069570, 158674524, 791741624, 61476664, 555689490, 530280590, 894299284, 455233930, 961639143, 731193625, 147138862, 284429750, 452322787, 583318640, 285989272, 487608333, 602610403, 880397224, 537815265, 82134947, 335011098, 215372578, 59847529, 690333023, 442374586, 665744320, 641625081, 541538637, 711743033, 362186464, 564119094, 270781688, 272071674, 669774212, 398769689, 857226832, 456906003, 358202484, 857872822, 528219717, 158045464, 443892546, 371057773, 844217852, 33742714, 639018289, 384071691, 858174695, 516567607, 730978370, 845907858, 358190207, 218618512, 575585678, 513271528, 508648781, 844305475, 128721689, 668488757, 722222196, 324074935, 137473985, 821205787, 658919657, 172627505, 210232125, 409346540, 645059610, 440625940, 175717687, 944261164, 170893696, 610444202, 105595788, 944906788, 196054353, 476674959, 583721609, 312113776, 709277413, 237094689, 876337401, 621055270, 20812177, 903890358, 421571210, 283791958, 603519612, 625866987, 920413855, 284297824, 632296804, 912262932, 686354268, 268756542, 252302926, 306047224, 967900918, 413988663, 316740911, 846211440, 709138709, 511852091, 578240781, 648553560, 548433864, 199662762, 361767109, 833079947, 344365353, 232903438, 634183111, 171927520, 29624297, 696706852, 611415673, 810190312, 170765927, 434066870, 715086594, 664699895, 549412717, 577087631, 950397224, 648081474, 798571052, 668448636, 678639494, 324982362, 568830297, 817457306, 864256569, 226604284, 869317818, 901588296, 842601765, 603175036, 933499425, 138705506, 182573490, 928654370, 354908922, 684903541, 328813669, 99616474, 706466367, 771595259, 56037296, 631445993, 754267397, 552533574, 450440625, 447611668, 446500653, 727908009, 548307358, 566862829, 409266493, 712618520, 461074498, 811132881, 167636831, 433878603, 450212663, 997806726, 481749091, 953424025, 331106521, 409626248, 122271122, 7082820, 83549555, 424397546, 400634116, 593823391, 878022183, 67275603, 238877573, 960422755, 669365641, 116122825, 837216229, 698681015, 95210205, 894244949, 923121826, 327210874, 913424471, 880774702, 448524843, 976141630, 116142889, 981311750, 627248463, 202413540, 667512066, 269403233, 222181213, 725524733, 16806406, 984138085, 975103867, 4819523, 883083886, 534910550, 295984382, 851393067, 898177710, 590150505, 446893220, 368663454, 73416941, 198592897, 520882049, 969682534, 388680224, 363825174, 225623782, 842701872, 870595909, 677547855, 162516240, 114850175, 408722379, 780861087, 3805798, 383590279, 697832107, 35454884, 281087826, 514534955, 557373094, 682727021, 269281486, 961579455, 994346932, 870942739, 661530382, 448624437, 219716873, 299244733, 358001455, 159154697, 470798305, 101172585, 909191275, 485666211, 189931470, 881648410, 141949108, 11458164, 208908318, 416695923, 801293016, 737374260, 457662532, 191664996, 861555349, 313016047, 829395890, 187376134, 826842800, 202116065, 856088974, 23650463, 538610169, 312859205, 812679713, 506135091, 280400223, 968166503, 242988639, 794016964, 152678811, 906439847, 662523096, 568914073, 870321560, 700678453, 191053060, 698319788, 32965035, 76797945, 154393056, 710259861, 280392128, 390887319, 929736202, 714171126, 157710396, 803826456, 776765604, 964018916, 187529969, 352627395, 835472151, 758687483, 700932353, 870807624, 167411526, 832730443, 437373231, 66338737, 230679438, 344609161, 731224032, 93210141, 298995461, 669518119, 576508220, 746042341, 300552311, 368797437, 486155076, 722988017, 305735321, 484284649, 557700529, 80717070, 773655118, 637748318, 95916484, 593993249, 836266020, 796484821, 54143974, 450184186, 973167293, 437559158, 464877232, 82361987, 481114696, 784942655, 69778955, 632031281, 974528974, 949960797, 74917022, 53245193, 235692492, 377674469, 902817829, 471144204, 849074517, 371269545, 748313928, 340298770, 522736496, 295946298, 223629082, 488883814, 818024135, 446625824, 551330102, 321674623, 850447127, 984725661, 317855927, 371481440, 914427954, 567413170, 699447374, 993013443, 507424957, 362066746, 42585073, 502389181, 942631938, 490151195, 94495717, 385042523, 316746853, 429161549, 895485178, 99160528, 192434884, 122609532, 771827242, 801174562, 253015498, 72898980, 578153295, 324829441, 516168686, 100802891, 520537835, 957312212, 999108685, 205942046, 231587627, 317825368, 33869437, 926226446, 143107822, 819920124, 897882870, 944461645, 946066538, 768008726, 322133179, 706375850, 618043936, 833806212, 841983102, 155601188, 211965262, 134983229, 434521667, 483350466, 198720514, 621250461, 98338647, 590922849, 423882503, 365190005, 322277352, 270641329, 97317468, 686305866, 432487927, 765656449, 66144142, 178766268, 379295829, 964802924, 462686510, 454152333, 726367590, 337434680, 722104544, 2165662, 791796747, 294469149, 862701648, 689594776, 930632129, 220544961, 846538291, 776562492, 624138793, 624855348, 95438676, 969103934, 156969538, 944020076, 973842385, 487997824, 934087484, 457891396, 241525955, 808433385, 755838148, 677321975, 418226807, 151345274, 922971142, 742500574, 71320535, 398111836, 197907382, 936895833, 969752208, 728018717, 22761640, 81209274, 136466626, 760052496, 404879806, 662732587, 844066849, 606400098, 723653746, 249619007, 636369748, 457903511, 568568201, 671191794, 392087353, 736834627, 634521487, 827852118, 320858168, 774438820, 459892931, 564751443, 339941180, 14216189, 636883983, 705981114, 80027581, 404060319, 456095324, 470376371, 949222468, 789049327, 853862574, 668257472, 73299381, 387151089, 187041061, 578121607, 789835271, 560938953, 59130024, 337479874, 514178868, 638184753, 911531433, 989152244, 836321341, 485598651, 868434468, 308444118, 494092658, 792494827, 951669999, 146461310, 612948993, 566672839, 617037974, 498661966, 397756728, 857888550, 335687222, 275965655, 969482098, 887609546, 127975510, 141732248, 41462196, 725555191, 805077896, 195009527, 997355498, 504632940, 452415097, 715461115, 413480135, 824677383, 461019714, 481794700, 842146470, 52292679, 556520966, 98081057, 719657720, 229623375, 562355403, 19260865, 437089333, 110465288, 909888433, 571693597, 168114740, 535684841, 616336093, 875739999, 10779612, 765311254, 813017795, 509286903, 567299518, 60817933, 278417505, 952091216, 843008014, 816522996, 915169479, 398791609, 618771803, 320475033, 343692462, 601955969, 250965206, 472648727, 200759378, 879035821, 589449122, 375920363, 30068259, 383197594, 467170113, 966628356, 397355864, 243296562, 892808734, 93660001, 630329661, 353476683, 762037106, 241433310, 677589953, 724814311, 292759368, 938098803, 585104406, 781497549, 274420998, 845191161, 376012888, 827954329, 489218444, 813761038, 486266491, 449883088, 913237629, 155447349, 64701348, 183402193, 454701417, 4701445, 405597911, 617554666, 714529135, 244066525, 782418601, 274382327, 897747362, 297527415, 617383812, 258881128, 820891533, 461764370, 124891963, 877219127, 378960847, 113190376, 509935406, 611486029, 160322661, 376979618, 389024014, 619071397, 545725834, 658433245, 489148026, 895136096, 897844335, 706407739, 400806682, 386588401, 954544523, 740158409, 837794737, 306591974, 322913416, 88053399, 623215737, 656521418, 401756706, 789523119, 152946101, 169327056, 373099901, 85130621, 644952058, 707311723, 866706382, 867902119, 343179554, 646818716, 779922882, 229248804, 905021168, 460917625, 243086105, 992423754, 691268859, 122675455, 945285762, 263165419, 293834159, 392293868, 940705669, 594351786, 771867086, 671693219, 653588638, 825472162, 85257400, 866840926, 105334510, 466469859, 312408231, 349368136, 244120214, 185404414, 456750409, 856811046, 677542129, 592415475, 205522829, 683525554, 433042916, 631457499, 734571778, 394156858, 816968664, 947663511, 886503254, 775901779, 206135702, 722817127, 178055512, 662831560, 727613826, 925387843, 774099284, 630268977, 4685211, 574037372, 749803451, 293600426, 481412106, 18484572, 789430885, 730649746, 731447766, 310982021, 997390026, 674717880, 636494903, 93445372, 809044807, 687031978, 987449082, 284565834, 615214123, 523887059, 799496873, 592982332, 694209230, 649664839, 401349864, 486563642, 703419771, 276372701, 803702556, 592880992, 806866169, 305867983, 983102833, 178258157, 391057012, 812474386, 835142715, 858029282, 655969320, 9236304, 614203941, 367652331, 77361730, 742971133, 628061190, 54091796, 155971843, 255781555, 360749028, 435908387, 245049787, 97119010, 450429400, 973406387, 556345466, 286561264, 87939171, 557728457, 409155652, 539576619, 793999857, 188074389, 120055952, 464505007, 175822230, 158436350, 75267488, 469763663, 86968883, 303186962, 419552195, 763102166, 827695328, 507174403, 248175752, 455029487, 303475569, 338107096, 936292147, 103984640, 946746145, 350044149, 704909816, 589337268, 48329642, 985151905, 692147697, 871331931, 549662182, 42231512, 457207572, 974738192, 236873820, 703664675, 468108351, 523103676, 448306735, 262547095, 757837261, 791270392, 773111719, 240287499, 185942242, 484255032, 165792599, 607683577, 640803334, 580476767, 198556733, 140989933, 818791044, 813854269, 267945913, 217500749, 14920661, 992173935, 84904877, 311472670, 794443102, 61019579, 123718211, 901998744, 655484139, 921824240, 936330986, 568277767, 776642637, 524565407, 734834310, 149589921, 501840303, 510705327, 559031952, 423699102, 479948620, 553169022, 195632480, 704015566, 802640908, 15561434, 717160846, 621259468, 210991222, 95004779, 575047498, 473798277, 852964313, 858231166, 181151167, 740889743, 691274019, 148217768, 842339465, 189307234, 525431626, 544202155, 508871667, 808159252, 96800293, 494037785, 700321127, 175815301, 519225934, 417621238, 658745063, 513727734, 289096769, 774407008, 150754195, 477418416, 473123734, 314475131, 713552233, 930141710, 869148917, 779259567, 610990810, 271607991, 596198654, 269592917, 499688886, 164068429, 378739636, 12175578, 549892372, 326514628, 724535279, 404135333, 616993728, 813152575, 861218193, 536812065, 319528197, 601275982, 928161110, 160959307, 434689694, 256051810, 949603473, 666009586, 505373170, 211047335, 782391151, 814605861, 843165358, 530949811, 925035188, 31359555, 848181588, 934288011, 3366674, 45629597, 165545170, 639092019, 814688562, 746518960, 301876949, 228293995, 216808315, 771506018, 329037271, 220735418, 966306046, 18359052, 492952544, 999607933, 283558740, 187768232, 698673524, 231534647, 345938977, 951483112, 255394246, 623496923, 377056212, 610829591, 130544811, 146353575, 646201594, 629855013, 207308000, 745300459, 227768817, 505806458, 101336935, 700789178, 876811343, 393882316, 482123771, 231037600, 756149534, 408472607, 716949400, 592929801, 807286182, 376683207, 257685466, 391029397, 888251670, 145089473, 768042034, 646148388, 675426678, 358651232, 496689584, 253219459, 28764185, 524900218, 520266108, 884604214, 846757312, 64224619, 235187068, 289076771, 592799336, 676891816, 608740542, 672829512, 567590726, 878213867, 62375282, 241731697, 305448305, 872663110, 40581630, 24081400, 299337391, 429004621, 341644030, 338284080, 201120105, 963535253, 211908072, 905614041, 395401805, 860804886, 629738329, 796216497, 222033160, 318843405, 991748262, 184480108, 243870242, 599242650, 61940644, 452399585, 273862435, 709683124, 105250059, 24325190, 576871445, 67762331, 786476638, 759764348, 936448544, 709991382, 735666715, 290898739, 404930033, 299676977, 419337104, 337634942, 894523213, 832430071, 290281548, 831972753, 418617674, 635697985, 686259911, 621974361, 987023011, 446994295, 7601525, 246552300, 25499928, 860876923, 293605068, 164903250, 453752419, 79950662, 945013056, 641919382, 792987383, 871106240, 7336849, 311817081, 825040709, 515203670, 765278242, 102524500, 79049491, 292623212, 494956382, 866045878, 903482630, 242592283, 524117237, 604827832, 42738042, 333335033, 81088392, 844248077, 992259155, 662741185, 538315212, 866808239, 79607294, 7180190, 780051511, 403543148, 534096249, 350343267, 302943387, 724183026, 204104827, 326421758, 451550743, 621002720, 156969155, 632276078, 204657330, 406745195, 863778613, 443363849, 207688519, 214625442, 913105364, 716914325, 85231306, 141486709, 808691008, 959600074, 848359927, 692783685, 14239741, 690807706, 932047394, 990874293, 170960285, 779590974, 202030830, 417026794, 481340136, 780440120, 181855701, 843177511, 806315787, 69521618, 704581902, 439953210, 699197363, 662699839, 767372362, 164168290, 531166380, 816678315, 276127391, 211080484, 164979552, 837120624, 64204174, 405493490, 81616891, 611131843, 373961056, 31887478, 941975091, 354291387, 14507453, 543624834, 239099586, 232850550, 364726863, 3378863, 684976052, 609045917, 176262996, 844104205, 636116160, 165987466, 307163798, 296014505, 627877825, 628338355, 258162076, 96847480, 414449851, 323653285, 173468302, 904475137, 887377547, 409954659, 465579015, 442437690, 646867859, 677025692, 471839676, 669781994, 747108449, 180829551, 867486199, 454418745, 660042544, 723329622, 84025690, 745316785, 436589888, 752101454, 992930453, 933567447, 481029695, 912536329, 615574784, 128863845, 466746007, 620918639, 975714452, 358768143, 325917126, 827968497, 396038248, 721243796, 832589194, 322393132, 671338071, 132608646, 157439281, 760067927, 686171482, 278458199, 238445655, 310752332, 838729440, 183949514, 461918843, 895688933, 917399846, 471717719, 653464053, 489609275, 577606892, 788697282, 6718277, 993067742, 787248531, 782934696, 855524498, 663028576, 45426028, 7776554, 869655214, 122705886, 960358685, 200033335, 83367856, 632683776, 730541354, 154317139, 213912147, 720950093, 775073911, 52231654, 249564525, 161849993, 712877291, 209895094, 916336912, 520829065, 273068520, 304404557, 287775473, 501787301, 824464490, 58249280, 843024209, 772035134, 231566773, 748677671, 885016506, 17206190, 227458021, 578806581, 453874035, 963183232, 638899771, 567424258, 825711949, 867369369, 123989332, 185612234, 468683332, 8786661, 357175868, 706824666, 710872769, 911016602, 242445723, 969452632, 733303638, 153635948, 158090183, 794249431, 918320593, 249539806, 94703591, 426549063, 125298616, 677995502, 944676282, 369385753, 618752511, 292590921, 942736778, 632496238, 512667461, 807757695, 743331192, 438409113, 807557538, 541022730, 110218030, 313088319, 544578735, 444289044, 491409065, 789291147, 373161667, 973072165, 165275669, 760557638, 447798771, 264908057, 611552674, 812877144, 501856902, 164960138, 752246387, 534524920, 71280482, 893811730, 778213788, 990691640, 83416944, 790517541, 723180073, 403016453, 449356557, 309326271, 461666443, 564080059, 172205822, 634134546, 569552529, 322268108, 688988771, 264143985, 544742440, 214963565, 98601037, 465988494, 929476566, 351851128, 705978655, 512075263, 287580858, 213155510, 347245387, 191845813, 428213659, 240575830, 502821017, 817016195, 791378344, 836033724, 532425693, 209308582, 939638942, 687170683, 684583209, 923510694, 70436146, 260511816, 653593520, 962975119, 766484738, 67819310, 491545842, 802992340, 412929667, 325702604, 202945042, 601883834, 866092576, 848681821, 337541091, 153584231, 247188077, 746955570, 852406812, 426944958, 752802810, 117552018, 47631498, 27157781, 742501462, 900953772, 804388189, 514168921, 226028010, 805540146, 570336058, 801199167, 357953374, 906932588, 328720047, 228659442, 203712571, 284371540, 643587988, 895289626, 627584084, 863441519, 560398825, 466899904, 561390709, 171608238, 100547171, 197668671, 246904268, 610700740, 597932825, 887945984, 550894177, 897308448, 107614889, 31486808, 579349039, 511182933, 155842532, 235510255, 146041069, 995940331, 29413470, 360584661, 72672649, 5740513, 912664498, 340870113, 105218394, 198237074, 115663533, 653621916, 85237302, 464847273, 878725149, 450018599, 34942406, 963212755, 579523591, 103407509, 616761449, 292278970, 95003637, 506239561, 858115631, 736840390, 192529033, 7288689, 787551336, 320719619, 815919189, 413364563, 962957041, 910854591, 889674096, 164511434, 979079154, 304907705, 404945946, 494467117, 975477654, 931500435, 952319585, 887040124, 849101900, 56474660, 54374786, 333199465, 695716091, 923831072, 455176676, 600455831, 94562989, 925542649, 187943311, 539442258, 928068389, 176490511, 107796618, 417367665, 485335548, 490763813, 131673262, 83980393, 429353869, 282380997, 20725518, 440834923, 864030, 2003635, 492408690, 750970990, 545089796, 87229848, 194189639, 965100245, 61292982, 695154975, 74424033, 930181824, 973052871, 269353100, 851881591, 987472882, 908335219, 510154037, 716902325, 330427378, 592969253, 808333645, 304970389, 825333051, 338126012, 149342501, 759120806, 373001489, 912386705, 856351377, 907145224, 563979277, 956325184, 376904742, 123568191, 833379241, 364672434, 120578546, 285872994, 410652394, 675399330, 252672155, 951828842, 283182210, 139679188, 176916593, 161839350, 318484732, 528029919, 98662479, 801514154, 380429525, 449051416, 844326742, 793089119, 2728852, 751387838, 288722186, 885682959, 832476040, 565380391, 895643108, 179402299, 918572663, 939945484, 604598448, 399813479, 279545280, 935137734, 430491396, 875101646, 67427902, 156083110, 262318215, 385270421, 269740968, 7220156, 833347926, 131554019, 518929745, 691684899, 613382086, 446449065, 405248434, 984715237, 217705237, 826942026, 518991701, 512917501, 855850963, 861158400, 840172803, 101069712, 408965347, 1447798, 268244499, 22675426, 392378649, 933452655, 83175699, 862742524, 432595502, 856877557, 377354311, 180858317, 318491465, 470259008, 324391064, 467114305, 737267570, 881223536, 482422258, 337750762, 38733608, 103318553, 484047882, 721206894, 209904333, 37887386, 496520419, 280995119, 286369936, 448769308, 133189586, 80152089, 253055568, 775900824, 92566222, 113859190, 728933291, 155007672, 543979047, 75439176, 345751717, 9304259, 897375235, 188862253, 464132320, 103703606, 740774257, 793107279, 437009259, 111764901, 528783810, 794107446, 653733677, 461302978, 29523593, 144557688, 498252473, 607164488, 630270905, 125532610, 59093559, 255559350, 45260641, 289697241, 890368485, 99406637, 146656137, 144112646, 273272193, 932537456, 681840175, 370902043, 912817842, 285233267, 642124635, 645882889, 11636569, 414701574, 708380940, 286980437, 796638965, 117163306, 446200883, 626050481, 5861915, 833478856, 389224079, 943594283, 590750087, 461674811, 502038934, 273948297, 483343728, 786315542, 324965889, 393696474, 63135759, 568605286, 882407560, 880678698, 392702077, 372518158, 67041501, 403776257, 672355876, 340419898, 120610327, 157478422, 589726017, 828445428, 708683210, 512296183, 289483193, 802245184, 681417648, 743296875, 183957219, 468130408, 150934527, 353173050, 318266661, 763174648, 400698914, 332192521, 108029463, 602565229, 753329394, 746184332, 153789778, 826831756, 848248771, 234961937, 612366190, 424089070, 656428030, 972577310, 29587977, 711359314, 44082673, 703605820, 535430465, 185002747, 681689196, 873437057, 649550415, 732725277, 74734112, 392316042, 699017049, 265668584, 318291916, 568482150, 724529740, 987518322, 239442387, 67038198, 342299832, 459473670, 554100324, 309800817, 203627627, 763817554, 719019803, 712297570, 787578601, 482709594, 319460623, 280013736, 478845177, 173604924, 780037764, 687116277, 755708642, 386764129, 353865212, 93364129, 74817193, 926395363, 722759031, 249821987, 706283234, 729134286, 144265172, 986596086, 53194129, 675111557, 965146163, 76689126, 105132056, 517136607, 517269000, 780380769, 257353684, 93049527, 649427780, 766866425, 159896734, 324603205, 16687017, 358775604, 676102244, 335275450, 531790642, 763772400, 528217623, 651865486, 826877985, 675215645, 475673497, 208359945, 114312269, 539370185, 908422229, 578788302, 543981335, 425656811, 50392335, 759898771, 839067096, 290119801, 922931865, 552696408, 82663412, 269803159, 68540107, 378519547, 455009581, 965821689, 472559526, 7654823, 830108119, 913377355, 599698802, 235573222, 389470662, 135895062, 420633555, 804703737, 510780068, 595816751, 835673004, 61544695, 842695896, 533355871, 768703653, 356163338, 676411806, 715383647, 673731012, 449208125, 680442112, 264837471, 497249538, 461497200, 392138687, 93492881, 502797412, 576226423, 229657299, 488706135, 644398127, 669716458, 671523994, 733686611, 119566589, 824952701, 956090608, 942789560, 274694166, 230948129, 990321595, 407557252, 769313115, 702289073, 456839780, 621718402, 205830827, 164483654, 469412178, 856103486, 239406407, 539296948, 101145145, 894657465, 567221495, 800091527, 49833246, 178647966, 398387653, 446259306, 344831988, 104335921, 982591434, 239871664, 110475493, 603540821, 335751982, 587964993, 220973760, 51391661, 525463797, 286274745, 880879224, 737256807, 20309903, 630404585, 221153322, 567664616, 214849802, 969192544, 701980664, 643500759, 45476123, 413813676, 877194394, 332342811, 7393615, 336390167, 826133825, 830510305, 671422071, 266038927, 72989761, 948366916, 951461370, 64138318, 114661254, 729058447, 209878061, 472028580, 422538539, 975760595, 528851920, 798046251, 49147837, 506519905, 450876508, 756749619, 212568081, 417733042, 577879923, 110397228, 653432737, 296725312, 141663462, 756381779, 297794187, 964609652, 764518612, 231680876, 132337383, 639223459, 183909542, 609203080, 962836005, 501528539, 133618860, 41549098, 114810833, 673272910, 551191994, 138898463, 552494643, 359714657, 395602197, 72977133, 467507272, 935781363, 462936755, 314723961, 210350102, 953523210, 180737360, 600849061, 758330599, 430942328, 521861481, 981572369, 458553270, 872438407, 894465179, 611543608, 584197972, 619428179, 831451977, 864503350, 296303756, 906788136, 729219142, 805108404, 423275156, 461508081, 481133778, 38855210, 762971494, 821480193, 900426118, 730785807, 914769109, 429845378, 163023158, 214310275, 575623173, 56358519, 461927519, 990389070, 119898874, 635686366, 376258757, 489545987, 247966518, 848452440, 64486368, 531190608, 639862303, 725270469, 174114560, 876094513, 900518122, 358607325, 541069603, 429093071, 46216887, 653187495, 896031710, 471432146, 59013503, 183153175, 11754568, 867322213, 110612822, 763281752, 6935131, 845282535, 352436156, 358805355, 111797179, 634452050, 658825547, 244203145, 71733861, 585903781, 83559988, 24515258, 187209021, 358203640, 949676432, 962075662, 414368321, 971001168, 714732721, 581891994, 640249886, 691674212, 305444991, 93831071, 260026462, 709908698, 868346354, 374175549, 539969787, 218710215, 944850244, 697392339, 537425057, 176222147, 160228574, 627797652, 783959419, 6986907, 353865581, 84166465, 488143416, 574303903, 750661819, 929783220, 50361673, 908901326, 22030935, 618037800, 186970987, 740889882, 190160500, 998810696, 45068555, 28050447, 877501039, 784348979, 80470232, 134585213, 713563353, 532880797, 658868578, 436523116, 124665004, 957175867, 331333273, 212752559, 27276921, 488764747, 805260628, 576609797, 349027776, 625848142, 694430909, 501615669, 50752324, 299476132, 747844009, 465739115, 95287383, 311957950, 504436690, 236765551, 200311507, 137914598, 274587737, 969769569, 209375851, 693313392, 347514698, 591579429, 868293509, 319642005, 706888015, 536601625, 87519169, 506144111, 92347935, 572230457, 363455776, 224946672, 203221472, 886521663, 622608425, 738522976, 555259246, 441111641, 812818470, 789433941, 273883034, 673340487, 850192188, 763949587, 609156850, 856948473, 966548816, 974805629, 128549624, 260096516, 527879019, 178706725, 216309353, 646157758, 632917860, 822502306, 289745908, 213064145, 618800803, 473527086, 222553995, 663719618, 555174116, 529484700, 197675327, 301681062, 835798057, 906132493, 415862227, 581593122, 55349816, 882420180, 295028859, 617529566, 795793559, 794627069, 592353075, 478522106, 968301844, 47540545, 877035678, 909923580, 626448967, 467563365, 196265619, 421982889, 285903267, 550435259, 816039673, 777679257, 80437119, 506484984, 474408669, 277216740, 364148016, 62170298, 912341325, 22615576, 499110439, 203470950, 93597059, 523920926, 903468741, 501743021, 346166380, 182496176, 725865681, 388655058, 679465019, 156676708, 446761581, 73491726, 294756861, 668742619, 303032347, 187303694, 688869194, 936121342, 412584984, 278202576, 97441356, 621042398, 729527321, 641752071, 368918449, 523434984, 967027359, 848268183, 208578484, 176890476, 137135533, 747173973, 709444621, 259080251, 900935396, 769931305, 54864496, 709297176, 692685993, 382383196, 691360773, 273173426, 140308849, 14939433, 746157443, 787883722, 296030443, 509604720, 630835402, 806174913, 15316282, 868184977, 663515216, 806698380, 696657123, 953656159, 890843642, 280980849, 765882623, 446844182, 327373698, 493349765, 45438492, 398452446, 215312114, 880051384, 204128587, 196792569, 78132950, 467852265, 852460719, 619725586, 604430619, 545967870, 765296677, 585638646, 402676850, 990332898, 903826872, 524213002, 666883746, 681363011, 698784106, 475059953, 814563175, 546597081, 703072468, 750195568, 145787964, 849938471, 783035026, 588835767, 331339617, 753325063, 584464080, 406313932, 521120787, 955147435, 474150612, 187160610, 732986993, 211496331, 774259669, 290104330, 229247733, 145290324, 784940912, 35356505, 443644620, 34445725, 803063779, 464289690, 760524793, 22831250, 544618369, 609610543, 325425342, 581220404, 308943501, 243663230, 285068656, 180251801, 571611112, 909870640, 338151481, 972098041, 17519865, 591741607, 976668095, 158179017, 727613293, 210221047, 853693627, 286617788, 694973288, 801791903, 882262200, 990268716, 578519597, 411582926, 991966666, 932004288, 984066344, 402234733, 914509499, 466651919, 218152853, 365177026, 524055170, 346678289, 432083494, 501742161, 558628899, 379554301, 565050076, 336298216, 674561262, 122228169, 673460146, 891399096, 631959704, 767791547, 488248416, 6230584, 803564087, 56250326, 934783984, 805100108, 456819672, 738879205, 455543091, 511586513, 799974087, 21996473, 238885477, 179445346, 509864521, 704713016, 880775009, 600147529, 83306738, 518118097, 343892089, 162074778, 258333146, 76729376, 570913007, 703399785, 48963153, 207695428, 172220197, 895360944, 406388443, 846251037, 708405321, 906614419, 122716614, 929530694, 734045599, 142273185, 135107145, 630161299, 873817739, 946434061, 428236575, 854169338, 71056430, 230343570, 54174322, 216025722, 260150837, 326897782, 77141658, 821087699, 836325590, 432290011, 904643949, 290880692, 301562573, 867770720, 867357533, 269340346, 238918831, 741936530, 907859595, 79071978, 602912200, 245151817, 369107638, 322841131, 605357396, 342428104, 740063920, 791005801, 184038290, 263229172, 452853705, 931325753, 743707369, 69522385, 239015276, 157787034, 82510325, 217363687, 467733873, 25085833, 540961051, 26434727, 922339153, 761507272, 429544057, 829303907, 130155108, 39629630, 287126659, 635227088, 619746517, 877448836, 969049863, 858395571, 223462115, 318814082, 512485080, 650333240, 757838630, 28452750, 647566225, 240907461, 915099894, 137058473, 229743583, 459039854, 132759692, 750295204, 141102832, 445339978, 762902206, 281142245, 568685461, 138989968, 358925848, 627273047, 857054994, 658846977, 778603902, 262141266, 717709197, 842210635, 70608544, 641914577, 558826237, 783716469, 905413765, 825560210, 955944062, 860484079, 565730753, 224838247, 968072586, 790448347, 117753061, 714942084, 562086127, 939598916, 201758244, 155135551, 796811896, 345133701, 391310878, 940351319, 246550407, 685605390, 770154063, 789387765, 999048950, 628185217, 627120666, 103616579, 614597180, 332930335, 876146589, 435239934, 911359241, 999491382, 610274913, 382605071, 129696496, 18734418, 899119564, 944125877, 767695153, 520624312, 216689302, 837926324, 984441656, 449642981, 974458779, 335245469, 329569860, 920140348, 647058635, 117893776, 824490115, 130935102, 331135843, 499598124, 648270774, 355572927, 684563675, 531084995, 75557496, 493388516, 882416374, 157515220, 347557360, 511735669, 256186148, 261453256, 998018132, 651225502, 979749295, 690734294, 520693450, 8260957, 278784283, 783644994, 461488691, 320458219, 475245894, 127600311, 616849522, 784408932, 202840450, 497553843, 149319824, 177173078, 732974719, 239065367, 942261965, 662708747, 828881363, 677117416, 292456243, 248991694, 120250202, 5767231, 425585354, 7851988, 899361828, 992358065, 730917617, 810842978, 316326986, 566243396, 488952876, 109707843, 43822001, 864754464, 782234475, 205513343, 714879000, 843683084, 445608454, 291972087, 675900362, 784326258, 163731739, 799688524, 876458431, 239333436, 260145863, 626505732, 333525744, 955514354, 140859287, 494209489, 16111257, 857009803, 165460895, 116830908, 416363871, 786722261, 368437373, 573692402, 6493599, 266193717, 647630053, 185219918, 769749423, 975373402, 277312506, 94897194, 598517829, 16169549, 35343535, 593134816, 960009011, 466410692, 808325946, 141626699, 950008745, 245572570, 516505446, 162173351, 309206895, 632118540, 514696637, 605555970, 308677320, 135272987, 741618676, 326555269, 57694607, 424897175, 320677939, 217564046, 658801465, 697151468, 838066006, 681747907, 513718375, 956130676, 783141785, 918867123, 983942629, 213596568, 147176845, 715927751, 273322386, 196443712, 388523765, 644323616, 999390151, 933870926, 446951577, 963628873, 368148123, 520245415, 491133342, 257459563, 528275452, 349098454, 976687978, 775609399, 398884456, 849194433, 721888500, 264978092, 31553452, 490583243, 340044275, 527014707, 863538007, 109166054, 64285700, 783329489, 557800346, 392999331, 53636596, 633338225, 348384479, 723289729, 365794827, 64138163, 845090379, 224573482, 484384831, 798618499, 619659932, 374448079, 812834831, 358218230, 197617218, 833306977, 825896054, 563707532, 977176744, 263349467, 893280694, 919554379, 628720392, 85972396, 551793944, 343563605, 525403393, 469651510, 916172456, 776288273, 161851112, 422288692, 770134770, 61127769, 962265199, 835182703, 668431003, 629339082, 862925653, 110816283, 64703552, 955992243, 436685007, 807375526, 662906311, 596522138, 652107180, 238410333, 16894302, 256851292, 317766003, 265034198, 887094865, 271918195, 590311667, 875514007, 824454483, 89233126, 188992363, 210850819, 796002953, 447544513, 367234555, 397308480, 70587173, 165156067, 185637328, 790669847, 619049965, 290568111, 560979059, 241633814, 452308073, 603015913, 694841660, 803812632, 406807358, 499486095, 629309774, 66567243, 135035547, 115714809, 112221254, 315945104, 320638727, 852610861, 425885586, 247439741, 250512979, 870431866, 881780987, 246036753, 993929539, 322903578, 197767467, 815336036, 779063422, 59906959, 587047562, 45808307, 57937325, 880693210, 519446348, 54507470, 25590927, 998596768, 474623506, 572831895, 220253518, 770088557, 3871081, 666075296, 299415193, 912929337, 793591488, 858767166, 764873040, 666798602, 476675568, 337412792, 706240986, 796941849, 969623500, 680530693, 928201588, 8227460, 379618238, 479143947, 704664315, 339893245, 205320767, 88034572, 395087684, 152929385, 21421539, 548346163, 126490169, 961726901, 219814682, 165731688, 971015593, 499163122, 199513669, 52199328, 195223235, 494816458, 585935943, 387863454, 736002625, 99639836, 627964799, 671838521, 234148705, 229789000, 539224135, 349760305, 70268354, 853752821, 609594033, 298002244, 162800032, 885705510, 843432832, 444690285, 149649943, 596537244, 916244106, 409706957, 618397310, 176350696, 811662038, 672774404, 975124487, 563776780, 929427334, 984813968, 517983238, 228377011, 598348089, 666227411, 523134413, 307605628, 500665712, 149414386, 677149017, 549436232, 899112490, 526775975, 303213264, 724811474, 726540142, 980091850, 306610830, 788466355, 758648765, 576321118, 940658783, 574987932, 915908633, 749435766, 310229982, 46535775, 958743925, 791390209, 275662611, 449807548, 972689652, 613161558, 319485586, 603184660, 719134472, 53667803, 918718739, 329031489, 990532551, 332673748, 146829243, 588697213, 256935384, 567465862, 33949660, 738514080, 893460709, 693833147, 80494333, 336450571, 471749690, 114533731, 95189390, 438582063, 200239994, 122075667, 645492364, 197878820, 947665059, 386956291, 682218043, 110898326, 119434740, 839037227, 892284520, 603247347, 632779088, 854419104, 931626984, 607056551, 818840077, 306839241, 546175738, 962600909, 114807994, 711354505, 937804745, 311693810, 23622516, 460414806, 862938287, 918947937, 347804324, 388364706, 651153353, 979991135, 530263810, 926857502, 751526785, 611161956, 875286994, 53719857, 51433607, 990696237, 221444073, 801469192, 144555287, 535378690, 900312071, 754851558, 545422196, 426213856, 47561726, 341992216, 998001728, 625502280, 352863954, 716142681, 754370256, 992357318, 875233517, 153482206, 59827068, 985895199, 24542904, 881008341, 714593541, 563282282, 51029856, 935978217, 47626491, 387226174, 787382560, 983275271, 605789397, 655698456, 934342095, 673856270, 276072661, 81412205, 530765858, 721010451, 829722604, 590883709, 616331196, 690722423, 319366997, 865197472, 845259130, 594556039, 659808930, 783450672, 320595727, 252691514, 60475723, 757402674, 747819498, 865858647, 213322724, 164176580, 527463738, 701007425, 594920580, 302972650, 19193525, 330738698, 119291385, 52750815, 966199322, 350704705, 407157877, 859453898, 373295423, 238599371, 901058691, 667095757, 867932761, 455059431, 254298748, 466292714, 651868912, 155173372, 881972988, 794942669, 185605088, 94609217, 204042951, 344878661, 301005603, 633677611, 853544153, 319667288, 389060916, 317200663, 575784043, 835902397, 235601071, 819751564, 692340192, 979300467, 954770278, 450766364, 157168073, 387795621, 1634777, 789984188, 38328844, 113697298, 555349379, 541154369, 951466139, 647317712, 259860514, 717933083, 815063627, 132447035, 417255925, 554036163, 283035018, 230327136, 112945247, 120617550, 894466115, 526636115, 511083151, 101813306, 358497687, 871435940, 667988272, 716403217, 865392723, 44106095, 12381832, 30021446, 500247139, 341500354, 612494542, 188690584, 655175724, 338728389, 315355383, 34132705, 989456172, 152994982, 507186233, 469120867, 331503626, 638787356, 84554681, 380867712, 981203730, 960074581, 671197337, 446322541, 375251430, 546390728, 636219516, 852536819, 822009710, 478628305, 657427168, 787742606, 652789543, 674010638, 720456172, 433473633, 451345242, 871625138, 84350906, 613962095, 810649733, 613441207, 54852898, 364434446, 828492016, 340322462, 963642582, 894078353, 531931807, 940921505, 199470301, 435405984, 316994131, 648235580, 315103884, 763662740, 907673742, 494302293, 958172118, 196578530, 999190662, 881995453, 17843910, 150126383, 867510246, 637835162, 223405939, 706660798, 936348570, 389534642, 550700423, 501034287, 264467148, 119781599, 248093619, 90866377, 137965301, 678873609, 905597277, 116316560, 643606647, 626791426, 562095934, 732598093, 892073246, 518986752, 342975463, 351409138, 216819125, 423758821, 807925258, 20881178, 870529451, 362011254, 853060626, 379063640, 193581913, 353557703, 336923467, 575371413, 644302764, 197523419, 631077425, 509533590, 411180564, 733719896, 513061386, 82787777, 170556149, 399888003, 708435595, 168007096, 36063767, 47902104, 325936675, 96335956, 135104363, 11581912, 9358538, 567021182, 587679553, 496969064, 39516246, 968367715, 286341172, 348082223, 556039005, 913791274, 157876854, 619889992, 702203254, 253470417, 15919778, 873919467, 229540691, 935950027, 893978431, 150716655, 304971645, 458670609, 929184330, 359198511, 540958415, 204598775, 663818257, 803104643, 53275963, 601336162, 286334653, 703151558, 351295411, 38926544, 869924988, 488381370, 91070826, 781694753, 374438280, 874635535, 973146288, 863506884, 105668264, 20599938, 415893896, 261886942, 536093190, 644653884, 778561899, 73840448, 926520053, 433255149, 483957559, 547748530, 985928040, 939792564, 872429635, 988528229, 863606342, 925944837, 593276224, 673604381, 484812588, 311195623, 718075963, 958716650, 733519166, 575120868, 290906744, 779553283, 457668389, 631060810, 92446984, 565387399, 892859906, 134519173, 215193443, 451431017, 998076245, 725634551, 990351651, 283372560, 368922858, 325765585, 906580202, 467411314, 6985318, 122978397, 119186657, 580795630, 425220006, 543896706, 745655916, 278484049, 980864017, 611651031, 208961776, 759485097, 368442009, 683394105, 534220659, 905886670, 851012089, 448153294, 97977100, 286454727, 105333365, 303281199, 51441183, 155988201, 504502583, 627318462, 125361624, 177886440, 397897954, 192996784, 804773413, 273139873, 328106368, 754388633, 765504801, 118213213, 399318512, 904915301, 791902003, 582357486, 519724197, 360166261, 220030616, 44488453, 887785425, 84587360, 726830738, 678201391, 565862952, 655425030, 281101492, 878843276, 189525774, 350036138, 916257835, 926194684, 372849714, 875946887, 129074617, 713747500, 80707785, 449712658, 959651471, 363239928, 793721072, 306128749, 17093453, 727970135, 142440751, 924626462, 14707715, 491391609, 444302386, 296053533, 586387341, 835877380, 834015938, 658955473, 643472256, 929662948, 602056171, 871117328, 669645298, 716439437, 494991420, 628574291, 90142330, 422539152, 724267798, 308574408, 864936907, 464932771, 939854407, 986202376, 341201022, 584379695, 734873756, 635813895, 573979548, 122739911, 472198413, 41422051, 871528334, 224275925, 740496966, 927685846, 194351525, 763231396, 670303541, 821856613, 431692499, 597290829, 955642262, 386472740, 740506255, 100423869, 748378040, 718352118, 696132553, 116234688, 652305300, 655891407, 591933437, 203954750, 81338561, 380133626, 985707387, 577037055, 50584276, 234936317, 292563033, 55333863, 96491418, 266272973, 295070141, 927979121, 982614306, 539714722, 350224953, 474965009, 569974231, 331281791, 922097064, 477078692, 572706351, 944160437, 969230918, 738347737, 805904972, 181191490, 692501964, 511826630, 865825234, 936331339, 748204817, 776445968, 873129014, 253569492, 692071257, 482810633, 599280517, 900811134, 389081460, 79315866, 425174729, 965830579, 792154561, 82955365, 8619867, 344019405, 993073488, 960184874, 905692908, 540388269, 556303207, 326837170, 395839452, 978701610, 899794849, 471586318, 494910484, 324505690, 569112021, 466092954, 400133318, 12050245, 454045205, 854545505, 938898032, 693976846, 646258715, 915783371, 134683087, 188004251, 300057589, 787005771, 142862763, 904483401, 589379195, 214637614, 614517, 915703257, 303347206, 537346776, 59957652, 281063882, 591143791, 999602970, 729890994, 161897330, 371869861, 805577459, 188901402, 982281982, 750922132, 844427909, 524120436, 446053981, 586988383, 571710122, 699366898, 584472797, 786045199, 561532485, 502234191, 737505170, 619209219, 947536718, 697321240, 584754155, 155578532, 396270743, 895114051, 706808875, 88087879, 894438678, 309181573, 729132012, 867406911, 977900352, 339556543, 209237304, 341365584, 811661858, 905274932, 318626859, 110932929, 889713303, 684965576, 335667175, 918861731, 306662263, 788191712, 114386144, 939937180, 248803593, 997195637, 837706712, 277804562, 403147578, 1722411, 451685562, 656403615, 212359291, 986148825, 574019552, 689647926, 124988570, 434321938, 440265097, 834488302, 157317200, 798193843, 251522313, 784712384, 346969544, 99284631, 899876113, 604725117, 93871722, 817927800, 360998245, 906072978, 726363634, 457847242, 825799406, 391232334, 770643336, 45458540, 740289099, 201428243, 806039751, 982767701, 363710145, 584066360, 96404925, 932604985, 755775378, 657264916, 547454065, 958674163, 841264431, 783452241, 904953953, 152215300, 634067062, 116936844, 283182775, 769935896, 566916631, 538936395, 584793856, 341231197, 591919682, 623113836, 715754169, 551030813, 993694060, 971889358, 155066405, 881591125, 633507133, 245660106, 984731276, 145171256, 790364367, 92225063, 701699129, 246357917, 756052223, 392036177, 123048677, 750347531, 133428650, 370212987, 779649713, 512248525, 468784581, 572402513, 191111732, 360603736, 198705271, 699994056, 904000239, 47024991, 249494522, 987231954, 979109348, 822736192, 411682366, 642087159, 78581268, 206064780, 740871452, 672853610, 743359664, 214719124, 621600964, 84926567, 401081026, 284627910, 536695985, 848710182, 985368178, 593463361, 725394398, 62774210, 80066527, 587323267, 999186087, 638945437, 754177388, 290298929, 981064760, 153898589, 610149236, 820914294, 573995626, 908117465, 252160931, 748767413, 591125953, 750653664, 547945944, 654175242, 835736189, 795081030, 693406983, 223699320, 978089239, 94263058, 269174726, 264828012, 558407938, 122004260, 517419020, 260220572, 482999041, 363751107, 287610953, 288792896, 615058849, 756759518, 424052052, 463944303, 99024150, 867066864, 767533361, 933618854, 46764759, 294189717, 580164802, 843841852, 582239514, 934214200, 555921605, 573497411, 662408174, 972695598, 847636794, 430169715, 685186679, 164172556, 365200614, 343211792, 219373349, 479791519, 271338414, 15496764, 263522665, 802671697, 461436793, 329011495, 687743892, 454461776, 327855815, 263533998, 90965711, 954147880, 932284590, 100195172, 12429559, 36577985, 719398893, 200421895, 818331954, 382366877, 521451815, 957479652, 278318183, 136731386, 852922193, 273592778, 233585693, 845105921, 944071770, 640364124, 294368709, 60433577, 158322041, 902718814, 759289386, 890762477, 368567230, 968790560, 159737326, 822564044, 192358673, 401857752, 576897064, 958081666, 147077233, 998286289, 466044942, 271332533, 392490981, 443083653, 986836569, 304948883, 752345834, 188302890, 638642317, 115466708, 941271695, 900762116, 921896368, 95387701, 825276649, 137348776, 275691383, 364136058, 675899682, 42622409, 202621126, 157123308, 393880416, 7996186, 697513593, 176582401, 903815338, 829948172, 165203074, 526546532, 418445881, 739380421, 299162742, 550905847, 461200473, 282781320, 737220123, 377156516, 419378577, 474142583, 426224939, 396095184, 180167890, 791689375, 575182209, 50536139, 817896305, 116876320, 539162673, 649503891, 839373563, 607355459, 399037709, 870551259, 970322590, 718420072, 1147164, 32387555, 249242543, 189683947, 920333223, 670950582, 411085988, 619387956, 810169650, 653565845, 315756728, 930385218, 546017683, 823791229, 274049411, 678249098, 923125562, 789538069, 70752109, 568304662, 136753929, 647381595, 913204528, 229971754, 514753514, 667300637, 316144833, 521456742, 819911905, 8970835, 79491607, 406207140, 103499492, 679125614, 25960468, 952512651, 236596617, 534444633, 826978586, 381139986, 829753077, 591800278, 689499765, 344436149, 619298230, 829084585, 732701312, 106297122, 555971591, 279204774, 642220986, 743058603, 589140504, 16051757, 886112776, 205015879, 603975182, 263833991, 734935359, 804258204, 746697184, 358370431, 734804573, 534770799, 964012949, 559907417, 275949210, 351560452, 97667338, 558626975, 774279545, 315689070, 987240052, 881457766, 333350870, 315163586, 411845278, 212424308, 513299092, 38194973, 631864237, 747836497, 907472812, 845776243, 819833959, 399934212, 94508477, 376420921, 215255062, 124365975, 219138804, 590658459, 670014267, 224632729, 396319612, 552955055, 106928547, 312379733, 795922086, 791810316, 358330555, 535105406, 755881199, 381728590, 635100570, 291597630, 486601769, 478386077, 628178193, 587207984, 579733576, 212450373, 199349220, 637420549, 712843426, 851212952, 424476431, 739452331, 462681930, 518901058, 676849557, 622403954, 403334870, 947041773, 303781834, 600175144, 704797757, 802082192, 165862590, 286311872, 552123291, 236897335, 197983231, 190551943, 403011103, 993039434, 709207722, 334326879, 224915654, 258707369, 238527831, 763107136, 844526404, 199290678, 588369393, 964801615, 440292225, 179831414, 896464141, 790348623, 652770854, 255902662, 971952719, 413988302, 791744810, 607145440, 371806871, 932490487, 893076998, 583205938, 771004334, 203599255, 690512657, 757108494, 75820949, 32270788, 296009628, 44544213, 655448173, 438775867, 885309404, 451727364, 477829997, 271700919, 460445294, 242949607, 773686436, 486428664, 866078785, 986010943, 265232359, 478689129, 293655375, 423046794, 686133160, 324432738, 491291682, 73423309, 715330036, 826561740, 417053564, 384189752, 477619730, 367734776, 922319603, 804091759, 728755421, 748000486, 907477861, 79458526, 253127981, 10614200, 485487864, 721142598, 654222201, 54901610, 436356824, 680410015, 730745282, 267317212, 984956715, 617290627, 505344298, 289890630, 465217610, 529436193, 792870800, 432396510, 669074542, 96399337, 387229200, 374916039, 378097220, 222952340, 255766696, 544723275, 920939197, 270653164, 703798618, 682480350, 705637075, 770661485, 34427175, 104406281, 188765476, 743884852, 965434131, 473111345, 450853081, 310409447, 887881310, 504477148, 387712926, 689315761, 568283324, 935671461, 286029471, 483502942, 458741787, 195166498, 679880676, 312317749, 292723171, 395496053, 686426310, 996075082, 704154154, 377681106, 51206924, 712575111, 706468246, 706101393, 16270821, 804871068, 287180685, 166580261, 187282088, 837186687, 657307304, 525412762, 183352891, 402479096, 425977544, 333410951, 555187272, 986100694, 603587915, 753167155, 75890437, 942756075, 800834620, 700685195, 466399033, 651266591, 597041722, 329479008, 954426749, 249810822, 517140462, 666209919, 532262606, 84852526, 927898365, 983718074, 176432362, 926809931, 71924190, 450443343, 324660665, 415423032, 865266989, 427005938, 697064383, 982510521, 481847811, 634698057, 270031951, 39040688, 838792522, 177462243, 261748947, 683413779, 703025691, 415645433, 767443793, 989542348, 271042576, 345061324, 448706598, 13793663, 811941333, 294317991, 737167612, 672604096, 180402254, 30965914, 805060416, 386232052, 792000040, 853508424, 311197049, 690838664, 242129832, 663135620, 234233593, 939935520, 623269287, 832248683, 123661511, 46471482, 703864141, 999146761, 971410495, 280854604, 526704586, 808765922, 251547606, 178181893, 707753140, 773161875, 612842241, 478770122, 31442139, 546221803, 364354863, 939166739, 116935058, 666771274, 544850612, 144121558, 821246736, 910248102, 169566417, 500263687, 492235389, 657900604, 511963501, 980300785, 721033589, 594837437, 720586962, 247800774, 879351982, 912546459, 402031308, 960070417, 796577935, 110614200, 690059913, 88584574, 630826476, 288572302, 959165517, 322462081, 598036772, 257808917, 535583896, 129696883, 561163979, 989903954, 11087182, 850519291, 486811258, 590294264, 188167847, 62476711, 39849758, 631570060, 94606707, 991779830, 665729350, 340089693, 303543758, 321454660, 613224775, 615340521, 893708189, 161407382, 803363741, 369059191, 121577980, 42451580, 787268913, 966916317, 561297647, 207909721, 210167009, 270431741, 376600337, 265853576, 944240023, 930201027, 842203581, 659400178, 733892127, 858180522, 857348699, 936557007, 652696701, 830829654, 186876550, 485423064, 374517028, 897570381, 973101805, 391928049, 713269102, 338907859, 292087237, 520423337, 864433647, 700013001, 421672607, 550958135, 802018252, 601958628, 242320942, 735440012, 501431907, 235170713, 889441431, 399725872, 129509577, 331922620, 440420266, 621015060, 459259246, 947141031, 346832352, 802679526, 264148184, 636410303, 835025035, 441453475, 338757876, 357385411, 412818738, 776472886, 349211232, 340484465, 287636055, 252625573, 675625906, 77858760, 708537683, 831770122, 151183259, 361615505, 38282697, 584998807, 525564119, 993492276, 347511723, 353596520, 54224448, 540998373, 723657553, 671216611, 173796741, 828744656, 478208555, 958799667, 453689959, 569352717, 57472175, 516063084, 813614946, 576612200, 467852830, 821212168, 598413668, 862384979, 605818872, 154249233, 33819605, 889686902, 635242543, 877891485, 429311441, 605569657, 628463551, 292147108, 824090454, 574542470, 881028475, 343940338, 76919883, 341206574, 307531279, 749861736, 751628655, 860020712, 294371329, 969486711, 378778391, 81947889, 229382360, 330558818, 798683763, 454250109, 178168263, 433164569, 964357484, 198506451, 597255839, 992886756, 363188758, 878558131, 694776565, 618769574, 510874824, 695633607, 458701164, 225913648, 623920539, 338208595, 254960842, 550234548, 99217602, 443149884, 535188801, 110445668, 802481075, 620454919, 879141573, 496465188, 208864296, 762602438, 96483977, 735556793, 32718237, 867818189, 548113652, 723780982, 993696519, 839046981, 622522636, 823659017, 444734394, 780129183, 517869291, 968953488, 968783709, 478635239, 450595681, 126457344, 691380843, 228864715, 287719053, 63446434, 322368110, 552732271, 262222214, 286967282, 828564131, 247046956, 599195393, 944776580, 236778018, 656356731, 969024272, 581864392, 678338017, 706952414, 46795492, 539991221, 811123921, 42212724, 429649176, 128534759, 31900802, 352836659, 682629579, 647622199, 708805786, 919170228, 209386948, 409612957, 430213434, 18567888, 713674270, 198440443, 170248467, 261952545, 371749334, 365610013, 572977544, 32979561, 215076649, 136922073, 248749403, 607281007, 75235002, 177160521, 899469301, 71344611, 527318795, 143811013, 974506400, 437111078, 344817665, 708751620, 721724278, 420132540, 705921331, 680536600, 410682640, 123933112, 448053005, 864494155, 405223005, 365146751, 161992311, 270447765, 955527219, 165887699, 460912476, 934866125, 790125039, 977304375, 711235290, 248242115, 178929019, 371159309, 193726847, 677577714, 337954943, 564604474, 165838995, 531612499, 79475005, 53368901, 322851061, 580360189, 829956130, 856339492, 791723310, 976015749, 150460892, 227104229, 668072017, 639220908, 645104073, 537796939, 844399989, 360220827, 268107052, 674949950, 427574907, 547033137, 443131171, 217263708, 726213063, 397458168, 695059275, 889408147, 225430703, 339120305, 868287045, 405125134, 124505455, 370077763, 424860418, 146364181, 954517667, 393253405, 988802796, 124288926, 702642292, 925697540, 715779805, 36087777, 553511641, 78637374, 724171384, 772029809, 286239265, 886096968, 758245535, 85062864, 23375907, 849437664, 417934265, 771557507, 269989962, 201416701, 368008076, 80587552, 672000349, 320772464, 723077799, 977295065, 791387381, 359328746, 205830986, 963168738, 227819294, 962488768, 37099578, 647126353, 774431254, 7687303, 491280420, 199368923, 236778014, 562635265, 559902764, 439693468, 790997424, 956655779, 415784275, 953429009, 156000872, 947814734, 978288544, 232690605, 960133435, 790199373, 444535510, 96120219, 771483686, 158503402, 573355511, 894400144, 574543783, 463996875, 652658718, 851641458, 686926039, 555133549, 896622911, 159017115, 5467080, 2485105, 849399427, 491655936, 516197132, 141691311, 82652524, 244460570, 292317836, 388752456, 820143833, 643051716, 141478469, 930592989, 685631167, 498299415, 400055351, 71517810, 172321193, 331091294, 774047662, 743050985, 762788007, 855374203, 268343945, 12854274, 417281797, 200373113, 978005351, 670566519, 95974029, 952790334, 199297260, 651930614, 455451101, 147630023, 110880355, 795521215, 356859334, 699145791, 312008978, 117867259, 273596194, 464009797, 728309067, 151508245, 991577919, 296646111, 974953019, 344051640, 503810377, 43951160, 14854003, 844208639, 889664218, 442242280, 671907569, 186867177, 112147414, 305853994, 675708216, 540474371, 862149595, 939988440, 784455558, 224406525, 289469652, 836516358, 6394178, 19432333, 723148922, 239865159, 941240351, 548929953, 825472592, 625813889, 391870898, 681651599, 898599557, 388409614, 786933183, 164068143, 605820861, 519165966, 337887694, 838311599, 151554698, 735544583, 15150386, 190975183, 514687536, 147451267, 370324403, 535804849, 350534009, 950558351, 264862127, 241644364, 866190029, 135749120, 793677883, 53559406, 572322625, 305270163, 295692451, 718173997, 235271893, 841955519, 874147992, 292959467, 291771133, 791188667, 141217060, 981391635, 652547117, 271999486, 485029868, 585860046, 249940969, 3835592, 547657178, 822927499, 194496116, 930572474, 527751944, 197703867, 294061782, 710256003, 510405858, 297131426, 836454606, 878679830, 631832348, 858941473, 330562330, 126773034, 275044957, 340619502, 804486392, 193446810, 787143738, 946534796, 914811214, 435493439, 585823736, 206122583, 821180790, 608189755, 307710160, 969553098, 72033855, 395711175, 495790320, 765293887, 72368139, 961017257, 279455024, 258249572, 646247357, 669884654, 787335474, 19963538, 412380102, 390124156, 287643676, 312428175, 161433615, 335998208, 886121544, 403703227, 557696414, 73105651, 94752273, 366877065, 456545680, 124991966, 239992014, 56986981, 156516820, 47812028, 104604934, 412632147, 660359627, 37833846, 310536831, 113591746, 126101166, 389409841, 953895878, 775361090, 56309479, 681604905, 656768820, 190848094, 335560124, 232879108, 470412609, 982649519, 562251834, 257457144, 471771100, 458218678, 404943010, 259262622, 703705022, 34155148, 755916800, 496420936, 314028575, 649543755, 218367856, 248534120, 938355167, 323100956, 644994310, 647507270, 886056760, 366078180, 810439734, 606098706, 270379076, 956843774, 530725640, 285305828, 282699194, 906621109, 946651507, 908582062, 940933047, 110496675, 431741760, 915988319, 534444526, 590370701, 946758788, 650032660, 917581488, 638596498, 524335123, 132386741, 562607050, 168887981, 85987061, 783733738, 145958356, 685600729, 492259631, 715864976, 860241345, 59948075, 39924696, 719685884, 162684172, 255554400, 601149838, 595198313, 857105844, 865469720, 734445541, 402979256, 793659383, 590612365, 44532603, 511477087, 374691315, 718342886, 590624049, 169819969, 366731857, 693905919, 437662101, 179693281, 689398566, 746281595, 202858392, 506254883, 96195983, 279992901, 403890539, 266343010, 581966123, 61086792, 857394286, 759545558, 871138029, 484818022, 890242574, 23609497, 663724653, 755499295, 245568153, 479993539, 685721765, 529245388, 150299134, 914545483, 146785786, 259135947, 90294348, 376767420, 838077110, 829514726, 291040430, 846034901, 9136456, 657287345, 265154335, 549963008, 321644103, 271532548, 653594756, 205833947, 674376515, 439890778, 23827583, 978120187, 727789952, 774574282, 907948007, 980696022, 114516906, 445542553, 310271159, 335251218, 766752643, 163607376, 617380373, 608116542, 344993594, 772741394, 132231444, 712897062, 212899715, 16726979, 687555390, 643258679, 697233105, 431919228, 230125836, 194635674, 731425293, 31263676, 607268150, 458934665, 320292674, 841316359, 608536351, 620247243, 7664194, 148960807, 823647915, 200837647, 94090942, 955501151, 239650387, 325309170, 103650357, 770960404, 895050264, 265838164, 540885961, 51004550, 191147501, 653842565, 331618596, 802129769, 751171356, 335739540, 839992190, 486654330, 272314216, 943867915, 624905167, 721475083, 519068326, 665239352, 208087861, 437754124, 66761716, 120900981, 136610007, 744865695, 486960530, 252924195, 463991442, 739188333, 33584277, 272826040, 716230654, 859313787, 825481920, 96858869, 562510541, 22161659, 865835993, 403708151, 33216862, 806384586, 240964411, 741251243, 999771445, 753892509, 210270053, 54677580, 321952588, 123763502, 415143475, 340828869, 827681447, 206493224, 798029617, 222387334, 221432656, 341835697, 581482586, 962994436, 359321815, 902847023, 254521566, 642259515, 763488024, 391103771, 947529059, 38671052, 294143431, 649485199, 943484416, 570761665, 714115242, 205256187, 359171813, 94975608, 222427002, 496777088, 100002638, 19646473, 604030433, 783579231, 408973845, 355033222, 696300687, 790525876, 966748063, 165843650, 284640185, 882562194, 724645952, 273347181, 893425497, 355037560, 761980987, 591240814, 357576015, 368935831, 2520294, 337804161, 576754383, 914933266, 293989892, 109959489, 496494271, 809497131, 734930277, 366764544, 363419016, 54405213, 986842854, 260127617, 457593444, 765100515, 703867044, 328076521, 463996642, 888897515, 600216105, 565894844, 737081776, 817905360, 202784631, 7440282, 505423506, 713292469, 569701241, 977909391, 208408619, 203284143, 828813020, 364118705, 570856205, 46452282, 722081781, 894009387, 870705195, 927661747, 554292313, 416688787, 870784432, 317403947, 678485483, 136948457, 217981119, 101121437, 573166549, 710740343, 674256438, 591075805, 899534608, 848108752, 15295066, 260578253, 897620989, 99497066, 478556488, 11384976, 808692900, 130483266, 59208342, 655825900, 803076335, 984622410, 786325712, 682650632, 188225434, 605458051, 367059759, 232470993, 768498413, 868125296, 660635561, 611261462, 750304983, 438917186, 344313041, 956087571, 481551980, 531974681, 257659373, 971041953, 918245967, 719928650, 106844888, 120854005, 72395356, 409996783, 793920513, 926430430, 725037325, 496299907, 576018765, 7362790, 696881178, 592765713, 452804453, 983207670, 447754149, 696752996, 582159734, 131200802, 662683923, 586368406, 846935810, 384833865, 757227089, 627455248, 805834053, 588397491, 956739464, 465585149, 313758341, 614590149, 758379397, 915120568, 769541116, 160317515, 623144945, 919962118, 44609344, 789661279, 576178028, 329094892, 338449546, 122033929, 284205965, 747441079, 186602123, 606519085, 538612898, 726783525, 202913777, 80610515, 717205827, 633982859, 679742123, 237149956, 103371035, 519648207, 922183415, 316106013, 811887250, 864694108, 521676723, 568226883, 363153031, 352971374, 312155821, 964326239, 836028170, 397311597, 290714093, 95875542, 360948892, 443508709, 521050265, 308195569, 589682352, 829457134, 961931990, 50619206, 685731353, 318345994, 716623776, 321018828, 747682361, 451041349, 702125915, 698174906, 484060169, 840457329, 172108339, 289630679, 636078024, 670198878, 909436101, 307826983, 778735459, 944307261, 945351817, 258709581, 511667078, 725247070, 240871499, 85529012, 209841872, 920124324, 10782771, 810898615, 22804804, 658643908, 839113418, 414834328, 800173665, 975159273, 502272249, 954717018, 161241987, 840985117, 662782820, 220519905, 605756868, 740963887, 614342491, 216816923, 554015504, 63702051, 621249905, 197759177, 264267273, 84788917, 143082115, 535057114, 562176309, 594530567, 703518702, 22167427, 453823882, 238974705, 621378941, 709499814, 841184315, 962770172, 636540405, 938617648, 369829010, 467526092, 912306488, 898324451, 90026559, 71021669, 844819598, 806985871, 915835277, 367407251, 276867931, 899751360, 369183564, 272116723, 426383412, 888090296, 272586487, 12935405, 584943204, 29540572, 763277607, 715439389, 787022132, 976788207, 681980732, 908554155, 278612808, 277907258, 309158280, 315158274, 472586759, 582495702, 536585716, 197731059, 874996650, 276931112, 202771568, 774972136, 768213853, 181098641, 983407715, 363490532, 977443424, 594300423, 812437630, 742236698, 527557103, 114650977, 282752030, 67731027, 231197844, 896599928, 996165085, 928511278, 149713398, 685136542, 701562552, 343348917, 573128652, 117959067, 408908821, 443666943, 321797335, 604397625, 444662055, 131560440, 303539746, 505598410, 618412995, 463345606, 636288043, 564627958, 383766642, 62564753, 193029180, 127168082, 920363363, 321050345, 521112746, 524128930, 831091521, 307545409, 966409985, 246721705, 826930249, 11791076, 889650898, 545397328, 444212727, 644402598, 548947614, 231636273, 708023454, 907683273, 733688459, 344683363, 339260029, 648678237, 702033486, 792724471, 64158496, 416537480, 936113868, 222225559, 649201417, 388357517, 584053284, 896619811, 987496649, 232714351, 784404145, 808647918, 356161753, 322426845, 208327662, 75142084, 393696633, 85661013, 513078136, 55950728, 937820395, 287114546, 629567019, 969009896, 477730802, 595558723, 850744377, 329495591, 785847758, 443207070, 6819787, 40201532, 831508543, 990544361, 119745451, 941521815, 465015874, 949063901, 241542834, 736555100, 776428351, 478326254, 168836387, 953802646, 762736186, 397851068, 935713150, 963744820, 779542289, 58922020, 769072223, 45409034, 489659811, 228156513, 563437771, 924235652, 424920050, 921182745, 652185171, 523633152, 946191525, 782606702, 76279443, 919387893, 61210383, 857556169, 151794988, 577444152, 830277308, 869593333, 386616002, 53479775, 1410230, 415986618, 483775490, 468736191, 300767327, 964768453, 168017215, 629127173, 654101302, 709277429, 938955169, 835475485, 710492617, 250573213, 559808081, 909720385, 969906247, 419478121, 715180636, 344719043, 206394899, 468838964, 996801414, 936376829, 39639378, 44162650, 709854961, 667035196, 275867109, 22375123, 755516923, 204183432, 16796735, 523882343, 64292959, 339923750, 53864080, 222711684, 928628463, 441903043, 920707955, 49603839, 90109347, 278292281, 293018617, 783295044, 533355384, 540671308, 857707783, 137399847, 872325259, 320532533, 465733083, 432603948, 14691491, 160959376, 884122339, 683859331, 97851806, 691413715, 433309283, 931799285, 478243437, 664569883, 517018994, 305335607, 121254323, 456803111, 694364629, 888022427, 8815124, 841774532, 246042302, 954417960, 480330085, 635708565, 773598164, 415189102, 739136548, 438956654, 21485584, 539297278, 507334338, 957407663, 282875834, 662750584, 979191240, 177920436, 866768701, 952710167, 416094252, 551790007, 19732732, 337479406, 167284750, 109581781, 222311782, 754246936, 209808871, 645907196, 109946660, 939324179, 335690855, 36543344, 42005414, 315505546, 339665053, 790112941, 729854839, 547689300, 717752875, 228537351, 428800924, 13354719, 757047281, 84229998, 318642337, 272058501, 664160750, 801277174, 865634708, 62623229, 686105246, 217857376, 311109160, 854458756, 886727378, 408790052, 666723246, 564684750, 110576097, 31959464, 659667291, 480181943, 21851305, 56994402, 86108533, 741144511, 486612284, 363960669, 907376789, 400725317, 226929055, 202582152, 960064052, 391283219, 826368183, 550258016, 633634877, 259567194, 405440725, 397354291, 472524868, 176062898, 332124611, 707896318, 773414464, 888550890, 585252475, 848296161, 468308433, 691326557, 436783674, 534989138, 7979481, 98757410, 651212020, 122456012, 361265164, 849646468, 202655852, 714947617, 661501982, 296334813, 218658599, 369710021, 386702788, 247631815, 419372186, 380969847, 93001718, 982805486, 234313404, 739535243, 639076856, 480428674, 860452224, 190890456, 550413186, 833504922, 700844511, 787466926, 815848320, 539718063, 414087799, 946321343, 100606101, 95897317, 272995970, 117577079, 42986462, 56141674, 807941448, 803782114, 304465456, 509752413, 137852996, 842004624, 546684561, 560439428, 895019970, 156013072, 248333322, 757951508, 763070690, 390340357, 443663455, 676530868, 361294707, 656702443, 8680422, 920903597, 452886597, 281654347, 734753172, 459450637, 249458452, 149447873, 947906862, 956150548, 90026636, 305959226, 950201824, 379171307, 924176542, 292244601, 132972106, 598206189, 493960316, 581557037, 791828547, 809799818, 568054117, 253108698, 643606159, 417806893, 956207607, 4140419, 962697761, 713349035, 646584750, 301464437, 449904599, 752010543, 3797990, 573655779, 582148126, 340989140, 505777959, 279553644, 157375016, 568739181, 692399593, 803761377, 863990676, 98663767, 421150182, 396457874, 705233670, 226028779, 496423123, 476528485, 995186798, 276919840, 839560472, 535891389, 932976321, 661940210, 298910151, 460223062, 312925591, 856175562, 728672764, 223550681, 636853434, 268315676, 437459716, 975312551, 829058067, 559212612, 390062271, 906261043, 955772402, 278502535, 148708245, 246070502, 666743986, 286716853, 944245220, 731750776, 624881956, 172964952, 559366036, 976722802, 938657928, 495528892, 956333519, 275736498, 285406211, 80813886, 20282478, 377255581, 446508407, 945234884, 721898833, 961463364, 359985516, 355415372, 624222539, 368070414, 887235317, 150682551, 891769911, 977207827, 913075185, 958428585, 636004436, 354446156, 601518797, 986903447, 489600796, 698469830, 921107383, 224793970, 293161178, 716177410, 652687613, 757997439, 309197582, 934636540, 698851812, 216392294, 878306365, 69314211, 224511546, 473713073, 929530492, 645076710, 689675470, 479848495, 273356154, 590215894, 723811852, 613519272, 752211193, 494656223, 19960392, 118234768, 651689800, 120272616, 94606032, 541100110, 609554137, 59613585, 944482324, 884438537, 929791172, 377346947, 106304862, 418110306, 326484247, 154916036, 420477202, 818376104, 60732024, 32682459, 16439468, 462921733, 48461959, 742315131, 294863513, 51066170, 176374696, 785496465, 721342108, 972306690, 690801759, 622614052, 332201110, 889457303, 798230369, 433376457, 126026287, 988671581, 823773994, 988877468, 553759253, 448341377, 782404283, 946226498, 993348495, 536718627, 160718842, 906726292, 694554354, 204537069, 240518165, 114848085, 377235913, 879133454, 567720149, 926918356, 561524831, 394968858, 542547895, 461416047, 107982762, 550108437, 113854116, 849088368, 829869294, 512243042, 791162525, 256932992, 530648791, 712583928, 873422019, 349596455, 42706105, 501028663, 731515081, 903797093, 625754989, 515436346, 337439104, 149397160, 649920169, 365813762, 314223525, 45698551, 243062820, 935539114, 237402154, 301986190, 60281925, 143210248, 663563932, 402596054, 530677526, 195569607, 744314377, 619544506, 691382545, 593694577, 376486382, 369207967, 782247416, 977437292, 5501512, 658090323, 84944689, 795024018, 834488675, 18807996, 112768561, 951084715, 541066877, 318767278, 241183020, 885124811, 113391337, 554484864, 407418391, 800902560, 893955234, 646593162, 799283087, 185557898, 759866193, 969599522, 387169442, 192103002, 503992920, 633062367, 332505100, 419283830, 876840304, 43339609, 833827849, 728593087, 287895103, 679807697, 22986869, 680889661, 198841547, 66972346, 228260328, 555431417, 70342182, 882346206, 934351773, 936687017, 829073773, 806070635, 882486313, 65539783, 79462178, 505971725, 613044125, 291749034, 215123138, 438937812, 320514619, 185803446, 724555618, 143204609, 643700476, 697210995, 436251497, 754401427, 213154664, 334334979, 852269215, 505559840, 282271908, 184507828, 693382770, 773411479, 6346891, 827039339, 795599626, 158255300, 299033709, 753656241, 830659342, 374361978, 261828663, 616923820, 720965099, 701863061, 436723049, 455468433, 141973728, 521044857, 710498419, 466177813, 759291733, 613755945, 664816421, 562104890, 575914121, 910527833, 793020278, 36062135, 493576879, 458741358, 735339370, 314327861, 24023287, 820144729, 129105157, 494220269, 658759716, 298949612, 46607795, 951113335, 113700577, 521777504, 415492318, 394031007, 894875060, 424717960, 874420285, 854553210, 823127187, 262184855, 575409756, 416266601, 993517308, 89374465, 558285020, 942146425, 577738836, 312856447, 121536389, 947739580, 457480788, 42077381, 4112133, 39901592, 734835747, 564886885, 831989492, 671884488, 605187630, 188049720, 328170963, 801317192, 361182046, 133939407, 152315718, 467555976, 573530414, 600925896, 697409382, 743080042, 159003207, 833413482, 105326580, 708703710, 738090104, 297595033, 99757990, 512314521, 581960067, 24136064, 90620751, 505169107, 866311277, 291234688, 238612227, 395795357, 300189782, 149368069, 943960126, 84626660, 379324484, 408591121, 958521846, 88747382, 763080428, 475490810, 89579182, 358807650, 341731640, 630937757, 204063168, 854590848, 750907391, 540300908, 702292707, 663833720, 777074740, 951783442, 653578610, 203898008, 12583432, 13702172, 276548368, 278892379, 236909060, 270924826, 962340244, 713030822, 463226039, 615916781, 771294628, 25016951, 965903607, 511981695, 808943267, 714350082, 694681517, 763733044, 781853836, 398078456, 624027259, 317162562, 552150788, 338728789, 546523858, 508562169, 92936269, 840145593, 404393593, 987963157, 213501871, 95853488, 294116916, 149941358, 543841075, 506962281, 414210045, 462058782, 15125725, 423631996, 242603094, 138134209, 898666850, 679790910, 903062694, 372642056, 616944344, 196964679, 576372301, 152135844, 903235318, 645732859, 697331505, 440130001, 610797896, 243301153, 24275256, 40027931, 507936284, 729094354, 337039823, 47826376, 663785844, 755413808, 781499797, 435709185, 954205552, 353016599, 170588783, 485504605, 625737963, 894115438, 226698197, 617100812, 897164555, 495455833, 844393102, 744604142, 183287971, 302645950, 650236145, 760698033, 260336815, 702370323, 835386561, 756718146, 772760503, 485115327, 883590141, 929116994, 365556301, 164005391, 404730754, 308515378, 725988381, 246535147, 579367823, 469373959, 368182389, 445149010, 986467563, 8968894, 167201533, 585309217, 421811283, 317590899, 178222878, 301657814, 544012965, 44433756, 73165452, 973095690, 137813070, 967501555, 765752359, 896718446, 424042998, 673240742, 345694796, 557021498, 726441732, 508362889, 20248975, 535100475, 65784806, 977165211, 907012924, 528171825, 1731289, 639267723, 474293402, 353932828, 907785347, 413943248, 774749555, 574005946, 778748756, 624774099, 512275970, 247736550, 52970621, 537561483, 590374563, 18659757, 471647047, 132421484, 539308720, 889597595, 81165209, 386334074, 609587293, 797999056, 423973117, 182180550, 719444956, 47650391, 685650390, 244697937, 776079685, 725801994, 386111137, 708853718, 701889016, 622694765, 523116271, 30762953, 31657444, 101036526, 435941957, 86128445, 592610615, 993551046, 309049320, 929719829, 66488718, 988319082, 27964512, 6472997, 748930981, 376036146, 661286844, 64773449, 283028494, 914900894, 967227528, 140480860, 610088144, 751524147, 407632882, 219028466, 374126303, 716656460, 333921348, 327391755, 39584421, 342684067, 156657307, 651336454, 884587393, 915787123, 465735553, 9140930, 600676406, 12393671, 76223828, 552411804, 460732489, 974411307, 532625485, 246937879, 986765963, 57197299, 738096293, 661386431, 236725803, 420984262, 692845579, 701918591, 476822583, 731848843, 626514518, 225705447, 332283079, 874783863, 552344544, 44847872, 665388203, 857946738, 525634489, 215753998, 256916891, 241178264, 56522942, 605034558, 972155573, 309840566, 122125712, 211887932, 862231833, 138051738, 779728592, 770939091, 314385077, 514402814, 385140323, 600213041, 792447682, 544167983, 713307425, 589796998, 417997257, 581812800, 339797405, 561831453, 380545310, 790862813, 958758128, 213037286, 409783784, 282646873, 696217635, 739328254, 300916499, 478197910, 852323693, 207253447, 734083673, 270308754, 773136069, 834547034, 487679860, 401064380, 611355617, 420381131, 774879509, 912024185, 667001144, 942337309, 472298584, 315547762, 579183066, 359217673, 269035302, 40866105, 860126459, 79699125, 57201779, 385485534, 131401351, 262232155, 664556776, 806531988, 894740737, 36968891, 842906429, 554649837, 505973901, 378500035, 919286039, 396090931, 541210840, 276394317, 940774528, 71872704, 180930206, 872462307, 692039008, 294538827, 412884671, 24982608, 833728994, 791128118, 509114110, 627316882, 115479166, 209375640, 792512985, 964675530, 602313355, 708176500, 760579437, 27543846, 701497203, 432662692, 248510485, 277585837, 601010722, 770645074, 646066732, 900812374, 185364854, 199263573, 111006792, 863124718, 113018563, 709873097, 535426899, 630966653, 3933247, 153850299, 236177612, 292074297, 688201810, 454028084, 829334309, 308430747, 498089641, 848225501, 846070060, 851957707, 463834926, 977985382, 206092106, 424216593, 361275333, 916090513, 492279202, 971226648, 19753338, 623122684, 290679347, 537182858, 578665004, 460683490, 845665249, 696238280, 693466653, 584199685, 480236700, 600286210, 934859, 464452036, 105377237, 279189525, 296244698, 283393553, 973151222, 417434933, 817140881, 99725434, 305449663, 463674294, 931157148, 521886540, 409023496, 874835892, 27796753, 74728363, 690507143, 944336639, 831702315, 740486420, 892444666, 811356379, 282809876, 812833665, 188005920, 902411382, 510871252, 547414856, 566178981, 7364041, 528636443, 802900305, 764141892, 88432366, 638039773, 654711964, 493293000, 328559767, 696547462, 376941072, 289593840, 788913519, 961549759, 423142689, 62238768, 558180314, 48852425, 119090551, 241807615, 458940877, 39469267, 729988787, 832711535, 585552458, 504228564, 632590427, 322824297, 14227390, 898103445, 675970231, 230586912, 355867044, 892691115, 554299820, 779168721, 745311830, 958900228, 122146048, 493682075, 667849754, 862834195, 479287439, 759536391, 803195452, 279081879, 343001026, 661214687, 272469110, 416187466, 825823443, 873377893, 858023983, 421993377, 637800229, 126066054, 279218808, 478466785, 512614852, 652081188, 797014586, 267917895, 235720243, 760802781, 509137920, 140608373, 361881613, 451763063, 112340641, 564945406, 50321451, 452108089, 345281145, 475696095, 177111186, 571499686, 275783812, 517285629, 369107623, 771101475, 648901483, 481251334, 614427211, 793804784, 77171457, 773485224, 797776282, 200961815, 175186122, 269585187, 855086466, 586421584, 768477261, 899216221, 555282317, 969037935, 655665237, 574859730, 965490157, 908462592, 783532870, 763044443, 481461245, 759440199, 49878949, 686012628, 222520996, 457205629, 976616192, 905700478, 888733363, 525428371, 892266192, 33676249, 94490046, 344133425, 167853408, 403911632, 425369434, 272522200, 764011539, 250606175, 845348914, 788637592, 505659109, 759123485, 326279384, 964400049, 920756356, 354770052, 782252853, 416869061, 893576896, 673131494, 871748443, 216424285, 281489594, 436319892, 241453978, 279478964, 413625500, 612286157, 384311151, 2169167, 47402484, 32243292, 447183255, 714727147, 368175054, 409635353, 298813584, 385644290, 887350198, 871253012, 562445494, 10005464, 381977374, 976811033, 777606453, 208986102, 367624849, 92170717, 184324138, 205123184, 330570069, 376817561, 67953794, 179020347, 694375028, 549837013, 761022170, 569430075, 674921460, 252922201, 125342160, 179746073, 90862874, 261450694, 115507755, 634239720, 668235288, 807917616, 644910260, 828330186, 552933235, 273614697, 733743884, 86990728, 440377089, 722189276, 212264561, 796805638, 229165180, 922558857, 970814819, 737730332, 607970323, 272470042, 545526154, 897892684, 88110735, 390917311, 787231801, 263396643, 769015204, 834076157, 410595011, 94196785, 64202716, 453085382, 224288422, 382013128, 244709436, 568316198, 412704234, 389038137, 179045909, 753082751, 58540694, 808358113, 43814144, 671526720, 695001567, 265437066, 459473552, 758802476, 246287082, 475559639, 50234909, 29880167, 610618650, 144823592, 567134717, 420956375, 361980409, 215505956, 985265556, 712228343, 624739872, 66135828, 952756375, 533102130, 49992901, 774412908, 492304070, 631158866, 479878788, 405241388, 383895396, 290207430, 601291522, 814067468, 880010186, 43003296, 176652398, 259177801, 295000467, 214468449, 921577396, 477772956, 872881177, 186847921, 581763118, 816540730, 604929578, 275125099, 885672465, 847323000, 279663729, 719852397, 725580986, 637376834, 668428478, 2162560, 103544706, 987654181, 616573634, 343640148, 871442800, 753606165, 887320587, 675007047, 813860002, 367578466, 439361994, 767968456, 19841197, 589443343, 82656238, 339946120, 279685783, 823228901, 996668951, 158572568, 173571841, 451206065, 298927788, 45957365, 438756168, 15825177, 253066540, 933172389, 778416069, 659889939, 361810549, 614292131, 593049940, 338360117, 47076686, 142153219, 319569794, 710509102, 403809455, 925009238, 84527088, 827661137, 820934810, 406457599, 259885644, 372152312, 331272469, 775467233, 783378516, 675607114, 732419654, 816756859, 337017122, 483701383, 483838587, 358615305, 279309737, 173010267, 502129525, 477417746, 145561092, 497134701, 135131322, 699082262, 815059343, 591584560, 716657425, 947974647, 347517107, 846868684, 76079781, 692700787, 406341062, 240372957, 574366406, 439090807, 338698886, 68287749, 608083008, 280620094, 287565739, 931463083, 901788484, 1254115, 83023801, 67694657, 196652035, 759281215, 632769005, 400143349, 223220562, 278062472, 129127246, 226465973, 343205338, 570027510, 357945253, 700865036, 603801071, 232825965, 600439529, 884589019, 520307356, 733339765, 798580993, 178503130, 535940930, 646585536, 893757006, 850486607, 271046276, 260137430, 530607097, 485953630, 736308475, 493741929, 314748972, 503530142, 968058377, 164747448, 333431859, 743111109, 283680093, 765880717, 747210034, 704329780, 854478847, 131431233, 260574956, 626198608, 51537962, 433225436, 604808619, 762141097, 444825641, 499738090, 199088206, 308612327, 515422012, 777967058, 442824455, 300674574, 432101484, 641680649, 438670391, 275374667, 749064654, 371677060, 702852531, 385083978, 754419679, 532128104, 672466512, 346856502, 506680204, 89234736, 421416074, 979674344, 214871389, 335494639, 57539264, 71452626, 880541195, 703434531, 72797148, 176079461, 433198055, 949301103, 939298509, 878641639, 955042635, 558151320, 631860433, 286600173, 291447714, 706223620, 763491274, 710509243, 781932105, 860480648, 482685701, 312648087, 506240645, 123405747, 786474510, 818397196, 402236782, 387141249, 230185911, 223348416, 185971604, 514641755, 303999607, 544049337, 199235749, 626736896, 595952147, 640290423, 13789660, 240352271, 286298186, 240339091, 305361072, 600518097, 786079210, 64530332, 497945835, 874427103, 933207382, 718358160, 115844513, 741629617, 431103764, 923937100, 404049583, 449576335, 586036811, 824003362, 746387864, 879910367, 117918155, 397909133, 381262263, 766726671, 605012282, 709248108, 468578715, 598313965, 547822024, 289873750, 772793321, 429259760, 760934925, 328961147, 480895027, 260011189, 313150308, 621787382, 457502484, 259374477, 948825381, 87012938, 711372613, 179279940, 584355990, 844103336, 599709858, 11987756, 54245369, 56254808, 715757658, 789087884, 454921363, 83948561, 125223707, 129386693, 274727590, 648962669, 820160342, 894669159, 264037612, 137426376, 613820210, 228803109, 976146673, 407057897, 293594087, 680796029, 205211397, 318668179, 48911356, 70456395, 849244751, 471628643, 999611936, 295061395, 472229116, 778347268, 561278317, 632112396, 106036862, 306937768, 398963858, 969390321, 829006302, 847884560, 433001374, 249744581, 534860858, 697750162, 194378345, 345863229, 753556448, 289686742, 28872115, 830443314, 203828710, 166485164, 935946673, 125590742, 433390766, 606330796, 557915848, 519522506, 844392292, 451236843, 751316602, 179948561, 774581812, 417272155, 676308950, 538682617, 328640943, 840242887, 906599527, 427614443, 4331171, 373535236, 966078162, 905837064, 30091389, 402371351, 768524004, 285615847, 434205369, 741057387, 390749372, 582857791, 149209553, 462619744, 952000462, 668532541, 104086274, 204958621, 142664286, 965405156, 781322532, 677853979, 939395291, 830857508, 573017780, 415587762, 950545646, 154316483, 893466496, 631615780, 778310464, 547725877, 411966830, 711060290, 526397043, 332939539, 641069385, 614169926, 15417903, 178241507, 489237074, 134733607, 509361037, 650681611, 432123504, 472918035, 8929735, 337862014, 625984527, 510753339, 588276601, 519906610, 141098854, 306070911, 139566764, 487381260, 348808166, 309589676, 749041643, 745640181, 461037834, 404866408, 175372726, 108787412, 157708347, 917471136, 709043959, 321037152, 11455153, 994691146, 788634889, 795977145, 698873012, 603643044, 284870745, 441180318, 289932189, 766505346, 586787312, 757829347, 34102684, 635782423, 420367002, 563080848, 51471840, 191426037, 108422470, 2532214, 38105311, 227695236, 156776171, 361206906, 540590423, 594052877, 33604556, 95457990, 331684647, 181111364, 526200559, 242800464, 655208777, 516534612, 16067955, 792758143, 387603307, 861806053, 494110938, 939557678, 407730175, 735285186, 907607250, 103236949, 808052440, 653692073, 155572920, 581119789, 796490244, 259141315, 960052566, 782798950, 114149305, 73980121, 599489575, 486134013, 444764097, 855910410, 953779987, 974962531, 900228604, 173341502, 236155422, 312355728, 468928666, 948031635, 862306904, 14014316, 657568411, 44994655, 905630104, 435925619, 505695187, 200470149, 910938353, 761639718, 174514833, 193438983, 62485997, 334780220, 572388999, 472602318, 571848308, 25134366, 54220226, 461122949, 795443414, 686073990, 603021436, 512697377, 321504412, 893187330, 888538100, 183730844, 88066843, 856994294, 405835648, 717911446, 387106622, 308824165, 194153788, 425296912, 673882879, 273896308, 141162142, 197868325, 869539657, 884151894, 812564027, 131648068, 188623523, 52655298, 616658691, 242204558, 617308885, 272419169, 389544196, 166754652, 506979976, 548943769, 971148486, 266455643, 462311868, 790798966, 565852902, 171650904, 790904824, 671016611, 86451451, 448144100, 921413400, 342955046, 202070955, 628142035, 361695590, 748972992, 189850857, 194011462, 474172042, 558694471, 543508470, 327590667, 2773797, 318184126, 543254721, 435829579, 382409514, 922551650, 825150798, 235949007, 48660543, 669098126, 324006519, 288408399, 237699686, 488892616, 749396860, 836200314, 772257007, 266600876, 74847199, 166579943, 961629448, 246712438, 375204917, 732822327, 714755870, 459531633, 703664320, 405543890, 371146067, 199087123, 649074450, 955659442, 28963471, 90849379, 204814495, 67118676, 837804757, 833459961, 703308444, 481201140, 72491614, 22893902, 18700186, 344051059, 73212955, 362559538, 789818400, 55280766, 923343006, 340242804, 35550200, 947099444, 693653474, 629739954, 963552467, 975039918, 246197826, 701161074, 374166463, 283551195, 928780705, 303514069, 597924859, 557470308, 762026974, 250227220, 229200692, 71358612, 691899603, 266114372, 281099819, 709177620, 457979843, 856816351, 726449052, 551842628, 664288136, 934516747, 116486270, 215284449, 137379801, 354666513, 636781922, 78158261, 711212624, 383330706, 324307612, 246442821, 292645882, 453941329, 706282134, 78454816, 863588158, 382483117, 706396401, 877767413, 874281453, 747741933, 370182972, 427968364, 834155857, 410524603, 972220777, 93878762, 493955665, 420463775, 131000178, 27702148, 160443219, 347699618, 881375006, 986691154, 177806524, 220066587, 806565392, 924501239, 138006445, 380348939, 680808551, 509347970, 254493139, 312607311, 887633735, 832434107, 338336032, 760193004, 946569130, 273204955, 676819125, 220609131, 345839570, 783685964, 272737294, 578605480, 543554983, 99706776, 144791606, 403476299, 334533042, 626484386, 163957145, 942813156, 799702710, 945214089, 251120526, 432281679, 917903560, 36216829, 363764074, 345420837, 344625746, 167803770, 650579923, 317567218, 321229450, 15154425, 200562537, 22620310, 835887018, 701537097, 371863863, 72272466, 643358330, 507069086, 181916911, 265058571, 104471395, 617599476, 310663038, 713886175, 286246560, 328304465, 434475527, 770085426, 929305526, 718335262, 199613025, 798293399, 810778231, 501450910, 590529755, 252434187, 377376691, 893675926, 224167039, 145161048, 557643297, 72505753, 889584651, 335341909, 980962634, 115870856, 433314136, 806479441, 761229449, 386094885, 766128350, 884741949, 324320031, 191107976, 9957747, 300561097, 257556639, 133744745, 409239118, 871714687, 379480591, 140133182, 531048740, 98411878, 366619598, 12622732, 822817364, 283749502, 23505567, 548059466, 788317693, 860593533, 636014095, 699515855, 843323159, 951097701, 217379682, 257422177, 134055386, 15976682, 837639271, 90240921, 360600234, 601000279, 534293350, 325749506, 817069356, 961793338, 588051888, 71412966, 136209845, 200296858, 276959525, 771715318, 988666023, 117847818, 191922265, 869269440, 272906704, 876472801, 750192712, 434105423, 237081422, 631444443, 788122660, 176543742, 375374502, 313798700, 983774946, 594868579, 477504327, 619057357, 767271815, 113121186, 618691915, 491271127, 11289482, 607380686, 624789666, 553515154, 659999315, 87915162, 783087007, 387877108, 969520715, 58797792, 281683520, 584089415, 718446497, 297515015, 676990562, 916864761, 542233048, 83420631, 847198002, 546453445, 445297639, 837844726, 473586218, 190827063, 92777597, 364789971, 293658854, 336789882, 567885146, 574221769, 300350811, 657659026, 742940650, 339967783, 151101966, 304651952, 392352020, 473764575, 716651954, 399587366, 395058749, 907253379, 584398320, 294357380, 337693800, 561816091, 985748864, 724029686, 679330648, 714395214, 222741582, 956255423, 835232235, 909032004, 138944718, 458691428, 951901990, 989049275, 700352087, 40982372, 421941022, 204268276, 356569154, 638786479, 791223113, 684441155, 822313455, 462691229, 941403, 725935892, 185186622, 627790418, 751933121, 838727956, 207778519, 210111100, 800989326, 60304284, 38957812, 677508162, 601548004, 705932490, 3108277, 644787003, 205807688, 922755558, 729586100, 638777221, 445323628, 610654607, 330613544, 568422602, 458130750, 85708492, 431554119, 305931922, 890162448, 22369061, 365471887, 605500877, 433304831, 336015318, 823584946, 906157904, 490477186, 570991716, 393088296, 483614293, 498372494, 210285696, 414112864, 983580688, 578306503, 882913341, 808899653, 303109145, 274945937, 592250312, 967452743, 539058325, 365281192, 938285603, 491785221, 484137630, 686248793, 994433418, 20263314, 818969132, 311856896, 154359718, 272273099, 602071410, 291092470, 756812441, 680359173, 84948499, 331667552, 905263874, 916850803, 574968528, 261234763, 932518535, 185944914, 249122671, 982294268, 133195979, 468346142, 89130101, 807837657, 79730589, 257373255, 429565361, 289251267, 816037455, 799786547, 932839700, 205919913, 277449506, 617652184, 849149027, 153970225, 447212824, 788477796, 797783012, 507200995, 515680191, 775926290, 159506241, 986562778, 402547745, 930939881, 291053590, 53386482, 242544595, 655609164, 974139860, 188828935, 358106453, 775884238, 463527222, 508149779, 675429053, 387269155, 842072729, 874116669, 240003663, 878852123, 364578185, 994128912, 318624128, 391048184, 662973116, 769847456, 354563551, 669717523, 230053606, 581505209, 718877074, 299325967, 908919069, 107721621, 414893581, 988415781, 522078686, 495130801, 628342357, 188919056, 787922322, 354827690, 447544535, 355030695, 30802634, 708258377, 66579981, 181948048, 11974085, 998531329, 887738200, 671420373, 993284683, 556732350, 462455833, 737785333, 342049654, 799427267, 371713647, 725736992, 312984822, 447397264, 94982450, 758243516, 963197598, 445384371, 751155250, 661581927, 69616881, 455081547, 411754083, 859918092, 148630703, 174681662, 827549516, 569393151, 788798849, 489629420, 139317438, 44774442, 131718514, 411180393, 505460599, 180449652, 162241200, 201520501, 724781100, 471123194, 539496671, 68099918, 372514196, 997146161, 402230142, 283056539, 677620047, 241012897, 317570437, 889064701, 221440970, 964983705, 672465228, 939137939, 923389531, 113874044, 609030411, 92847283, 888076323, 645427195, 961841227, 192260233, 367225199, 203391753, 666130461, 492641591, 674622747, 838091315, 345701668, 572641117, 150565521, 890885809, 774667551, 65781930, 849344505, 801843613, 656968143, 471680620, 724330752, 562231870, 774607936, 58993460, 791085679, 203191098, 99747639, 792144318, 643984564, 522530512, 941669926, 275795150, 788341856, 801239793, 230326719, 524217417, 518168765, 128536419, 122947235, 858385767, 212272345, 653498122, 60548963, 79960468, 941731372, 429911608, 34956782, 856406229, 708355468, 578463294, 455928540, 648327860, 33252933, 962250150, 504037419, 467234936, 656721569, 930095535, 146370478, 414720258, 278073361, 846231867, 986184394, 678244271, 557148498, 369654956, 446044698, 848763618, 270509598, 395881472, 741801931, 745605492, 922471066, 650288097, 404116759, 816833236, 572832074, 494569170, 363277305, 81839578, 623219832, 649338736, 81560151, 799696115, 144512855, 856838982, 695361374, 927887118, 777358006, 425736328, 195123105, 56127131, 493905192, 56585076, 928015941, 759088397, 536546983, 930833411, 344479695, 963031034, 871673043, 202120654, 854947323, 260840053, 493606745, 593707870, 655167307, 278819638, 993077831, 365327803, 796296615, 52546841, 818882678, 115290529, 655999972, 296620403, 993521400, 279987078, 278971274, 821420714, 426528164, 365529883, 741663505, 684246079, 610554740, 632271847, 266962097, 519431112, 320487153, 632194476, 675082274, 568402089, 175645635, 955501148, 791532518, 285320027, 236230355, 405671910, 855252506, 577706993, 85753259, 761663677, 769337278, 265532212, 651241877, 964966382, 139244433, 85317669, 479937622, 235495347, 304993175, 474454905, 199543225, 968184937, 697310917, 772562846, 73861230, 84126705, 982547940, 217608506, 326978152, 767973896, 257369410, 819002615, 963766708, 307652914, 457684012, 701944502, 773658251, 240266562, 688170396, 368526345, 792953132, 843631854, 563556844, 19431214, 660374834, 190624815, 696009737, 982382747, 910135202, 954010372, 458573115, 230578009, 256550815, 330841512, 151378394, 41974103, 811532143, 99199648, 87739241, 152486174, 701863213, 495445107, 855613699, 152642070, 115037004, 547194297, 275329586, 319007697, 86708238, 52996990, 535693670, 703101184, 425369972, 929506634, 93836494, 206828403, 275798316, 872731525, 459197222, 506360193, 173355219, 262465708, 14292650, 411729182, 502839112, 132600864, 96995094, 938070831, 947849031, 561633477, 750661261, 960879195, 271700403, 710023125, 567343684, 763216865, 962493783, 442303519, 439200193, 173894155, 888117874, 239406117, 932685486, 660600751, 281044303, 265053586, 531916260, 843649569, 220502684, 246664509, 321652816, 152805669, 673692641, 106951511, 661362471, 55883614, 355840260, 867196101, 984256246, 134571786, 168171883, 223705041, 436102755, 81422480, 976482578, 320499032, 415503974, 353342988, 911129101, 743040565, 49362729, 304291056, 687098895, 113744361, 89247887, 648132321, 91832104, 633609787, 820629289, 936885565, 46382551, 465385277, 119056599, 256870285, 901759200, 294710175, 78429452, 984408110, 472506157, 492560228, 982777910, 128428359, 537453290, 54217101, 203779700, 713163871, 744096662, 324142657, 418786247, 403956248, 850834638, 11307527, 1446226, 8658429, 997069458, 676078034, 467552722, 511733837, 44186598, 396231444, 545036689, 472135273, 72835731, 476461355, 334771741, 99254568, 243117985, 170238961, 380052037, 955475128, 324191193, 999428702, 758020015, 583905874, 404746908, 249056907, 385309296, 181659765, 72518904, 646158253, 271102202, 447494660, 639891247, 937187803, 594319265, 698651896, 692240416, 512095475, 793657778, 263071274, 715848083, 878272386, 548275515, 969946895, 176306729, 620763738, 555524505, 975694036, 924133031, 926541595, 145696818, 217913654, 709897938, 586210824, 326187774, 841554196, 753291897, 442601882, 744520647, 632103914, 134363826, 38297842, 568667239, 438106356, 957091686, 783395634, 26759721, 664213927, 386609156, 909419100, 118676940, 80978865, 837443154, 926056538, 780001004, 781479143, 968869451, 985128460, 965309498, 479868178, 407135982, 960541547, 577186802, 788981080, 585389656, 82671111, 419860062, 579759459, 800702105, 710040212, 286401221, 89151606, 955699895, 459871412, 547002511, 346222894, 581308964, 396434355, 8674866, 573492104, 56968049, 146450359, 656984565, 398678974, 615022090, 789783889, 104781107, 470995959, 161284437, 870677673, 12543779, 644769316, 203626548, 586514424, 303365395, 498410405, 780800051, 576540091, 498455990, 845962291, 89691064, 71665325, 96941133, 526671933, 233388136, 760610898, 375147503, 453415351, 532321869, 674366876, 566769486, 727380678, 962892687, 544371508, 545674605, 243499674, 627640633, 285351977, 71089307, 940468583, 103322736, 537378240, 93859149, 943881396, 931039145, 257807905, 11179225, 582297121, 630007994, 909219136, 16482101, 898942393, 950323895, 101771292, 198087403, 389673340, 735889514, 219981357, 91918340, 30334496, 371859572, 786314185, 229171291, 297596192, 535950523, 372523276, 105148745, 691018520, 85269787, 617894973, 289223296, 913623978, 385209035, 423762827, 392154502, 473956674, 455242335, 588652132, 118882446, 289552573, 955455260, 256271172, 566617085, 539329864, 44621770, 499334791, 856522280, 283859540, 282838086, 272541442, 348158651, 841641932, 293942610, 909570652, 669398583, 748938078, 285793646, 527243333, 312603821, 818483588, 45900875, 760162478, 289110040, 127751140, 811069103, 137950137, 469862765, 844083404, 663305881, 74481951, 55573165, 243500576, 415929427, 918467927, 439602504, 65393468, 661169025, 653441785, 782192784, 745945876, 419515981, 15949267, 155645385, 14112280, 508573339, 809947140, 588204647, 421592726, 725329341, 72240861, 55036862, 532134155, 263278080, 810234301, 414225755, 311767852, 388558783, 642018275, 796480231, 241918148, 215607272, 273918272, 279688912, 641187386, 635256899, 830812697, 243184039, 62876732, 916165174, 398170412, 128579743, 81672721, 38735502, 111745148, 77074384, 856620535, 284759276, 936134524, 733407075, 731944081, 372438638, 757619509, 117613768, 238507978, 738572559, 844686857, 794520737, 305216335, 539053178, 682134748, 138219687, 551876763, 124674876, 273281990, 92301873, 479552931, 755853862, 870771317, 176827946, 997242174, 223075395, 544235678, 592814270, 419712611, 586552102, 816450057, 160280987, 423442846, 786544678, 241805108, 285000255, 832181082, 78273762, 241553383, 928000107, 992221872, 870309550, 372769793, 559220294, 286624820, 910632506, 738407682, 673305590, 832731049, 925065763, 798958380, 571289529, 716039418, 460111084, 442931643, 834565869, 753180971, 798327417, 136235805, 534902834, 450398161, 391774344, 50754905, 667791039, 672654938, 585897525, 156593442, 291474541, 956163222, 776360398, 713668890, 130616961, 518715854, 419837404, 608699903, 228128335, 44989815, 861582751, 557798161, 739955460, 480429438, 973085608, 57068232, 611619449, 685658421, 576337782, 562054890, 905341259, 851944624, 124029891, 607849459, 904419523, 342216640, 186472063, 428194776, 310127311, 217928669, 104894849, 942478135, 82860617, 914379827, 6272035, 845127428, 550503540, 507284647, 725809793, 829719214, 500334325, 630736019, 700559857, 563717506, 926491833, 334595136, 944974768, 761525371, 554799587, 852925407, 687124366, 704663470, 584631014, 443241064, 889236111, 92920713, 355211694, 701442456, 282403005, 194978790, 334568500, 569993003, 182983790, 326722007, 32484065, 726115710, 75583982, 675269840, 194782241, 193531668, 807429206, 201336702, 608412895, 878019975, 576950184, 314032344, 928682079, 72720567, 614601194, 559626769, 923451932, 566372478, 363245497, 481082731, 7700644, 412682190, 826748793, 514636077, 206284888, 27548009, 108637327, 603729425, 715030295, 904239507, 452235665, 380433241, 448460107, 721526304, 367451478, 291915303, 522432763, 663439567, 707420179, 666417974, 453148186, 734091437, 105972349, 176718518, 903102332, 79272891, 407727213, 977133236, 188629224, 61374019, 831472353, 471039929, 710958626, 175511379, 932696551, 21483046, 896074248, 470327309, 289686917, 550737515, 288642058, 954177444, 331776519, 343198449, 540884598, 358328301, 16298511, 551089789, 680709747, 706054035, 284488949, 339068171, 468385816, 457149343, 504603310, 372074467, 225739942, 690838490, 415821568, 281657299, 240287826, 872608573, 288283809, 580648300, 630549361, 103060788, 61084082, 608627395, 253178974, 455172207, 67191891, 637702750, 259010701, 599149746, 666867296, 332849649, 312021132, 441670030, 138505338, 10574404, 291969233, 391450703, 708255072, 189040231, 315082430, 76690107, 476325948, 473759053, 127780006, 26629617, 927926811, 58234982, 100406453, 576696575, 736081278, 597615630, 754983153, 206646631, 399464358, 428482852, 618645251, 673850161, 581304336, 176494641, 391008595, 657642686, 105329285, 764141202, 527327854, 926014740, 350318161, 965908719, 717675806, 629006706, 39327314, 155965420, 500367493, 135655315, 254762585, 831266742, 612589017, 86682980, 52855511, 857582622, 786358309, 65625496, 880451812, 557343016, 332677794, 359800956, 960052513, 493198355, 130781310, 402910289, 580106099, 32582047, 197798282, 57035838, 102856697, 816628110, 623985674, 794544647, 332939908, 68974581, 522038384, 444982455, 413171398, 180520145, 633000421, 824583663, 39677728, 385956826, 95237031, 875609087, 453542544, 389885441, 941964180, 31622166, 697180097, 459214509, 449184719, 329184003, 874035104, 432143489, 238307788, 249855279, 95899955, 933496233, 80358047, 733474425, 768680068, 891421008, 46209982, 114734216, 559567676, 298897564, 740792193, 645253702, 783837702, 173700067, 185306879, 548551596, 714453777, 87738803, 749627356, 217773846, 624530741, 188658478, 611522158, 724211999, 783243469, 80183566, 186453503, 687613619, 414023186, 348634392, 823694462, 892281078, 467589994, 405714020, 483530694, 87926926, 8938421, 172754815, 140557978, 506402880, 288567681, 469930243, 638700174, 786709673, 918253825, 614850266, 189044890, 774789308, 529947074, 564258843, 447746603, 495360218, 921554263, 117834444, 684925892, 911597370, 44897349, 444942488, 934210809, 953060704, 171888708, 562798300, 807037599, 326265569, 160501845, 806216786, 897208512, 685344663, 64820880, 255505126, 45821165, 598636025, 650712844, 296624439, 161632296, 398608940, 126319863, 721140225, 884719471, 870708439, 642800176, 166165273, 630279762, 355174887, 472269477, 298335487, 898831547, 754706648, 134460496, 631409078, 919186564, 685556628, 889558920, 946201609, 375947375, 580853593, 502133382, 601775543, 934851750, 284966272, 536972312, 379878339, 202873387, 851592795, 728485505, 610207069, 913773560, 282989436, 218169735, 482323863, 111212667, 449669985, 650035322, 386487096, 450261845, 980388337, 633717048, 166365520, 521497859, 308428180, 915440683, 797349584, 392292477, 106400335, 447435741, 760748355, 509621380, 611886288, 470424519, 6768630, 676487621, 759177872, 727933946, 985985174, 545853084, 980264628, 533387169, 367710619, 687417763, 342502123, 500759904, 396854947, 264214395, 868519906, 158005987, 710375349, 759745030, 402056055, 883062044, 414954130, 523689548, 172341003, 647409855, 404157414, 374382959, 880364038, 670056064, 47175015, 688355290, 380356929, 693276686, 346422923, 770872842, 976924974, 782673344, 759198204, 605496438, 968911070, 399078684, 629376502, 575643430, 553092175, 476364059, 353723737, 971174339, 561877830, 411814101, 730592562, 242026454, 375309461, 507369078, 247037074, 566358645, 482202238, 931830265, 167717332, 260541710, 114476871, 851399224, 839352940, 721124975, 654680223, 213184932, 469526346, 638377040, 636950604, 121002509, 366872025, 833427044, 292419611, 216796830, 282295868, 727951650, 608665009, 223761856, 458578882, 624367013, 2759941, 659655321, 603149159, 192715293, 724617607, 151563040, 549402501, 479414203, 314961660, 226805995, 124462560, 143142435, 714618670, 284492647, 447276812, 184706743, 780827946, 157138114, 881919134, 169631785, 463345939, 216578228, 928117422, 288102763, 408142945, 506286932, 903638612, 472970761, 173722407, 567144132, 406703822, 774385555, 126828250, 172748260, 519842538, 547863357, 952131592, 50209175, 947994557, 770577834, 949238221, 754052672, 249521920, 981823148, 111675098, 149103245, 512065945, 358966477, 493658837, 562702231, 546029126, 993039543, 69333393, 51661434, 533748633, 468290865, 237357610, 657104339, 48414950, 765261899, 63904772, 740453721, 202170331, 997283979, 345747175, 429451550, 938455489, 768824036, 805990878, 391750901, 594998009, 651975516, 94743107, 262858546, 568479548, 957463839, 36452029, 695128450, 812547413, 805273388, 491577649, 850787548, 901198768, 8663673, 266135675, 258485951, 123587427, 671946870, 974141242, 982844070, 973230670, 883728186, 788766331, 683951745, 301109065, 422661282, 69969385, 908773743, 370908316, 82089902, 574800234, 876739155, 136506614, 641163597, 874629967, 893094514, 136468507, 260274298, 64691565, 683116700, 501568385, 764528026, 376266948, 188964300, 48451843, 387614344, 294556818, 363124739, 716002744, 84172541, 591411684, 333064979, 622706747, 92226809, 308836481, 400585193, 90133861, 304667554, 583298529, 723613360, 870233788, 969039370, 240082887, 825702533, 126837547, 661381785, 120045680, 224236946, 480422152, 309657362, 146577913, 931435665, 752753442, 710939922, 116884908, 451679000, 845745889, 612506489, 978558497, 328570875, 21207076, 603700492, 235796839, 608738359, 616601219, 204888039, 292360041, 707392712, 476604998, 520673910, 856846727, 645909686, 384992410, 694027849, 565678081, 659260034, 466906748, 513288446, 80832931, 962094999, 864095993, 127534281, 691075210, 283879863, 723610298, 92484622, 685033065, 85661920, 994046551, 346835961, 102197138, 621146627, 581271568, 555085355, 473902759, 964569622, 741232963, 831549138, 552990523, 80497378, 582912879, 693218242, 723547311, 322322793, 814997049, 190672996, 390420144, 784490701, 632957257, 737478662, 529372994, 38676769, 932782973, 578815185, 593161956, 425901774, 289631270, 582472673, 848406367, 679950975, 597684234, 382282973, 336174236, 591879770, 189347884, 737464934, 446614287, 930519533, 216444084, 249196660, 392234775, 276680540, 805928526, 352536110, 406747250, 951241423, 235822662, 145451640, 385037908, 889664277, 551610443, 566803096, 215946200, 704872314, 638157878, 217313186, 914953673, 867456159, 482745220, 95356945, 993005224, 540878466, 447463037, 68714995, 185119882, 474319734, 46431919, 43416677, 939386330, 980412373, 299728257, 412684880, 292459106, 814244805, 754638640, 207641321, 577375210, 913030768, 672717534, 659085479, 41925635, 104745222, 975461959, 384694486, 455022439, 440543583, 839520816, 254281617, 346286457, 551049571, 189047522, 737823499, 771322302, 252599336, 613429971, 214484471, 377025357, 165532627, 966420022, 840760244, 577400522, 674236217, 473218389, 142987848, 233652984, 733072059, 525263799, 99927435, 592208257, 237926871, 536018767, 242749020, 619254711, 81336471, 398759112, 482491203, 423941106, 877384060, 55522690, 370705438, 323680159, 126571961, 789085000, 26307035, 351138731, 155859206, 405549296, 725982551, 823983174, 8514155, 565394842, 727558794, 641887943, 541108928, 946401618, 656764630, 356988069, 684821787, 21401245, 177794970, 931226923, 179908046, 562124338, 585963040, 694545169, 631461944, 794407996, 523224127, 359232386, 809706494, 74286594, 258348432, 948356258, 37363262, 929376399, 777869135, 940115791, 383809831, 458982971, 194790785, 602335937, 408191726, 35614578, 443641103, 457034311, 225262107, 424340911, 717992587, 281890886, 543243493, 290075979, 317319223, 452606187, 68447036, 548842763, 361941368, 915953135, 929685394, 59018541, 558475799, 316789567, 714061807, 736935944, 437798307, 457124144, 161129331, 735411843, 814764157, 897141855, 257296957, 935034489, 158957176, 965050584, 216441000, 674955584, 880495796, 418620832, 830047016, 9752339, 679682600, 753703379, 741527834, 667107147, 865477385, 122328382, 567948922, 641375913, 125973200, 685538944, 186219150, 929159906, 270352877, 467537911, 411046655, 363892080, 613965640, 889379677, 735756962, 294732930, 130808994, 701604784, 118972897, 873868925, 229071931, 941555673, 72983191, 623225506, 363260641, 800731029, 727180960, 464265288, 182951191, 330729520, 131653741, 823369277, 864986247, 229174978, 982244437, 66203954, 178123304, 119202570, 149360225, 955251996, 791701748, 315548983, 734011630, 361996356, 357097693, 701414176, 943448688, 440032292, 784287386, 756211874, 410428034, 552452959, 256175938, 908267008, 391791008, 709980663, 184771599, 31189213, 21223460, 524424487, 409741504, 832586926, 392178555, 238595176, 988874807, 311620571, 540956877, 736406048, 285219854, 223480967, 971823440, 583823134, 560730091, 12349271, 623727553, 52762406, 658500075, 987863400, 708116967, 758520840, 946193559, 665281255, 435715767, 570312871, 369840771, 254081416, 890692839, 234125474, 64757128, 501112689, 63644366, 399113802, 919266786, 140749470, 861468431, 781748236, 584866739, 560746593, 408848177, 29139421, 768731410, 291193826, 469577254, 871236175, 116876005, 758331457, 112332837, 617679626, 265291426, 572376935, 376786107, 311434222, 959282345, 356602353, 664192947, 849644310, 659894626, 892896437, 113302441, 192484075, 743640278, 373741958, 25480702, 322534196, 898027876, 727326862, 983862182, 327003683, 306940920, 763325717, 95700248, 473794341, 810584104, 624613662, 259593028, 105852270, 361598766, 333977697, 592835978, 984605363, 326428289, 455881052, 169960819, 242008298, 928620687, 339963266, 247151741, 116820336, 351647351, 731408238, 461951886, 524154653, 637723490, 169444802, 621520214, 587510790, 135137944, 811433017, 177890091, 235064405, 538482112, 185244685, 967390601, 181768744, 774298588, 55776586, 417874786, 538371748, 918372281, 746569335, 975941223, 597956986, 927985073, 155370120, 110502370, 344966983, 584747202, 362151728, 302409348, 586442921, 427657749, 135482325, 482498197, 994214969, 298018446, 585194395, 299680228, 202557723, 20580478, 467325793, 828505711, 737704299, 361093661, 268193124, 757201026, 54343551, 630380248, 366370808, 89544130, 921872791, 403808978, 174560700, 680411380, 675509965, 235435553, 998493717, 471098185, 284883122, 562334351, 964663688, 799224930, 559412921, 221228363, 929528294, 755202929, 339375932, 679658581, 731899923, 915645328, 457234922, 199464427, 821523689, 563332210, 770270132, 445540278, 537542520, 553761741, 18733665, 970677040, 217991504, 483594951, 812683217, 541752247, 268061546, 666292442, 990010752, 499731188, 633792903, 491904363, 319609292, 959351124, 783084344, 970184961, 867237059, 787729102, 582868029, 214988509, 352011514, 191358632, 233831996, 159506988, 117888704, 998888704, 74190609, 639248000, 64374083, 566956435, 558036724, 908264602, 84652191, 348835670, 823354337, 512881960, 771082057, 840271714, 946080448, 35960013, 255254411, 700164465, 279786057, 962723397, 50508797, 604642986, 753573528, 803523381, 2742742, 479877648, 3160011, 553101152, 915441324, 518072490, 660537585, 533283571, 685687211, 75822915, 564603948, 444301933, 262590803, 525120450, 716540207, 991495070, 29307683, 453999146, 794083214, 832020528, 868963892, 870449580, 867295029, 435021674, 485653016, 7105765, 212682211, 3810917, 341235421, 522214099, 815333024, 789079176, 484402764, 63186093, 153820556, 473194130, 807486764, 764737981, 626475964, 675111080, 147228445, 369321062, 226205216, 544283213, 133482949, 650652355, 354255273, 319151870, 818348474, 643031072, 226154932, 481476005, 72216507, 96815696, 320941197, 144402378, 140500711, 811624890, 986542842, 660085810, 890646434, 583349046, 140804530, 352323272, 257321398, 645535823, 764434944, 713824130, 47966167, 877849551, 664511119, 396279861, 627590846, 616379719, 838559266, 896660377, 195139451, 80989509, 657169243, 141857380, 350478449, 597024278, 202951080, 746443721, 765651021, 707647767, 865769673, 376255320, 352026869, 826365189, 133949683, 774840809, 94368801, 584457483, 859769043, 794770348, 354781218, 233012914, 788382908, 160241496, 823475175, 841754024, 943263723, 682242949, 154691973, 826405833, 744869184, 121612941, 547456131, 125237992, 914055976, 269520088, 356225108, 864475027, 306439146, 656906104, 391910314, 565798867, 567940272, 776210113, 938291550, 585114909, 524722856, 707058344, 7828958, 466018760, 475644352, 93633268, 621626860, 858607777, 303767806, 861707841, 330124768, 624960358, 633072280, 14701721, 615772595, 11511857, 228336323, 422483260, 354425997, 856889566, 43782115, 167173576, 855740637, 993453211, 339458417, 950640987, 192766695, 563699517, 348492626, 708605442, 841953512, 683064334, 21521661, 726130124, 848969680, 79017583, 352078409, 354379569, 542944232, 173437566, 749269971, 623099685, 908661013, 454718915, 325890179, 821164653, 309093509, 486886498, 955514915, 919080176, 527370945, 505933072, 361658779, 95355949, 559571701, 817202451, 106318978, 303023130, 525054429, 444509509, 912830286, 630729002, 900458888, 717772906, 430488713, 213760019, 698155163, 71824393, 526678215, 643152905, 41904447, 980327429, 589571147, 735118489, 88741694, 44623443, 422560376, 950956189, 483172988, 912788155, 706606097, 54467950, 921704728, 59954256, 805222650, 57682685, 662129409, 744587476, 50124512, 787153919, 51434322, 791429152, 604330241, 859370878, 68741507, 641547455, 499343035, 338676145, 456453521, 208065587, 446909957, 196656596, 89930981, 195005552, 838747029, 612376943, 462384661, 328333409, 209471918, 220296296, 19695217, 757515635, 509101043, 126932587, 190779591, 719073937, 135217519, 776612203, 727580915, 859414808, 742024883, 740876259, 480090481, 508411533, 383117072, 938831522, 200831360, 600589392, 605257451, 506930295, 981323683, 146748053, 311654019, 501567351, 38219860, 903273170, 86661067, 943498479, 587967719, 812772018, 516176840, 271097410, 321605655, 768528589, 138611163, 772646229, 305837812, 43580838, 850303776, 247880391, 573049874, 488779977, 146919922, 345655661, 662289471, 465972208, 391528698, 296382092, 197250614, 41220164, 784471109, 701785168, 105099615, 271772733, 371884474, 451159656, 911752686, 522994391, 981432548, 458786063, 623963315, 643849248, 289209758, 989865800, 158270226, 558711084, 114830446, 77346750, 367622182, 188356459, 450695063, 741527677, 411764600, 35590216, 51267987, 234260391, 540306913, 746076334, 214306996, 509483431, 546164556, 778551254, 609907365, 745726201, 391721856, 295684625, 933987832, 948492204, 527813240, 463539589, 464306853, 209481251, 857924383, 986603764, 240508574, 769331227, 289289367, 745260976, 310605890, 500641887, 733877994, 200900087, 828000140, 455738094, 137843712, 455110162, 478027119, 829688311, 689795907, 169264284, 758214020, 731804615, 382478393, 752197658, 707948035, 590869157, 524386407, 305022928, 25458284, 272724916, 528294979, 734955267, 65641117, 579406078, 909342463, 56345292, 439403072, 710572653, 103820479, 880946627, 574825704, 675380841, 497376192, 265516206, 121020946, 188619390, 77793209, 772507238, 82440776, 879701750, 359215209, 878540491, 874470804, 90615382, 161400999, 578305838, 7428517, 200905969, 508274131, 74137501, 351267729, 677136400, 283215481, 30270210, 722882051, 10869771, 823302665, 782842777, 369634569, 682680410, 930837406, 577617317, 199342831, 932998799, 190693849, 321052498, 633487824, 803230647, 811710590, 538642155, 945457398, 973754344, 720883725, 366047991, 904687321, 27091119, 805884211, 759390161, 191667619, 948274800, 99911318, 75819910, 303035908, 33512529, 254277519, 965458280, 702464845, 497049257, 635981048, 64592333, 694602167, 457076517, 646865542, 544430492, 869260469, 663311092, 622101827, 821023600, 681954162, 329270893, 328135117, 543585978, 345789622, 354474894, 522081, 273534807, 360276316, 908338174, 499723386, 357161355, 321592492, 363741583, 888295504, 372023908, 850965484, 40358199, 70241691, 309112539, 622907688, 917447838, 908806027, 416004861, 325559281, 522083713, 572458768, 243627970, 37496950, 871272846, 670690097, 988318429, 862305690, 186730032, 736323354, 991358027, 81765352, 820339657, 421117754, 519336824, 972584572, 695996429, 772816496, 67330632, 618698998, 171629235, 853895781, 250928265, 635105501, 518815614, 747072182, 293790453, 651148714, 786117576, 266991507, 907865350, 520939614, 64985870, 940820016, 472145990, 364424628, 291094939, 216582232, 339098330, 75213472, 336119052, 310938899, 461732853, 971927976, 701991268, 808637813, 380078338, 993380544, 623655866, 372744596, 637044784, 133246129, 440774108, 546137525, 31165157, 699501434, 909733050, 529657495, 802667242, 556702641, 765288015, 392943418, 61439586, 778155777, 594939622, 385929401, 966972386, 406795390, 112341529, 282198353, 606856290, 379240903, 658345909, 280891430, 778205611, 120869024, 723130968, 405526920, 446421246, 262195478, 31961558, 487140593, 89212644, 562972479, 814350007, 272797636, 139507756, 372291523, 548071683, 522143224, 752397242, 322761499, 366406588, 908252960, 63729400, 480601146, 578590811, 757461190, 548924909, 720137572, 654729766, 659202707, 684503372, 608811111, 906219761, 66069406, 609267068, 134563298, 836747423, 588073934, 485262152, 907867620, 370503017, 119812437, 374400739, 907045772, 461655619, 403562519, 921691504, 971611265, 106405857, 100573558, 682237181, 100171123, 82155142, 807152106, 214225285, 846691817, 331781232, 881039865, 885178018, 906749189, 798586968, 721474157, 642704417, 865071472, 28371670, 334709939, 793961613, 160910897, 469002418, 41337414, 415483744, 269984427, 256447611, 752288329, 637827275, 60918262, 91967587, 47642616, 262421841, 964376278, 785693235, 350337242, 302433009, 688843570, 785544512, 208188622, 43625805, 282277090, 365659625, 495989152, 570805262, 654360899, 968637594, 988017004, 921931488, 348347267, 562787138, 782359947, 125888585, 579813193, 336444365, 499481193, 926985475, 997496778, 285707365, 588803420, 184602588, 775930999, 989671356, 163508048, 429604675, 926470395, 666697848, 354521191, 789949153, 458093047, 963453483, 545034656, 383498155, 657829261, 981871771, 821687655, 936122263, 67832720, 872517065, 566909570, 117964561, 346591306, 255177978, 83546146, 615413464, 80224190, 101577118, 910570657, 670192751, 179147437, 580232656, 270965916, 28552685, 457726743, 981216507, 315169692, 166413847, 90917199, 87488335, 513515839, 636672628, 449966640, 169964233, 619118576, 986286012, 411537966, 205660010, 879267947, 468342146, 832892379, 355966217, 734532571, 183914649, 981731207, 989375201, 822556038, 298862985, 773802900, 93321369, 281093788, 207889407, 527710566, 110861305, 666778682, 612625043, 146639912, 14050393, 263293820, 381503910, 585497455, 617229231, 972354078, 553344633, 611850319, 668780635, 150718736, 777174333, 859535546, 731005995, 128865853, 771370068, 479715474, 269143861, 237062802, 166425178, 240152520, 374761523, 654795110, 362906812, 343822020, 975087596, 243758590, 103616468, 768993180, 460214549, 582742271, 442763293, 687728894, 928427487, 761481452, 615346546, 569346912, 979616255, 163043921, 400076262, 822092484, 654067119, 886943878, 389468529, 665814379, 763131684, 634876782, 574736125, 209282245, 363175996, 542922056, 509034021, 102026008, 606776664, 387380574, 858355891, 357394343, 682728429, 181088499, 703619892, 698234311, 554009163, 568500699, 743414745, 237099165, 59532987, 674810291, 361152492, 803028125, 255864757, 918763941, 402459564, 997345264, 700237727, 728777318, 378636778, 861157642, 816305250, 737925429, 25788120, 915855424, 857021550, 254920028, 637205074, 136298953, 708766457, 182157121, 176438482, 940845227, 599277733, 988140949, 524925293, 288665274, 335555674, 43421117, 351196572, 692862380, 155335290, 24166572, 202186570, 450188822, 823094054, 690193341, 717501239, 914922538, 543835329, 305517572, 693136729, 985026209, 947116663, 88692899, 310172378, 14260158, 803884322, 650501377, 118239084, 422021001, 144654587, 138283809, 630757937, 778092876, 189694717, 636808233, 499762810, 447321668, 717201290, 123699212, 704559506, 69806952, 20343015, 579019377, 157682339, 636903861, 467188249, 529856632, 594870600, 733067735, 540227106, 827168200, 567858256, 23619517, 260767643, 800289786, 223935175, 496817444, 662907324, 343925673, 174896937, 958573187, 720369715, 472130590, 659746379, 572181553, 245028755, 782553985, 510376402, 379872170, 818489362, 294219265, 222392592, 155182236, 524692720, 92462782, 467587334, 196900835, 392891728, 120023085, 19276078, 310142354, 888532237, 19987039, 85037171, 969157055, 245760323, 901267773, 64329447, 903614507, 942617286, 766757878, 777486000, 325190832, 544966059, 906309004, 844582253, 603144976, 627309925, 416391122, 127453188, 484580535, 458856005, 428518650, 523159349, 305737830, 101707478, 118643394, 912560783, 377272882, 214565206, 538091783, 332437825, 13090184, 490291445, 311458653, 61559741, 919545900, 193208227, 884554875, 205488641, 295405049, 537764084, 496387843, 106414520, 766837691, 943928770, 286916105, 605798918, 696685188, 542204031, 66576714, 814884599, 423363455, 308922464, 838405864, 837670272, 427525256, 713246425, 164092912, 338434050, 103725364, 954419366, 265069662, 637009630, 930300748, 397905587, 355218747, 486587105, 951706251, 544039110, 950352673, 387652160, 950164538, 365941092, 39428977, 119506965, 39014780, 891765433, 540538887, 567212615, 594545840, 862285539, 476548155, 850708524, 183842802, 556360706, 756911695, 195648623, 377970821, 598930097, 317372216, 567762046, 777566776, 399773674, 669524325, 684334882, 226719697, 984203843, 77177158, 886179031, 392175153, 302607726, 279721821, 300328751, 705032854, 9436345, 997245559, 459987126, 173522417, 142523020, 925510295, 535136362, 123614616, 645049106, 563745762, 251814207, 259531717, 680965490, 677076711, 599257586, 934338839, 579780421, 417233389, 559469485, 136295689, 232983744, 821798488, 188743777, 901953308, 692944359, 66806117, 925048994, 717742517, 983251759, 459356761, 625010098, 1302488, 858502379, 938656634, 383160435, 705483341, 430367130, 379632470, 668676294, 806896416, 65630419, 769007754, 27529246, 960490710, 924589209, 629931051, 183259975, 111894486, 309998054, 106659489, 75206079, 461179503, 970550193, 756659489, 328859185, 927568906, 25041258, 82131125, 462209385, 875938330, 243632129, 418836057, 229324026, 354712616, 350790962, 884681120, 583395019, 922308327, 958473162, 853120234, 682939883, 330401095, 102460406, 98206381, 929064005, 310710106, 228414934, 613415554, 324021574, 429285868, 766498155, 332958670, 514289176, 490512032, 466542909, 843339733, 130606034, 556427892, 409564838, 372854202, 318741354, 701665442, 234757814, 952396239, 741880541, 479957427, 61790655, 903055131, 673463216, 307789504, 623729033, 927357885, 878253060, 643877365, 592122747, 932572168, 773481437, 22678613, 817168695, 777645374, 721547123, 179974218, 638085476, 913496662, 755937793, 942792946, 75612671, 247172613, 627914686, 373238272, 446831170, 389329029, 958841890, 925986070, 496251189, 812329494, 360615962, 227919366, 735969270, 536582397, 725158948, 489045, 170299166, 432562122, 729419095, 453128514, 561628010, 408593720, 752021254, 70117954, 871749268, 523583083, 157499598, 143146077, 110951157, 622026656, 579506700, 50071270, 138847794, 667325579, 592514847, 820590966, 462216299, 143059294, 454116980, 883113819, 282606787, 448539308, 850860162, 33409253, 850797627, 847705265, 922150940, 755465614, 923460613, 251141299, 658352338, 863863077, 944774849, 790600141, 586143319, 798049117, 276475025, 670606275, 110594048, 555065688, 331879325, 405875121, 483423171, 784034267, 429720565, 774046637, 217493344, 415975350, 490467102, 99501950, 364794239, 403172525, 744767494, 425805134, 233079944, 9350240, 583649438, 415831530, 846596447, 44551210, 473952853, 350735821, 333690866, 284025664, 113981386, 219893520, 34223347, 819389053, 995346451, 719381599, 52159586, 527425702, 52318133, 370607700, 566471841, 549497561, 125561735, 753014415, 191690692, 862412622, 434778191, 519463676, 360902234, 61458832, 551342436, 200332687, 203465933, 689705299, 697702703, 372662547, 754314790, 106072368, 13974458, 912567482, 105061166, 876566148, 919216429, 317512484, 217604768, 295749832, 778813657, 370565161, 480236195, 438151628, 154241853, 77314245, 728496026, 117482414, 963275766, 424147321, 242683881, 485859683, 747209731, 170971752, 846680290, 819052540, 92699326, 881255644, 21174623, 519254822, 407447265, 604134544, 317346495, 224633851, 296323787, 143410051, 306570681, 920337559, 646534983, 286326221, 829992895, 997290460, 303372556, 320330221, 317636861, 725101230, 510475356, 289119022, 916250699, 795216156, 848963703, 519013636, 203577813, 435709174, 431599074, 820249350, 342258929, 748250930, 725534685, 989494175, 257409447, 917607792, 391452656, 143635574, 23075410, 783067034, 728804276, 362561295, 44743754, 541957244, 633162010, 462280669, 515887969, 739270922, 573663768, 941735028, 987481603, 867750105, 579483935, 845553825, 652620067, 835096928, 116038860, 84664028, 626416114, 803476599, 803634842, 82530990, 926900054, 783543000, 590782320, 241713520, 422300076, 218505096, 402239925, 817733493, 214413840, 150279207, 443531208, 51318996, 878231573, 944398377, 941828375, 259751090, 588326765, 115921537, 259944436, 272855437, 570092576, 26567588, 474727048, 864509399, 628698722, 915774956, 87152390, 252636159, 915078382, 890928920, 592141674, 984001733, 975427865, 702902824, 261368749, 71655224, 809000620, 522335244, 94819353, 940696026, 14437665, 41255587, 254270677, 336686875, 193199460, 285083220, 567244895, 425419944, 584375869, 402958185, 171568732, 183258897, 622719744, 441211916, 941034285, 468902646, 329379293, 16995670, 768126559, 610216045, 232376733, 709200848, 347396059, 238576822, 800588033, 560076398, 365505391, 718176164, 757189187, 273452087, 12850052, 59173136, 495539928, 966385474, 597286783, 161510174, 795658757, 911764322, 373988410, 703133184, 304735719, 179645052, 20657760, 535928356, 849473718, 698387366, 537026526, 394385784, 289626302, 48005723, 276161583, 689065412, 657310929, 452552418, 70199393, 806919462, 312474490, 218168313, 360425539, 238922096, 833924099, 490225226, 187585611, 588962578, 350762780, 932388416, 473346273, 448625830, 147595427, 578322469, 162665514, 109904116, 7857807, 965089821, 540359234, 86660760, 382585892, 689897441, 331267672, 309057575, 214375200, 578708192, 395071943, 190599434, 31934786, 759609302, 610467570, 268450088, 182237894, 321979175, 178358436, 555541368, 126729597, 515594659, 8819927, 616190258, 203838536, 586578487, 571086379, 483006553, 406278327, 899182294, 608439498, 202090314, 459214377, 650337648, 765801185, 387680214, 886398951, 577614583, 353574168, 513299242, 110439828, 83669976, 88909169, 802548607, 179832890, 528868734, 817106061, 878406510, 252490836, 407552170, 622718584, 256062877, 670336291, 868632373, 563362107, 372727038, 640525121, 234426647, 818758843, 128633140, 608069755, 398880234, 963598555, 846698036, 219500351, 449450289, 94373891, 117567454, 53280530, 727386289, 317197217, 813456323, 938650123, 297820609, 168454731, 140018397, 251060648, 858596924, 717778030, 233428954, 782898527, 484051799, 129974093, 778790348, 419855844, 474770939, 95728854, 429811995, 585343260, 753307773, 696408271, 400353125, 583147848, 494006499, 642373824, 805665744, 646322852, 490768429, 677922076, 21438150, 310732150, 696508496, 467055112, 736093576, 63438648, 873681248, 935712736, 13753859, 918961187, 573274977, 91551137, 460878571, 611415046, 545713346, 738773719, 469699670, 787417719, 192009639, 302455295, 132941159, 387946426, 598573200, 430033908, 254301804, 780770476, 276382416, 484055259, 984333506, 608666361, 649635646, 718740357, 61662773, 609641648, 718446745, 298772096, 860936179, 813036279, 615068275, 408557983, 692507553, 796719730, 123365016, 997458905, 318599715, 824683372, 420272231, 949416352, 212736727, 641958529, 661867858, 818184859, 608743994, 159355043, 217514132, 485692524, 868523328, 10998941, 95607070, 377719334, 10137387, 308858066, 93178433, 526418313, 562536687, 835706142, 542832894, 654037639, 28708291, 944575645, 923456058, 528762183, 4649944, 623697020, 709400489, 496728937, 80519206, 913432022, 779393740, 348608497, 692041607, 419438915, 408011696, 35928771, 486491625, 853576504, 983807949, 374532663, 763317583, 714628755, 945717649, 815482931, 796743974, 952545962, 532748739, 328448795, 457255171, 181487645, 905062205, 587454788, 638824654, 584079792, 826782574, 830364506, 342717728, 168630121, 870799904, 424917987, 778454251, 274107118, 807763868, 728810602, 263616245, 614241345, 160720939, 176426510, 335263244, 756593604, 330416079, 753171390, 770927386, 700088647, 93969742, 245663343, 258965632, 77536622, 822334844, 515457834, 865916813, 351715825, 124682522, 1739778, 226499333, 398456875, 83289749, 246191781, 724760971, 376001952, 443959568, 234880372, 863738784, 741690087, 147076202, 47868782, 794752822, 136950393, 442354243, 238801841, 442471802, 193024203, 780533639, 910217580, 808186817, 859846950, 991183722, 359507004, 490674099, 21351229, 814652858, 750317850, 381127464, 721316465, 538066381, 424880538, 421462319, 409828264, 837071222, 685568876, 378716599, 725738718, 613554094, 181901137, 249248801, 780032862, 563125070, 345318623, 186202415, 269923817, 673571488, 552005456, 977578301, 266321861, 279337121, 837508214, 44324335, 415024004, 666955617, 474519896, 236405721, 196601335, 355598944, 536820161, 537367938, 474217098, 645990501, 807597296, 356891148, 212936685, 877257329, 949030479, 78243651, 938993383, 448779062, 950040983, 332627748, 394062477, 872558731, 99401587, 839992817, 618949884, 702436624, 835065853, 661154165, 779729809, 563454886, 114257878, 422489843, 380042668, 392117902, 942896432, 66979782, 4045787, 215892833, 931832248, 619079034, 231825979, 848984827, 879304879, 453799244, 462204509, 64040566, 678130992, 128041999, 109254027, 354777788, 59027455, 904914155, 450060527, 292612886, 917256256, 30757257, 963551474, 148364520, 98043351, 230263142, 403234508, 304202669, 619171792, 388023898, 295002928, 338188423, 682400653, 204949013, 996487497, 897230192, 519253174, 666703647, 985006723, 388045526, 541534785, 864550228, 93077689, 721284325, 681099659, 70425751, 611453189, 656280296, 73462144, 951781779, 401518368, 689642269, 137761033, 380048483, 697652161, 793985618, 278592714, 715872180, 499428019, 710959447, 438045158, 964960172, 100647963, 744361685, 984126553, 387851937, 576896353, 52686281, 344817138, 417519901, 195210595, 22236528, 459749197, 666705228, 736918814, 190660558, 401433587, 517137736, 514030829, 935909887, 451266794, 822439719, 58487579, 91000342, 484438373, 906440949, 399150738, 96346058, 701742188, 299612315, 453191346, 375429933, 651470749, 348544059, 514290713, 84961389, 1826715, 482271982, 465626725, 19882869, 574201737, 112509689, 99470304, 25614128, 789624440, 111708015, 288066018, 40862238, 409944515, 502606085, 446888706, 410644872, 895793213, 130071005, 417828250, 178584670, 380547877, 329866296, 776971438, 682706523, 46218804, 334566861, 556118334, 332222298, 691181341, 489159059, 81449982, 326532688, 909846509, 322767434, 34456173, 669852144, 619641089, 159448491, 44761934, 346678631, 718752772, 980888830, 819788182, 439032791, 754582312, 258113513, 717307173, 580028095, 826655108, 387190493, 354262551, 356049589, 164240482, 778673242, 174396189, 207555209, 107573794, 336565349, 506116331, 657224015, 429646374, 570261085, 78057989, 692391489, 395370504, 511225676, 661131090, 358415460, 819747239, 816156242, 956729778, 946029255, 926413208, 158229340, 961065516, 204392969, 656075926, 130115666, 936666980, 568703385, 207831769, 839046034, 164213466, 541288084, 2446768, 488881951, 42841692, 850358278, 306896226, 881928858, 73902496, 233137621, 21110902, 376687414, 221917531, 172020367, 857746989, 40143572, 926833124, 933253881, 954604197, 64781944, 627724399, 333602913, 450981933, 478919719, 470424152, 292911296, 480336543, 727472456, 404950798, 86978660, 150176142, 304096592, 856612186, 948735096, 861096190, 55823972, 350546046, 489111404, 82272145, 805605309, 253472853, 980117401, 515498810, 840556672, 666973325, 768228460, 382025089, 347884982, 138402977, 128633003, 506196192, 839181217, 601995514, 561360503, 47912296, 882880556, 673635592, 977248549, 263107655, 55845747, 21530528, 120070361, 478166502, 954876332, 781415739, 950062123, 358270345, 969236245, 115096507, 395988106, 931928490, 552097362, 23288156, 469391736, 22370982, 203416730, 437008855, 386698622, 161365603, 770431816, 920304950, 450917919, 824150454, 550949212, 7032000, 562060260, 580367807, 982259365, 467101792, 7304885, 953747818, 438234381, 629524400, 796168896, 965499909, 205674930, 830614625, 261667667, 650462769, 776956365, 364988030, 921128920, 176800448, 779451253, 737890567, 907353274, 118734106, 734196421, 390810877, 874519799, 813134111, 463776500, 564768462, 627309137, 353599051, 759992562, 704834596, 597963492, 348047162, 169057352, 859872403, 499074733, 363726589, 555396475, 122479183, 39998854, 937395366, 272242313, 929038309, 857790920, 704396001, 633263283, 509410242, 427371890, 47641311, 131732860, 550998767, 168378982, 950374899, 221155089, 123681229, 783088875, 380968030, 782757191, 865913203, 745329573, 327840641, 559079653, 180572002, 691684509, 450682268, 484721601, 70092866, 242080966, 253166295, 401918039, 798441892, 427318726, 880149745, 912838902, 821230913, 942422271, 129448101, 45505176, 923557972, 667554854, 690314499, 338916219, 348583543, 193449878, 355902484, 916583177, 485134024, 172581692, 275729319, 512463458, 773714367, 554908344, 671660864, 469654371, 818329528, 461881421, 121275552, 239407183, 544561451, 184463922, 38175145, 952171776, 511910770, 705986336, 38234444, 297792968, 597655744, 724415362, 413036646, 366140292, 542260057, 470769421, 325523844, 436341209, 383143471, 640736019, 314054660, 342195635, 934038015, 384790486, 959790621, 438554501, 511703788, 204492380, 735919136, 210877874, 325012044, 492729921, 918670144, 3375585, 374727185, 22168584, 366086818, 36315204, 903066644, 621330345, 262021247, 681199948, 824641238, 429761967, 57949372, 432653259, 57595324, 82245851, 414730628, 344096528, 178389011, 784784372, 601308869, 747536804, 633771776, 454252982, 818019850, 931238883, 136531076, 879222543, 998897341, 82397290, 324572888, 384427773, 548551249, 32395805, 901621826, 698644304, 204996993, 348285292, 497449987, 518488350, 495638337, 815574944, 93595480, 476418332, 303868704, 908562755, 761965877, 905286477, 209991605, 226049765, 279991710, 128717233, 990106945, 137429205, 965375054, 637411420, 838331641, 880610104, 559074496, 752172870, 305183910, 156286662, 249324700, 79904662, 869853215, 597834045, 543843858, 44929506, 175854673, 183832158, 473441074, 491701789, 993805454, 842439004, 659866924, 169243278, 257095215, 133202733, 335062948, 991981764, 329764, 293634175, 451938936, 694501085, 933954079, 285510829, 725595656, 900854328, 325393979, 504570171, 30983350, 442592670, 535333186, 340026711, 170680571, 243458177, 183433355, 676413413, 351050248, 35607737, 843746857, 664321372, 790494525, 569185845, 352147843, 989221180, 979569489, 405857144, 326134815, 200588008, 926021089, 548636451, 630745513, 852127110, 247585304, 745647996, 194162029, 664160464, 484900321, 872999339, 551221230, 591710298, 604497760, 439372466, 131430055, 190530062, 864422267, 26807612, 555580877, 438560132, 265047051, 981507525, 835601952, 510294049, 407149599, 51963015, 521017025, 719704527, 846454082, 723013988, 864130489, 319953407, 949692305, 909605105, 193929440, 203560613, 671943656, 295576171, 510310638, 479218241, 496193637, 87381535, 665341475, 662721806, 474241875, 612313416, 307062939, 429221503, 83960734, 641680051, 207994491, 345377154, 507484765, 320326745, 521939379, 823203475, 939732231, 491621275, 16897581, 213938020, 942415300, 69929400, 267157420, 811892008, 510506048, 549316538, 160480895, 737794415, 495920593, 20833284, 547932598, 264645627, 914386897, 770271460, 734210895, 696631775, 420147868, 504731793, 459311794, 838336908, 995136807, 588762325, 736133105, 35259700, 715494003, 773848967, 61043483, 893959647, 13673955, 826444271, 682465567, 356479814, 74698029, 454996499, 961062653, 752800623, 72553670, 423088654, 209958762, 945724927, 722484090, 514620481, 99080441, 478095871, 938443032, 359495017, 518152729, 909667297, 882170462, 961913285, 128886158, 328646485, 346461130, 674916829, 477667114, 878070123, 571935313, 849770687, 80802844, 630820193, 540835524, 698584789, 941813061, 796229806, 127361592, 934148119, 601650173, 53610623, 908717317, 733238095, 904181872, 415887579, 901265844, 820864274, 396088888, 617615155, 849340815, 657398554, 555271119, 644570859, 852015032, 101555566, 482783052, 208498723, 475826886, 449874332, 637697431, 153453776, 181722732, 671233731, 691187301, 961967909, 909626806, 29431344, 863484304, 100139791, 124938755, 318634219, 503888696, 966133347, 46999407, 720379005, 788657275, 377036871, 45207325, 945452406, 39844709, 155863951, 898784376, 202832490, 910964153, 657879190, 43509581, 841737683, 721692782, 800328105, 381567322, 10823927, 403737858, 110741974, 820045518, 223045784, 779100232, 123253207, 961066136, 397799613, 325452864, 282193670, 590468074, 537989911, 233582873, 447099563, 875023939, 650409711, 200478169, 167844527, 743966205, 665536705, 937540753, 228283889, 580161038, 273819989, 887199929, 719829510, 393830299, 982755931, 446341634, 924463642, 990739123, 482389246, 537810381, 188457586, 665291266, 90719783, 93414364, 860727206, 56253992, 985806999, 636420622, 440649314, 912523243, 273888967, 917310511, 179626873, 199135503, 468034512, 500317397, 352249522, 820686900, 160115447, 237648847, 202960930, 334813011, 438288014, 66984625, 224047142, 630693478, 137206667, 68228754, 691436378, 262369001, 833804388, 664031690, 594077278, 493058681, 812530446, 329009455, 581815964, 994541831, 427858278, 737618135, 677673433, 700871676, 303740911, 772071405, 849731627, 136216968, 924711916, 357164859, 604799038, 976384505, 681578358, 67209391, 184339441, 408367627, 589239610, 583574420, 435897754, 679491059, 768717945, 296426223, 356932464, 642038488, 420203007, 612917094, 77213817, 38194928, 342857294, 880093620, 241112670, 964396581, 604401826, 242240572, 391276964, 72481249, 344563282, 177320118, 792075369, 517924441, 838093858, 77076400, 323905638, 352847591, 868858656, 288412144, 50744504, 46540626, 13017455, 411499646, 718705288, 452360996, 103266498, 972990737, 935131787, 578406604, 737628957, 505652661, 37250824, 510555977, 418235199, 648833883, 785521728, 351215876, 76677674, 222625044, 263985046, 884042135, 566776995, 186224401, 854778240, 837838561, 198856578, 141376440, 522753419, 672905107, 333127285, 744991266, 400166709, 375624414, 573467771, 650590357, 619706835, 829536363, 374129249, 174925478, 68216803, 360948404, 621683272, 854588774, 175968334, 48824742, 710394860, 282460419, 407058688, 711832340, 502604127, 611003128, 824139428, 329493278, 919607535, 463674144, 994106667, 462663106, 735132195, 328285805, 931462837, 521607467, 528883579, 11292203, 280090759, 530564208, 569577299, 73605775, 599060643, 854832527, 304787000, 534377336, 896125900, 418323776, 160550214, 390326237, 91640271, 424242910, 454412087, 215798695, 227418114, 530971114, 962191982, 182589179, 72085184, 897803393, 17162452, 9374843, 266131800, 552416711, 749960864, 432864926, 586383511, 670057017, 961294036, 91725578, 856598305, 124127374, 721529030, 616993752, 138256963, 609000650, 866821898, 929406299, 130120250, 917898206, 804929399, 195500966, 174167339, 338214426, 894729665, 769608281, 537984653, 327254885, 790469705, 137160014, 424642209, 84900673, 168734761, 852047678, 708322485, 977396155, 325328831, 637103366, 66141832, 274726355, 119864428, 185757156, 889976439, 417916629, 594257210, 926542088, 196750192, 957098988, 179963455, 953834268, 195139450, 744030155, 435309297, 35914737, 697754667, 439860454, 841100907, 623647454, 961016616, 103421567, 238735042, 874486615, 95553990, 867138900, 548899662, 883827610, 628299971, 931763573, 708293715, 631003822, 230506941, 988989630, 676698484, 527619415, 625604049, 132454679, 973757803, 307517332, 757194326, 897632130, 529898408, 211008296, 846703658, 816139450, 216553429, 292930759, 626632385, 619450783, 30958783, 430936537, 808079458, 208100058, 380711508, 358420451, 58189435, 558399082, 667259357, 937401026, 400518367, 335988790, 903329800, 779021306, 180312995, 862692883, 330072944, 347876758, 176568969, 530059958, 558571112, 966747401, 429935819, 309050579, 795167725, 535245719, 305242854, 426356657, 666913656, 576519922, 825077099, 174742405, 987829431, 951557057, 310193233, 990156391, 604072104, 795988464, 625770782, 800733342, 546899461, 769537832, 65331251, 537582179, 365760717, 369580373, 148820245, 322756754, 651974120, 915573615, 746350591, 506538102, 83012007, 45852106, 295295972, 851461463, 517883520, 833217866, 850677424, 481223900, 858431907, 120363117, 471003561, 66651660, 905082361, 494271149, 161312250, 534838733, 157568870, 532749670, 25656285, 464663658, 392491407, 250952212, 8585955, 146979483, 864677680, 80116346, 143274413, 807743291, 441749033, 5134319, 795257746, 465179827, 674097285, 519581272, 733579857, 552663697, 109147997, 317112177, 682117, 963602388, 534408799, 924336702, 679980874, 394766903, 462604377, 924223030, 636457293, 622448964, 151737439, 72559297, 941302790, 458649909, 755175954, 314502717, 665703862, 893815602, 406839008, 533360157, 622257496, 554727, 964008379, 405912548, 226805358, 68832167, 788467435, 521735698, 766400120, 394238369, 320977192, 184185398, 520029761, 746619597, 950758811, 466018063, 201096112, 297314340, 653917352, 529314845, 871056353, 485881648, 217898528, 571011039, 477595711, 949107572, 288762633, 209384642, 341241733, 145655346, 395080877, 612852862, 876221055, 602858358, 589029139, 766057409, 867961504, 415001947, 47379195, 372868690, 300988088, 585980414, 435164025, 739223764, 773214452, 206701586, 71905435, 285822100, 289857040, 806690131, 988371940, 913247023, 479316872, 709539686, 806970142, 108840359, 745918242, 486232753, 590658918, 796849380, 400489861, 235968380, 732150883, 164148239, 762629348, 62029770, 242570434, 208558680, 5478678, 162565789, 757511484, 39725654, 344098714, 669912634, 349250192, 741390304, 993947321, 535088687, 511581323, 514544440, 915738396, 173939140, 872514003, 611782939, 604668674, 636688566, 346883821, 987222602, 136820717, 227520756, 591775910, 360910287, 48423208, 206204547, 232534031, 728191709, 785668495, 451959921, 174069072, 825587363, 365171904, 468732731, 252745148, 866191134, 681817214, 755330429, 561006058, 692634834, 659128003, 319116111, 200394896, 602643552, 739693978, 719453418, 217221045, 641171091, 927858577, 619986969, 208209060, 984904254, 666869480, 17066586, 410115229, 23192253, 29588823, 714711078, 7824859, 866026662, 360221054, 920773298, 19794377, 248076201, 519327911, 918589006, 356175625, 698007200, 994300778, 482752931, 830955736, 446058018, 576895003, 923895396, 310370983, 85010323, 74066700, 47527184, 715647252, 477799362, 448420227, 571632608, 438509680, 705428760, 427989379, 79530913, 349949269, 807107263, 809599856, 433795061, 540720769, 312731089, 757993204, 387258525, 735043250, 981470280, 467829162, 663323628, 84023821, 516691844, 893799239, 606695614, 183599373, 935883711, 153951809, 844128341, 55978877, 371072398, 300868662, 420947098, 120835874, 842690620, 228571905, 377240829, 223049192, 422736426, 353270077, 836386274, 484719735, 633629365, 127909610, 727739494, 533367012, 950717807, 834033236, 202066945, 542071943, 248761664, 34516893, 165784925, 290872062, 397827637, 819537252, 675980772, 1308235, 931817465, 144645985, 74718572, 174934361, 711843510, 279382220, 893327775, 766877192, 865314753, 496863497, 42638907, 28198505, 717216917, 146459087, 660896045, 390744377, 52402050, 295769349, 13898852, 135071240, 778389086, 534662045, 337258852, 908786032, 591066355, 262467840, 299870112, 153283350, 95542972, 737364165, 793658147, 473773671, 118313096, 295288025, 584805492, 790130874, 89761102, 26037378, 50710319, 864861579, 264547087, 541957126, 525730713, 931587381, 228066924, 736630327, 713538168, 459222295, 694444590, 724297454, 761055351, 14977321, 779069892, 682921229, 321384286, 129084916, 280289626, 639369121, 266501275, 545935109, 720920441, 349610396, 401530261, 341822981, 187408721, 372836046, 991676261, 446402046, 589380902, 613780734, 863740862, 367661618, 715536978, 758831276, 426642407, 872919929, 600828307, 649938288, 313487998, 351765553, 467997620, 671616128, 592341935, 807347471, 766586663, 639323249, 127981511, 440599618, 900078647, 108977548, 647882353, 336739122, 118994331, 603925142, 353390036, 829628767, 321479335, 295827894, 963638915, 69985981, 559016756, 908121148, 98434935, 500765266, 582204570, 930548842, 781885933, 375170864, 547711667, 545950196, 669423069, 668687921, 795683848, 520604845, 29659349, 39457055, 888977196, 773102134, 694188721, 87091041, 996169142, 598419828, 561820026, 205050428, 248113764, 278984059, 977604084, 717684140, 788151874, 469252356, 762773940, 315683933, 430402665, 96830156, 104428086, 669314998, 789626870, 53505403, 367362170, 268104497, 681118044, 760060900, 816284078, 924104702, 428499995, 924921947, 766125860, 279797940, 533637314, 319244643, 284293347, 408094258, 511776835, 271520011, 813858860, 153132302, 460353003, 299570690, 387423784, 33613956, 920622630, 378102135, 644092178, 351132162, 696229766, 469327873, 469535692, 271528636, 811479908, 94214343, 329238691, 117456233, 209020911, 316294733, 222215045, 794521118, 628232156, 378335434, 134141278, 693034519, 279094659, 249449590, 610393434, 910500143, 1937553, 619127005, 975117530, 552005584, 251410408, 640824317, 413729963, 242542340, 366125477, 330681820, 980308462, 995739110, 933788155, 43238177, 817944079, 926333107, 837735920, 31648786, 688117489, 562694943, 709177674, 200244359, 219023119, 134460595, 903447951, 155491650, 864367763, 470368942, 108638462, 753852643, 474230711, 109241131, 104464252, 791399241, 81624185, 732082561, 563400869, 621484313, 713657601, 206299461, 387157255, 170625063, 193044128, 895812483, 595174719, 456359084, 410360629, 98257206, 508396887, 768338259, 75079949, 604716300, 443390737, 385692385, 832779018, 35213387, 847151088, 548465297, 151206828, 363699367, 726393625, 795138299, 91073192, 118601656, 660225044, 751556950, 775135792, 36328816, 658581391, 565738898, 29978079, 543131583, 115167397, 606423828, 982097769, 794546864, 163217333, 820812779, 792992559, 623616146, 848119790, 246959824, 36483825, 174446650, 953607185, 16178149, 608460011, 290692118, 226962710, 940624396, 318529827, 177405340, 236952611, 445582055, 524794658, 657162795, 463505643, 960990632, 9715455, 987605191, 446223331, 647316514, 790251192, 674471505, 777132452, 162560677, 910810371, 159213366, 245122683, 892541780, 130397287, 780194128, 926341912, 869447663, 560453414, 931542262, 122768114, 625407069, 135848588, 190604020, 801219247, 912868614, 901981358, 24389810, 255777779, 835388581, 694524521, 181491232, 615966566, 797802917, 197163867, 31954691, 870077625, 283102310, 448543628, 701189391, 945319279, 964070814, 252470152, 378999082, 790226905, 132424988, 630924917, 982918405, 628204076, 346816886, 762882294, 770623435, 726883592, 282682036, 331488996, 39867526, 296937064, 575103771, 518870916, 625513033, 427425449, 666319657, 936304340, 737273743, 880692625, 319346195, 586093494, 736474484, 78725685, 29962515, 401707593, 675673358, 152040722, 451638436, 645389602, 718801361, 774821488, 957262464, 575754368, 537155759, 59780563, 738592167, 66611990, 498422299, 170123732, 7694789, 474361944, 893284508, 463260793, 719462484, 542424125, 885997057, 763600329, 688829491, 571181193, 359249482, 531058301, 676522366, 37491072, 16290799, 418834068, 394544604, 677169051, 685665636, 696370480, 269664826, 310430310, 186185469, 831268915, 28579100, 630734170, 908383732, 394451163, 690011398, 190573311, 66939596, 326462180, 49031494, 843561643, 237273271, 359415884, 848507901, 837630875, 810823082, 469845623, 706548990, 656157322, 689322621, 27808508, 581083137, 905630301, 916868181, 720802837, 970410192, 467240145, 641750196, 997485858, 507474407, 873701111, 982454770, 3072122, 286416143, 127061811, 872292149, 485710645, 998350487, 950433451, 482319391, 399914314, 892488772, 882790044, 408551568, 246319338, 153438506, 978327945, 401203224, 672226984, 232287632, 805422908, 145558067, 60163614, 54714493, 29196436, 615676726, 525135591, 372887459, 97517814, 57634943, 273533026, 578310712, 816549552, 263360836, 867755954, 143605312, 100197545, 741584592, 196149675, 133939174, 184725603, 301079767, 934112227, 974296238, 721695936, 827233986, 156576990, 81765704, 537016117, 916383647, 771053683, 437719718, 353518245, 791418653, 722483438, 397285199, 71095467, 228318961, 907612853, 162757358, 104250267, 340188766, 526232175, 731493888, 790700255, 846242662, 212530728, 179875886, 476993445, 373800243, 817428129, 931534372, 18693178, 340848273, 760444751, 435926287, 965725655, 565975515, 434878489, 545104312, 45394810, 969988786, 186990517, 583077383, 724613907, 569370427, 998904826, 636158093, 618107367, 429690928, 609235697, 934620017, 755566395, 892583233, 381624827, 977628446, 550600999, 964366728, 780251106, 528337553, 6322210, 258329849, 56966806, 512508004, 291482522, 466938319, 241594916, 720024351, 893027051, 967822038, 256700037, 37627494, 929411852, 998423877, 236357415, 812796170, 16943925, 527164593, 910349289, 738407321, 138653103, 633490608, 253910755, 518547541, 726329364, 682134110, 908562556, 64911812, 784573570, 403886090, 533274436, 906090700, 529868109, 761103804, 673097427, 22395069, 716599736, 395625190, 771666325, 908178303, 456314381, 822651549, 869360595, 67327028, 61366460, 961348233, 468884806, 216629357, 415822345, 391203477, 328970214, 143793067, 770024026, 394731736, 661579666, 637353464, 504659272, 535531851, 368048221, 279370484, 839404907, 278619672, 238018606, 108643221, 363136494, 632586172, 649873626, 973843363, 755265466, 675733979, 346719411, 77047441, 118217343, 349637288, 712169740, 53698171, 670424218, 361765964, 883735049, 855193313, 324017526, 322948918, 293926840, 29884200, 640538535, 908515864, 750704826, 809061422, 508478816, 124624974, 705490669, 560610565, 732805214, 52732274, 461124146, 686037485, 302075914, 973310427, 610133319, 263394441, 75150252, 969698225, 427712928, 890266347, 822973295, 949307512, 668124367, 222503122, 851974037, 384505807, 970788702, 209020525, 862893691, 98235056, 621676837, 106149451, 989676131, 452054093, 435673617, 180137232, 921522120, 864050015, 490062213, 968812015, 434534393, 412691744, 699236607, 616430889, 825251607, 293316545, 657567596, 707720005, 242677012, 400381791, 487430425, 548267984, 924787258, 646629791, 380909433, 129807744, 974213507, 896284485, 318602039, 303137470, 793032432, 201204773, 300318465, 582895249, 27184771, 980929667, 523684402, 588686837, 322403613, 886958025, 678240769, 950100887, 52199136, 754237736, 613623980, 115395108, 697059160, 491454816, 448864534, 380887770, 612493231, 372162207, 147475526, 879481987, 349073537, 319356336, 403598909, 474536995, 613109806, 601933385, 452437540, 706584063, 750847590, 948143328, 394695623, 384305098, 208091033, 870008097, 992630432, 65297531, 4231608, 454307203, 907588359, 106643018, 737676377, 147047975, 486164029, 349130439, 20039123, 292780798, 479046636, 457106984, 86411465, 750018783, 130877658, 765565810, 775245563, 968552681, 469097540, 596789088, 885442134, 301131977, 231722487, 880794670, 745804921, 493138986, 883088434, 677112180, 659730994, 127412585, 601369340, 630156827, 159768348, 374301930, 39861525, 736035720, 838814180, 206939296, 188450053, 416658928, 142518778, 52259101, 516616325, 529679761, 68547699, 737733882, 141716270, 462454607, 129412766, 713984778, 786460212, 318659421, 939707415, 64389341, 762211919, 961685392, 774457376, 374329136, 416496327, 795618617, 163044978, 744798098, 149973061, 778979844, 352794547, 797503674, 77619298, 999368783, 40596160, 63704664, 603930434, 460538773, 417904919, 759141853, 44336136, 485051383, 364854257, 292688592, 679979599, 270932876, 271281762, 677973130, 338470070, 899217021, 597536965, 708998878, 675732237, 284249335, 419839994, 261427068, 726908276, 525019476, 930704766, 685268287, 1190036, 517656650, 19355253, 112419260, 203987151, 95343236, 443996305, 989458863, 793243899, 473324567, 866938577, 759951812, 966951569, 830734464, 394717859, 291242703, 134008714, 623009052, 454032329, 83722000, 187425589, 905768515, 314481976, 824175311, 349051465, 81144670, 803855360, 358259281, 342789709, 45292450, 545272569, 62770614, 463554921, 849645070, 183333704, 346535217, 767784374, 510942300, 823997781, 259815260, 765956925, 962137547, 189081457, 864238769, 739555372, 412312902, 581033696, 753954954, 934268780, 291730345, 332227187, 357692600, 613793653, 109100817, 887392154, 553208743, 72165852, 90443062, 681760344, 736484203, 301057020, 965573311, 56176994, 833960580, 651519630, 264331330, 485795305, 137900245, 778658984, 295385122, 754205085, 473129232, 747836574, 181961327, 739659072, 779400849, 931494637, 777455328, 272639233, 313522076, 387603172, 88720, 71006875, 683771804, 532651252, 779362487, 486860138, 503044377, 360890978, 143719473, 10366993, 871901816, 952539559, 382167781, 834710013, 922583348, 203077643, 825789083, 477164751, 544451771, 706910881, 997243726, 866317655, 252587199, 645725418, 451011230, 606746467, 73508278, 774695832, 832977419, 691208536, 99655235, 519866914, 925086838, 246953020, 887596099, 951278277, 203223258, 526763385, 30665154, 345003005, 869151461, 55932644, 776599760, 108186318, 4298661, 560227495, 267519471, 442855538, 967194173, 775177614, 565637564, 126097823, 483023217, 815345950, 588599493, 68500891, 782092495, 20522104, 677815547, 834784686, 187363064, 317721296, 251129218, 736902043, 486880071, 169692355, 66969848, 139554997, 430229500, 79118034, 298307818, 46318394, 251428731, 763181028, 447655210, 526699958, 266126343, 413780348, 793656657, 978392557, 640697034, 419730556, 899538813, 352545618, 651235186, 97324150, 981848501, 431469911, 410907652, 464500430, 559640237, 865153123, 297629636, 163691378, 143020833, 971633524, 936584455, 486602841, 493653920, 250083211, 223815852, 783191830, 159959094, 123163498, 738707636, 733598670, 296491053, 228725664, 800667945, 998194424, 806368716, 219619689, 591696033, 602502926, 761329375, 802236392, 585258087, 655621405, 443843013, 932360073, 458333855, 259981010, 487989971, 54174233, 954835256, 100903921, 789545995, 582679455, 575973605, 389537356, 682917503, 438474115, 23344811, 973105044, 50399450, 378212451, 834469308, 744719345, 811721728, 47094182, 924336928, 102928795, 196679548, 13665503, 33124753, 888170617, 346661213, 423996492, 638766959, 245074271, 234122703, 396034072, 31404572, 717722989, 420602770, 929984478, 108009456, 743034452, 490821199, 168814093, 372068521, 388978165, 184438262, 382796983, 323783249, 87467129, 545817932, 467950479, 380190934, 829342628, 920547394, 764149353, 188629649, 486424359, 702849212, 802975790, 318460774, 919465676, 443809946, 464655712, 293195568, 440990739, 237112365, 509991260, 194854217, 395740902, 919141912, 809022186, 530908092, 209893301, 9856554, 396163043, 222577855, 235863003, 109590840, 942941931, 984203146, 441717200, 867728679, 222321874, 761576413, 817304227, 133036021, 383895832, 837402267, 187201407, 470668481, 250241600, 571179487, 923041077, 879192292, 632523693, 959517168, 773309162, 308620905, 615571881, 725923100, 345972132, 528360850, 927846413, 916603321, 94528665, 803181096, 800167499, 650703968, 875358771, 759202267, 524250706, 528877307, 524263164, 859920826, 55936697, 230941550, 914214418, 549717956, 121028249, 843203787, 296552259, 235253856, 874200191, 870962467, 3297258, 863787949, 354211691, 323426039, 210234910, 934166608, 849389415, 934225732, 149832367, 794170978, 380107498, 462288160, 79740387, 953450186, 155571553, 665079218, 901613966, 780265368, 743080433, 317363705, 300299922, 864592542, 88049688, 616161430, 948138015, 544794653, 637065461, 646877179, 589718373, 848405379, 655801473, 493558327, 885861827, 19177546, 715692740, 733124663, 797848756, 863235974, 233292143, 766643302, 897781798, 833810436, 412862344, 547848321, 681620993, 397726568, 709356048, 616568773, 182019785, 84091822, 707326442, 93673122, 329705341, 582832345, 109813007, 205330209, 670672504, 428363695, 959115361, 551777799, 584977307, 936333742, 636806778, 553896859, 962189174, 704354100, 582008273, 402564870, 513129512, 251281756, 683954761, 715221751, 147972366, 545686775, 171473204, 101244963, 59206413, 245467642, 484435445, 882160647, 348261121, 416261033, 322097019, 713308009, 895193409, 29033614, 139744971, 252438817, 525696793, 862623925, 96386443, 105950010, 378224274, 708713808, 865324312, 861923166, 766013014, 894490112, 142071902, 230575514, 662484883, 484841901, 394896014, 683991284, 588056468, 991495411, 774944969, 943976657, 695541544, 715068418, 146230827, 897033236, 365950846, 431718294, 924640273, 637140515, 947230881, 282875978, 465105296, 589138357, 714306871, 226930165, 320323023, 501536993, 470857379, 397491759, 848530379, 559748326, 170849518, 733615492, 171682553, 944897503, 981239694, 254330614, 203618736, 685806800, 835960828, 637737455, 644477920, 493479423, 571422326, 793713677, 20109794, 813733443, 143148893, 208860799, 10672500, 505541814, 793383786, 356849837, 625509542, 453838169, 686878644, 841345943, 589447831, 640851614, 334382255, 577053769, 707707152, 94558534, 389417646, 204406336, 887715619, 42963490, 438724573, 491575985, 21925741, 661401161, 386330374, 742308936, 14498972, 864907959, 325921148, 701431004, 770285290, 51940514, 327739169, 793795141, 185926814, 661659251, 129363621, 108280504, 704342069, 693214835, 743975249, 601180679, 321083280, 285717496, 42792112, 55535097, 761179510, 445867605, 111969129, 549165767, 278995494, 972147558, 957497491, 573559950, 608651557, 14697135, 781286227, 676552196, 636981323, 17939958, 59361136, 961179870, 991350341, 764590076, 362423072, 475211015, 872106709, 444212134, 377184372, 852579928, 495901504, 203997851, 677732235, 343195911, 585585745, 240796231, 722294416, 800775903, 455213666, 581622668, 848148823, 790797137, 932603137, 555116899, 134639290, 339963488, 66602379, 255358161, 741012309, 181426817, 26527835, 269244639, 570502802, 880205685, 599500610, 413075376, 691492927, 980628398, 31914534, 799915051, 823929434, 920140232, 706249279, 664619811, 207368089, 302719263, 844381877, 811372849, 101383835, 253381222, 83272778, 472927507, 59755801, 613100599, 889548514, 794551807, 806114648, 344313114, 953243474, 541735399, 875252802, 216408018, 564158760, 960708595, 892082252, 431356760, 432502772, 224326165, 319411194, 897266376, 981846983, 324551206, 745231057, 668825012, 628941177, 39157556, 804164121, 6609062, 400722367, 198623864, 668916270, 878275924, 52114408, 6381182, 247110287, 422135845, 1771750, 678959904, 114533111, 756179647, 499828450, 680511356, 72815423, 327604902, 53266583, 875745686, 324631028, 112853459, 163341329, 696424577, 267469824, 497332281, 885276361, 509526536, 504713897, 487392615, 357617095, 350638865, 818555881, 72288982, 895468823, 553970240, 439205289, 344471341, 908236809, 169646124, 742820406, 720841919, 376344428, 452966456, 211677843, 247105428, 446749114, 900067850, 546875145, 127702371, 712767641, 194563493, 126636291, 706810046, 708959490, 884018693, 760545057, 229008957, 199705460, 10696131, 542071634, 383808788, 259578975, 168639927, 881811358, 182956073, 161613478, 56650608, 976511825, 624081423, 287771276, 337523005, 142536891, 899054319, 672437289, 677360978, 286340806, 924157240, 455683022, 419986469, 602458926, 746156276, 25332140, 950625114, 853771704, 947193752, 648037270, 254744294, 48454233, 402932824, 158952426, 880215762, 211830663, 351781482, 827372016, 594193095, 468844676, 797390103, 466000635, 771190878, 424580861, 398290610, 782402349, 502539115, 951052750, 659784314, 555625525, 992073216, 546473094, 238724021, 852435416, 228232843, 783384488, 635677017, 370269092, 3588724, 671726370, 772512871, 654011725, 111008225, 308082744, 228806887, 311990431, 638229072, 236832698, 595047585, 70232079, 132748030, 334505677, 383782760, 68319339, 472687821, 928300845, 111120657, 26904457, 336597159, 56880606, 826519402, 331661968, 501810170, 677235371, 233454431, 126418395, 599110960, 649279839, 4581036, 263478942, 907136438, 251427649, 775496317, 78819681, 833353767, 877566761, 200014335, 472345606, 518916662, 347424410, 912984199, 853592399, 261435455, 552432811, 511057891, 530089466, 613542527, 220826211, 315067162, 655755135, 87999061, 862077257, 593811638, 503062540, 350384241, 687272706, 103211756, 861197243, 572976274, 281208405, 7274615, 24698947, 603512891, 499138075, 592481936, 116875571, 470217826, 676712984, 175423921, 102561288, 938713451, 375434504, 218306464, 571797990, 865041012, 653687760, 493034674, 500242331, 691353592, 647045826, 671177410, 390048539, 826631559, 953268420, 544285687, 228767202, 246502577, 698887221, 79532185, 754793810, 224945780, 218093, 677093287, 328139033, 503524095, 182967852, 37920945, 16047767, 536376956, 871530133, 642216536, 834545658, 347607840, 554177547, 796779440, 526719999, 231041436, 589061707, 115895551, 996732194, 872760206, 878167467, 279876670, 848475045, 586933962, 587044462, 110862515, 663427932, 829584193, 206198183, 649418728, 884979837, 335954346, 66479273, 261974537, 394966870, 40669375, 806507168, 337251398, 81434315, 282938066, 420996001, 725159976, 638450785, 216326417, 217481539, 726796182, 60029608, 329472603, 339098077, 434282995, 673204985, 699907624, 661222381, 466765223, 255782695, 515789187, 665597759, 659921122, 508812214, 584565007, 833703998, 534934693, 145966267, 989313864, 718773283, 491674357, 314539864, 266105666, 371626449, 421408529, 471881231, 206880301, 460817957, 742766640, 91151002, 807877920, 93706630, 665624286, 893649673, 156929795, 765053798, 50617524, 255073948, 71696211, 376022919, 806892448, 666580500, 624611405, 476574848, 332612906, 153086081, 469956519, 552340031, 978949808, 673785349, 25065285, 691327598, 426327621, 180173052, 108132732, 201087929, 741601754, 863583640, 75910067, 503756390, 701582239, 512031176, 449729055, 173023023, 908331498, 553744053, 19992506, 779172898, 672092763, 768778567, 318388043, 910319854, 502291497, 227106444, 280635474, 962401514, 86032432, 215704631, 215399351, 781352813, 588813707, 317885969, 541671897, 209010793, 37154203, 588933335, 725969923, 565939505, 457288050, 938930224, 559556607, 414439379, 207558282, 443967511, 549575212, 451807586, 962097418, 514329005, 57766391, 585083334, 220398710, 374636844, 619641115, 849181732, 69660845, 345241115, 157378799, 932562340, 47041944, 817555618, 196447526, 390809778, 778868289, 270434527, 403846332, 6461505, 979110078, 934727581, 248945571, 279037906, 530466262, 139507656, 466980690, 881563426, 405199754, 911210919, 34255738, 489038960, 487640657, 298385222, 929796354, 383350675, 660243292, 736376158, 409644711, 718023629, 639446682, 607678970, 942919793, 672072169, 154295704, 732804172, 403929489, 896863858, 655985578, 374222159, 576040482, 368348442, 942520994, 241468543, 37615160, 616628807, 194232855, 946269663, 454570328, 305054626, 314925862, 705516328, 610790725, 795786875, 249105524, 324994221, 433701237, 377400556, 797445773, 742981434, 378026897, 395202502, 826557975, 912519495, 616463126, 528251804, 225864386, 157617931, 183737162, 614269750, 120660901, 460164149, 159670219, 149282017, 837039502, 535588921, 569667714, 103519767, 552945075, 651912890, 97851273, 712523294, 545735651, 599089429, 308513267, 66369647, 543909969, 290197557, 157389768, 887618383, 309549439, 181644007, 809368006, 470033474, 676170617, 58828919, 128820192, 382349908, 468356020, 464308262, 129505516, 887425423, 705677725, 388415228, 990431481, 516815010, 906686372, 914065616, 512386965, 425287279, 103370619, 63843222, 467765324, 122374211, 432713288, 535046654, 620091659, 220641594, 350337913, 790139212, 527462765, 36262673, 644160414, 841163231, 838523748, 819906496, 962080433, 136252631, 883945517, 602224442, 844407175, 917786893, 91918885, 103099303, 403670662, 436641382, 68837775, 977180999, 272428861, 985476993, 71328841, 447229146, 97836253, 367884248, 86431645, 751131963, 959912389, 828502059, 43567292, 601473951, 881042583, 512438563, 65645730, 847570739, 745401892, 360361245, 340268738, 338939592, 355799311, 285393457, 276380996, 12575823, 483695449, 175272946, 355200554, 579128238, 936902450, 569075309, 185741211, 180563815, 651715330, 341031193, 194202877, 93019633, 150895453, 583300287, 147502475, 998097305, 872681588, 505761480, 413376676, 750490012, 602596904, 30639467, 689654808, 523639369, 920966830, 641780033, 296075460, 746984804, 946501348, 566578244, 750623939, 267288919, 229530967, 599234991, 412509720, 45773696, 18916700, 489527299, 785690095, 322194784, 551820977, 231294376, 241400355, 166571716, 238483030, 354050303, 511152220, 247000044, 93652739, 64552504, 799876319, 660675598, 958654130, 355091724, 450771613, 611300178, 687789124, 386456396, 669711189, 414080499, 417653233, 396995798, 334885081, 296980663, 740189580, 643281995, 800282446, 533649336, 514911198, 700552001, 808229703, 272862205, 420873265, 406753260, 284836811, 907495106, 429397059, 100422202, 104976025, 297671413, 491835286, 245116874, 412441867, 798184240, 142464756, 995675797, 596570803, 624219127, 896485268, 86295924, 966899297, 745432784, 790312022, 159072116, 479971788, 257780424, 342212877, 145187968, 393629462, 885462331, 496408179, 101775251, 199514654, 598243427, 504845110, 689246788, 894745162, 895815840, 833610927, 819284777, 925827311, 23684225, 163525066, 494261909, 822347323, 225163274, 752924352, 730609797, 193879916, 396600377, 680501988, 364804752, 978107672, 463245597, 520240369, 342354851, 796526199, 594495443, 79599456, 516555383, 53292040, 305930859, 885230936, 689899816, 718311099, 622623002, 941247655, 707954222, 181579987, 519249730, 213106886, 980610832, 48085157, 248758289, 819447036, 165975275, 752784359, 164645172, 364163765, 341609081, 11868125, 341973558, 49483523, 976204066, 260363569, 327351060, 583844996, 556057215, 481555886, 701485794, 544620779, 357389247, 920774911, 916380569, 940092953, 870283426, 519526924, 85021308, 772774591, 381447052, 140041272, 952803458, 608004435, 429848236, 284183871, 832236604, 102752747, 847390663, 718951484, 811912766, 458893253, 435279470, 630114206, 653556650, 544516246, 871479787, 849244952, 702102627, 663477874, 376091704, 815554747, 108151912, 749495987, 696249992, 466030330, 67441023, 685175280, 855368022, 826758221, 815944891, 314203016, 357903412, 659187444, 903630943, 559224474, 712295422, 34403497, 224655539, 81450999, 417737596, 279340361, 573365685, 833343588, 603230765, 253260955, 28947366, 623545956, 84347911, 119535963, 117844311, 789896684, 161475072, 44607326, 140942625, 863149124, 665970368, 483340807, 959001974, 428915108, 470365914, 90868398, 516058939, 587516442, 648690659, 488515431, 709146753, 763587394, 510946067, 505216306, 223464721, 447485246, 411517176, 476350796, 759987472, 33434691, 466677823, 134904729, 620514257, 706642584, 751159750, 769125859, 331373092, 58279117, 457068282, 83978400, 797817640, 539419606, 722095135, 53548900, 399819987, 407652940, 317678658, 407999449, 825293025, 932709803, 942864137, 590695343, 470663995, 970692595, 31311278, 544685106, 919193373, 720170921, 28649039, 85796436, 162598893, 924154465, 163928887, 407159437, 41492385, 319559332, 186578275, 202705617, 308574244, 468889031, 801013927, 19438333, 185217719, 532241470, 833856415, 796419865, 730380156, 494630991, 214394663, 556770970, 415558675, 905970566, 873493784, 414225885, 755994318, 661804536, 864753215, 196817822, 415538859, 641372643, 230423683, 783448801, 693001402, 418394740, 873868006, 176437089, 694489763, 355706908, 839577049, 543601237, 909391420, 613696584, 657770311, 939991162, 176260628, 391508178, 961240955, 861126791, 92049225, 726583268, 319574051, 197428447, 347544147, 66353557, 100828384, 601726177, 611976042, 111890979, 698680376, 464273230, 645357841, 508436139, 552975221, 244401583, 224009861, 361421093, 284670338, 289851789, 378025251, 744462668, 504802914, 631695288, 45410302, 559754903, 179062969, 152798256, 192794705, 306440254, 66058444, 412368587, 467002717, 59414134, 687777398, 765754690, 715758591, 471618021, 733776914, 989895824, 580957695, 358676395, 753175946, 231668340, 122795230, 631214980, 357424495, 46541911, 217501408, 898833739, 363236136, 680796815, 243506403, 947210618, 942397142, 880354446, 680837309, 337818128, 654924527, 487884891, 286119638, 919661439, 824684699, 32368409, 460849620, 55652306, 435640534, 383402828, 409151181, 149658453, 925676415, 588487629, 683759190, 854371870, 854880032, 329967710, 758977305, 473400400, 716135211, 681737388, 623762653, 681476048, 914784008, 825534630, 882375779, 964074284, 343837696, 171434950, 398086817, 600245995, 218630397, 552582622, 202806267, 570265321, 393527342, 593380002, 583722118, 829526125, 204711598, 539057915, 550431810, 647589445, 396650582, 747209215, 560015352, 772476263, 279240873, 36244305, 756312769, 478391658, 118334066, 614641541, 824791470, 752366278, 893893226, 588069712, 680460685, 624407516, 698198079, 857326874, 457577637, 657567430, 988308259, 316986344, 58218718, 456715336, 906796198, 929465427, 778767492, 65455359, 201855242, 583662499, 415118382, 560330429, 373441425, 46867121, 970266375, 406276762, 116506062, 119666611, 924332660, 61696075, 630883660, 473054365, 478939160, 162742067, 48306482, 499103806, 995856366, 727564450, 272736703, 249143999, 301647076, 983355423, 846993209, 651731802, 459438255, 885656958, 767350298, 79710569, 108427225, 354879961, 278456683, 679333746, 556409301, 698208842, 85432587, 897216718, 316042410, 135727445, 974534694, 408588700, 567717454, 849706653, 701524434, 425672122, 93943205, 721437072, 48651406, 982152022, 867001095, 562737782, 210736789, 15467384, 675198164, 902076702, 111722430, 356102450, 913814761, 130632336, 18825467, 97028537, 229202189, 673104792, 290649402, 908174082, 266615163, 366677479, 99415482, 826601909, 10638627, 724884656, 933815699, 370824973, 479958377, 210136217, 87428082, 115411519, 425936014, 76780614, 69134089, 952091138, 436981198, 326307941, 761170736, 643624447, 7155962, 84536199, 289559689, 730149220, 349163913, 374937153, 229536086, 417476969, 278498468, 64409378, 394709489, 896745839, 136934425, 295051821, 601693551, 151620138, 119432717, 253327235, 646722014, 85151262, 387947927, 987331579, 105072079, 410573875, 782205718, 269556548, 550125607, 560224412, 273998303, 845258056, 774761002, 338297848, 77742514, 950317807, 31250051, 276498875, 649007818, 274720487, 768416008, 728807983, 296584881, 864663723, 103546143, 599236379, 666748613, 136232629, 145683114, 306661228, 719575680, 268008683, 693964280, 126469637, 692576650, 977440035, 483884416, 634844077, 975857346, 465020924, 64187078, 894864687, 252694361, 805824489, 81747873, 323891167, 786886318, 852783856, 337207484, 824503141, 719157396, 957671180, 215348382, 232951872, 121069133, 11757817, 537554322, 521542411, 901608371, 902469223, 577072285, 711357711, 423900221, 8639620, 808842021, 130694569, 961668747, 805119318, 337027655, 604422134, 412268359, 380695151, 186907419, 766265506, 350044190, 955530480, 261028224, 342721444, 163186336, 206717602, 785256285, 866149268, 429720987, 660194538, 423170993, 843089195, 54489145, 821479385, 472723446, 979336251, 582131520, 962570781, 206065042, 300119868, 732368106, 693031170, 157228234, 728357628, 654898545, 602998357, 653966374, 742521981, 122836599, 794956453, 616560140, 694566987, 474503312, 343377984, 692096583, 924929000, 902747692, 953731534, 457001094, 288547765, 365766400, 40766249, 225154282, 468633905, 631723582, 662337609, 732614414, 868543348, 477198415, 548556338, 482186820, 687593442, 675252940, 451847304, 404782484, 300700402, 9511204, 64484118, 199779440, 740377746, 431095912, 797786723, 701013751, 157470395, 46776603, 542212535, 201539987, 771121620, 686158710, 366788023, 994445095, 878832785, 815554663, 652569970, 882218691, 925361218, 822965583, 713632253, 260632837, 201053683, 353646737, 214892058, 158733617, 349394705, 868661542, 806203633, 804880974, 928687353, 520841622, 607135826, 21085338, 958783583, 383145721, 15973859, 410046376, 166535332, 211963669, 842705766, 669619648, 113490568, 281838945, 603833439, 466195467, 346016214, 347019681, 647065657, 489611062, 667730289, 408205377, 467602949, 153872336, 408746647, 383719587, 328877371, 990482722, 621943220, 767690025, 693961479, 41439877, 713429022, 605237955, 151508014, 345247609, 127640209, 874576946, 203224848, 879611623, 466326306, 493663132, 417095377, 368806343, 417033724, 683679520, 329592349, 681721637, 485425969, 13958122, 735559905, 583886413, 293587370, 280117707, 875360555, 627713932, 963318005, 712735106, 956149337, 375607649, 962025931, 711884250, 771059951, 720723696, 281269537, 16845577, 874780620, 996233696, 60376799, 494263163, 211158398, 284776637, 831550317, 62895091, 887952587, 598264975, 162355028, 897832754, 738113560, 728990113, 362327185, 384465847, 848772263, 546022492, 705728494, 661466515, 344645709, 456213130, 35057911, 207468529, 889033280, 118710251, 259170549, 325914781, 888940631, 492265143, 481681895, 311024225, 374614962, 189598348, 812585024, 379641087, 870865062, 560547083, 596532056, 423001168, 164469342, 450272359, 838163313, 107406643, 550471160, 586300850, 509372110, 342999054, 891022822, 189914805, 804735147, 312307835, 501693207, 91808411, 482540381, 835677042, 883543327, 862577679, 85036293, 467650975, 497280559, 125368031, 266729691, 286725100, 525150326, 529568226, 198997420, 24488626, 103118969, 444697486, 700759533, 576643211, 142444294, 540693212, 318139300, 253973950, 605969639, 528172001, 257019162, 566397788, 579766889, 435527367, 337785064, 223475152, 453526292, 839776556, 85342300, 86009966, 395912971, 802324481, 960050567, 808555345, 262623180, 651786395, 727620170, 202200495, 276588261, 539328603, 615896095, 157543133, 873798207, 545436230, 999730828, 351347054, 164354086, 244756935, 793058453, 452919885, 223317352, 145160148, 376688990, 934829, 208566202, 184123259, 279610690, 717046071, 375187735, 413618462, 530948135, 855079921, 867235829, 182972565, 220331066, 125550964, 817926123, 225895893, 96206239, 456998554, 278744229, 712035553, 605506420, 800508413, 353837659, 552121905, 473364762, 435569982, 431908095, 290031788, 450893252, 753226014, 627115207, 584625472, 267852999, 351508523, 219899759, 350101933, 34118171, 63412355, 580599099, 610608022, 911430619, 804501686, 756500007, 380172997, 141529772, 567624403, 674444468, 261642284, 160319992, 788398137, 813240605, 55921771, 806927891, 64893879, 394109894, 213555788, 873647242, 447251599, 553572756, 751235305, 236801803, 716442227, 592985904, 239591373, 220857165, 128028606, 286404420, 328440916, 272499655, 499251253, 960648376, 664379504, 27384421, 709349848, 336772726, 958273395, 547856610, 535095784, 999176168, 393004176, 654383521, 72419812, 976439196, 638224033, 976963484, 631197819, 831014578, 96070962, 694293691, 435551169, 339064158, 497334631, 434973699, 637947809, 904587366, 266694582, 6977913, 723012690, 973062717, 541970395, 723408431, 216826345, 86884231, 175925039, 124117317, 700438351, 398920318, 257316886, 320350004, 185604084, 588405535, 795638287, 515247480, 968557757, 256071339, 144329968, 274079915, 240809089, 392252023, 785175376, 103934284, 713467902, 434991006, 498032877, 450019255, 205385873, 461351526, 151061816, 786391520, 121059622, 257804643, 492054926, 789628742, 291392076, 395967732, 536149441, 380690033, 870008546, 391458263, 790908284, 306274615, 473755343, 85077297, 780217470, 160889891, 270907898, 494786430, 365055960, 837621991, 911032527, 6014056, 914578261, 438574013, 897795371, 342094347, 786940284, 945463200, 618428905, 490127920, 516488728, 731222566, 57699854, 518239744, 506977671, 701509758, 331583885, 83656115, 1148942, 386516161, 5954061, 582483327, 888066604, 965678601, 812120855, 610122211, 174933773, 262814662, 841717422, 146058118, 65107633, 304738968, 441051589, 891272127, 861997420, 230968485, 993528498, 537569661, 128130987, 31356309, 484971071, 280291195, 985456016, 202773058, 871637135, 859734315, 110240497, 923474305, 148406859, 916060928, 923337296, 386752465, 996965285, 343495766, 677398349, 60973132, 869921541, 882018111, 828466925, 934684459, 404949064, 672657136, 274363467, 687302322, 637371659, 152051867, 811945215, 959431206, 443309400, 253701364, 131388062, 210044817, 442451757, 446179496, 301981191, 335639089, 32723426, 930459724, 535622788, 342351047, 459801861, 133741913, 31023966, 136163996, 356902185, 536967237, 399008803, 559627322, 217415962, 364076580, 896635629, 240938732, 354792705, 944920777, 586949464, 430794448, 148831051, 113617798, 285444627, 452635344, 959482231, 501170568, 831672629, 696183349, 308326812, 197546301, 180055546, 49665713, 439749507, 140497392, 629420375, 549200642, 218594693, 887313047, 87445140, 307824266, 694055823, 115362023, 575395899, 947417252, 231049262, 186140265, 924424236, 362264146, 664322342, 808173869, 702345194, 112936661, 158147237, 964365346, 973589338, 638132704, 510366422, 210467410, 306436756, 258379195, 597569056, 131530545, 167191371, 484654342, 34171419, 810329541, 384936809, 169196448, 200594180, 115196780, 695872326, 901409196, 300006858, 715319599, 572664159, 371830613, 579373898, 158719340, 547831841, 314202059, 46884429, 637903800, 819148232, 149729102, 258071089, 280921426, 516886190, 730334585, 118574456, 930489617, 63973622, 414627977, 697506421, 472938057, 498211936, 102953349, 532181127, 128220260, 24898572, 17030634, 332348647, 587234360, 286356625, 660758869, 199738298, 289777852, 989370042, 501994568, 454808875, 814213182, 282025059, 338743957, 695117370, 958575119, 588845735, 710753242, 300119487, 226277464, 711600503, 670124081, 720377752, 148081087, 824051439, 923909911, 987700525, 815965140, 230437307, 339638119, 405772631, 191846064, 903999221, 527767004, 415455053, 421103638, 874718940, 226991886, 408292229, 987458848, 867599426, 541752055, 755740854, 966088739, 629401396, 337116525, 214200503, 898718969, 690147275, 815959307, 60892508, 607702313, 353026288, 735509550, 950487887, 831833744, 981051427, 549815337, 692086716, 622976213, 107703065, 909026687, 267009292, 517411929, 286126537, 99959414, 160478266, 779890338, 692192660, 613817974, 930219826, 897375975, 463224018, 307363208, 868320107, 185910666, 482582971, 972240924, 889692576, 234945128, 339839, 481944542, 66982401, 566244266, 227287149, 644561864, 443152771, 957703905, 452650179, 187177003, 621744680, 179178443, 369667729, 184712948, 279172950, 498615202, 38656833, 696215454, 194453338, 493226182, 50085937, 932306719, 720681276, 460557436, 239131212, 259320362, 433517237, 731359120, 797103180, 245271107, 602236495, 589587012, 962194116, 478608712, 797770563, 118502209, 71578038, 17970003, 930061893, 416248031, 844662031, 590155111, 318963962, 17999880, 542073330, 916214129, 671033917, 60710860, 420623669, 197303290, 560571288, 842301383, 314153323, 329373206, 508500441, 738556688, 681304381, 518907239, 869597974, 540347357, 227806927, 548816056, 443248040, 114775649, 813119460, 289934807, 824442730, 739531836, 567561890, 510171613, 362376847, 258302963, 382435989, 432618127, 365145060, 832485765, 835351339, 378845873, 466343844, 22888339, 144117760, 890527982, 465310575, 369251107, 494276571, 626649596, 234627615, 784524016, 224434328, 768010028, 514258163, 595143841, 471762924, 992231329, 356191287, 148889642, 709040292, 196887272, 318904464, 947169224, 265320953, 533093290, 439776091, 801647586, 849065407, 783090737, 758229082, 728351372, 621732880, 636565798, 558856768, 219287980, 389172225, 897648387, 451951797, 199260917, 217034942, 378474108, 286222503, 64954733, 370324699, 856623900, 401191233, 674751153, 969603657, 59996583, 604230761, 992163899, 924530978, 135349241, 918239917, 384235043, 574259239, 570430997, 53757498, 634047248, 730188543, 330891043, 963974210, 687250209, 938305654, 935541210, 664251504, 862471204, 432496721, 166065984, 107388839, 885038500, 347658384, 25638862, 366484113, 917295641, 144134090, 350355741, 782480103, 726336663, 352239065, 812216627, 926135540, 923847530, 226711429, 103796327, 789634589, 581769194, 534592116, 33840342, 239948492, 53567240, 870570487, 204850794, 814213547, 889299288, 202930869, 265015244, 616914853, 324025355, 392527568, 987556577, 531168877, 309642902, 175052382, 732232840, 213874896, 109367691, 675266588, 351576760, 159971808, 447556524, 288994525, 284206609, 56450504, 85311243, 375409580, 661747543, 185355007, 467591749, 180392039, 838264966, 361189126, 696055869, 657201407, 667442716, 676743563, 539809780, 624680352, 195529088, 922090693, 505064645, 249189591, 94014804, 722064880, 301894836, 341127903, 797877982, 691329802, 138050722, 272595774, 741214025, 841378809, 362939762, 450230976, 888657561, 91876509, 389673599, 577123152, 834759435, 153295481, 569213738, 825472550, 947814517, 134458178, 512254414, 317857630, 673027715, 554954269, 103999272, 920210199, 59526612, 339165763, 351321317, 255848540, 568903558, 723525969, 588076313, 635637632, 925963978, 967229399, 712906064, 957810187, 661135095, 191863811, 937590833, 670902357, 392876193, 50751281, 370352955, 669496886, 666153558, 269354283, 466514950, 992646235, 959553884, 200882650, 49414220, 308572397, 692827510, 987541738, 804663671, 172910126, 511180058, 445756130, 254493230, 106623686, 63066417, 878784507, 530167508, 766381709, 913877581, 272492178, 478545746, 625309476, 526468509, 518877741, 536279155, 714272260, 748563395, 449368035, 140956937, 243291311, 400834113, 90137691, 386954789, 55627199, 317673802, 401435409, 689522274, 651156582, 601610107, 310486739, 790289276, 390886677, 971915375, 604615614, 72968631, 178056061, 432069075, 359625949, 717017883, 203064601, 116388377, 958602563, 269328655, 187253194, 958392959, 258142862, 668312016, 146420500, 904761980, 869216287, 327272446, 579712824, 671068738, 188050405, 436646982, 929783406, 616698810, 562910443, 780871350, 871562905, 63254868, 894766952, 149314690, 612469412, 833090841, 649014038, 840195433, 821969482, 728861665, 688122131, 981868083, 298633409, 732130875, 703981773, 743281268, 356054048, 373142242, 935193569, 159183695, 427168459, 765249617, 660939531, 542012381, 814844233, 985207000, 264245534, 799973132, 575048677, 175581446, 871872982, 481183692, 612054770, 268847094, 218779738, 816249069, 114053928, 44106056, 990541897, 242344747, 506603650, 220904287, 966817439, 579026825, 269247146, 654267225, 475464800, 506297152, 170922450, 580141457, 636968085, 495512959, 647195484, 918092160, 668581726, 30358800, 848824888, 590782290, 329759741, 228244327, 212135833, 30467395, 116020553, 965545615, 573516196, 194199032, 915479801, 3609689, 631889871, 11630263, 828554636, 164202499, 567709047, 273907934, 88840263, 10329026, 784992446, 544580491, 318099591, 106265523, 286923122, 139494323, 291095070, 220925838, 188355890, 818083617, 656859406, 600260104, 132877925, 799872548, 811823847, 63217393, 441452957, 339135560, 227088248, 676069175, 929069768, 47220994, 824986551, 644534260, 206482329, 920312473, 654962442, 577166569, 669439504, 378113730, 881307929, 470017976, 422304306, 810985098, 138077923, 257220248, 837060679, 590129122, 803863173, 275310590, 135142974, 678204223, 4573705, 484519076, 958196502, 310282000, 719246600, 356062891, 882688317, 548219822, 682350760, 731406993, 507823770, 857622612, 406222645, 794119847, 3267763, 436573994, 297037435, 943406676, 218041276, 541752058, 523760175, 217331347, 109648993, 103333870, 256247618, 78566048, 810486075, 662037764, 666472823, 95447690, 451078758, 472334558, 348096523, 654704803, 741996876, 957811757, 263230404, 428889158, 170654704, 400238489, 177534493, 792401144, 137170392, 837875584, 349764988, 829984782, 156666841, 686842678, 709298116, 649780492, 877161632, 891795375, 866268352, 382332063, 446496677, 921931787, 233367695, 761465423, 456813714, 150453883, 751114203, 286354517, 47538690, 736924817, 557350223, 408082066, 606088348, 743210751, 255024472, 517798698, 347994233, 971024513, 390121299, 676001827, 546210526, 150351329, 314386569, 795897699, 537127834, 525033211, 860797016, 915120292, 508526295, 928668101, 810267339, 573712684, 991432372, 44463342, 759880228, 860523912, 669200857, 949009850, 227268038, 633951646, 883300104, 963561973, 100788948, 372721118, 178492281, 358173185, 430023978, 247269166, 437965999, 851740796, 777803692, 399773984, 781379706, 96117438, 499564876, 217193911, 186086938, 155128638, 294557477, 68442489, 144492616, 317487988, 850062648, 161426306, 67845726, 376508726, 756668238, 596166762, 768816810, 524575761, 405546927, 515420574, 351986818, 867053848, 142900088, 447622057, 633141623, 860653444, 937182152, 547010177, 896835207, 776218590, 141345069, 730547310, 787679229, 246646119, 528066016, 506427134, 666100633, 161523134, 879236413, 31713693, 219019727, 652798254, 444367384, 397424202, 38148104, 609405724, 617662089, 322631018, 422293035, 581181132, 317771318, 637544406, 412128729, 464963195, 393045169, 439603692, 419233684, 643493746, 976069921, 54539165, 817921794, 577806071, 192296024, 197474293, 364167735, 69427667, 980725484, 332924755, 48162713, 49362849, 12263, 573678118, 851227118, 789580228, 771749548, 171855060, 601850109, 134327110, 876975970, 185990546, 331999933, 199783059, 239646468, 683225913, 190997382, 512141492, 667906585, 748334918, 771844280, 791026109, 317492808, 953257699, 266705817, 109633309, 131763006, 544611194, 414178438, 986340621, 361787247, 224248869, 364566035, 830279955, 756639429, 634113802, 183138679, 144765437, 903767780, 832638385, 701103296, 549282085, 497335305, 70333166, 397712394, 346363840, 663568817, 934461293, 814520245, 673563555, 3528449, 350418926, 603082463, 924849966, 643639002, 410066038, 892752259, 597211134, 727464793, 316879894, 438588574, 318842317, 239761497, 1083354, 157996528, 6792539, 869993603, 969856327, 426040789, 754941735, 84377802, 495560786, 487642145, 406309791, 591063765, 245887425, 980247485, 690463712, 93993205, 325184034, 432588791, 416108113, 49407556, 487203651, 187029703, 954468060, 219165631, 599324985, 265825609, 771183778, 617738576, 101768977, 444749874, 682605949, 486794703, 372987921, 293190423, 573633675, 279437892, 407203575, 487685329, 568040879, 740725405, 83245209, 752156343, 928108850, 405557714, 325494617, 992112101, 580528897, 584644642, 653799196, 110185193, 219525039, 780680363, 655107357, 350231547, 536051763, 664019450, 709187243, 130028508, 861593618, 544596616, 524616300, 503978644, 403804112, 865178196, 239908979, 794669449, 235111693, 592234220, 536659358, 69163801, 743416249, 477408924, 452730968, 821686978, 55977632, 457348224, 773191523, 142306439, 52287101, 857842468, 566203108, 156055631, 178648693, 418919778, 161969822, 202453290, 74884053, 77325147, 472530788, 411518785, 896071584, 334589232, 216998530, 111392355, 87293289, 442803656, 409727753, 527849065, 917434663, 399429492, 136670791, 622218947, 686944335, 786053531, 772304507, 260417607, 585844300, 569837898, 379953146, 211759849, 647601135, 169379893, 664595334, 869953829, 303596330, 209807339, 594030574, 838207954, 274851234, 975758010, 855913670, 784261778, 985829840, 418774829, 268704314, 387683673, 230725831, 862964740, 974952232, 141677567, 265552003, 200599735, 248403895, 649330557, 666666272, 747194634, 243136113, 783218861, 538091045, 660348355, 441231968, 89872415, 52966951, 966786740, 655302837, 322632443, 914738998, 950327747, 210792349, 628538202, 843647345, 781887347, 229576377, 645023171, 85479515, 256070964, 260383905, 460665869, 738749586, 804801431, 161471714, 328916253, 247902012, 330247611, 991240714, 151673211, 622957024, 22297652, 278620479, 684357943, 342053699, 985777121, 26787830, 729156396, 619240187, 717921811, 296389248, 465417413, 161736000, 9457521, 778565351, 18263431, 858308087, 465714375, 363775614, 346009078, 587320403, 680341515, 21943562, 275928220, 488837494, 586950436, 351761518, 891920702, 863946052, 662987069, 64211652, 249286385, 537341857, 399419821, 574565866, 3366368, 280552127, 307688421, 848009045, 877069804, 925212408, 778225199, 886917996, 478023392, 638752580, 993424505, 736934450, 848909185, 207766405, 141861218, 705051506, 319899055, 630977941, 522396688, 960743529, 238772668, 961941166, 759862332, 338738682, 418056872, 453487509, 835305824, 772409447, 81855430, 27783013, 853561756, 51871484, 710530814, 735185832, 489004892, 120254020, 467360767, 598743162, 839138149, 937182105, 17109722, 531380783, 106104578, 152073575, 796535673, 805555891, 824168774, 842286975, 392013048, 26451211, 948522971, 703541258, 681280619, 321191429, 881441849, 668225309, 741450204, 654659325, 180112544, 864174958, 537687165, 222626842, 365402220, 488593438, 241591211, 769258795, 267582398, 86654373, 710235912, 83498720, 879439305, 771708880, 95209588, 929130726, 3201709, 310297438, 596073594, 738401271, 25712313, 345854703, 492284547, 994917401, 705301075, 969938125, 452372826, 80630933, 336689511, 107512594, 282302936, 764482354, 544476266, 505194050, 667161835, 937168205, 598298652, 125075924, 791547600, 7975061, 748726486, 90623408, 373093481, 898373650, 397611944, 583089764, 782612573, 144354860, 339269051, 358172515, 217800245, 917594219, 499178736, 955961061, 393368243, 999919624, 81276514, 747495117, 629982445, 565515598, 155470713, 491198191, 876262837, 502260730, 804487890, 333417155, 612068393, 50488290, 436791370, 773915319, 567463251, 129694401, 164631533, 215869400, 942741856, 319811956, 81932166, 417825775, 963623128, 878425507, 43808098, 172757206, 142510992, 633597262, 764334691, 123910079, 390398143, 10167584, 823082173, 446660938, 975346415, 609926039, 177787371, 671363051, 405129936, 477963872, 624762755, 411389453, 59392801, 796905256, 281936491, 439044866, 804401546, 975418014, 663282820, 890548285, 934463929, 969711124, 246494633, 227221642, 773565970, 696789171, 6010117, 836835504, 352370932, 896090335, 145663363, 694145716, 435939081, 891248262, 544928969, 646706780, 465641121, 605808114, 165085429, 346700873, 472348282, 953518083, 195079252, 739466383, 614549943, 558072518, 863416217, 954088376, 643347541, 102745791, 710283352, 469873646, 280810823, 709750334, 540469655, 308929206, 362171021, 814462414, 679459691, 395480919, 739329633, 312808939, 41050696, 875926841, 574637506, 807887691, 839071329, 236906766, 181373403, 429769491, 73500160, 467913568, 257535196, 199733626, 927057851, 626966554, 48938093, 32029395, 643988365, 549520625, 516546863, 349119588, 626889575, 191776795, 633711633, 691041490, 94366846, 573724242, 198186983, 208470099, 453320859, 293001138, 934329237, 109226740, 901572587, 143531611, 100752917, 481749486, 997358688, 151685441, 200772746, 121159171, 936217736, 732034923, 336029961, 732545325, 939200282, 903662570, 631770966, 159621548, 480647665, 339560473, 817053827, 791356361, 447419888, 498176483, 496391193, 560736425, 961049309, 759403896, 431860263, 305513117, 595021912, 283307538, 97072365, 3048908, 617591728, 705522854, 548462545, 311478515, 716485486, 908849657, 92903928, 993210068, 411123689, 417265503, 769232323, 586500894, 659948577, 815475005, 768753313, 879446739, 863156423, 97494411, 23274815, 35642118, 806711253, 35971671, 593001892, 25740961, 440663239, 163144060, 404384452, 982536447, 983291361, 59028819, 207076699, 372191430, 148969964, 842701570, 644632041, 489429094, 239262168, 523111961, 743866052, 37280944, 358362297, 850299351, 774868979, 505892868, 752922132, 807757795, 849316500, 759342092, 915222398, 720076934, 676504135, 521027396, 804427446, 161975382, 708680829, 254889284, 104345153, 656554868, 236025621, 677426203, 32505745, 244252138, 858794301, 326070955, 190276087, 184253676, 299534123, 303756905, 414431041, 968378996, 165097958, 765935776, 223107606, 989128847, 195852597, 754908730, 767718534, 141446902, 794773827, 369615256, 769093645, 77700913, 736686590, 797262715, 14857385, 583493084, 366259425, 892773209, 89625303, 107477493, 946617684, 254607830, 876531914, 20703005, 309133182, 725014080, 333527128, 955845469, 919226755, 91408843, 824240432, 829496577, 191323609, 555228004, 131381608, 71217931, 998063092, 3718961, 501640665, 266057171, 986931657, 15830165, 677495148, 788820903, 398309283, 313179803, 131846505, 713158802, 42893010, 586146004, 922524858, 368647988, 889064005, 474826937, 330047250, 404085395, 911982806, 285273290, 830574732, 652723905, 831100338, 24995241, 523534270, 183903101, 327768931, 205097348, 779384970, 153226413, 378862181, 929435760, 988429093, 461840114, 737015339, 440534644, 386260179, 531959536, 522734372, 6571235, 721210669, 897778962, 467491664, 107528813, 389400454, 987609908, 661692713, 139808396, 662694713, 566050308, 169361417, 703252622, 451715080, 520327042, 146527436, 577954516, 279407908, 99608055, 587255884, 387653450, 531409045, 155019093, 851886782, 802481277, 445572780, 960162144, 259446961, 984673428, 710492586, 802014389, 940822956, 564408917, 138565152, 569770944, 196192397, 95394872, 615131628, 993835647, 987057499, 828069692, 756123814, 989004373, 953360509, 783263334, 215440530, 705598286, 980736851, 113352009, 803091313, 118926395, 901034139, 459084586, 342824106, 595064317, 858725956, 353817253, 16142159, 167354259, 783040315, 794816737, 349523374, 281736735, 745677156, 663820368, 146144814, 639043544, 668977968, 447482914, 373100673, 49319162, 308897399, 143956211, 575695310, 827358309, 517046988, 349180762, 304920568, 480380351, 847931249, 818792726, 454450107, 452724948, 563455777, 704708298, 698616821, 466183359, 120975542, 758960585, 286824531, 400789354, 13335570, 785721383, 69259312, 602708656, 191459933, 718720358, 810953578, 125723549, 935572120, 621935813, 94124093, 450424499, 811961869, 935912914, 173008013, 179085277, 334608150, 949151668, 917563822, 922419340, 898088514, 739876763, 18476607, 670813203, 495705274, 889864503, 116123907, 515614261, 352845391, 820130588, 388880474, 98738669, 464803701, 478443108, 242718387, 953759166, 777504026, 384418410, 311474723, 953733539, 160485742, 420943204, 762813015, 596011100, 869324586, 567919882, 645590176, 296372335, 840256096, 316705626, 314100403, 480619004, 948375720, 53996649, 638393995, 359195454, 82195971, 197502726, 995594888, 95222983, 971183802, 108765641, 639314266, 711703975, 820181988, 947830120, 479108416, 582211297, 53035903, 726336809, 372006496, 909216965, 563874569, 385274964, 556004393, 853076903, 125085239, 281236391, 215748395, 960330446, 534412195, 806836930, 722471959, 165967515, 159159607, 776750687, 599812538, 444750618, 844107213, 525636785, 844830098, 531701970, 733277552, 86187218, 252530317, 198903504, 808254751, 621542094, 365021275, 469129796, 885662163, 946184097, 242910181, 95711996, 223419395, 302394041, 138803347, 790957623, 837382531, 456359153, 10265440, 877704999, 230300383, 955955797, 67825330, 350392642, 43273897, 716170734, 163463569, 425437110, 850880032, 680828015, 739621587, 845316738, 70882379, 507335894, 287944659, 625653339, 558123166, 59875011, 559412244, 119356537, 734060349, 201344565, 254708343, 427878163, 785423011, 481331722, 116331614, 837811049, 192621171, 840220597, 558932490, 852713145, 947296654, 743290313, 995414338, 999640496, 397586793, 227976602, 118639271, 890201015, 33429732, 584702191, 726802309, 189342243, 854867440, 318578145, 348188476, 279283630, 844535624, 525034275, 970590343, 152138229, 514020504, 999398437, 58366911, 361143003, 907094698, 577760052, 512995596, 195858964, 850704903, 355104915, 319509802, 433660938, 264812595, 731291935, 942115718, 742569989, 280149482, 987030150, 387496640, 655094932, 72725017, 386413931, 725744968, 51430012, 256356019, 43475705, 122251589, 643229499, 648513202, 30984177, 792074547, 67510089, 741209609, 990300163, 478043325, 56763014, 772624023, 325931546, 861270945, 218085742, 794071141, 77761530, 15183894, 250915584, 142536240, 564161538, 579843640, 534267906, 324857763, 763104702, 247119505, 923072529, 580006373, 715362766, 646577127, 231504558, 55108344, 863125916, 5505389, 334307454, 286373556, 706952772, 378861636, 759549455, 332976607, 545110628, 663284547, 346570649, 203703454, 921727782, 56448674, 315316990, 162930472, 350487393, 615791683, 166820655, 682586816, 624162405, 959471322, 471785801, 478665966, 845314072, 435917944, 612029243, 925363981, 414333872, 478634449, 304367178, 967120818, 121324449, 114673582, 205716099, 897923380, 588112692, 282291959, 962604364, 597216326, 654977681, 887476135, 322105454, 562767949, 808734999, 971721830, 498583374, 693652750, 703114240, 493502413, 599625926, 720354452, 303600830, 122371337, 535628498, 446817371, 791548584, 378268300, 452802647, 781524578, 60012037, 574148689, 228273000, 5523268, 708553081, 622017641, 889467016, 651916091, 566293151, 764557621, 559901493, 288208023, 768796926, 276061417, 87160970, 654992010, 197189645, 868834160, 377711860, 621966438, 3444174, 155076035, 135829345, 440938609, 720478023, 670611800, 643290444, 981672019, 907802166, 600456971, 961525460, 929467274, 320908407, 765760223, 819545912, 864180560, 651387547, 330561192, 44964247, 285573076, 847383177, 896281608, 204689070, 72985210, 315980302, 581980767, 285729416, 549828198, 345950300, 64480850, 383636718, 978702957, 259943063, 288206432, 265566885, 815265116, 499319314, 899816037, 441525678, 706439870, 385721334, 871143034, 200002830, 150127247, 636797906, 309531941, 624879154, 324848177, 529106450, 236008602, 869521513, 245088554, 164884435, 620343633, 660293395, 969876561, 407580624, 785504675, 186899451, 272880585, 935750127, 241053701, 163046937, 465856027, 826631311, 761003708, 526063796, 106549558, 905140536, 934708673, 365503848, 352619472, 853080612, 499122569, 560986903, 921053666, 571132599, 892436172, 865163089, 263034064, 381788721, 159268915, 125317391, 151212832, 846477082, 327468162, 172308925, 745275226, 75705153, 256939341, 761064477, 867966574, 532494027, 944627950, 178978935, 274218008, 749507351, 811599913, 466519057, 325257050, 606449900, 989803390, 97415386, 884192273, 458730074, 781996395, 402744710, 317431782, 468104899, 346682712, 46320478, 61342774, 162941219, 254914965, 816694214, 770516870, 726454914, 538045169, 901293259, 792999260, 208012726, 846086697, 878113242, 889986005, 875366029, 137182474, 675571528, 252537005, 405377899, 414055469, 854075892, 948985152, 593689882, 940966841, 788231054, 213701748, 809927238, 268559902, 84130789, 901261814, 697598464, 686092420, 694938637, 598090714, 351596404, 474075250, 299237443, 236397741, 665360251, 263109969, 375977516, 726417865, 858581914, 727828137, 802329188, 44968233, 82664960, 251497962, 234584131, 811524921, 316399218, 607543275, 340779828, 900054124, 831086590, 66728381, 53818745, 675476817, 841248371, 970347653, 30180968, 225717189, 786289896, 345277647, 411274247, 796851112, 703471088, 987283302, 684839254, 410309565, 212054770, 812856224, 323330004, 874496163, 878784604, 701985916, 934690030, 70340891, 966112626, 245987848, 917781315, 798669926, 961217674, 369687617, 435862048, 951350138, 901449952, 777685024, 691764173, 548232323, 657014882, 804499828, 852333326, 188309030, 202058196, 7713651, 552542453, 901339614, 717744630, 284921907, 705806717, 966871048, 358879520, 508370867, 481843932, 596391929, 421246957, 658126763, 7610600, 544281092, 510211256, 150458180, 580339554, 995822852, 823460633, 101345923, 305602649, 921277588, 649611350, 721669405, 160956348, 222126559, 546931909, 968816949, 555510962, 755261872, 772257847, 851319905, 732334009, 430410094, 13482206, 52266617, 992111049, 173217319, 695671113, 867495876, 930340555, 432970027, 550980715, 674535838, 65631115, 481456219, 277622683, 622736685, 763197954, 934509117, 637820510, 122990492, 99549870, 957841217, 205048149, 797507322, 476903378, 264936759, 512635037, 570050125, 416374795, 679681031, 309750230, 473171769, 998259940, 73106018, 865900272, 705090658, 453403102, 977847077, 484935447, 625749402, 637496107, 243328419, 818744455, 133651185, 131976536, 781146890, 405954006, 498126269, 503995014, 244416881, 838677482, 624545420, 742843288, 851059539, 651107225, 216857472, 528596926, 928119475, 725768363, 862082694, 510908832, 872911522, 611975601, 976404963, 496312280, 800076827, 537398834, 176340652, 578553150, 594825014, 837245889, 904830769, 196780758, 519284410, 312303202, 363078233, 651649469, 374320599, 944699410, 763937602, 576060395, 627827227, 919465634, 119292121, 498893338, 270500377, 737125317, 547754395, 816574815, 632405352, 476088967, 493019787, 736847825, 31602514, 388169295, 348650578, 105785413, 229412157, 163635167, 404544940, 430949076, 506031159, 288240067, 222603187, 314802866, 725810722, 777567283, 94717043, 949836210, 977185285, 195257021, 20375739, 272155214, 364640877, 997182528, 483993437, 824256651, 123084932, 968667671, 148013692, 55340973, 975735334, 493057770, 662522899, 442888326, 128015534, 876439165, 667287425, 386210357, 754836207, 741740530, 319546243, 555362625, 809942926, 998590315, 495193324, 980153603, 803251742, 729899629, 150400259, 511645066, 330748487, 644794357, 121458598, 71275438, 432494059, 846557579, 141564449, 791301550, 423405571, 947083710, 575209403, 476148472, 950781928, 188241778, 829988877, 62033924, 216665873, 138101501, 180923128, 714590537, 108982639, 41556130, 888240241, 516074454, 306522312, 291212114, 924280920, 857622390, 988387171, 791063541, 643553724, 119566314, 577653977, 292552525, 268689427, 528917373, 133279951, 542732739, 136726771, 611597605, 907439248, 379864770, 184417262, 206485764, 654838285, 640060931, 855875571, 390960377, 721453671, 522947632, 661013306, 17635587, 82166825, 659477046, 694403541, 130612189, 292083961, 7678251, 986735252, 147177396, 167647407, 498489338, 705284789, 235207310, 15116458, 208963738, 87476288, 939859740, 339455647, 309835613, 130553223, 783068260, 290866751, 704853811, 330212892, 397972210, 448145693, 474860998, 448699461, 739849538, 830466914, 61023283, 17207444, 176960351, 946141580, 755620569, 100595393, 947068835, 875162526, 972024145, 656032653, 846946843, 624696603, 307832026, 996445614, 778054590, 171675297, 675916194, 218912322, 386948062, 604449442, 424066523, 588794345, 297591850, 646620241, 918168250, 722679098, 494440378, 598687130, 239385260, 679398583, 369747102, 441050056, 575462823, 932269474, 289300533, 973637670, 903163555, 507698623, 375678829, 848429367, 461738292, 340334951, 175201524, 177647774, 431972756, 791899489, 714816548, 755413113, 553930644, 100773248, 755038591, 724066071, 592107533, 44913097, 818931488, 482326607, 994433203, 825502865, 837339238, 876895447, 889905423, 730245569, 583004142, 585453590, 767956571, 624909184, 935949357, 468160714, 875005849, 928321774, 331545095, 246621339, 738491211, 56086154, 66269790, 295068503, 996477988, 373744070, 891959743, 254842058, 817346662, 675726030, 60829322, 591470729, 980451626, 391837259, 142735352, 600482964, 484968791, 581728512, 762106247, 102540921, 840558204, 376303114, 116725105, 363525837, 862605872, 400969096, 347743869, 341209467, 314007565, 115979503, 220778654, 156139597, 765628467, 16260876, 861268412, 607849172, 441388473, 784633016, 7538090, 766808044, 334750098, 638640551, 327846286, 154614190, 835849214, 881023703, 583220155, 322696588, 351818098, 98654530, 437508911, 995500130, 30522374, 269026412, 880275061, 598988095, 18470183, 65713708, 63401914, 619332769, 607521242, 200903425, 907964540, 396765706, 143956720, 573386285, 923462896, 808662944, 838791333, 934756045, 567037471, 932600339, 276779263, 743634762, 746876281, 735311231, 683334646, 765650087, 458961799, 949859241, 92969538, 760352973, 424283984, 749168520, 437294975, 78427770, 37566154, 625198917, 406673488, 251555798, 927292356, 980840550, 693723227, 525654231, 491738831, 476919183, 645606063, 820077808, 53443070, 890924042, 227012718, 95533518, 350502051, 364595686, 125907650, 45306378, 271457765, 169107946, 257343916, 430402152, 5511342, 158365377, 452347115, 677080960, 567490522, 367487835, 910562228, 541675441, 584374288, 677526140, 660799395, 645433639, 402495691, 929380472, 614096169, 68760299, 633513677, 666328727, 520159981, 441066684, 219376102, 502036604, 677573433, 987655151, 122238188, 353973969, 569843701, 707289660, 711215047, 617108653, 554342491, 950399748, 774985551, 430079882, 183106164, 767648765, 74943610, 444493665, 484554192, 111434272, 909723176, 383874486, 650805735, 836567966, 892262051, 814824828, 43100856, 130476151, 811772130, 940513795, 133929003, 494664311, 285033317, 231714060, 349853213, 772517240, 685580967, 771371588, 816181723, 528800171, 794089402, 351864205, 248032799, 696776838, 522711384, 728058177, 280344282, 973639924, 831404417, 89830466, 20297988, 650744668, 374544397, 732401309, 673135018, 469811444, 468972469, 778064238, 175590225, 693880979, 688349640, 779728998, 79749663, 660545411, 340417576, 455534669, 331541674, 122794037, 413955981, 565778029, 248988878, 412350612, 606597105, 230406111, 533127200, 936985335, 911566092, 231198313, 956146701, 605193461, 938841752, 329244627, 825642469, 462588765, 362683522, 652771843, 199966915, 761609651, 652389437, 949785084, 933110663, 717171964, 647702193, 910680915, 879950487, 486341445, 866016665, 121745815, 630847480, 139903641, 985251744, 910149571, 958722544, 259961257, 484306530, 272292037, 690549441, 433380918, 285561749, 992257265, 184928596, 379362276, 156657743, 102596891, 636225610, 897275310, 531623940, 184556784, 6278666, 329250520, 150715646, 805761592, 619672778, 446057181, 707051496, 567113614, 500545251, 514455777, 533690447, 557223392, 206342656, 375084607, 564799652, 505220316, 814719999, 932244049, 333058693, 329745668, 115599240, 213855382, 306087472, 320698294, 215484696, 386660771, 726975723, 397612365, 634409177, 55296717, 911383499, 361114532, 25387093, 363616158, 163314637, 228476239, 764888265, 141841986, 967112141, 74804087, 287477918, 485981832, 802666912, 853870196, 759529750, 680985382, 734768053, 793199314, 717483564, 136218695, 564439204, 844875620, 153192145, 688143654, 736844212, 136453288, 937668457, 863305704, 363940890, 955625657, 14176446, 367904574, 479018339, 530202647, 217246546, 300238245, 991326399, 633894885, 964166523, 289318952, 262065068, 645650735, 927356215, 513620950, 866478534, 741822699, 34313649, 805501434, 949584769, 535450443, 361594813, 757973157, 634916453, 285808220, 565525617, 24629883, 171402242, 541150880, 191877356, 456912803, 399011293, 373707157, 629142560, 39307401, 850655921, 663831517, 96189047, 835945472, 82525692, 667282144, 794369629, 252197141, 660541959, 970371789, 692897125, 578790193, 282465252, 334569259, 930929205, 603616698, 14006114, 22049637, 630266044, 905727162, 163283196, 918918550, 511445756, 801369653, 147288163, 478564465, 184131965, 656473185, 431680391, 261605778, 640788551, 659127213, 819711564, 44612686, 713545298, 514465144, 545513257, 255489264, 879087964, 225433319, 734639787, 534167176, 670713112, 245034451, 100092062, 42387644, 304917170, 873472408, 1085844, 122897715, 881835387, 851960721, 881351929, 621274250, 683851283, 805565648, 355279925, 937711079, 34635050, 168839093, 349861231, 429446791, 460180856, 96456209, 659201867, 400928086, 148965866, 932074813, 73340453, 116940988, 343258750, 200413875, 927648203, 603840640, 42161840, 830061900, 898531371, 399005108, 964444493, 128083285, 135629855, 257107802, 39876489, 292431960, 398814732, 921118981, 518375226, 54491091, 445937936, 101003864, 6466342, 951947982, 590815678, 124346027, 410767721, 640481724, 28688639, 569511705, 494385684, 514432591, 131865234, 996257162, 214680027, 686542515, 177992333, 417515832, 32879134, 311329875, 290638107, 444556393, 777731910, 659229561, 312976158, 405480940, 763428307, 87354738, 398232774, 808663044, 575240032, 589989628, 161966658, 629540993, 653787840, 188015913, 349809599, 257276746, 86813442, 195708302, 850069030, 952215174, 303213123, 150328352, 61836119, 721931688, 171838937, 8794829, 670123719, 308569155, 778969414, 246347741, 789452965, 728600382, 751927724, 302674335, 201520482, 219283128, 258102026, 284284694, 985913259, 642441157, 379349634, 464187981, 422226325, 519131592, 722986077, 900264759, 675084846, 628445279, 331186839, 702000461, 228680197, 652930243, 241128648, 648494811, 352306512, 523506349, 365314611, 806738381, 67947599, 363249052, 794645730, 740789204, 563496515, 646151899, 221314378, 516748207, 492408969, 95398114, 488775644, 528282166, 687132467, 401379381, 887431101, 921341991, 404497595, 25095678, 132765855, 413137477, 148088668, 635029345, 836769850, 128593900, 257718635, 187321374, 486228960, 819022669, 11118839, 542762640, 633018920, 550167555, 985154066, 769170372, 356245336, 38478017, 954885362, 592856395, 149375625, 739110327, 969660486, 399503937, 695781091, 793550153, 648218356, 210532950, 620276353, 106801967, 19813213, 669351617, 168782550, 642365024, 288055946, 271873248, 989747599, 772427066, 745961257, 766044909, 17053624, 571911403, 77473153, 610688498, 600311573, 888843209, 103993212, 552476174, 883328263, 417014898, 17544864, 83375709, 99794336, 717406813, 507305492, 754771509, 5024458, 912360943, 927596324, 168812157, 486395025, 879817263, 474116458, 711534992, 786992747, 896786537, 602914991, 782244740, 627563090, 354658134, 711620311, 83679627, 175783194, 295445828, 590233190, 784810242, 461264396, 778930308, 801610791, 669700395, 441883623, 689067868, 489017917, 446247971, 490289144, 67884442, 378187688, 446412103, 829698471, 581048744, 792124512, 662048220, 519823900, 755265649, 326318214, 784332139, 78770720, 545631654, 548250526, 109149531, 425549163, 157651670, 327258194, 715043886, 442940013, 162877057, 971216257, 334931258, 928303260, 196672931, 46114864, 98615553, 520675993, 762619146, 498615187, 569678714, 505336260, 43070133, 342865389, 424828158, 914534278, 168504335, 766737327, 514964145, 151214467, 432213878, 59470022, 918238011, 935422377, 228137611, 221977538, 816291883, 761927055, 635773070, 747407085, 399506530, 313042816, 880348024, 263543605, 436265351, 145145111, 997150656, 585439851, 198801355, 785373285, 902951398, 925010895, 2536964, 573173235, 25732597, 584396777, 453138671, 365986653, 893867252, 770178673, 47515462, 729070847, 708506723, 173710989, 448388270, 136037811, 927564158, 826644124, 416780452, 819697154, 308046302, 621353405, 437055657, 110942941, 396790023, 530290896, 904144100, 773095416, 408371200, 390713875, 605680127, 759411736, 448764057, 4093815, 76236475, 828213361, 481086545, 56527610, 985470867, 714635788, 564080033, 75342193, 484365583, 993928562, 711994446, 732462637, 190349794, 149165253, 35463551, 793335608, 617627264, 324361618, 449720442, 319264253, 149689122, 93162530, 541149169, 346569028, 348547799, 199730595, 144017878, 974329168, 104485690, 672783677, 62739262, 863870252, 658291602, 779940232, 120838168, 629753993, 736901945, 114538242, 982543413, 561654205, 271265288, 162287605, 564565861, 738886263, 389892930, 405153371, 973777160, 459530483, 331015392, 525061817, 416553333, 758919540, 174755989, 726163383, 792399903, 84355459, 709125402, 652494040, 777547516, 19168734, 336723334, 696365785, 57250614, 19021992, 91631605, 232645413, 537221590, 581799323, 385156586, 463044052, 7241138, 822125768, 394539833, 607311890, 348026520, 894233345, 126850366, 143093930, 331998158, 877988831, 717004440, 820676414, 960584422, 878840610, 407906826, 891750708, 788895271, 910086683, 429825285, 441747525, 155024160, 192541405, 85468704, 255557120, 838264509, 735754068, 657586312, 661820606, 288727003, 901396682, 172616633, 39686963, 544105477, 191103501, 299043426, 968474886, 863542098, 746204214, 275926536, 587618653, 433391826, 23726578, 319656697, 60040004, 766527714, 670345492, 680706123, 441528215, 400093403, 935085093, 462462004, 149140405, 578970976, 748924623, 114165983, 964611054, 641464849, 494364921, 378430577, 98683586, 928641351, 149924710, 818376359, 658754283, 378663159, 277899319, 167899554, 477707790, 161527705, 205894277, 735175017, 963925090, 511425381, 594655709, 670863732, 123516409, 929623344, 534410781, 533548184, 241656029, 119949610, 284404291, 597757480, 425947760, 124409388, 99176914, 131971489, 824747107, 346576047, 584047995, 151237190, 655068883, 979243614, 203343641, 25584629, 993873779, 356128435, 386203857, 883158566, 374551811, 523883679, 285812893, 152331712, 949085995, 135198285, 645425221, 817190017, 223663054, 852119182, 924748991, 168384434, 594152934, 234706834, 69445930, 713332345, 653922550, 893677377, 858620406, 892752855, 377063208, 681041676, 119692579, 145561260, 180388980, 742287407, 197914983, 302099676, 742371829, 72608017, 379314392, 165729481, 718198732, 861318262, 719390507, 713886312, 592206251, 141222147, 754797622, 173700029, 607341207, 306276042, 490214799, 986301888, 715703138, 804424477, 822498975, 150492629, 370679904, 401544836, 562502395, 147596354, 58636098, 139123470, 15036252, 995921879, 621031129, 973673467, 929441560, 949682761, 181976327, 27709311, 20282454, 333243817, 519400720, 349666331, 876913943, 80918337, 937507523, 228800580, 177315981, 558324972, 410237460, 311830517, 681753213, 560508736, 968586311, 384975341, 265207018, 740182667, 733490616, 948730809, 271679185, 292626318, 736050621, 740080105, 169283032, 130035206, 228120437, 563605920, 604328171, 998619502, 953632227, 664003570, 588289393, 900806378, 513510410, 650415834, 117025949, 926059778, 70589380, 669766405, 268682234, 891616751, 247517215, 73376093, 294128057, 87702110, 848558033, 785703607, 646729760, 153795970, 374277845, 261425763, 672882579, 44466097, 33628251, 577859055, 804767271, 586216150, 491932447, 549676275, 67705502, 391388465, 317675477, 456952148, 8695207, 839133654, 763579643, 147570920, 54266988, 349464798, 52014042, 290845623, 815500375, 167932488, 620203360, 196844405, 619907158, 660531746, 855928180, 712663156, 775822308, 321475941, 435395308, 60356441, 382947322, 538555279, 653020761, 944710907, 223538581, 392128, 871025525, 820747263, 190666099, 126310455, 26788996, 95882555, 497689886, 691839386, 144506687, 661185708, 226575798, 296685739, 975181978, 123258442, 651335950, 746931660, 95044849, 590100463, 469851762, 381260280, 78402974, 166703098, 252262956, 902530452, 772960221, 428953944, 462790342, 134295950, 711496839, 483872440, 130037412, 623757337, 779141244, 829583190, 114406538, 247686269, 717231369, 242463419, 773660402, 451820038, 978816219, 452093337, 387300469, 562300376, 20759260, 173682213, 877887778, 41381910, 532623337, 725128997, 636501132, 562653520, 924361809, 100504324, 378364443, 133702864, 37456819, 59287974, 109377705, 402672288, 884262475, 31629055, 951850808, 630381462, 175292698, 173936828, 874446859, 204218834, 651006259, 917404863, 37065848, 585645193, 416756724, 870785074, 451693555, 180415140, 996615853, 907296643, 663557380, 881164512, 390855961, 532341630, 777328230, 307263161, 761575154, 618246131, 884859797, 234061712, 372459083, 872656208, 517850384, 665627715, 970522058, 130626660, 415270700, 937225629, 247637924, 875381407, 296525093, 344397968, 232558967, 432488049, 628783566, 794366851, 884329387, 376816508, 44776418, 891809258, 394601061, 113613001, 726073715, 9006292, 96726013, 21920218, 193724617, 132949232, 952318515, 824972590, 418837575, 892673554, 825512014, 343139157, 789063804, 347254548, 785805572, 821993658, 283885130, 142496076, 947744856, 627237181, 903692928, 688502522, 808071473, 290050365, 282840593, 425952899, 348065858, 885423010, 394620368, 48358321, 438150987, 427735463, 76326408, 67559701, 684689089, 584222390, 387330834, 962503330, 622896634, 288302656, 515175425, 629931698, 953085564, 612614333, 142122219, 298485662, 855746890, 973243824, 89374684, 276520971, 482286843, 497543396, 183736884, 392767610, 600425609, 394961676, 728518367, 881419092, 528093489, 69722939, 38023314, 481207760, 559700711, 535646942, 133858060, 715991023, 195638949, 405831771, 907487816, 385118313, 986841353, 562164672, 645759165, 872571246, 199530612, 437182475, 597509087, 466907996, 705944895, 448698616, 948208277, 776886476, 399301511, 587728926, 662648870, 902408217, 440445648, 838985292, 254342100, 837129147, 181476997, 571502603, 890458431, 643614366, 408244855, 997809332, 356512369, 488771465, 752011709, 438265552, 453075896, 733252369, 841359434, 573157434, 750950745, 587406236, 855822022, 844109803, 130611826, 909007619, 840355762, 13081786, 318204459, 924644105, 446778896, 31401184, 136448904, 982241361, 512344199, 916313079, 718024868, 56888030, 880873968, 102695621, 606928060, 78917009, 508314830, 802414397, 642957846, 180496990, 285527230, 271207700, 522532369, 126491878, 32676327, 821260375, 392729486, 715616191, 837310725, 15933190, 696404969, 742840686, 932249207, 980122706, 202435611, 651508475, 970437663, 760478444, 448625334, 931526527, 519514342, 463144841, 792477145, 750380335, 54353628, 361778548, 242609349, 442000564, 519446167, 352625452, 87034233, 696375222, 178253843, 472087122, 587055721, 619297416, 811725817, 472437117, 669150456, 810396751, 146984761, 948444585, 635577477, 201244405, 702203456, 701538057, 197927439, 91802114, 133749192, 605465613, 115273173, 497786874, 499309615, 840311487, 213877686, 108155644, 864826591, 220600524, 437889568, 696530094, 707358808, 693048528, 481071109, 383723759, 176055615, 332062965, 573001860, 558508429, 756038082, 122077926, 283092911, 890730241, 209502615, 845779756, 171201777, 394024224, 75238586, 358670688, 611702754, 751270279, 306255899, 997467938, 198906419, 342797532, 136164153, 394623994, 724779496, 388493265, 812415886, 381090192, 115261980, 479573779, 65539207, 99437773, 462178213, 752126555, 446246649, 246997419, 208209251, 319932173, 984362751, 279292947, 171074023, 79607033, 63248343, 873738080, 919806046, 742580292, 486038152, 791720169, 314348372, 406123302, 539618678, 282418896, 619862429, 818118031, 949277825, 283042701, 962675629, 791955758, 8608097, 569535984, 30982988, 122879634, 24862567, 427310501, 185455992, 275348411, 195731508, 631679852, 209977915, 516091010, 969318714, 507134283, 733131298, 378939157, 955444727, 575638169, 678981688, 32612400, 575116072, 749482324, 87110912, 293803141, 79065771, 169526834, 283486421, 149790303, 211563953, 498268367, 405531175, 727669086, 395396905, 682486005, 826867725, 33782384, 102550965, 984451440, 598928979, 347571325, 406530045, 958171629, 81830992, 73898060, 96534465, 877384367, 530523730, 562594172, 294110436, 917499074, 605481786, 488487536, 161951979, 590751556, 237985209, 351105530, 410793540, 111777011, 659982033, 786692783, 357410934, 144761342, 106372240, 147093193, 317100086, 80627898, 126016564, 575216947, 852146481, 472452452, 344751741, 500745233, 295451353, 349068473, 726929194, 899176059, 611717012, 582257643, 448581448, 794266257, 233179172, 310785955, 116518880, 921845480, 371986759, 601102502, 418900770, 94235148, 638841432, 990221885, 202547624, 487049923, 943296520, 108480703, 319354037, 712399365, 695562524, 654867971, 829141828, 699884407, 560176418, 357883853, 251591824, 655684279, 94249390, 368125147, 302891428, 210977886, 333162228, 570846850, 59164464, 556488648, 632707487, 414149446, 424379067, 113653113, 270939855, 575824918, 510301443, 325613982, 857803472, 280310737, 464688676, 460805818, 479275247, 655474292, 540822341, 501116307, 182415936, 564840877, 490920222, 55115818, 961955052, 432516861, 880813541, 944029704, 773407669, 465712269, 512251645, 408570019, 873036359, 79198798, 630022242, 723915102, 74484973, 787473294, 983971088, 675208545, 311035106, 832673817, 52858429, 765092376, 360789491, 251054345, 976185224, 974649035, 376459722, 880996805, 435423819, 961425306, 422388429, 267187498, 749494279, 79984291, 894949802, 474902240, 583598242, 150341368, 937277816, 250654170, 367496225, 462969241, 489539526, 297903022, 596867065, 264276611, 334380168, 873269037, 234293424, 595608102, 209196920, 210308966, 842893147, 206753807, 680944135, 413626463, 391698072, 825727186, 647392596, 939889979, 548654303, 964053892, 703790553, 411780008, 286296745, 610002131, 901693762, 80971991, 968802058, 217226940, 316701764, 32251717, 66573010, 166626516, 294093887, 345901800, 623690218, 19176428, 148021413, 236889008, 225561399, 629327195, 359885299, 392834618, 449086945, 337617514, 737088307, 248256574, 782852220, 931582014, 295420133, 752427567, 496038713, 167519079, 73269666, 438868958, 712309298, 835760418, 254126173, 326196082, 960799582, 271716146, 395957536, 108719224, 195338862, 845671840, 582287512, 350692610, 335653166, 115325755, 987071803, 478978429, 102919923, 703853507, 825744693, 726171030, 341086508, 21161766, 291871836, 229223341, 534083303, 494032474, 444366284, 579950732, 573523601, 203406847, 352056064, 777964422, 890713068, 602271383, 648005910, 329616811, 351267576, 562921378, 750805901, 573326999, 826077811, 429601421, 376345973, 654825113, 606130609, 162274775, 996736008, 573587937, 594021397, 210867557, 431341761, 881310109, 505944790, 976852199, 696193372, 767158040, 831173305, 500401493, 592994221, 360324700, 423873525, 18597437, 407583778, 439634307, 440778440, 123783853, 57818290, 750690552, 423824998, 370368994, 353961610, 622161848, 694512492, 326172360, 667365521, 640548079, 115097649, 983141492, 583014860, 398158407, 44844738, 795860153, 905129158, 649064103, 745969920, 59238784, 366360018, 190717001, 669131426, 619466798, 554487202, 195809956, 205815655, 718313100, 57159829, 237542532, 908531234, 748861439, 241202827, 522612407, 916446209, 707280830, 570902422, 283239570, 801179225, 576200062, 557928111, 518146626, 825820011, 597537880, 812500583, 284806839, 607841015, 182388180, 35216552, 495064052, 59093967, 836765420, 765428385, 345334462, 437080479, 69991305, 336409418, 861856978, 658234811, 875765135, 611371534, 725023795, 86561856, 446464480, 789659785, 46735607, 330813216, 373362689, 229651389, 772188203, 15716314, 741478283, 67505201, 186033952, 74384544, 370900783, 210011122, 626189967, 902136811, 640406644, 329458335, 432946991, 18068360, 790931471, 805931513, 435561996, 193262880, 500579556, 449602406, 955694249, 358164006, 204548331, 50835089, 811807924, 175419382, 98358560, 216440129, 287322625, 168271670, 931366777, 977240683, 345093529, 290375356, 22412320, 353240963, 686275170, 16252453, 185986262, 464025365, 169300836, 912319194, 921451812, 915841056, 297343537, 742169224, 636250061, 538050820, 373938896, 595721121, 703644936, 95175061, 819191985, 340758115, 17507570, 599135227, 912711220, 49090, 871673404, 392002529, 307904937, 128154417, 357708988, 880617811, 969567968, 431673196, 417142875, 357259185, 728107921, 703424289, 770613904, 628165174, 521772615, 696537274, 210892882, 19076512, 908202231, 182829253, 413891735, 612623923, 852080520, 236400666, 584808814, 421921275, 912741269, 867059358, 312892658, 793988699, 298074240, 441702069, 258964114, 865511673, 547172447, 607665496, 18742638, 804975369, 408172475, 175877103, 931043388, 216113938, 19814250, 193709854, 314099123, 104589974, 13533557, 101320806, 890397305, 714356839, 576817168, 672135962, 628145249, 906269925, 546480338, 461144698, 527245690, 308973029, 124168799, 942086140, 667451068, 499059943, 524043328, 781457597, 470647917, 619812503, 700358604, 426143453, 476927752, 366069143, 259044991, 160129114, 893514962, 60286306, 627296966, 537969172, 177540309, 326057524, 290855023, 970661061, 613598128, 489573866, 901595405, 430038022, 176957388, 53939199, 404499115, 413544151, 14398234, 175719792, 444582340, 658673946, 482209240, 240015670, 763740848, 908479967, 155879933, 801776042, 543773034, 310552613, 161585979, 888770602, 64456899, 826876915, 741372412, 941461914, 872679136, 103649570, 309898087, 877260466, 526285787, 95430128, 128781558, 517219453, 736884941, 769079664, 380096331, 130857915, 870972361, 222713162, 592003020, 252826076, 32360707, 816542575, 425050444, 569848366, 748350589, 70879730, 44598656, 448806739, 773687527, 103986915, 240349260, 583292359, 467719229, 202138531, 146040177, 219044970, 555561020, 57075853, 986050384, 105482855, 550294946, 224913203, 554323948, 66588238, 952740892, 405216204, 335226802, 280984695, 334861539, 147712581, 302705772, 443490629, 589201895, 315725354, 295374357, 355096407, 317465086, 487861209, 764224368, 488422337, 729262686, 17280311, 241312002, 770990890, 843749679, 952073041, 261360775, 908078517, 849227700, 521237523, 55397867, 868283071, 307266034, 340874298, 526185729, 432147767, 908322628, 376238213, 923529099, 511566328, 864458127, 654972865, 978612421, 651331674, 912556923, 994521621, 494881818, 998805312, 39623445, 516464044, 693312744, 60295549, 622643172, 479251213, 252824734, 592686347, 625097964, 625235934, 610579700, 260466348, 765047341, 533734288, 479433358, 972507024, 418217288, 793895200, 421614433, 548630525, 996530873, 539398660, 508013422, 222371226, 808528300, 382041510, 488756935, 767242469, 405835920, 912637864, 870042324, 908546691, 479112236, 24876922, 780108678, 288063938, 300195121, 446723762, 304894789, 490303335, 133664206, 128027380, 983138212, 700430105, 248701537, 781150028, 993353900, 298847751, 707562634, 439309264, 798440729, 83599219, 273850503, 282754713, 156760921, 298634704, 969717181, 558192793, 268068170, 305212844, 258861144, 723283067, 656129528, 609995165, 205308461, 397150099, 638003045, 310197104, 714141104, 27367567, 414306194, 240974732, 723637467, 1240473, 156237343, 56349655, 409056255, 265160919, 415264265, 269165856, 674570144, 580515152, 148577492, 79793618, 856796837, 834487787, 172651803, 421588015, 91784377, 647636818, 629776778, 754209324, 751974350, 467517804, 493398747, 275449749, 372617611, 851494302, 344215563, 371240611, 504650170, 28891635, 500104388, 21123737, 983358062, 814952461, 162743882, 235643791, 918908027, 272931954, 106685481, 790964205, 983876792, 809516225, 999252486, 241133247, 560161757, 780702726, 889219888, 132624353, 565700032, 861020299, 151950110, 881834263, 89443560, 836662167, 198375987, 636393248, 988873344, 897057421, 462901953, 912206768, 170568754, 971542853, 768646789, 253162295, 273343756, 267988581, 141474791, 370214160, 966176036, 636209839, 842005468, 136131856, 184228280, 481492491, 896902606, 503674909, 376865245, 769608527, 828007742, 258968469, 96994602, 155403607, 357862073, 910294514, 380960811, 950238724, 588938581, 194191808, 647845761, 252686133, 272441520, 275144149, 907088018, 507256156, 711832428, 680167854, 735652556, 585486645, 506838711, 354222819, 464159541, 488177931, 755187345, 374050973, 750493000, 821479089, 8271878, 281363106, 679654861, 505725860, 531922588, 687112182, 926743181, 482682624, 360640581, 71685273, 306004260, 412259520, 626944493, 915148114, 550830199, 901331354, 774578070, 15736774, 18887804, 430964818, 685835899, 662015893, 427498127, 944959687, 687948229, 596030591, 810308391, 427982954, 359519755, 73776093, 605565851, 220852119, 475723330, 900894362, 457057449, 925040568, 301287079, 480550911, 301647259, 974381253, 56503038, 143071667, 629270323, 554869008, 569799797, 478227169, 305918166, 47602539, 313338400, 95679923, 106021028, 991584315, 959771021, 15726121, 328971390, 473303806, 697656139, 517030620, 591569647, 983385752, 496424185, 129391502, 701048911, 820461941, 15424388, 499246375, 194493107, 54083514, 548882307, 458965119, 64304126, 339170394, 287764255, 117036087, 437249233, 492868459, 249149309, 946408051, 685313087, 364760673, 897567358, 440144645, 914356097, 513900039, 345385433, 59561591, 333322526, 809569416, 405846076, 519901697, 443309699, 342364182, 326159749, 430435779, 94962131, 761229489, 465237616, 773697940, 238146837, 927817108, 487920365, 856968653, 996089463, 951926032, 613691645, 164366483, 381337318, 261612785, 46882248, 715448425, 288736567, 273970784, 248076914, 352657290, 66567998, 76484126, 374054604, 758994689, 630633003, 886718479, 984025205, 492179767, 659520588, 347514925, 982327, 252066865, 321649939, 287948268, 10530532, 682100203, 363062923, 319985713, 581578348, 839365034, 474494377, 128421547, 152065207, 116222095, 25952602, 219590346, 484214360, 449339367, 754499638, 204915944, 531961369, 990236193, 735956317, 965759852, 52867851, 778998565, 918133789, 767732614, 24293501, 461205180, 129642095, 995998901, 213093117, 128195261, 788939417, 119020641, 424396984, 111912819, 976700936, 845864670, 526445742, 268342011, 213441841, 433062501, 298225850, 913705385, 947055209, 644887058, 869722347, 204040305, 642942520, 412345517, 779379565, 768256187, 177430143, 220285890, 922944728, 770123647, 439423922, 177422594, 238898345, 530702333, 668773383, 740813468, 199404516, 381043570, 350610029, 397224165, 280674823, 397282981, 382013646, 964444633, 584453134, 281077022, 227046913, 295123069, 757649773, 168323999, 890067717, 494805655, 416264316, 697566679, 329252346, 462039755, 511556091, 224878076, 341758254, 20267686, 671603507, 774780753, 552595278, 433994935, 520600448, 373229972, 942430741, 680203161, 85415220, 713176990, 907112625, 475547151, 356950965, 581994197, 840595024, 460703563, 542586150, 500029326, 393451434, 230471299, 999607740, 736692809, 28183618, 578229700, 695723084, 221084213, 531029761, 160264396, 85681248, 975970646, 335481804, 840066528, 584972566, 587674123, 858990461, 303000294, 926933442, 385652618, 657492139, 476083170, 58306243, 271517543, 836253634, 378751553, 993447821, 242721382, 113055677, 166150055, 712094659, 941727322, 327963647, 249763084, 720876317, 386970249, 106305301, 759902675, 15475846, 947831179, 70363337, 199912354, 845210385, 457094985, 890489070, 368117237, 564072461, 846961611, 759554379, 300794718, 585962950, 645516586, 531779625, 825280902, 306344308, 696010247, 249008372, 471404244, 324668888, 229810786, 587699166, 611728988, 635248624, 293914633, 944015962, 729062028, 44463721, 771729625, 885725027, 691486385, 216395223, 634510466, 608916015, 528999546, 345812788, 591051349, 692780302, 487524816, 922865397, 589720080, 656755509, 97222793, 685402970, 329329170, 106717200, 46188739, 91033099, 746663274, 400460196, 75132003, 196185729, 248194380, 304651565, 386046552, 964847689, 303167330, 316171188, 741513374, 412501846, 911904584, 696353323, 65995979, 586130253, 863245370, 11655802, 151538450, 875151514, 308305396, 954799779, 730092366, 939466448, 118338692, 288704005, 489731738, 896930876, 669284855, 707784117, 201992404, 158869833, 203019443, 729555538, 835107149, 226236649, 757859168, 134027029, 282721544, 101768794, 888459652, 50557591, 238256523, 90823120, 771238989, 357624479, 132661796, 242230260, 519285690, 94126604, 704808439, 918500103, 413855510, 574455711, 876097076, 847453012, 347921658, 921596692, 370659045, 682949173, 890621707, 351590903, 21350131, 613472982, 846623258, 381773934, 623275015, 367290215, 580703207, 881790252, 329222414, 690185758, 572635978, 119736553, 303330619, 659187912, 20700818, 287140981, 8048285, 263623106, 298078687, 100357616, 899462913, 704879922, 184129298, 846734574, 218611189, 901695027, 608856853, 306285785, 143854713, 605694614, 426652464, 820501930, 216869589, 995584985, 466447699, 352406778, 157913769, 432173029, 309080648, 323112665, 116054555, 487779528, 782342321, 145193623, 887414823, 674078375, 610057654, 836874055, 876041013, 870712254, 913221039, 786232566, 30358412, 165032951, 671749610, 299921984, 331538419, 905223618, 107346015, 826392627, 314342122, 257562929, 356883706, 824920150, 475642578, 211334847, 955936719, 467714019, 799851487, 752739138, 722868542, 116143572, 499461735, 499485164, 753734380, 339794878, 548497155, 35370267, 242336596, 149693123, 657671996, 219507968, 908241354, 57964394, 225241352, 997822547, 622563244, 999567287, 206337719, 573131911, 351766780, 68713918, 463125324, 198892914, 389326410, 283523548, 224051972, 60243545, 452385774, 637305167, 786599641, 211337834, 449034954, 533759967, 580688145, 102286113, 710025936, 209256709, 717294276, 380383335, 919920943, 710691120, 370453945, 287402103, 972494211, 940856168, 597120479, 65152116, 913522657, 651170375, 159683741, 617345682, 297652752, 641619395, 744344037, 201353669, 114780280, 396189002, 347650323, 383587788, 299074067, 625519766, 817148014, 131418022, 959432522, 758395617, 117949290, 73217207, 654842737, 141160976, 633422623, 894909339, 666991790, 17181443, 293306309, 896751643, 921115857, 644908457, 25600715, 851897409, 963456318, 139258645, 851790526, 425546795, 703053642, 629771989, 538738687, 125961144, 285198888, 339462578, 895073023, 596344703, 186246569, 67207877, 314647110, 482098912, 457036227, 878408299, 185613400, 281214918, 201571105, 744701750, 166407056, 90427246, 765020347, 218039058, 350674573, 473158147, 93775070, 112583973, 946422086, 844623064, 585482935, 354215371, 915971584, 298631133, 356765189, 364283051, 730496369, 856106131, 699635286, 635691792, 842088092, 531082403, 990469769, 153366474, 570608537, 955336370, 533179034, 519957708, 225260339, 160423405, 875395715, 15832623, 406167171, 662441920, 673551555, 106392743, 883627908, 642417415, 112720353, 982405344, 623208906, 803174410, 870516521, 487689802, 388339679, 894348494, 742192853, 493650862, 367608071, 404147055, 658707883, 975978159, 459748582, 8215258, 404933447, 771026116, 701528582, 979746685, 604539513, 699511955, 466335505, 531069506, 306225488, 949480867, 30301543, 240396111, 878893674, 629585362, 619380663, 919422393, 531201692, 940362234, 950813326, 47625766, 508606815, 896914572, 14745761, 357023584, 884675787, 474671207, 281646772, 984399373, 716819285, 170454233, 37010328, 692792853, 147144362, 270251683, 520322243, 771250247, 697150409, 630989239, 3245099, 542462508, 725617772, 316360437, 984362309, 992289141, 455797992, 210758187, 995027438, 276931356, 109848247, 611816542, 331814038, 280057363, 172543652, 305504327, 178295351, 242681199, 935111787, 876599668, 828454956, 265498664, 526551780, 178419318, 102175454, 790743032, 620448663, 308661954, 168863906, 171191675, 662965426, 536719369, 108133327, 334299501, 590272023, 163793490, 694314601, 204475490, 158119079, 241388837, 988750613, 386346146, 996485230, 695681613, 283155151, 431890958, 154893798, 422569447, 874947327, 171786551, 954830323, 599024819, 105184888, 549838429, 468609998, 34264433, 920953039, 135115452, 57341301, 834218624, 467214139, 210318112, 575042899, 18004712, 872445538, 676140679, 261568959, 230671556, 681638861, 211291995, 863372961, 530936160, 934603000, 387791641, 617308019, 941635511, 829248492, 209356597, 421276967, 550107902, 198654971, 334450903, 420037102, 968943765, 527275626, 679121458, 790482052, 683403642, 130668864, 176686511, 258140657, 645522551, 60577624, 128151934, 933650741, 105673023, 65814947, 823733601, 981165997, 290369434, 410598936, 393148008, 964454615, 950252214, 619091989, 262997702, 20436205, 447298659, 443961715, 372492903, 762565263, 505921050, 919347788, 220091922, 766983849, 469545587, 595202763, 454562263, 529093412, 94520601, 638745688, 480127614, 318307144, 177301071, 244504280, 146308476, 160814377, 238493159, 962837493, 29459212, 439737427, 250472875, 104240620, 653008177, 416097172, 805591267, 651671351, 119706307, 576053128, 190161032, 993387730, 968540351, 457479829, 369172852, 311615825, 112622235, 545734939, 312141771, 996426481, 343144520, 252374943, 68080797, 465188987, 600359802, 875984103, 904065483, 796671740, 557565743, 304995544, 661196952, 26490121, 86541946, 641235533, 506855440, 153249016, 922350397, 171255682, 751220755, 459624946, 740177964, 798354113, 715195573, 3251635, 896612065, 247254749, 83576755, 55430156, 816767065, 629997594, 208320219, 203428334, 864491757, 909138110, 277313158, 357611211, 118577384, 599760630, 907652956, 614513261, 289154000, 514030351, 629294492, 828745977, 736460358, 856262789, 451029447, 896503255, 161738060, 349514418, 785612559, 395287077, 627648125, 314846808, 573942195, 345442186, 297360777, 208001415, 506953481, 994031330, 667996563, 730923580, 858463803, 302506438, 512204730, 966965908, 747162623, 122477118, 748854501, 692884328, 412465556, 956023041, 272663354, 447060915, 55197615, 969193414, 399350166, 364295594, 199697120, 689840122, 22481299, 769865841, 857269285, 560551467, 180783085, 991204970, 839197445, 876773696, 903088878, 367755690, 508485070, 630351902, 702589921, 994716012, 38029039, 525144153, 832624750, 310248659, 191637366, 997366193, 50251857, 771880410, 945558939, 392320618, 400509077, 121408585, 888819420, 611135748, 878916981, 692296229, 242427662, 570802867, 78810800, 763230361, 570476204, 227863970, 776162659, 718866716, 667522567, 937776548, 555850120, 500179653, 582735432, 225762554, 181835591, 687129846, 215402880, 805644428, 832394506, 600486159, 195867210, 298592020, 793311077, 46087473, 69007768, 758519440, 491704702, 845423039, 904131964, 486220, 729386210, 379208495, 524904086, 646435516, 153832362, 629898021, 801500224, 31443169, 835435662, 310715393, 546676321, 412842317, 934284409, 971000152, 915452869, 212239371, 370063351, 2257476, 644535123, 293148388, 141292006, 369361791, 135383889, 660171922, 608875410, 284921080, 557037612, 448327083, 972690411, 430656371, 237313963, 842830918, 641331826, 691927181, 302186681, 60517407, 280988, 148810616, 765639929, 384917259, 247229434, 754615083, 123427727, 438858474, 969254828, 229739275, 171905968, 684268077, 261192107, 849487240, 290379897, 292315417, 15707110, 952558521, 116593774, 959819774, 827115180, 908782504, 663665255, 336080412, 293930360, 967659106, 768478244, 762746035, 121058485, 341236261, 820212668, 618053885, 214041329, 979198870, 657995806, 417820220, 519666966, 708170218, 822341517, 582367622, 805470214, 353549931, 68891216, 353568394, 962962018, 433141109, 166610314, 190369244, 69079611, 196023002, 780394539, 190019241, 789872217, 528820741, 696042549, 530363069, 56481387, 216356865, 372155925, 411603168, 948135678, 369906868, 213224294, 393793804, 95120043, 444833721, 607011140, 15349086, 686405137, 99684695, 947554039, 310912648, 719924932, 667110756, 315289251, 330635211, 593911012, 714336298, 27592415, 80852128, 415836941, 757188718, 432799246, 343776192, 450273132, 669982541, 29156363, 168653250, 924514516, 92000381, 241767553, 693239924, 302255869, 470970689, 470187832, 481131042, 534412722, 16325271, 132991870, 705647663, 847564149, 205485221, 565478017, 781854094, 919095372, 596841396, 663340878, 615623691, 900503004, 206068923, 197930939, 438374818, 257700266, 137666798, 611288155, 914489936, 726200442, 596091393, 864193887, 525177201, 514128373, 15788019, 389863665, 690200834, 942419344, 788692451, 296088079, 297605893, 683174824, 10456083, 8057621, 530086200, 191927432, 495120479, 797766898, 793950282, 946756131, 805997803, 764274071, 822077132, 297739280, 894102897, 778336966, 190015538, 193607998, 867935299, 775640546, 755231303, 154180236, 951983998, 468772090, 413141672, 608950560, 380208475, 64750496, 422863271, 655649605, 307810112, 130874672, 922724495, 789492663, 398425783, 967408964, 546908697, 748690281, 308102281, 485495550, 499543458, 995298109, 117014967, 617450504, 211851761, 152246251, 655065858, 924216739, 899148033, 492529225, 855175308, 357601384, 537954553, 171015318, 409906804, 663390495, 18254365, 622773629, 858089245, 738745110, 241563142, 300561658, 61011281, 441633979, 472283031, 403783928, 519722578, 189050448, 942185310, 655195923, 921509755, 665576485, 393578423, 725204603, 103436234, 792372345, 47477414, 131927015, 390716399, 4766449, 503163677, 896610088, 234389295, 561348919, 468651298, 620537771, 39629233, 258662474, 323020285, 618954527, 231522761, 591346172, 537906791, 142298745, 281103377, 971535060, 29717770, 868050962, 322675006, 90249349, 339515662, 465497928, 601500724, 572958457, 569824600, 489849878, 322870910, 915109414, 700622536, 182064666, 749022469, 667030498, 442296624, 279322608, 700993437, 338751294, 534898895, 855278279, 701872275, 506178848, 33162733, 190391550, 436245201, 860516219, 349511821, 856226134, 588309058, 312342244, 875441738, 674455816, 760888587, 164475738, 658532383, 428528406, 76187192, 875287845, 829147942, 490545657, 509423743, 922820804, 367498987, 333480246, 337398980, 208259163, 324893783, 836142105, 691406259, 98215404, 671839518, 204056875, 306993268, 378282253, 748159402, 994276153, 803949551, 225379640, 365753585, 879549360, 23566142, 333614491, 973444149, 593271292, 89949747, 779066667, 158080606, 96145451, 72389577, 338532396, 279698958, 426298382, 907000456, 76750053, 885208058, 987381621, 285019840, 750513635, 362377540, 647894715, 324918482, 372933786, 241108517, 188528658, 963575464, 394098908, 859774398, 923286065, 982985124, 189249647, 147714030, 948511715, 780889430, 216177899, 377250107, 499108094, 834620338, 610550979, 582844390, 253678666, 960980892, 340344445, 292842357, 112169667, 870662757, 317740909, 869051436, 587237921, 250108686, 349716133, 287280343, 536702063, 685554134, 141309894, 461852093, 508621769, 574736914, 100054784, 431265602, 948860670, 615174900, 315820048, 306980223, 31424396, 442956283, 157202986, 86105123, 914394253, 602341346, 261546639, 864267949, 565306684, 743883014, 785881295, 5955681, 601650141, 618656573, 431336102, 531758739, 402692429, 920984286, 474168385, 580047347, 242012725, 369901611, 83649281, 516051143, 65576755, 6273577, 261676398, 708115335, 953287522, 743497683, 160640774, 723671980, 463668463, 996588797, 264453875, 692140020, 323320339, 931646460, 498685544, 250662996, 487666041, 282607295, 687148419, 514879415, 356546091, 409163977, 658954864, 364586872, 813299625, 777969429, 142724340, 386751862, 97088581, 744140585, 16076343, 838648998, 874169839, 637723454, 195786063, 27105753, 176727301, 857523600, 261154322, 882890002, 404124250, 675090853, 195691281, 45221595, 161443993, 408878840, 836456623, 298678655, 390467258, 708483267, 673915415, 361571766, 207699070, 238650695, 493368814, 397947402, 137301923, 823340462, 947553764, 136091428, 700635908, 232611256, 261874708, 369481438, 323062868, 911614062, 924781184, 855561542, 727576798, 420983176, 601725169, 420971315, 516870207, 914443256, 75906679, 430919878, 867064556, 714244790, 667456162, 299013902, 222247142, 377999426, 81685319, 186629826, 874190376, 319640570, 110950251, 926519619, 327193771, 519712117, 240131108, 369286546, 378318481, 569292912, 16047740, 405230722, 332812886, 800969398, 436205093, 320329599, 620291062, 915775451, 131145315, 593190801, 459252257, 209786975, 94763353, 693836377, 838985122, 297745853, 209331991, 84041954, 445369983, 629051134, 10964862, 627458440, 168150645, 620847431, 720105659, 375545191, 908395536, 212036418, 974828378, 222337866, 383718756, 739498052, 492686127, 378319986, 89163533, 187181229, 455789805, 513847513, 606571027, 246128368, 871954847, 42363804, 328547990, 353962092, 597941427, 182891680, 855499876, 424865580, 135035847, 265649031, 756719877, 972313153, 257069140, 62294739, 942431149, 621917540, 285878417, 854070502, 790819826, 588429249, 213470504, 492208665, 213015705, 309643188, 477636207, 579026077, 931649300, 737446547, 386286123, 287516536, 62557453, 728219892, 52369983, 730317430, 470251533, 15388859, 517706664, 264586772, 525826443, 948406771, 977447317, 145386997, 702604733, 730152787, 777870837, 775506225, 835639357, 960010423, 151504783, 95699010, 777163851, 412093755, 825094249, 344994141, 73511397, 403272337, 932826273, 126468768, 880051720, 474463784, 536034635, 101613553, 962468539, 497188964, 701191508, 416156541, 843157720, 919109466, 698610618, 346163565, 142021599, 98466628, 357380361, 657443171, 788587732, 913798255, 221336366, 58520741, 452349497, 247759343, 679066862, 302380965, 999298562, 541421114, 574306933, 556073405, 960930721, 139713625, 641082765, 19835241, 267555964, 840441153, 833519085, 326263122, 650841318, 898682001, 405161123, 649006146, 539581935, 53664696, 437286720, 649677134, 139484973, 114837939, 729546164, 944438637, 89259698, 537236140, 832942049, 889161271, 768509731, 167337155, 456476295, 286003046, 27521794, 952370458, 271230191, 294907626, 344042258, 489975968, 818194530, 886640414, 569354988, 224378727, 297176551, 978702555, 881076305, 70083533, 791407673, 163245553, 186357622, 432356842, 646536711, 982540240, 789750429, 2319582, 171588876, 295718777, 401481425, 76837430, 321871679, 458668147, 558338825, 251536737, 93215373, 172678680, 279384286, 793658279, 53690872, 546227430, 964786645, 466648152, 341521345, 616648262, 266611668, 51401097, 421987488, 295823955, 476349653, 280055771, 915104857, 351414647, 853973966, 585420620, 993750543, 775610545, 122525891, 624057702, 353765556, 142915477, 408348464, 543548110, 605836625, 906288260, 397772405, 886587265, 630554074, 890435447, 569018838, 233552163, 219059484, 611777523, 299332056, 6241721, 241153007, 203798260, 843996181, 480608047, 349286164, 130767954, 852382384, 75743655, 276019995, 905838349, 341426899, 381341143, 308834551, 335691900, 156379662, 212703701, 130229502, 448867769, 417319411, 462653543, 98681248, 911132406, 441579221, 456906542, 472393221, 930383676, 57971556, 914316347, 784754045, 398959318, 399948184, 745057347, 605064250, 501654307, 209348565, 475368428, 246273290, 663162358, 336831368, 663699694, 698729820, 417388736, 865353408, 290392049, 244225711, 406763866, 148047501, 165808962, 416685750, 847567197, 333744383, 281070891, 294865405, 795163783, 661051560, 430715847, 926358177, 231287366, 594794468, 956832268, 420917616, 835130632, 472670536, 205990903, 786111977, 476545450, 670769777, 204048593, 587690088, 62052450, 552020756, 732898098, 613331338, 931048225, 855127884, 744120822, 527582828, 247750763, 954557712, 668021813, 827226179, 401444594, 143112365, 513481592, 712532456, 462790812, 15700567, 211447292, 917683837, 480456444, 173168384, 291500012, 189114250, 804750872, 89869428, 169616107, 845472559, 739560136, 953415140, 60711480, 185058011, 92858980, 865775609, 336596137, 636435306, 62417103, 395908477, 267224103, 640044574, 20828272, 532096165, 531484349, 623029919, 510641588, 269389720, 7637167, 871501186, 78352220, 362784768, 638375958, 592485029, 509300871, 181468879, 119706452, 292543125, 143570789, 959864782, 916146556, 855376142, 85138280, 52967165, 340150621, 252889648, 826706129, 805521958, 746356665, 711448851, 404395184, 288244411, 484802476, 914566647, 351205582, 919008783, 959502807, 301676031, 410218, 281791733, 839544767, 398646309, 707234079, 831639787, 701134585, 810360922, 904355408, 165628514, 127437187, 995861260, 951375917, 142790226, 973609416, 888894538, 759958842, 999892211, 801592297, 205960480, 856704509, 798957840, 562175553, 736613105, 614520414, 751004545, 670319020, 803213398, 988646901, 7609924, 302124669, 497336533, 163529770, 144966155, 606608529, 310785344, 86900945, 54977928, 249527853, 958122738, 666632075, 223734586, 796670668, 999277739, 427113964, 548334638, 747869, 911317554, 495633905, 773014932, 894338572, 433089560, 949710724, 790225700, 189745120, 601283093, 500574159, 766362897, 558011299, 832576329, 997148407, 175964591, 819423895, 148838891, 191184482, 725553103, 814141558, 164726467, 396785973, 396220560, 363156716, 515965365, 755674796, 879451786, 536794254, 917841880, 918635052, 950301412, 978591646, 728820474, 83147018, 53522781, 311733603, 849079920, 915226893, 516651422, 832943729, 940443604, 457047613, 108959095, 384607251, 205726483, 287924369, 987833300, 440371558, 242541933, 981800837, 34571354, 205396401, 97545537, 544369131, 543356979, 188497927, 935873114, 797465858, 317695667, 3922991, 60231163, 923793200, 74883223, 897785869, 463150446, 998184936, 718822507, 729680360, 103695033, 813521124, 283951085, 731876132, 149030547, 208940256, 315604732, 960173485, 685805633, 406356631, 54238236, 521901276, 25540853, 775324499, 188963554, 790805014, 353166213, 850946975, 418735160, 122274741, 1947322, 53345487, 216702937, 763062869, 46834796, 551113245, 318845048, 876486387, 618066575, 467261029, 505295232, 202778739, 264231976, 461594701, 904455446, 208740221, 280789271, 930983091, 233098837, 966088971, 723747921, 969172508, 129665837, 814833878, 38365354, 644717362, 390595051, 382095961, 493514689, 530644011, 92900424, 67299974, 125255032, 703257073, 511859679, 205919033, 179852519, 442510660, 184652144, 139978229, 477815028, 549713554, 793101260, 239632937, 503558398, 739032305, 3005119, 791219784, 566023093, 476331273, 521786301, 703993747, 957949524, 959364982, 338593089, 553911586, 902467178, 161204603, 944726027, 632721542, 819617783, 636361505, 576541243, 654403827, 159732807, 10460004, 322746411, 180816928, 61174537, 638228577, 23344396, 223282841, 537578378, 755271391, 546225863, 550311424, 745075200, 800813683, 193660734, 496458469, 221541508, 128356351, 691633468, 184581756, 874111510, 487353387, 374824898, 513426637, 179501621, 956052067, 962759462, 995781953, 260217697, 250981800, 178308723, 979296099, 662144710, 842133056, 784525195, 134818011, 939520171, 380649679, 123103019, 184675961, 107166425, 874167375, 949525344, 440675305, 988248602, 532002814, 782121982, 980222578, 469571489, 696061573, 709132382, 323224516, 301964534, 328769667, 172531788, 190641366, 938169393, 126195500, 922476670, 989899690, 783505002, 215121835, 698211042, 305012986, 567967841, 726180555, 231559016, 45616542, 874089814, 732971145, 509501418, 148087738, 874001692, 303556143, 900945207, 413211392, 855800447, 586146989, 813278083, 73721284, 708639306, 602029006, 673202398, 735399139, 26564799, 672795741, 111557904, 863995010, 480522620, 802762908, 331672858, 704274541, 538598083, 498150006, 732191139, 849951134, 517736112, 219549535, 31167089, 193657583, 457402341, 642752173, 646775612, 970927049, 323833756, 346798678, 165706559, 984174950, 883436244, 532229786, 232373905, 100555208, 861868324, 251050426, 739716950, 450278155, 402081504, 460817491, 72993323, 924709794, 710527647, 745326957, 195602270, 227026646, 85448283, 600576339, 272229680, 869746713, 490972562, 477161838, 325458459, 307055283, 783514382, 194040866, 963374212, 304746282, 442950892, 577076852, 437956631, 683248671, 328472917, 722257807, 406935335, 383515273, 356495856, 661204470, 120939468, 297658284, 263342928, 105299047, 560644927, 993008093, 321325295, 730934639, 779949228, 363910298, 652359773, 984465577, 931831568, 492622891, 491729247, 596840639, 677524231, 383673568, 613158503, 60934533, 833647361, 425995144, 352840633, 478814908, 817249942, 957853004, 385706344, 993407160, 40381496, 895938738, 724368665, 514194796, 914805, 241390520, 51357977, 514344636, 779527981, 4352995, 762557323, 932116905, 729934779, 334670242, 664799536, 906177924, 190207991, 679337856, 407735258, 45742008, 27372104, 498932235, 716197749, 837100949, 702342977, 87751452, 195046557, 203431384, 283053358, 673662403, 154118091, 793407260, 260809516, 639801452, 260591975, 551730951, 205250936, 197843428, 636865147, 726845778, 162758907, 706850995, 286995376, 202288793, 105929610, 400182934, 900996581, 763058979, 736452819, 797075634, 995385609, 977795349, 994877136, 835577815, 564847638, 203604228, 446594680, 554034390, 946920204, 240272690, 495856205, 547598890, 452440688, 948697558, 972855039, 662483847, 368628296, 124284946, 849286808, 621242171, 374621384, 619394316, 817342838, 631017007, 321895955, 787556160, 446629219, 902424565, 99966949, 95208649, 465521229, 450680542, 637225064, 770453625, 813161712, 937238574, 768692088, 596841255, 577929571, 768406950, 812651927, 951568626, 105797000, 222260395, 44775519, 859082170, 380421758, 448038279, 325255727, 939314809, 325617456, 284485523, 18550350, 2768498, 560116121, 415789766, 296974786, 391654583, 378084258, 450968278, 884096648, 928802852, 590353241, 444600980, 787631960, 111220618, 847866550, 124758172, 627335851, 173513132, 504457597, 823594235, 529933689, 391684348, 631646466, 455411963, 317924351, 987342855, 814113050, 147617359, 138400240, 303138642, 220549432, 786751699, 8572389, 424640261, 715780143, 634523956, 534374321, 227097326, 293400837, 716297802, 588881385, 610638758, 649154459, 198682221, 143218451, 654429599, 727937680, 530544911, 490014966, 165335429, 177409333, 762509267, 432859814, 703822913, 7043287, 778513310, 428739456, 973110488, 879604472, 790800988, 856712165, 894869603, 694022432, 504354867, 704758525, 871522500, 83199041, 480183791, 837501982, 582133368, 638702920, 369511524, 990359794, 637487765, 198171454, 753733107, 654021536, 506535101, 71865849, 189925716, 883836195, 145064433, 615660529, 123943966, 104412783, 697042489, 589505948, 438981856, 949400746, 695317437, 391705921, 242305010, 8501341, 932047590, 246007213, 50537636, 366249788, 529684514, 727762700, 964244240, 580094928, 13082269, 871549736, 946269932, 556473689, 167232811, 938815350, 419680187, 105758783, 671119863, 119398303, 568808470, 882121784, 782436628, 408979492, 160265481, 651765846, 543822106, 674627900, 256476155, 538435389, 664492962, 911713960, 986197277, 908178730, 822088232, 472112661, 547911207, 173526222, 516067307, 734365366, 849782561, 219013751, 289097837, 130281089, 525537538, 954337119, 752235646, 923559126, 790165879, 533418353, 582275942, 574993700, 348628918, 987419580, 470170042, 877247767, 54081247, 529324985, 714426240, 584789829, 801424418, 707819120, 288401999, 414117649, 245564293, 832584328, 311811829, 939080767, 793524298, 216448927, 150461345, 446892652, 423449275, 715802339, 661007240, 328459045, 304592017, 605407689, 92245711, 979735974, 165120590, 597305465, 489489417, 657078667, 263351909, 999281641, 50236595, 282691326, 617368397, 830252178, 739934042, 663056735, 948007114, 346187198, 759264012, 482266891, 863955915, 529762845, 932924219, 577301432, 953473227, 839509949, 793496433, 200679104, 426318671, 958083385, 365636627, 515655011, 975938970, 749254025, 103287477, 323516906, 783265346, 809766912, 423300493, 326178740, 340787545, 361631188, 649453310, 490108842, 102499359, 434049807, 636813050, 479290063, 687610015, 921987750, 332965937, 687889351, 228933883, 901414890, 773461149, 917240808, 224895541, 707776220, 772392018, 35809019, 802104691, 478729896, 671386847, 46207948, 36580939, 633104271, 545637237, 411838598, 29059638, 917294229, 822460380, 81949284, 742500379, 723177591, 830360360, 913614415, 619239041, 467594188, 224283424, 589529018, 488736626, 471454376, 525713562, 454637583, 846402237, 880243326, 823255045, 728259444, 45131820, 781956162, 229878183, 764778327, 322254405, 318332243, 97144571, 93036946, 797576653, 379829775, 357240296, 694103493, 39709540, 333047568, 440349639, 846499136, 231658180, 123944618, 608920535, 566243423, 525081299, 143131670, 976272653, 256098712, 674406362, 386626747, 660385398, 264075592, 254140355, 381152621, 31693204, 800114785, 679082068, 831802314, 155829793, 459472685, 337329932, 270719175, 626770719, 205363334, 803785352, 480258200, 74312704, 198349641, 874107961, 652276424, 907891437, 999309401, 92232689, 579378194, 696152630, 515363624, 234032662, 358730008, 432817453, 868202725, 171732631, 257787234, 720464186, 46978844, 182669428, 619876889, 253378329, 171246549, 28774707, 48277480, 168999687, 909093736, 159444475, 175031972, 146251379, 624509625, 864752095, 476732461, 236153858, 634714004, 764275417, 214079820, 506804788, 977404560, 477638924, 736281528, 467577632, 384876425, 222941784, 8674872, 485737865, 555325848, 251466852, 235006022, 167851887, 37349624, 546738050, 246812080, 660602996, 929718704, 439712422, 816602993, 546002658, 754757284, 383887909, 578069545, 199434981, 794873808, 623965248, 390492641, 110460315, 152962451, 202399969, 555160382, 234845910, 730019289, 926531808, 444425250, 606541191, 931693730, 835141128, 957970550, 762517632, 781112264, 880742659, 155635702, 387815054, 149656235, 744947016, 594456670, 184764228, 879269811, 345976732, 208761405, 877208758, 569117312, 615724503, 423702721, 255595257, 511526483, 3025649, 183487202, 470355170, 600123336, 650309107, 559781376, 811353307, 353681412, 412475406, 189272138, 693190305, 259536952, 277168395, 84118223, 425520348, 86447523, 752799379, 429979094, 262365826, 53765049, 307751765, 842676755, 604817663, 350804697, 479586459, 418227855, 84898673, 911837559, 888958084, 217933466, 122593483, 669655593, 726408355, 34089666, 614130989, 944131633, 690527543, 384501573, 377284123, 410457299, 910290336, 312986539, 665963201, 716316315, 699835134, 621526692, 593549624, 145345026, 420716410, 811442217, 674466077, 964751024, 230271118, 492487919, 188074, 40662910, 447952035, 761264895, 591929660, 845445143, 649663183, 907364696, 250110545, 600156878, 722639310, 819743496, 198759678, 213033813, 975318433, 898658289, 843482011, 219191443, 141091330, 355716035, 901455064, 805206700, 95731940, 448772794, 44155709, 789159253, 510108658, 534284169, 127289125, 765382249, 100070424, 520271046, 755990479, 968632966, 472472889, 567048927, 306210378, 203333749, 862052767, 424774944, 972728637, 241747638, 224435543, 104925877, 808814776, 376886006, 921512071, 76889354, 680245762, 291998655, 258368191, 608313736, 840386566, 80328155, 14703624, 505215513, 137587720, 187300693, 309730941, 170725943, 443475594, 333973781, 431400509, 866502794, 703820012, 55156079, 721903328, 540802158, 714832741, 952773869, 510516136, 350470866, 472191391, 328295440, 102064809, 562122299, 408743221, 433710290, 454520688, 719767043, 843330351, 236139325, 947154292, 331201484, 582876815, 93679521, 340818943, 54638264, 175332273, 514298840, 571582513, 38187293, 385262961, 412052667, 437079433, 119310316, 445636511, 946352694, 992114354, 432169939, 761638852, 355654508, 494570510, 396183202, 370892784, 486864060, 231381900, 564688620, 366751594, 914431845, 188603241, 295432037, 631961879, 941148154, 915193832, 997925461, 369416140, 823759596, 751338562, 451507661, 354470758, 804699648, 151609025, 532116170, 535726324, 258902607, 905723300, 700533496, 371233402, 276381172, 893498416, 265244264, 110659274, 826011942, 603088689, 167282839, 253914733, 374554314, 723564119, 772758206, 820367543, 883436420, 249409305, 863745633, 183380053, 898350424, 97687373, 152661932, 611665978, 437712040, 518066658, 246989880, 364362945, 177829735, 69561926, 964916816, 530105509, 612923062, 167979024, 913314008, 172394192, 809417605, 743998762, 839193675, 362168471, 85697499, 179474172, 603422777, 608375475, 301963060, 222297709, 554040284, 292837398, 451997014, 59542110, 279617466, 70492066, 419222420, 541416879, 471668922, 792969363, 584851249, 271103919, 938788606, 854402598, 100484841, 290128011, 281283489, 266067244, 66125799, 324223892, 615193007, 319142154, 694263533, 858356548, 333677623, 714679368, 806221574, 540637444, 526633302, 714854580, 725129411, 264962894, 317463436, 820403522, 136647929, 533434500, 972151613, 521659466, 343690135, 458709110, 236502130, 414871191, 648497839, 923954387, 676033885, 935011971, 58332895, 733034967, 934268609, 454279722, 813656705, 502665043, 278634953, 217032221, 756081680, 419239928, 169372627, 785437939, 993700500, 854953751, 114180079, 826997615, 861902200, 688316436, 978531917, 59275259, 864426498, 363915594, 407160907, 861621962, 291475634, 427965934, 698797483, 633832943, 177182858, 806181560, 272918549, 274319120, 687606618, 653893839, 594458861, 355355532, 936387141, 861049595, 634679677, 360357866, 852646475, 529084680, 818523974, 322913924, 671176698, 690435086, 81206684, 683482591, 94398469, 91107415, 635162697, 979656686, 272822509, 324886858, 257700360, 299630406, 307277267, 712210047, 823526268, 226302783, 842802394, 506790081, 267164673, 537320076, 339988240, 331896171, 799997322, 310120995, 379042654, 766220196, 359458322, 369281878, 967409908, 443501394, 954523051, 972979065, 592014454, 141922862, 353649124, 583317973, 258657242, 529757196, 645279012, 781781030, 395819635, 383522725, 726308690, 175735028, 253889500, 900206376, 99763726, 550541512, 451819703, 300719924, 534715570, 27595891, 446764770, 621487779, 143935844, 686789061, 125132483, 442523326, 115701544, 661240178, 145217129, 787589966, 147473289, 308024475, 855153111, 519259692, 588361104, 102301823, 115578971, 103565307, 897517764, 143210408, 127742941, 139572871, 216749402, 240855517, 663220453, 293961349, 458820548, 938725159, 434684066, 342521425, 993926418, 373240055, 64928288, 68445850, 773622985, 599664003, 908887132, 672018743, 305564036, 190738343, 674104605, 176483721, 182247769, 387644734, 769666898, 384679160, 298061393, 650948033, 103729863, 619203910, 90289056, 450540942, 186696350, 315219664, 987240757, 344857546, 521832407, 580396992, 668916892, 312719373, 461188872, 550364514, 294372869, 469636306, 399752696, 494850206, 697784618, 425650641, 779163459, 232622420, 434070540, 7572526, 469109264, 709768081, 388688866, 836708862, 378783961, 914675090, 652506299, 663725941, 794611317, 996041517, 423509700, 401516358, 943737622, 251162808, 2393689, 563857207, 591049180, 981781917, 352710497, 33493769, 675920358, 734259800, 728857324, 219154530, 925793699, 117133282, 297260327, 305361271, 849775250, 422378083, 773337724, 738004095, 284042674, 980095253, 979817098, 705921243, 85300583, 27278555, 39291347, 210681064, 361133757, 604791397, 949860220, 233206518, 46986161, 178961579, 517381771, 869920455, 63456843, 417511119, 589076905, 639352989, 890454376, 411216981, 398155027, 931409548, 853465662, 358520599, 380020735, 856897442, 72227645, 310667838, 829793844, 100942395, 771118581, 159311277, 426341236, 570556068, 77623691, 803254861, 190284703, 177857117, 111711811, 265046756, 50810957, 31577188, 778794386, 793423309, 478034315, 893649915, 431452858, 202710581, 549629353, 173027389, 285014655, 359827184, 591575752, 528381264, 441106999, 625822211, 257045954, 138172233, 815185122, 915357722, 306979232, 24842598, 940009712, 560542092, 572204770, 773403074, 103837177, 433937508, 354031545, 42508968, 5744613, 462437508, 822855155, 577459628, 370766678, 14079151, 359174350, 787331455, 408203541, 978598930, 339094807, 986067166, 831368568, 690851427, 557499538, 860572049, 223252056, 252265222, 211685661, 952172054, 269300999, 195557079, 30984586, 486223733, 443344467, 314258952, 3057378, 246788512, 337940837, 327573015, 547854379, 742962098, 957340046, 633456148, 255399957, 428766070, 792006905, 368511332, 31478169, 644423432, 134932224, 711085746, 102120106, 47203633, 18985475, 290638826, 821780143, 204091294, 737971321, 146117979, 355705571, 851160573, 500568492, 770460317, 284060121, 359615260, 839441348, 595010415, 32730637, 671628622, 35599032, 797431387, 619913992, 546291468, 835621997, 940917957, 975704610, 626083758, 576005302, 354520444, 648030782, 655673271, 996851231, 352735072, 431794774, 528871026, 660858484, 645321973, 753088181, 17943153, 193574902, 928114911, 28426389, 396130797, 798391042, 819188293, 960041497, 995369465, 380160335, 337643295, 32486827, 762435165, 946406456, 297822479, 675230394, 565168281, 691255515, 320488862, 490561595, 786852695, 703109523, 793693777, 104805848, 539234996, 985042897, 787203636, 372417737, 154190922, 206436667, 713053786, 697659470, 510510232, 575203100, 239884138, 728855158, 342061591, 207282209, 204964203, 244144203, 348255098, 85004446, 377154931, 479003301, 939931856, 720862391, 105456643, 873656032, 206536967, 18483415, 956383843, 471115677, 75681098, 155908622, 739387824, 401700333, 717250245, 908724107, 463779200, 293524448, 372093398, 576080473, 354477341, 727022570, 234967127, 766993011, 877285837, 481500991, 901754949, 917683788, 599609360, 561388554, 336403281, 720547585, 230864870, 334394996, 996895775, 584037441, 628157297, 800106360, 798062097, 385090719, 833435395, 244142963, 810369805, 535159569, 998564773, 726001828, 147988993, 852392229, 567534620, 116765557, 882728108, 65156078, 292247109, 682237373, 235669702, 734113291, 498906301, 970224773, 123720721, 148766266, 914863313, 27188609, 909227628, 647276089, 314015861, 452578179, 889283614, 821723594, 879608455, 647823725, 840960416, 545833450, 11142108, 353360506, 870730896, 48300274, 611590962, 938990960, 49302883, 761391138, 586416601, 4996135, 617817503, 150809010, 241150336, 546419343, 134872618, 882062108, 525224836, 979980244, 886829453, 792484556, 318554847, 850062658, 840589288, 13644000, 788223843, 421467663, 28773449, 11563186, 375930445, 189071077, 452362571, 641720118, 446772051, 273141034, 881809814, 424910261, 605682595, 924607187, 387788033, 980494190, 296476780, 42649086, 415285752, 755666412, 718972871, 608202561, 480214793, 736087657, 661694051, 332727571, 88571221, 321253549, 126981696, 21987493, 247403167, 296888964, 121461921, 570080187, 906174585, 589268037, 425830551, 964653834, 692052918, 719593446, 596394772, 550006058, 844610712, 282205748, 122727055, 930930433, 337447640, 191625925, 52575380, 53231965, 472202090, 311225039, 841309396, 603062921, 690482486, 113736678, 629176742, 155000546, 201780457, 44025517, 360426459, 523380025, 326841126, 789881916, 255943810, 127989988, 209344409, 945404384, 702933861, 817305923, 913245861, 465325991, 275660007, 286252154, 650695045, 88821998, 303044398, 560887854, 91537658, 161868280, 220721064, 206940695, 886983352, 833426741, 522478918, 127593734, 956414644, 985291649, 981553612, 141241771, 484999828, 35616192, 847780725, 624279160, 987462431, 554574284, 837506741, 724284369, 967219976, 262564774, 398899882, 228195092, 890218476, 974092861, 13725509, 901062173, 676857317, 260663849, 327815549, 425529732, 235213484, 845129810, 871593969, 488453430, 263684190, 822634301, 452910859, 308103011, 170491202, 798481532, 657082483, 27481284, 582160500, 285189283, 605907557, 946049455, 443728829, 185936912, 322453391, 848989172, 137484247, 484690622, 24363743, 948649828, 347214699, 445875288, 783111966, 655280373, 337836939, 318088956, 309691417, 616338846, 570137038, 810487350, 671672673, 494070580, 298813048, 150974672, 593229115, 474980102, 276111493, 327038699, 946771302, 488002969, 882575341, 951193110, 619157932, 939138982, 905947608, 493348291, 823590712, 254948996, 671218075, 522201002, 286982116, 572471374, 845123692, 56867156, 369055154, 602802818, 477501187, 384570354, 55511899, 712748203, 63697566, 387842505, 248613350, 621130260, 939009210, 594974556, 138489377, 504894651, 891691113, 968678354, 343895842, 739576306, 800572898, 32705483, 54273569, 938036835, 331990297, 750527486, 843556253, 551218935, 636870273, 527420471, 529589850, 767910282, 793844288, 959427502, 500181503, 650005995, 658657053, 357918337, 847326224, 724433611, 178556889, 934155578, 433255441, 523179543, 481629741, 708596243, 192233432, 561207592, 327763094, 534806663, 470239270, 144057628, 810692598, 972716813, 548194715, 268059178, 906236711, 23584860, 254427518, 932674017, 313586608, 15267960, 112746810, 477254040, 908400457, 514890388, 974551620, 115438708, 451318199, 944527457, 390551514, 344970119, 781706289, 33354586, 800629109, 15973392, 918105711, 728310209, 91473636, 200650991, 88529598, 549394131, 716919209, 665450907, 985421369, 760645574, 764135204, 911099312, 141744537, 431973777, 770713756, 434188156, 152911769, 857747487, 459588509, 657467467, 805421333, 497715218, 979478163, 79018844, 421111554, 265475872, 915543584, 48785140, 834228277, 618001321, 37485372, 828129822, 822970976, 933873370, 683156808, 62334694, 151346579, 873144704, 332956895, 820174755, 648071410, 418143207, 168214690, 763576374, 521679717, 948012310, 606108246, 659331199, 516862251, 813555137, 715378584, 382116463, 917871919, 375203924, 560866625, 531673745, 935228417, 465146599, 546182391, 666277920, 366449178, 383420732, 990964811, 847457489, 304161584, 658285111, 284116125, 338108897, 457659771, 968766885, 661887155, 32651377, 277146094, 490176758, 127023121, 337949023, 282918717, 549914651, 647165696, 499685101, 727072710, 441040758, 954046849, 289716984, 24438617, 584147106, 206601205, 218446231, 855466085, 599041769, 992954887, 864898776, 488595263, 620714254, 902191077, 42230026, 489246232, 500224586, 906339939, 534114984, 699870415, 404002217, 971536983, 609053185, 640266528, 466789232, 765618058, 783126661, 400570787, 540999302, 312024936, 373044862, 167384677, 141977859, 198746527, 385000385, 97554660, 883642725, 347128848, 574338065, 757321426, 393989508, 980944661, 396053390, 591152478, 920131849, 653898326, 488558887, 160217852, 870875375, 988139298, 930932941, 41335211, 509204530, 660760618, 553863066, 490919385, 561536535, 567809444, 556127427, 354153144, 349995868, 167262890, 369136559, 245707072, 199104099, 694960885, 689569643, 529679097, 164659269, 345114852, 975294724, 281699450, 834143084, 620201896, 969715001, 328771194, 45820583, 780668238, 141185527, 599480152, 747390845, 236055014, 202224068, 718328832, 937595600, 830557875, 684535341, 409086175, 198495091, 159834084, 112020678, 224432558, 17151023, 111074342, 619869312, 332081131, 393453326, 729200262, 994366314, 661933124, 768889446, 519812726, 105133644, 52985774, 704921104, 494803443, 813500458, 108928972, 30446925, 935552205, 593553153, 115429004, 745005141, 42191478, 416235060, 957515884, 302408413, 934482001, 55342977, 62280744, 10037530, 537974494, 457780005, 894331541, 582524427, 360029924, 95504912, 262573143, 824991333, 450184411, 9349845, 771816619, 835309593, 456067554, 634413260, 211626329, 377718299, 290932529, 954085780, 370873611, 165881470, 923755119, 283821773, 361407771, 226380983, 756852958, 255782126, 749989065, 274095310, 237547682, 121727438, 663674751, 477951483, 43250497, 641857496, 888476609, 359504815, 235251599, 594657589, 760223705, 968738976, 541132210, 546495194, 527937879, 581383954, 935867129, 794785105, 485692673, 514135985, 928328990, 554716772, 601429458, 904813070, 737881592, 965234032, 336631720, 261385135, 165365104, 789885224, 124033288, 662606203, 350027523, 251996463, 780038397, 871689271, 326737865, 334035835, 527256304, 704603529, 654191654, 920445247, 639235934, 92690336, 370855823, 904362408, 274920000, 251830576, 697998812, 990087245, 744288943, 966569931, 615110591, 503907701, 143922146, 366275091, 195257979, 763258249, 346779259, 941157974, 154698399, 161989571, 790874303, 4463137, 836153979, 238066486, 61890835, 255915863, 110148906, 927221710, 233864142, 145366973, 56314991, 529084541, 417147691, 514351097, 341022033, 661349618, 463003414, 981288895, 446055641, 471732668, 110412256, 847755155, 874686226, 28301778, 469271488, 50462013, 459473193, 518648746, 620009103, 187419504, 391487490, 295957548, 81351671, 494761642, 312869478, 887343046, 736573345, 109565510, 254081044, 87844594, 222746846, 909567724, 881423033, 495787132, 941901216, 78777278, 941229567, 426661257, 8766748, 717532600, 759825180, 655832394, 206377959, 798213726, 860894228, 737106089, 776129358, 648726858, 714770269, 645093883, 408032106, 62379145, 609128775, 833348103, 802371275, 7087328, 329480606, 789033456, 706185013, 841271657, 115967306, 375951530, 154057469, 404001082, 56795875, 653023215, 638094905, 938758177, 55345594, 909383408, 676802993, 302258968, 614298374, 866297902, 268103611, 678296029, 861435441, 349815054, 19125346, 353132858, 455262762, 677634039, 371563702, 501356186, 720417875, 274556754, 199544652, 148414091, 18438631, 395321686, 780294169, 795221844, 367075080, 927542324, 485514329, 317957764, 878268571, 527014945, 658201871, 207798636, 725843655, 152671415, 792327187, 234870208, 806245485, 485556730, 5199918, 655779357, 261706999, 923577160, 206314759, 601055008, 11703804, 871549736, 650446718, 624610346, 720274409, 158696123, 341223298, 976411455, 214194556, 814365189, 512536076, 636972582, 789999098, 489020177, 603254636, 344526539, 562822702, 544624769, 204718415, 511139536, 538265498, 853622457, 937853594, 906476350, 99190183, 303464689, 713079846, 776484371, 418144830, 890576693, 89246592, 143534514, 75944013, 642099102, 199585624, 967423571, 244315452, 790912844, 729358495, 880764501, 596572163, 75812709, 250290445, 94703465, 982766927, 38507816, 428772104, 306967518, 639604468, 962556069, 724188224, 17637726, 272501403, 529587966, 120881226, 394784047, 938229859, 485080081, 651171480, 154860784, 116634233, 597038502, 573567285, 132600221, 907046323, 814843214, 869717139, 914759884, 683225709, 775972824, 729153454, 563512246, 415959424, 726575, 998646601, 273677386, 735615379, 359279652, 222567870, 577925791, 992583651, 727725557, 561411759, 392318512, 339914773, 483547320, 788873075, 219054794, 542320846, 758923198, 152687133, 784257877, 977505743, 175843386, 987928855, 493498508, 975671139, 13336519, 139696753, 360868402, 682560536, 835510011, 817457046, 728428809, 271638310, 525414642, 9942780, 710763609, 266371188, 597111953, 264446726, 896904886, 444091750, 369561917, 658078350, 583600006, 28660311, 444151236, 800993245, 344083224, 927793867, 828572658, 192978040, 972255920, 954140287, 436101248, 603798081, 686576667, 708132577, 866299411, 177125867, 852532805, 615934784, 937313293, 839881262, 884124204, 780535277, 447114324, 215861122, 389844618, 942658196, 486895528, 23935616, 237383791, 218617752, 556328759, 436568828, 281802058, 552539718, 304123698, 962154099, 823195607, 176258908, 132889992, 323019488, 172191029, 900089657, 624466490, 466586214, 933465121, 74868003, 987272897, 996428752, 558201820, 147567638, 868259414, 894916002, 658068344, 881491995, 769844218, 565335154, 411525557, 115752533, 544265107, 192180075, 230108762, 336344631, 10238140, 762817858, 728478272, 323461212, 328543293, 144592356, 366370031, 175763453, 450359175, 335189674, 677455932, 228959317, 916287530, 682082266, 873657640, 780239878, 155021046, 530701732, 343220611, 733403968, 13645284, 233150115, 842997422, 119301702, 368204623, 237248271, 165835096, 578609725, 317423117, 914063868, 945691725, 487791423, 162360474, 693559617, 29836052, 738680212, 40394276, 778364565, 683597734, 25951031, 678635942, 409306317, 257551216, 418967160, 752440965, 980178871, 964157696, 893601286, 73194032, 88679409, 282644390, 318595099, 961246002, 646332224, 585431456, 88499928, 842881228, 413449171, 735265215, 733077280, 476787243, 429351867, 902121761, 767425926, 352649939, 332847362, 619769283, 286886601, 974993424, 678813502, 930198591, 609422758, 190125297, 789636034, 2834383, 186498506, 842388593, 695772524, 245629732, 134554, 663367350, 865633723, 885138254, 586492593, 327970672, 479963026, 617208107, 282385401, 743776369, 852568330, 423038649, 841774039, 881834118, 335481518, 849566198, 923616131, 619284290, 355963245, 148497052, 930749854, 108148773, 776290556, 763770357, 659525852, 197398213, 48027336, 143125875, 976671212, 317768225, 342994741, 358820283, 128409409, 115715625, 884912155, 833645199, 428818093, 20569179, 532243826, 543642342, 204391808, 268253494, 795602211, 679897587, 468325692, 468111322, 52595836, 478805605, 141691993, 719239609, 31875783, 653702049, 279520619, 333366655, 28858134, 343406621, 859748179, 436093397, 713626045, 293329475, 676857489, 161483681, 245199259, 350939572, 695282654, 727545266, 236291545, 542478523, 319922447, 371927704, 520210573, 404914057, 776130437, 312335773, 610661694, 963572411, 426260522, 701133829, 65591154, 252518759, 433762579, 580354584, 365536106, 872606417, 672267756, 88248225, 924953095, 398797475, 71755749, 344523202, 559864384, 430852769, 776713002, 53144270, 429145866, 567184634, 464577895, 586351802, 894351472, 698044342, 497896500, 639548698, 231263972, 165290253, 20187949, 630235000, 697085380, 849463774, 832021918, 689923951, 413968453, 798986113, 122324640, 676468886, 385524658, 337373902, 525349943, 225919741, 677096804, 218685042, 902622093, 677160339, 879015154, 682560418, 636558203, 917102018, 37596372, 866557669, 376463897, 500355923, 555115304, 644793309, 202103244, 513579752, 11250660, 883982613, 782089884, 936326414, 833042395, 107837044, 253056907, 560416421, 780200310, 102635874, 452147267, 686068398, 379143528, 495882787, 620737252, 280254481, 334224928, 467730371, 760941069, 42105874, 378157833, 970610597, 380726916, 414575644, 749301499, 814919342, 381120392, 581825493, 144909936, 355411266, 34206405, 983710743, 790227698, 92656472, 581721928, 518478811, 608265492, 822234023, 66389767, 154903432, 144545575, 438059251, 511227209, 238898492, 226291237, 314119061, 352448709, 753577391, 811269436, 867408776, 779563910, 769890318, 465064668, 704166855, 262590172, 505825571, 157893851, 813434300, 671963952, 509574956, 994735316, 312601441, 661111047, 1818299, 579479990, 418257471, 94486215, 156660434, 965105148, 427285606, 370117411, 550769614, 161365467, 745721697, 714303769, 451287859, 717991669, 665033448, 449931036, 60952398, 329576740, 354631204, 396456090, 801500424, 582639281, 616198475, 929577899, 726074633, 712889177, 430600337, 623479894, 525347996, 92141924, 988010412, 18402649, 744133781, 838467170, 378663591, 322284229, 966381645, 640854825, 546886666, 556192363, 867399187, 529631605, 129479154, 753552425, 805245116, 852455381, 610745160, 867113496, 780705224, 313402507, 296605255, 931016357, 636074142, 1128596, 280450928, 975263721, 833184486, 668274518, 898467126, 83913289, 886324135, 641832661, 759295992, 247585439, 240493902, 656278202, 628155353, 98005253, 296216683, 795710096, 824776513, 971267045, 252578605, 117202815, 43208488, 544671706, 950463532, 358407232, 237934809, 500765816, 673324550, 652181764, 884313258, 927439352, 566032496, 3423548, 582566290, 865747983, 265390187, 7561626, 367089754, 526263230, 22587493, 363259792, 950188655, 90577308, 61176612, 590955358, 786476393, 714920274, 855084927, 7723011, 198956099, 506145490, 492152405, 87220770, 759785275, 551694121, 32596099, 389227069, 247154681, 815007814, 408296469, 299793479, 851117591, 842355519, 624255275, 824672653, 184138640, 331272936, 669166760, 523141368, 889456308, 925632525, 107467959, 586419968, 713171630, 686338965, 146490766, 616292511, 27361010, 719137062, 397463397, 220638586, 28029882, 521569759, 624564270, 704020841, 468255452, 448396543, 684195526, 796973938, 872696597, 658622741, 974119241, 913481274, 208283191, 416917111, 560634807, 302973026, 505926060, 597015673, 968849448, 855006140, 862931333, 100175924, 380809992, 521914991, 139928466, 913111648, 909202318, 252860613, 633191037, 900567507, 359645344, 404088615, 348937566, 278613466, 554914748, 952547462, 982285617, 866426789, 845249546, 940127945, 993863696, 400629891, 349852570, 165709971, 417737163, 889349461, 558071597, 91285523, 796931778, 744314143, 27229945, 231594945, 847135675, 893769562, 769615232, 191113433, 267120688, 95528203, 289147927, 113382826, 194894341, 269323758, 220217086, 131751590, 833455158, 544933205, 178004326, 14172812, 192380289, 446976683, 353296159, 656908225, 545124658, 84480014, 579345240, 281017741, 510315165, 671001689, 613546625, 503618405, 531838382, 392662298, 287954956, 690189013, 161593934, 287834338, 349002870, 342783832, 859802196, 485703970, 401568463, 570035142, 107642187, 221174266, 132523567, 896184687, 697045043, 526195605, 540980715, 642762033, 99965376, 493807317, 872662397, 238979200, 540774438, 540129535, 874744558, 369035475, 142164878, 750477080, 843756963, 677159075, 763420729, 148989886, 213406667, 772933817, 368107812, 197220137, 895584592, 213708808, 199829018, 168226387, 363526180, 904141787, 572432440, 219309161, 990457287, 581308715, 551743496, 299061038, 171394532, 814161808, 440260313, 103251636, 358944316, 696039756, 835096861, 540148758, 55242900, 866646463, 237115594, 144466720, 161930027, 402854859, 764971006, 195793071, 256512859, 995644430, 807895367, 901169354, 193158038, 538459917, 841627649, 872142405, 807400660, 251976672, 672099406, 276464871, 692292142, 591536487, 555744580, 133323182, 384743038, 959694248, 423803297, 925666370, 794271799, 418750726, 888422898, 477622774, 612593557, 72847516, 262247327, 922685860, 558678976, 950377767, 54545539, 311427479, 358087367, 881775773, 517336654, 236362926, 45850404, 3837520, 220453432, 165581294, 988623122, 711957647, 811718583, 337448536, 668740873, 636229894, 575579608, 847366764, 669815663, 827731200, 997993139, 120734879, 284727018, 963246356, 226294446, 904577972, 528246041, 524339667, 574355425, 697025704, 48508563, 406836153, 471660349, 18861069, 109631126, 140466847, 922654350, 274441159, 134332846, 238212519, 771620294, 725498084, 835436466, 982643830, 233600298, 269571816, 280562273, 106117517, 919622208, 107318818, 244851827, 717431444, 58514827, 157799830, 309815167, 63927239, 373690665, 794572413, 310577157, 355410608, 432627317, 416171802, 455632007, 655526923, 614124950, 580101788, 502100281, 298425726, 16607396, 896344420, 264296878, 285851733, 314189977, 560140952, 560017963, 717800217, 397118686, 722655690, 490093873, 164887100, 381326226, 545927925, 976386116, 10867070, 704578629, 614584863, 277211208, 137466950, 594596164, 973677004, 26582466, 471113764, 186334283, 442983986, 569985194, 339032595, 943361175, 18815993, 624216605, 247317155, 461341939, 743371734, 678886793, 215720661, 8384441, 682668532, 456324885, 328874079, 653159237, 204653387, 779415074, 786122629, 210381472, 665279912, 282483972, 474660127, 548959058, 627140276, 18727911, 50891954, 296425657, 486523299, 898084227, 255393209, 943723389, 296427351, 267961740, 116597973, 592519597, 2034305, 517355869, 512950020, 335775059, 663078606, 302720467, 137170637, 898456990, 926507011, 622118146, 824003105, 534679571, 707663016, 843930347, 459959465, 208300759, 793100273, 979451543, 868617436, 687449402, 866836518, 673966346, 344919717, 210731807, 873443119, 559959750, 551718232, 943237381, 937403367, 496713351, 545040074, 615835463, 756724336, 515727166, 228065678, 795213224, 216287953, 412624793, 61836563, 770476793, 420143146, 136396976, 7239374, 641454446, 27344316, 246928736, 381217652, 526053097, 527107895, 634060870, 898270493, 139853065, 732904758, 454833604, 327876685, 350608485, 455789989, 56266249, 786191582, 595434658, 101587362, 305329276, 978148482, 335149875, 964936126, 385069692, 169103905, 534832091, 561672655, 578578567, 318320747, 591952940, 693663985, 395756103, 466050243, 246760686, 352295045, 856679596, 619922521, 160012579, 59049434, 76217345, 111600891, 591064016, 179592410, 745932810, 844257003, 287054886, 120646771, 494314507, 247003172, 6418954, 768939750, 503110789, 984949200, 675189340, 560391906, 325765946, 797205991, 397257800, 436337703, 540492699, 838101130, 683202086, 158670941, 20998812, 934344478, 339885465, 658769125, 82675849, 411675874, 802927302, 391686414, 796403716, 949957208, 118026180, 116458293, 496967890, 375221835, 263479296, 495655606, 220011514, 970514698, 66870702, 143378663, 809931163, 286382473, 471452175, 379001757, 208752998, 573320374, 717710170, 12508541, 806403206, 41247871, 150783185, 550711019, 588754557, 835622990, 949145265, 592409001, 696507792, 828057201, 493921028, 487343676, 985010320, 335550750, 539371083, 171393569, 348990940, 578838142, 485282999, 487513036, 906430246, 932118545, 546831566, 251765657, 234641869, 188799627, 687669603, 285435810, 127196940, 679373047, 437646758, 782623065, 135710740, 539537145, 551074496, 345908897, 850568331, 355474745, 767608748, 520665293, 223130616, 83918420, 647196444, 282768308, 998313312, 715399147, 574943951, 800546062, 55035876, 100690578, 899787454, 743055269, 344877732, 770377554, 439246992, 421620909, 890124409, 903253326, 777177235, 45271418, 557188778, 718209350, 778131982, 232066290, 544799860, 710173488, 583196534, 991518665, 419070798, 573640005, 906394974, 293044311, 266274679, 321352716, 686114339, 374357218, 58517826, 90112696, 216068271, 611564548, 607477876, 989579021, 109152235, 287042669, 663801074, 244553850, 936316976, 805185859, 655665221, 144330896, 576097320, 414721003, 959361632, 874027124, 607314262, 115742944, 7212504, 160578513, 21064319, 845130548, 442019049, 553201167, 728286139, 810705609, 660449512, 883293276, 759316800, 415190707, 930586730, 519894570, 624754590, 402637620, 815005152, 96718753, 81693910, 826188700, 212672318, 428258073, 182620547, 154745459, 123673500, 512200168, 497008091, 931162773, 217129319, 793160460, 514347990, 644770896, 261292753, 2992235, 135060645, 257976899, 918310307, 256943206, 91615021, 939178096, 755729982, 885042444, 792670454, 208475038, 410510825, 17147071, 519330617, 111687040, 564069400, 788105028, 748326417, 463855820, 659943278, 120655964, 169127291, 781482163, 703077116, 390819207, 107022181, 437179107, 264948988, 955059370, 366535357, 312830890, 475574952, 864612907, 263137490, 259973489, 824650541, 938482686, 780349243, 3812826, 76479466, 677676416, 220322298, 395073927, 723339802, 170366463, 832596296, 508001492, 501313922, 711211943, 336495357, 887599122, 450775146, 879233686, 412318105, 220950154, 765649088, 972939513, 814999699, 246321085, 564558307, 134740005, 577961984, 838908126, 749189264, 644586046, 292599911, 154338805, 416488809, 501927148, 700613881, 195616378, 890100940, 486896268, 124980053, 752890042, 460159374, 11804513, 74245605, 189762148, 34341401, 389816553, 360772076, 514917613, 609691916, 875112109, 709568908, 173044971, 802652706, 303999389, 331207271, 428502887, 596634289, 22729430, 478250049, 836130806, 234515769, 517405372, 53709331, 220991993, 707084329, 197744067, 994131612, 963199653, 269297602, 690768747, 941167624, 938347587, 762838814, 231857753, 285894216, 68076772, 684386140, 261394979, 81929201, 679503525, 255568436, 503342380, 392605155, 237615736, 94895426, 200436686, 198520274, 577917861, 419231650, 417585513, 173063154, 22295193, 258379797, 669906152, 971131084, 909433863, 820850862, 242657966, 834386322, 511275502, 142813414, 194300000, 171163138, 412517842, 286646115, 345508691, 797705558, 772200589, 920308840, 336558510, 505614832, 127103418, 549119759, 978735047, 150781608, 168658896, 868780045, 522238984, 672412429, 126085594, 600802502, 120149370, 628463881, 595118727, 420390110, 433659915, 859856742, 630625570, 642562053, 998638457, 657512476, 614537550, 8646619, 961009501, 355782085, 234717087, 437664884, 642534572, 661806032, 715764650, 770536600, 298790530, 651827469, 119517296, 897793531, 96251102, 882334066, 311003153, 278102986, 517460408, 844875554, 942822138, 325604882, 819149742, 653944959, 638204046, 424182636, 738716723, 495254130, 99655085, 701724536, 193695127, 285613358, 390581628, 958409956, 389490812, 692424179, 288972286, 47832724, 546451224, 845196309, 713699334, 630766105, 62598893, 557585549, 591186301, 295144621, 766512706, 18956555, 857359493, 872955061, 17433952, 662669987, 664243812, 279411336, 496225037, 168622370, 921775569, 582930849, 241346470, 512455818, 742506129, 372263957, 241461422, 969081892, 697667299, 831041698, 845636624, 307501277, 26672450, 549811558, 166527580, 418645901, 516851894, 998405578, 534831457, 458621483, 499601519, 512120476, 137558025, 606029484, 672665543, 701101110, 994607199, 560431388, 616553949, 671050677, 817776814, 140497302, 661336513, 905698701, 253090735, 883192400, 656203486, 879452377, 85354062, 486310394, 125557268, 998456504, 157144145, 890324399, 987609926, 484061409, 705861947, 992411419, 806976956, 688710989, 864111339, 180530317, 507138063, 333806565, 565942252, 814267149, 762507053, 14774197, 64712226, 997466735, 963763740, 62861386, 118721961, 663208832, 329101405, 410706088, 587722003, 633910596, 123081026, 160215154, 787542912, 127096376, 597312957, 370423521, 957573992, 991429444, 126079270, 885944708, 351257332, 585674413, 493548643, 184461996, 227521037, 837577135, 687702758, 57372246, 50932370, 16439903, 516314858, 652400007, 347730534, 201813239, 243435686, 613447622, 731747273, 279292681, 328665461, 443549347, 212304599, 719847283, 408540638, 728239826, 219997117, 933353393, 774668089, 157761427, 422212189, 448906937, 147388339, 193412860, 282160782, 878235748, 139963796, 854072145, 713924768, 268284497, 408733643, 119879543, 740894433, 310164585, 120494324, 235772891, 909074173, 915604822, 860558651, 127560069, 16418339, 467458983, 745446641, 401514611, 123740853, 932388005, 358693505, 878539407, 397466821, 190388381, 89852384, 525948469, 244600307, 118867300, 263297772, 662333211, 816911229, 550870382, 689561230, 283159684, 704040187, 201115010, 195451057, 182851457, 136158615, 197157641, 32739661, 621228410, 803804484, 294520120, 689706441, 820059339, 783031213, 826536827, 886719150, 676512856, 148984521, 875395507, 911777002, 181643194, 224088989, 583633223, 966130381, 779131048, 641087525, 871366071, 661940245, 700489347, 898727342, 924610179, 800773016, 485152307, 686431051, 504204423, 395442454, 968053585, 172157874, 379445385, 423755705, 823902455, 952098650, 801946820, 97609009, 757083001, 738657161, 155179093, 950561771, 135045535, 51668081, 734705989, 549641158, 251002792, 699649945, 59674641, 352886749, 616388681, 488396898, 900794085, 485968705, 639762853, 176417895, 519337285, 925270702, 834203865, 591955593, 73190131, 439894126, 130644661, 768320499, 785792331, 751705895, 972794546, 420646152, 241823247, 18269163, 853755278, 975145638, 218041546, 565976162, 959482917, 673301454, 736547146, 795067492, 30806485, 661679340, 123194076, 550562532, 141497289, 686746986, 709479345, 277026026, 950366483, 870587675, 697235836, 440843954, 629404226, 614033882, 485534247, 986405989, 56141939, 105591029, 804157856, 429215497, 683309371, 29558244, 123957549, 399333814, 824997124, 77149123, 46614732, 808487110, 421083400, 802871221, 556234798, 480615671, 124612930, 213612064, 903784593, 136711438, 473140864, 250147333, 170361205, 353636343, 368470875, 563632781, 968191477, 141658065, 366735262, 284762014, 190576260, 284911123, 31820512, 828577629, 185216242, 206631659, 736308409, 630713159, 947896406, 445925741, 781006630, 833061785, 75922049, 360245644, 559974468, 927105222, 956490599, 452849601, 594815629, 481079766, 210892543, 375491835, 677478827, 495760931, 67076071, 156140574, 705882057, 384255065, 504800644, 324080805, 449576876, 204718654, 318943826, 416682526, 84514283, 537172579, 619026832, 236241978, 680176653, 419435494, 378789199, 676535341, 12265310, 396741805, 40460350, 663863924, 996743076, 292609126, 915959767, 680821845, 909774527, 850226076, 904294427, 981334455, 7975452, 148766780, 727036180, 152604159, 161459852, 532243380, 136768973, 813736928, 588322847, 460275437, 156659929, 384164322, 459792711, 789197993, 157445979, 25298668, 300541547, 275624858, 296638274, 814253581, 302554600, 335757562, 940220228, 37487851, 956340288, 257679040, 239065360, 623128864, 598966629, 857698337, 182567993, 758769081, 47072794, 232988335, 831727302, 993223384, 562154625, 210204376, 168360281, 12510782, 657326539, 360802458, 707788332, 747371840, 45900970, 106682903, 340275909, 461918962, 973728827, 498002411, 147524212, 12588997, 342699713, 324137037, 697187154, 287233778, 530623182, 343442892, 814797114, 663591614, 920504682, 965025180, 291767218, 731038451, 480024512, 499213241, 783279249, 553080493, 480454984, 748316324, 616578836, 901866708, 291918125, 268442132, 422399232, 141964192, 991618948, 687311922, 385090581, 319690201, 367544881, 930098531, 164591561, 650803010, 555263758, 83779439, 146900237, 757589733, 729481859, 531972538, 481644635, 172260584, 198486753, 145830969, 423751149, 567965437, 943045636, 527721945, 987486168, 929594975, 970035890, 38189219, 973879083, 316250132, 876828364, 432089123, 745224764, 936161970, 605090495, 513702535, 30275534, 332426816, 461999928, 48321674, 201587973, 257183227, 485536036, 30742670, 740831084, 189600755, 401581931, 800507603, 455602355, 130623156, 494145121, 591653575, 826843078, 160742165, 32421032, 428507686, 685951965, 830850348, 678854230, 61167554, 3236180, 819186472, 256266258, 836382268, 683886666, 407267129, 154468715, 43487745, 912034094, 152472930, 797447540, 97335799, 979734405, 712009182, 709156322, 301829159, 330815440, 75456842, 504992512, 817954232, 689742414, 85255192, 953881087, 792999834, 421210192, 394967242, 857257566, 712911392, 501241014, 367389687, 123622662, 109533883, 432834031, 973200386, 326772771, 65885412, 647187500, 347895086, 706717286, 725418551, 740806856, 24862874, 351285067, 390527051, 518457687, 887853398, 843707116, 225222801, 360337718, 761154283, 938264493, 482831094, 348950153, 36584014, 718131365, 348906385, 265871019, 219939568, 351697657, 737116783, 862104021, 240602407, 1888451, 63302800, 524761637, 828324104, 868169813, 358476422, 17256994, 779518694, 526055075, 394552593, 447899568, 159245153, 965883623, 533426986, 948467621, 351854515, 635880523, 738017779, 45171739, 75943535, 700608222, 474846112, 552022380, 337928404, 456516408, 911190121, 418436745, 537300675, 379935078, 280897360, 138713282, 822810109, 525451210, 755106241, 640057424, 506646386, 887443587, 266645906, 316090487, 720736107, 829043576, 896783843, 68528200, 134322177, 46902779, 156293984, 27257823, 897805913, 740340242, 21190808, 597674484, 11964865, 61406426, 538282093, 268453842, 954744247, 82753659, 423921795, 76007782, 301641512, 844079338, 825069741, 391888635, 896268228, 816221297, 557275174, 819696929, 662088954, 899295605, 407186767, 222768612, 251040281, 619620789, 155988346, 874242977, 154248698, 278116914, 85222606, 514444376, 651997333, 413135706, 332113154, 159100087, 146244152, 980681820, 723438354, 688550719, 870010746, 99136463, 116299609, 142104629, 625977805, 129473733, 528095719, 457520914, 838948913, 822877534, 254782652, 74528337, 486604607, 885438849, 536882877, 595071694, 602095890, 657548942, 110620080, 172139769, 188546169, 902450105, 170518421, 932077213, 91872824, 855310500, 395779377, 82701783, 723267962, 686620186, 812865957, 361675155, 930430074, 910014433, 598117605, 477568727, 391177255, 546671901, 7451525, 422006030, 97507242, 908621350, 276646098, 441340378, 761612078, 977167097, 535517776, 33292294, 960042418, 941361359, 526761060, 625069076, 346468942, 483367539, 95343148, 773351622, 639708709, 950449979, 875896072, 986769078, 994159906, 524009447, 63366746, 278143365, 493511489, 18665592, 244853555, 199670328, 167532094, 44614742, 987714285, 123310394, 555568844, 811221423, 529115883, 426102384, 261491775, 872040402, 495260700, 380460619, 497114479, 963655556, 734415072, 974422779, 585954832, 675966981, 20825284, 157566140, 238896162, 839767768, 969131398, 168048086, 798784750, 308177594, 857817328, 741642489, 518863069, 793063996, 797618900, 825227432, 124767150, 389551007, 608509678, 644735236, 584046758, 554315070, 636690325, 391694080, 59877482, 891783855, 921885212, 374062775, 581244502, 145308915, 720726344, 841206752, 662976688, 521930335, 765751625, 124446045, 265001079, 690591606, 180917884, 758935468, 412524527, 505095837, 83197519, 495161268, 451133030, 8202062, 510312950, 509927014, 278735265, 345314954, 835011225, 423041062, 785920920, 300751413, 405265573, 132659555, 202560440, 555380, 120711921, 491413325, 567853465, 358706472, 348573384, 114582588, 665278708, 14441499, 807094074, 531808323, 325220225, 906442910, 956496319, 511274823, 165055662, 622421877, 702423576, 291312432, 709751044, 92659136, 97745786, 458434033, 198580245, 74556624, 545275044, 512994601, 526788525, 353757659, 976028609, 764173687, 379039800, 53776798, 930202710, 170217244, 191162533, 287983287, 986084606, 529258703, 23476675, 645031602, 645468214, 937487306, 573882280, 271760366, 281451569, 320107238, 174822187, 296484392, 731372497, 604100213, 470176429, 467160188, 41974717, 315144833, 114573, 581677739, 375448603, 707922031, 761067141, 649686997, 776968661, 292705832, 206854244, 151494374, 764086016, 601626153, 426804000, 335022785, 621631786, 28057560, 816824231, 816913015, 909020775, 925712752, 162374104, 588671946, 523496718, 820774632, 544217533, 730083577, 220687823, 508510760, 252690720, 749779878, 661215138, 500048801, 840431481, 326381542, 698703678, 180046106, 316673281, 804500366, 265507583, 890202860, 9415451, 611403042, 774652806, 800745249, 608836965, 378751954, 672944353, 557327510, 499799983, 200137972, 942153452, 610956505, 81703794, 396304175, 377388500, 246048278, 352960840, 989465855, 330640360, 522974602, 403322596, 442774868, 535740368, 512407893, 922772322, 202503308, 794175199, 908312695, 623474292, 44213070, 822723071, 698539604, 302722882, 986985113, 218677072, 840985177, 609757878, 652230969, 340136985, 148759480, 639581308, 323454308, 873038855, 466905080, 781517734, 191276230, 165836138, 42699096, 311526526, 269785955, 221266185, 147765707, 898696074, 4436162, 760494264, 945527167, 6330213, 857882584, 160524323, 596481543, 953864967, 393926470, 461107288, 328988250, 168208237, 231045890, 139401661, 35875871, 183761442, 826080147, 865097046, 930720563, 691085509, 351537666, 527348754, 905333045, 140481469, 291012575, 152422504, 893283127, 321479711, 479676081, 151162861, 682939235, 391950943, 332243425, 505269312, 630573870, 354368268, 423499391, 543219155, 517341423, 146697891, 497975441, 532249182, 782853380, 222815702, 647801651, 404746765, 976660845, 535107300, 412224714, 28617892, 737516323, 172274458, 589396089, 901128430, 396113130, 161615598, 721376359, 421923081, 908665450, 358876685, 371821647, 503520967, 520387760, 365003135, 287963308, 117783882, 829729961, 160246849, 577528586, 987148165, 919091073, 299504653, 778748502, 270715476, 791762600, 625227151, 490495693, 475467784, 183874175, 854591007, 32145050, 443286314, 286610204, 955911728, 485540018, 716000431, 209371296, 597855817, 20365393, 878744125, 377463739, 100877826, 95965355, 303600912, 611077301, 190132925, 888585539, 505793294, 872933323, 483553917, 3594159, 739492139, 940005690, 305647306, 350898919, 960610541, 837051304, 653240083, 934771338, 123255740, 166028123, 199506701, 605863392, 103235945, 642299940, 863411139, 487421076, 529904730, 532331532, 97632426, 934515352, 280812305, 831932338, 615985604, 520104322, 683032383, 266500251, 122308393, 101938851, 908991790, 655281969, 210614275, 269510337, 165084912, 167906407, 343205212, 883616010, 122131182, 746500950, 45337505, 156589423, 959098162, 689402707, 683762306, 909290727, 357339343, 392986754, 720201567, 716697166, 314864374, 116666536, 563107994, 174496304, 811485446, 149137428, 951298000, 969191679, 563308411, 256280019, 912273779, 372668346, 831544298, 864410122, 153767557, 749822081, 355141238, 430909483, 477369194, 620430617, 875606512, 799182939, 684134580, 91803454, 532931194, 649697266, 844063400, 791142173, 556646031, 528706394, 169847404, 707789017, 822701182, 803602128, 399081831, 454763095, 965590435, 833850614, 513646592, 411945432, 66623349, 137053282, 134493125, 532343340, 569578467, 167810461, 929583741, 597973564, 457251463, 35375099, 225252406, 323628422, 123119608, 818977848, 804538010, 7100111, 199799419, 692740730, 855726859, 264235668, 566809712, 204523226, 794472598, 14758207, 495377669, 295239356, 150086737, 541707035, 301030815, 312892059, 958428462, 608722672, 77209918, 565951876, 249982232, 463373894, 52251322, 768243114, 836067583, 271250676, 112509870, 707688323, 90074803, 67518180, 926563826, 498372772, 35070852, 661008861, 976738715, 488250302, 423241734, 822083615, 820084623, 865620549, 450922813, 771548203, 861012334, 133146736, 266955353, 329152270, 504889707, 574951465, 148054410, 64741380, 414935747, 722886789, 39546548, 808101257, 346126809, 460956850, 20080306, 654287519, 894597654, 10682312, 87109199, 550610053, 643750527, 278583155, 361293501, 904735258, 91471854, 62103471, 170415738, 889831931, 729638177, 490807205, 36279682, 553066375, 125072926, 549331502, 546289442, 516607642, 367679037, 387736363, 209047709, 582286697, 692012810, 26113599, 921543976, 341418084, 128805667, 139879483, 813668729, 900200163, 174707539, 727240346, 727229923, 593339672, 3096505, 119229292, 753924154, 608803366, 873619662, 232713931, 592261657, 82605017, 369546140, 997556090, 442449209, 106244969, 611566832, 594794050, 852115124, 217485482, 984494347, 155952022, 644051577, 342550495, 852638479, 393490844, 590677385, 118022706, 363303713, 187586447, 265569321, 919948307, 214997363, 867759881, 965002121, 430359308, 779182689, 111178725, 739129594, 493189244, 17274096, 102196206, 598313174, 712897090, 24073167, 762166898, 176279487, 113546064, 649847244, 330447978, 992813502, 145663867, 598229596, 168198533, 32512339, 122069853, 25402165, 329275079, 542851239, 771013181, 834307426, 168665950, 9749848, 932020517, 224446790, 392865294, 379179864, 331922172, 303678946, 279198338, 511426383, 418343894, 625965053, 280644839, 44003238, 609516975, 173839114, 965720668, 449900517, 577675369, 302342198, 353744450, 663375119, 293704049, 149309618, 765319909, 9948413, 299850270, 60595456, 738951559, 979280508, 662801855, 990045532, 393882906, 671719411, 202062627, 149976686, 358529472, 351958898, 558102376, 955060914, 890600350, 586824808, 910818237, 534027817, 903558891, 188052119, 505896000, 211535938, 800166874, 929296484, 906947108, 973685522, 76308575, 740905600, 39408253, 395917291, 791900130, 866017603, 175606531, 977988125, 381047022, 822685131, 734030945, 29524909, 899889534, 263224348, 397101535, 264516509, 788872527, 513566134, 941912697, 648278136, 772588110, 978796530, 315231954, 790045912, 586166988, 828022179, 666985562, 475863864, 104712517, 903376257, 691692413, 127912170, 57206216, 135520698, 337606472, 602771590, 442936073, 453408209, 278711560, 455013550, 361181753, 963373669, 215150270, 581504632, 834777238, 472372498, 708083973, 322660512, 251272838, 483029895, 846195617, 370158704, 133714261, 66542895, 676818422, 771747987, 248670930, 968877690, 975877719, 86180113, 971889728, 788073273, 435669727, 623882812, 571130302, 856184092, 394048266, 608108307, 411556941, 338432203, 697194182, 527434874, 498060089, 47673078, 125234703, 492960331, 134277050, 486624970, 534887127, 419488242, 273188686, 215585521, 900175318, 945513006, 519965312, 792905072, 680285218, 277126600, 684366000, 965893397, 924356324, 4872132, 510680950, 292773568, 381007272, 727193327, 229617615, 519144597, 656319443, 232903461, 482552374, 448048208, 615947740, 949369425, 115552944, 476497288, 167051229, 232776159, 617603471, 875246066, 821329964, 887363753, 67645571, 289257360, 178093041, 559528268, 95780240, 5263049, 861345370, 436984717, 565845313, 535780022, 114710181, 178009102, 933199289, 775993269, 733390161, 553434053, 489790607, 893434466, 709029502, 710325559, 589771145, 410105437, 786062681, 382525396, 745451893, 206940511, 979249694, 299593942, 600454454, 165346539, 809284557, 191182480, 427854760, 462924391, 954142511, 469726040, 148996976, 906308617, 47860301, 47070708, 507030084, 958813770, 898860792, 630540448, 771464215, 453158597, 61019096, 670834063, 423286062, 469762703, 920652753, 947680029, 396899237, 88208368, 415723430, 825529528, 963308396, 822729692, 449781205, 963025368, 44574836, 33610010, 101192086, 76868486, 49311149, 530138154, 205951225, 393396846, 123818748, 139785043, 260941568, 53589096, 326019506, 137834076, 38621406, 675507423, 496574857, 796434257, 462548848, 927199583, 675910236, 885165979, 485320286, 664452332, 456570627, 392065357, 631517009, 764979386, 819217658, 919283138, 411716941, 506693934, 815309765, 570462718, 65244372, 883762037, 199626913, 384691788, 450710655, 561726685, 568072421, 453776098, 782622941, 675798792, 117922332, 836109198, 583452283, 962921058, 209020979, 3838248, 586754951, 636709854, 741663078, 677283036, 403550986, 355704443, 117982257, 30609151, 94787619, 66496298, 81344118, 35869029, 831406882, 87176870, 730018388, 668481106, 151048876, 938550633, 397804828, 635435640, 634903888, 78301720, 350131455, 464002839, 963241145, 323108636, 660503469, 4607852, 221248807, 412946438, 232197182, 944784530, 99213436, 426032692, 928570046, 110536325, 164900913, 75608871, 703725318, 352667419, 213344854, 710497746, 209668879, 66036366, 725011991, 726164681, 97259048, 995596573, 62922781, 845908030, 631804554, 930014405, 765868378, 260804418, 632735113, 681765188, 32369523, 560596472, 435527163, 920476819, 498380801, 455635880, 314402734, 164039753, 653097031, 234520144, 53252601, 864530152, 241059723, 793901420, 22294062, 473004832, 900385183, 636290446, 382317257, 327699723, 247897203, 192522539, 544878873, 458231160, 361940607, 405247514, 437776251, 47834983, 948093365, 942072851, 136944223, 843736851, 813983538, 50147770, 200344198, 188201318, 603309834, 445362615, 550299445, 605664535, 834480757, 974771418, 543109548, 785595273, 814968547, 151231670, 671888685, 649951863, 557455534, 413033755, 261706446, 193522170, 579065517, 660932819, 238516109, 62156129, 625680547, 448945114, 604217245, 783069754, 89061868, 262265403, 291832697, 835840543, 332807097, 981215162, 283612233, 859346767, 430595809, 181044798, 596707128, 924585716, 436138735, 727234557, 37819152, 903503112, 393382650, 474063013, 389612290, 115206652, 893131983, 682958875, 887714613, 804780768, 215575142, 294386322, 20226731, 461761340, 285396087, 60196635, 877597119, 539543605, 267655134, 97381795, 283363798, 595306579, 335901997, 839892248, 120791423, 246490432, 838359633, 596041881, 52723994, 670650221, 296253918, 922064637, 105185482, 261254216, 709991103, 239333631, 332728968, 186489706, 892988831, 793371888, 834738434, 654698134, 342211632, 704340016, 140400514, 591111380, 901116534, 360166420, 75097687, 697361393, 431458564, 220434513, 169716055, 255214436, 387746113, 902468215, 873015685, 939528255, 57298761, 80117861, 925530043, 663587968, 347482439, 700312850, 10373265, 34945136, 247823178, 864056222, 223714347, 806859100, 485764608, 893522315, 130333717, 518917052, 850029792, 218726392, 612628659, 195621432, 152971427, 783570107, 338763703, 442054708, 394691598, 9665967, 30988218, 281140099, 715750295, 77929907, 291531999, 219223214, 989588354, 703901668, 965066206, 165362579, 344669117, 553236377, 439740335, 200992349, 205937852, 482109486, 536111014, 78432698, 834151737, 320678168, 248342587, 455354763, 779334573, 12044960, 662933947, 615227576, 175317848, 294964638, 788404764, 344732477, 306078147, 604691378, 646979350, 971850357, 622583767, 380161623, 783755390, 115363923, 208197686, 262029556, 818716960, 86372240, 550277712, 785439459, 786021980, 343427004, 819855594, 969194367, 447564537, 182479365, 315706693, 909681886, 676320199, 660436818, 304016574, 608517904, 297681951, 79089027, 588482856, 676888712, 732636595, 774335478, 547470560, 488905146, 843708425, 827714143, 324301208, 285351635, 319852414, 91072573, 731765464, 938981370, 780681722, 377624508, 262915195, 749233475, 333824476, 985984502, 571806944, 774787299, 654479707, 122263395, 486106749, 97094718, 633979293, 444845848, 828755730, 205468378, 97062621, 654038114, 103447877, 768213834, 539869607, 20543563, 869145278, 270905002, 153705221, 777201988, 464020839, 620648630, 649397388, 870829017, 390468210, 838135909, 252427001, 248588119, 296257902, 175142551, 559807393, 743670367, 235917553, 153115309, 762861494, 617485066, 587021971, 231619501, 838756564, 625426979, 115059371, 463989932, 946889190, 448013998, 308395155, 868889915, 714675476, 690863247, 190650087, 102578832, 798607340, 40165098, 639083365, 252650374, 772434556, 696273497, 793034798, 377288397, 903201102, 170975515, 130743943, 81938584, 573585810, 788430120, 751604271, 518872247, 683942349, 358623787, 878212000, 503669951, 850029038, 958868811, 683496743, 341252802, 28464094, 278960021, 565153267, 460077945, 761374792, 534522707, 823001787, 893131409, 941309641, 186807416, 787015052, 498646997, 162016374, 823529919, 724955639, 684073611, 124667487, 162739728, 609344849, 946304725, 684811219, 30216413, 393520933, 662100860, 563685951, 171353284, 709607368, 161957491, 343781482, 69578541, 665284204, 661496937, 526151133, 618402054, 198759500, 639297385, 165736782, 549120001, 985985484, 560320075, 185247074, 47024685, 752225827, 521744812, 79059974, 632186030, 865955612, 726238812, 45731729, 68758644, 699335187, 711662946, 192249408, 693335003, 668699939, 897782736, 550449511, 838513974, 924271171, 14926333, 142810876, 122782919, 497244440, 611657799, 136586629, 593639474, 74991529, 475768164, 605451096, 707405961, 702474607, 445449918, 126321504, 176605843, 685466513, 805673855, 204048956, 120611170, 57446077, 832601212, 744220322, 404985060, 264257243, 530086674, 84664012, 196214932, 2148813, 265848177, 351243715, 729350812, 306107473, 455657370, 19166278, 682331074, 986808145, 876513127, 705400987, 732422851, 380176595, 307061171, 422093752, 580460817, 164285381, 14156122, 699246870, 749366601, 977133748, 105184685, 282878702, 641749126, 219109062, 370973880, 393254035, 502631233, 290614633, 902804276, 749132890, 909593848, 44968926, 58446543, 344468204, 68626207, 378877379, 758835128, 554253154, 432020360, 876766111, 213357286, 645016510, 416150453, 950859710, 303230706, 314225118, 430185033, 988225915, 646915656, 637657630, 108196272, 495141717, 882827017, 664872694, 622765102, 801135710, 12529830, 54378958, 248389694, 271294537, 649234826, 898546598, 618488957, 53531785, 853675267, 381229124, 429122569, 467180000, 332450923, 944862660, 706457811, 941937397, 41791503, 981198298, 785734052, 305375120, 28136883, 67099973, 172455123, 696499132, 659838802, 360539654, 151564263, 372088507, 686858180, 62808423, 439260975, 538906892, 349418519, 837801790, 295496703, 321086866, 467808069, 131598722, 198133725, 992250677, 821013820, 722517029, 294489623, 156299786, 768892738, 644505026, 338511053, 543542927, 664272911, 277428025, 908033801, 681710589, 891565533, 58503165, 342601795, 645875711, 270490786, 824685359, 126638518, 585357409, 482025513, 233718524, 694110187, 335557835, 701340646, 342133506, 712369178, 427104393, 448115195, 186111367, 253184162, 737879216, 870454702, 642215759, 368300727, 830254759, 425840047, 56553671, 636883372, 372055318, 689009401, 964107599, 57537022, 52209559, 758177178, 962531059, 532018915, 858740680, 900554377, 274296994, 652391995, 998660262, 191576574, 480119704, 939960801, 869248613, 152971043, 758095770, 900692167, 449843867, 491525185, 216074741, 174997839, 134131669, 222709199, 216902571, 949787781, 91675634, 659466297, 654968597, 343337819, 174604107, 433386839, 11768901, 213871759, 162450871, 395841884, 945425558, 252580543, 590627509, 26250196, 288406329, 640643761, 12654849, 738855025, 254630583, 922581325, 571782921, 419123938, 595901417, 337054448, 449558060, 961084315, 660855410, 533807549, 336893224, 105430308, 123443722, 467147682, 786457124, 42873198, 292442675, 899475924, 546180422, 377705163, 687854913, 606468108, 93793136, 986691283, 689605986, 760022041, 184471932, 214929934, 912507743, 125211025, 53770279, 137142527, 130929298, 57928497, 728521386, 301451488, 375369230, 452732094, 500905755, 364541891, 856818304, 607558589, 404173382, 639218406, 638055848, 796057173, 397406688, 883358064, 473061671, 469336154, 461893355, 768736434, 145908771, 931737923, 664674258, 315708173, 447037328, 50791878, 237473109, 569942051, 779934912, 646617388, 950837772, 808440183, 827449255, 979209993, 270096907, 429343883, 886418236, 32210279, 812774753, 72747033, 249539218, 28657737, 244080374, 772839708, 841643005, 638741916, 227124351, 771815519, 132961635, 282786276, 649318544, 667362175, 792588844, 82568475, 134793439, 513364045, 289127764, 389466968, 159930654, 78109287, 386364248, 673791556, 628559748, 655330698, 126735060, 738211354, 471210633, 206062921, 399808869, 465372931, 127484426, 94002593, 597789742, 816797021, 397653956, 905444091, 70860012, 212128612, 966922168, 91125661, 125232203, 165865556, 434007941, 353092854, 496424512, 558821104, 764756336, 382313649, 283105393, 830828253, 78836287, 654652764, 7070075, 315397810, 681263142, 110012769, 436951705, 57460420, 893567808, 761291410, 108834561, 350992402, 514098228, 408757859, 456602395, 74197408, 505986409, 773530482, 851691121, 865311962, 782084754, 78195629, 278596955, 985812969, 809272655, 132047928, 782188664, 202467505, 444234803, 810997061, 313989963, 363098002, 470043344, 676508288, 125678334, 219939660, 685438009, 197480567, 369775685, 843404420, 683717117, 486096370, 97221774, 853654178, 247914254, 781274936, 622933836, 199062799, 214908304, 385612535, 780209373, 406171262, 48619043, 580795399, 831251394, 510398718, 165765475, 611324595, 769365784, 65354339, 805607711, 570829448, 862851620, 905019050, 995866970, 140129, 579164963, 14229804, 740879098, 120647644, 502846948, 867303727, 541528950, 449504647, 306544039, 11940707, 642956858, 258851147, 287318844, 343112788, 999711208, 213360260, 266747215, 376340754, 889248699, 139199558, 750445020, 321748489, 539576572, 836351604, 644306333, 640194443, 970452125, 231385702, 383359417, 690167070, 315143876, 335102251, 215889394, 57556899, 863122543, 410850717, 555404031, 208983588, 625441155, 604746055, 71526639, 264059489, 25667075, 820434804, 253637122, 305268724, 326408668, 597973898, 495150494, 546845648, 700520528, 916088483, 336075659, 280578906, 872374756, 277492844, 79127795, 271207718, 145248013, 407944680, 343369933, 592415336, 672207539, 17575675, 221721814, 869193865, 290358584, 702147987, 690641563, 741027079, 791051283, 948178884, 527066586, 548330671, 586747863, 677227032, 896668582, 735242632, 109375448, 122033636, 511375633, 413354759, 446220699, 19299587, 510544817, 858088774, 316235241, 490488170, 475383005, 268349966, 924515041, 446601146, 197692157, 382388761, 223121433, 356754169, 522320962, 170231145, 546931612, 850753355, 378550398, 329276811, 218011561, 741998680, 544557707, 98326084, 105842004, 229546389, 192072466, 246390433, 508107973, 684929083, 579185527, 528538033, 202531816, 92374018, 981664217, 813451785, 592961282, 698110892, 306600424, 378931771, 121062082, 339022334, 802879221, 843661085, 542452934, 315103169, 618950195, 489762023, 600685367, 438108068, 566907464, 484505773, 671034024, 889003653, 891431743, 943644126, 414870314, 793414243, 368983687, 436595391, 607493434, 987144403, 316039693, 350930736, 480879397, 201826265, 391486837, 905066272, 733439772, 390820250, 377114661, 845699655, 366641901, 336281548, 232665619, 727676418, 528033362, 61704929, 485989878, 476815983, 244033524, 86223187, 813961758, 111634696, 469177159, 60777177, 700005379, 924640869, 905971007, 664975842, 962296711, 488142225, 446072295, 690900284, 979845219, 550977859, 409817720, 503568027, 23704085, 351477769, 220457198, 66011545, 861662112, 160930649, 727532310, 186722819, 991846201, 648116264, 893249711, 171552158, 665187583, 255955291, 761799441, 5939428, 152698191, 559555937, 637376623, 158015588, 718629765, 178528322, 684099949, 498424249, 959401737, 575022450, 399670781, 473515045, 406706173, 614227150, 103717718, 463122137, 505204233, 576830939, 903146049, 366359997, 240640180, 592913432, 771858640, 799100493, 588740000, 772914789, 167404351, 911365638, 501771313, 654061224, 606197075, 101931778, 339745119, 97848327, 557448685, 171465213, 652340914, 50558745, 792411994, 589079022, 568067918, 305277302, 29456354, 45484486, 836981516, 156054981, 598543728, 862243677, 514740716, 771854364, 260218292, 464713916, 449099007, 319200211, 626865981, 806407502, 301180205, 229229754, 280420322, 376066008, 549487630, 559782816, 477693154, 966760889, 943054686, 594909656, 400322625, 451883599, 743294187, 625570754, 303076477, 851364162, 308777483, 621800605, 780071205, 604713132, 86320945, 840180384, 675753931, 138495209, 978682396, 217707559, 680006034, 814494972, 275743922, 764169243, 918856977, 289542794, 636593225, 976443533, 200776805, 708692918, 104496211, 718691926, 241573023, 151807623, 961491125, 241409660, 902519763, 760949447, 915091477, 258695701, 317104223, 621366573, 335833694, 676811850, 162493197, 806026071, 729791708, 641465838, 989777397, 834161789, 486653469, 279832640, 257295186, 394160875, 571201326, 440226294, 125539345, 389949962, 354384223, 30415603, 650008649, 803378118, 139131039, 696876925, 471330345, 190805603, 371517817, 461566214, 163670172, 763601747, 952054983, 329551684, 970966925, 503084491, 261251811, 266003505, 403832795, 21601937, 446284078, 702047433, 287735027, 519044400, 201275253, 862480774, 446574481, 494907484, 467240313, 554712803, 128936999, 609927514, 128734733, 968021992, 508048401, 767138087, 894888723, 720496763, 804209894, 249310973, 334030309, 909725703, 436561422, 730303664, 49611334, 203730851, 94213657, 152611687, 589919387, 382517105, 869669704, 949670182, 993758720, 881951796, 430773788, 142032535, 727289330, 656516946, 503125637, 60175280, 585766837, 390441173, 265954520, 18151209, 973388525, 568397513, 936459607, 302335674, 552399987, 178784578, 773205039, 169691857, 876323425, 731562541, 158279263, 71377035, 484951548, 769717561, 121971709, 599885694, 363676289, 638880802, 468751174, 372224799, 128646412, 550898234, 797374250, 145832182, 994048032, 295672540, 612458033, 4613849, 362277327, 599987284, 324816972, 257284462, 507933062, 757441986, 233833155, 5571382, 354925769, 942477607, 414711093, 466183629, 322291305, 181678411, 822332817, 802869905, 897758591, 382217077, 725406196, 503437593, 999441797, 276540395, 705219277, 615860281, 71681212, 839389841, 438980827, 65890801, 524598624, 738273393, 297743850, 578176149, 395398825, 724349406, 788452544, 98244450, 850600966, 983782227, 659522164, 225925482, 239949766, 38677020, 787094719, 809539478, 50437362, 460781812, 79099165, 941981777, 197822430, 158288450, 713330086, 346165719, 828447100, 713185683, 568196853, 664349620, 592268425, 199810384, 104498033, 933525679, 904792837, 90327949, 16384185, 627053760, 308172978, 862460729, 224169626, 710835555, 497918867, 630776652, 134019217, 18219898, 2257682, 985043256, 533542980, 861665058, 561701668, 853302147, 974047640, 561523194, 887430710, 822182326, 437306523, 465695823, 873994394, 505421817, 288614044, 222917990, 341175788, 974789224, 27534575, 492459007, 146897734, 709474680, 341844157, 987910318, 585714777, 398471903, 324228232, 809463721, 868731061, 419178760, 333036775, 196065265, 822632359, 702150766, 516200280, 509641885, 778415880, 860413078, 483091160, 292721163, 713587969, 955233374, 437538760, 152142888, 458922189, 152655650, 820628592, 691300882, 959521329, 452347506, 368284894, 632453624, 42551953, 203077480, 675261273, 997609146, 266852083, 211609121, 721200916, 401747891, 510743749, 330195074, 561852672, 301480512, 977060317, 883044823, 648337131, 732786126, 872228523, 222229092, 886320524, 544968279, 761050432, 57713290, 134502606, 64258535, 286045526, 270240621, 144399687, 187039594, 24717667, 206978685, 79348341, 62105647, 757935277, 621616674, 389407538, 670977393, 59686629, 371572732, 351791635, 350544005, 184998832, 378407701, 305384357, 986497207, 88206322, 452482746, 986451353, 652660012, 344791967, 411895, 401934309, 834014027, 609866633, 628021291, 588067252, 269826364, 13565894, 721067366, 306832130, 867723439, 620486138, 994221075, 583100620, 383417076, 69069756, 89280470, 871786586, 296059857, 208179198, 231743956, 419162300, 911946858, 44133516, 269575043, 490398153, 479793807, 1511886, 502409740, 799672113, 772788972, 36541363, 51408127, 39139009, 511579979, 339141122, 844839279, 196153287, 748199854, 408216358, 734563474, 911238499, 442838524, 385030589, 53764333, 766811158, 854967361, 624348581, 231281945, 357719610, 122563587, 711535689, 391702528, 51681119, 207601664, 466018019, 534199297, 913312403, 901390597, 8220796, 400632115, 369086868, 512523712, 106380258, 13265594, 353973553, 985219990, 650479139, 697662324, 680178355, 588184156, 658389670, 297453409, 852985822, 606733392, 369619126, 577577830, 434020021, 563598348, 903472792, 761101293, 604591750, 737143415, 67309778, 636744861, 79700999, 119880139, 528533731, 914627402, 299552223, 633792308, 701644103, 231474437, 36396547, 82147929, 279917628, 953304385, 395336517, 291946715, 263480300, 990273046, 765703690, 434173468, 348653720, 175308761, 488213783, 59767558, 181067724, 963859923, 690765416, 515329596, 735021856, 980785889, 563977884, 1883380, 336379980, 351677194, 265889388, 429538134, 429647402, 259088626, 683995494, 540347798, 315143565, 9916475, 275102887, 362708097, 553045611, 81708266, 16362738, 296729160, 97748118, 373677050, 104240512, 179117792, 360450743, 273521221, 648574625, 332843760, 638684952, 917049207, 412604508, 615212730, 24486290, 826211475, 944334196, 43024616, 411563088, 613230043, 42774107, 513095444, 766512539, 543195065, 296195773, 236658056, 855582939, 178019128, 462760105, 769778755, 789321444, 484678660, 832014357, 694030588, 234453988, 344197073, 754073937, 265337032, 479322553, 609717528, 224884640, 270997022, 639458005, 714060993, 193652893, 194742306, 855739158, 407283659, 607717294, 58212004, 280434968, 154641331, 799288701, 54808996, 241861930, 837797159, 222477187, 925381273, 983632652, 539158825, 517451323, 342292911, 248992859, 790953274, 725224147, 932334770, 581008989, 483462235, 376161124, 987703817, 215401983, 317328535, 46429877, 833118807, 79223772, 680738440, 360179600, 357853608, 622494936, 600681589, 950424803, 954733577, 292851411, 915042343, 777833033, 960848823, 333689767, 799237246, 202298875, 793003964, 69262420, 701624417, 790207906, 833539059, 992134959, 735278696, 980543836, 725875350, 760993863, 799287501, 637396052, 792267856, 341422601, 964052096, 95428797, 978884838, 97322831, 976216278, 467705814, 238909364, 142503801, 808280613, 253043093, 603024616, 919173230, 687715805, 267218215, 519066705, 54542704, 178381109, 462005250, 522212428, 256521764, 165989654, 665818302, 709059757, 813148923, 976258729, 714685801, 939513657, 125169670, 821078977, 884186211, 56154153, 799370669, 190506168, 88580081, 715475702, 771683774, 362348627, 359618381, 521404756, 318143737, 609812405, 35813899, 184976812, 72159999, 24457251, 364172892, 135938260, 406261892, 917924791, 60725642, 635188478, 647953471, 327571888, 973094586, 914645800, 237193967, 908327013, 118290619, 82230271, 894875698, 433944016, 991223878, 421547644, 215323386, 401919367, 645980386, 321832776, 841445033, 772709267, 667528416, 32577712, 411754125, 526139022, 834928152, 407218804, 646665813, 224195497, 576623157, 580178119, 76597402, 768337688, 201176273, 362806833, 125940171, 155041184, 730738256, 541821596, 576011311, 351149149, 486277550, 346114866, 800335150, 967206048, 757822288, 33282744, 832536204, 788916758, 323332532, 933631178, 580551593, 988882644, 297259197, 747438792, 840910011, 463218083, 920155237, 868911410, 674320775, 934824507, 36426036, 909918859, 431250019, 389183673, 632660163, 123551172, 277407274, 717689207, 522440079, 220624443, 818509465, 373498888, 246435662, 731364454, 827123852, 610827925, 982069012, 349134166, 868798593, 867076860, 868984294, 838239064, 256383197, 964922442, 736954314, 32155212, 646628274, 227883747, 920230676, 623176584, 425465317, 541080607, 831839263, 3345340, 446579636, 261739975, 304073992, 185576102, 151934035, 672085201, 244754830, 339739319, 781214414, 272933079, 314119575, 248634143, 634350969, 333583733, 783143906, 52596942, 657957218, 365497610, 340086347, 713958232, 90146924, 850631462, 308498613, 168266935, 72499893, 756763589, 847865903, 196619299, 932027346, 298389088, 968808590, 935851011, 927713964, 112376244, 770208806, 244133988, 920041550, 389723827, 276098310, 737200824, 322989780, 634110958, 74515199, 841892515, 757452189, 710478179, 969329725, 146259970, 258598497, 999550279, 929847168, 369784721, 847858544, 778305880, 141490414, 369208942, 244282627, 790118900, 710819308, 570157818, 761501220, 615117884, 511946532, 75740692, 962358306, 536088503, 131710835, 106817557, 705464365, 710110883, 545156406, 654917063, 616077581, 417491641, 881508641, 707977808, 289687086, 774246868, 6203562, 738517478, 105335042, 507266698, 495881870, 699216428, 447803171, 765559069, 310743173, 582760753, 797149749, 438181235, 868247274, 61131239, 918779973, 274535854, 396316221, 538596983, 122514729, 715944747, 967465255, 885218997, 928003085, 705932235, 80570705, 716890449, 875449541, 836677137, 496336279, 43447147, 941331116, 527801458, 64602660, 306253686, 714409919, 186890639, 935015848, 398256201, 324252393, 160221754, 656298575, 676322310, 25857413, 408501039, 638325403, 171228570, 944599338, 755676766, 421597867, 837908677, 9057684, 737538490, 82961193, 471975155, 459002409, 822436611, 420119466, 26269257, 17533460, 186369255, 451219256, 546776327, 61927504, 185533147, 309663097, 978943200, 843964597, 457749023, 580822586, 282779877, 190884750, 816444207, 398069959, 325599527, 638076864, 850751228, 224409015, 530268667, 187456406, 241896045, 704440992, 264313064, 937199295, 285700939, 754027802, 354855215, 625070562, 614159849, 234549387, 982695559, 632370656, 94976121, 456601040, 321272879, 997569455, 849465623, 248266949, 596408910, 541759104, 189134296, 608595664, 593970945, 583452903, 898950904, 71491792, 696107281, 510517457, 492948603, 479747859, 422995923, 57653110, 545532999, 618758122, 752528568, 817378388, 777641162, 211618834, 204542074, 348013459, 250189275, 287355614, 570082777, 895662110, 97521944, 296348773, 105727805, 327756355, 864450545, 170954108, 831757613, 864459541, 234771849, 681150908, 503784070, 518170782, 351954970, 132514722, 668671286, 535255381, 587504752, 818860683, 345287242, 911361352, 462134474, 89675687, 873890803, 678799415, 275902598, 583206735, 718175513, 818900978, 888524566, 978101733, 702263143, 462127465, 313711861, 19038324, 312310779, 826496121, 384065205, 286460552, 629604187, 590315849, 382981597, 70357219, 1389078, 743070394, 546723104, 147999374, 169343239, 653806506, 300593592, 656657952, 810116849, 740011391, 12534648, 129877698, 313668310, 993192184, 441237082, 603189894, 924573408, 169810428, 540977414, 680812537, 585446574, 590794881, 958573949, 446589188, 568768158, 780041365, 399904373, 610139787, 299109364, 120539083, 289505555, 789211565, 547647492, 477280769, 386382188, 566011183, 540295638, 700737624, 969118523, 151007731, 105631257, 21903008, 913992226, 805139311, 365543686, 737068985, 208826648, 733008738, 438874103, 468356149, 549535357, 901555873, 671244176, 98162312, 119243903, 6650369, 897345595, 801766685, 709354838, 957655750, 483230837, 871892910, 378829857, 628502156, 161231357, 881360875, 473799000, 468378818, 255480367, 728164182, 994130631, 99510700, 152326891, 712323783, 262055533, 998245725, 899392628, 828622941, 86302399, 870455955, 678648548, 576773860, 303717189, 710089350, 822232784, 873281508, 596483895, 191185774, 518764482, 195368959, 153252954, 169108548, 635911003, 850077607, 433168312, 597769602, 624970732, 593041959, 579204945, 974200901, 789907177, 650937023, 100676692, 637493526, 962303428, 788879521, 855702825, 235847996, 143736583, 432220385, 599214143, 782033782, 554473264, 476305138, 108657388, 876054804, 422238608, 768600960, 926612743, 31070978, 515034777, 334770446, 797636411, 77346440, 689871828, 310063534, 758960940, 669852578, 147781884, 769799809, 863085038, 464775471, 418776409, 625981446, 548008525, 977392156, 57859258, 853538867, 205759600, 817682942, 924723792, 64868379, 222527957, 968721937, 552649973, 907256113, 889672392, 172784301, 979587402, 214958658, 658013331, 36429495, 769437849, 941263801, 699886664, 374105773, 229893911, 472895761, 426918632, 805413322, 105401815, 874580042, 825296397, 911520647, 225372779, 295022731, 492426347, 798164316, 521200946, 270783493, 689949984, 638642995, 647027753, 779824970, 535363027, 973666865, 759932409, 358651217, 529828562, 96857724, 533200631, 265208090, 470965767, 302991091, 312080197, 728040587, 570222899, 462345986, 885489919, 782035479, 512815144, 436106560, 984514697, 365566364, 924014737, 38885162, 907704022, 502007443, 239038652, 815215152, 924100404, 899674691, 264956955, 759324719, 722415831, 917875161, 588234338, 193659777, 846378455, 151041024, 616884030, 566011642, 898733500, 874783691, 507171247, 974067052, 194749259, 152136757, 612513760, 909266329, 285082019, 335755123, 200851225, 589729664, 608509321, 27129547, 208625425, 139246123, 627329986, 574732422, 374444472, 678232901, 702091652, 530849997, 520183728, 85762564, 977455351, 423646145, 954185457, 686278756, 16857772, 315742175, 895135013, 65809169, 737501660, 279006330, 294048326, 376297444, 825953275, 831541610, 378711677, 15097239, 914776160, 401963985, 180187541, 349132655, 680741473, 324499271, 117984294, 490943240, 905139301, 63376609, 486895780, 325957761, 975494965, 735783950, 799924984, 908876490, 90699290, 638320787, 896941961, 891785867, 972047011, 976691938, 887481341, 452665020, 841819236, 916206734, 989066433, 842762440, 111397732, 645101155, 268251865, 264383082, 917941077, 586947004, 799470466, 326010895, 292305233, 692448161, 636365807, 663281103, 399904559, 371784088, 509853073, 759422401, 961366141, 913980231, 213978054, 2367941, 65590445, 411607110, 983751518, 883402372, 177436356, 952876965, 359989653, 474753083, 13278200, 958376511, 317951610, 345889133, 358566243, 769824112, 815120672, 269029468, 439160502, 347300153, 993667726, 584553366, 99399366, 985203657, 77217149, 102234154, 393446529, 3520106, 793098398, 942528225, 127760313, 126282913, 830323329, 198595904, 853189718, 527177867, 123574850, 124199904, 422440645, 856833978, 5059045, 766539296, 370702960, 433160887, 967580861, 558530918, 57417190, 749693404, 390794900, 233864491, 238958439, 568712873, 966438739, 750698710, 223331373, 74548325, 213231787, 957496458, 581283168, 734558017, 818963965, 739215040, 506887430, 13601256, 31106020, 895952772, 168946960, 105345815, 440713564, 737426674, 623795288, 67818931, 68390951, 691600866, 524528667, 354279819, 19544312, 43063708, 221994371, 120777006, 469568431, 663939349, 498503213, 923587908, 71094577, 186642305, 208728172, 653970437, 583799391, 541976274, 521029896, 699123431, 98854301, 487327445, 587841273, 91926646, 158005476, 508183366, 557257003, 3075793, 836891104, 649829364, 57199665, 263127691, 631842203, 831480590, 256166490, 373759924, 994637985, 540998001, 326044948, 159046158, 122503658, 547818601, 428374546, 694052183, 502767129, 340338790, 252847919, 628425731, 524938389, 243263730, 636617153, 552031733, 909591530, 174556573, 975060222, 537876355, 196892283, 359445224, 284622220, 529473460, 127363206, 193107775, 864827536, 309491131, 889184882, 858910918, 746295625, 863878169, 853258417, 991218301, 189861305, 181430570, 836488895, 185466934, 844679517, 214378714, 633481848, 377313203, 279247647, 473229824, 595677101, 143029805, 586544254, 218307893, 196344065, 322290848, 843864103, 326510783, 842320788, 23017944, 453660644, 520443831, 642595169, 21260406, 991982736, 608413746, 350046135, 604991170, 553655385, 980805789, 180493405, 738333746, 315309440, 3035452, 649936711, 219931281, 646146823, 459187157, 261206394, 408802646, 258969699, 342985904, 258882025, 545647431, 278261923, 669512261, 171861894, 717280026, 871795810, 155444990, 602123233, 702231529, 847068784, 725719974, 529732679, 692254170, 160623120, 413329789, 859555519, 496484343, 683928644, 203902936, 816124665, 81095178, 143750620, 544576549, 33364781, 538990919, 646618322, 982204572, 303847210, 364805813, 768180575, 952878609, 78697700, 133097610, 526367543, 611242019, 582996024, 508375772, 867095052, 940618319, 762537121, 901492351, 853557281, 648341506, 542348762, 555952716, 191737617, 947297370, 956761272, 795307237, 28474698, 174155346, 209446987, 868214184, 636853110, 809256217, 463760853, 545096322, 825497371, 884623718, 828850664, 701326173, 355394705, 872404458, 998083490, 655902429, 602373201, 547262713, 68822447, 921138869, 999727979, 686244926, 588597193, 1842609, 625246129, 3653726, 339887217, 201631064, 817135478, 233604891, 324833111, 234273510, 156074232, 291625945, 545684717, 219971890, 492940244, 938103699, 843239920, 63242772, 434076307, 718393688, 822855450, 798658329, 428995164, 832448994, 255537567, 875852575, 101437504, 320414307, 438322270, 725540969, 764446812, 309627606, 973663201, 400979707, 986607071, 316606526, 506790747, 542452541, 449225378, 621832587, 634393478, 673875915, 856185903, 560267408, 307648120, 868313465, 314935225, 668905400, 483574929, 644210350, 551777064, 502033776, 737899802, 931458372, 738533467, 291554674, 401861665, 821799813, 263180332, 425794735, 339623221, 57739796, 423972302, 326971081, 329239871, 851375830, 619113367, 657125860, 743517843, 790159949, 390003290, 800649152, 224909954, 924263510, 11188799, 385607928, 480826691, 790505301, 367540505, 599631991, 252278757, 512755207, 350987174, 50109941, 627993713, 510082588, 754869274, 933951259, 202715626, 697184966, 970135220, 68352243, 147680151, 91300569, 451231676, 419955994, 1176686, 595234583, 646841968, 235844917, 359438841, 250086414, 519320801, 66999365, 644628239, 124282725, 895877290, 647561492, 390995338, 948953887, 687686563, 790276724, 760755427, 110154404, 129065414, 752082790, 210199082, 283786773, 751998089, 976696421, 408407155, 129030073, 20464316, 51762934, 210480165, 714018021, 443809975, 52575645, 20178304, 690946835, 4186058, 212365802, 508993386, 830596381, 688462101, 634993620, 874821049, 471954092, 881821164, 340678490, 889580521, 382360658, 28123461, 180958257, 132722433, 40884087, 632370443, 590626574, 783365355, 397910580, 752419236, 916235934, 929899692, 252994559, 472456706, 674637578, 826375657, 444258744, 442664747, 112615636, 242355380, 12998201, 131749110, 935832835, 982978670, 728574053, 271063537, 591018824, 406329182, 816818921, 451718913, 61984679, 212755580, 597468136, 470520563, 969140015, 712030667, 422369824, 436804284, 360322772, 693668490, 581540731, 718997284, 885665205, 683937104, 622512273, 454823976, 529647443, 765968021, 104491436, 283638714, 30353070, 678928161, 331678998, 648937620, 545143403, 574133365, 723084350, 335656225, 8234508, 932963948, 488480793, 440327845, 934147512, 850513662, 16966955, 215259743, 997597200, 267298916, 715103569, 977125817, 216650038, 145080410, 663869759, 234154236, 249087830, 586532399, 176140318, 52051719, 954126709, 406637989, 312088466, 688340832, 130331392, 840405378, 30617029, 117492875, 80977688, 926202704, 819895591, 283473222, 25533281, 805763784, 678866292, 376458746, 868975958, 64053609, 958783137, 694092763, 393750871, 179316507, 944937802, 879334535, 505428285, 895459359, 563915542, 515974689, 811419007, 237492476, 852636982, 513745083, 224340512, 602911862, 970103805, 778506857, 946322390, 65212196, 874313190, 244474518, 810656177, 515897670, 167175786, 271008503, 480323163, 651840843, 499121596, 103834450, 123170204, 619099062, 665496624, 824875272, 870680560, 319228026, 17787387, 922110732, 190302929, 498222316, 162070235, 514818259, 270221284, 551337301, 129709258, 689401390, 851940519, 787459471, 603150099, 698616144, 448374401, 898067178, 863173668, 814944927, 257006891, 213884093, 961239430, 615218600, 987006885, 500424467, 762339516, 122844838, 863436908, 758107879, 391918350, 391503339, 413206482, 20736221, 725097402, 119651134, 905844428, 596658881, 913969027, 660970959, 99249512, 905857249, 659674038, 762407993, 620679765, 459596341, 816248687, 50552250, 335037264, 372609696, 593952694, 143666154, 69562454, 778450314, 643201383, 370406150, 595242353, 290996805, 971185792, 912787650, 635083605, 303307431, 505957014, 94198804, 950244951, 278736180, 771227874, 409297307, 618069908, 324498317, 742136103, 216889177, 351467032, 635338552, 133745640, 277783347, 939805362, 681467989, 346007916, 354057651, 223405121, 760349448, 316102796, 601628557, 786127330, 752339307, 764631092, 726796552, 669283706, 494037809, 98003134, 937655870, 50063227, 264684893, 585010709, 462245999, 885518049, 612579428, 443928921, 472259269, 620422974, 562153360, 899656647, 725631704, 149016714, 279510985, 351735518, 793181547, 959312228, 585700640, 81078502, 92634693, 283907919, 625081157, 786250555, 246238346, 799565944, 926919989, 676887543, 569533107, 787340398, 282410146, 39311884, 610411348, 964241347, 570452799, 109972054, 552129892, 978369849, 70482046, 812820556, 642882903, 856956789, 484069775, 600716920, 659684985, 921616189, 179859219, 650320985, 501111107, 166479005, 36692259, 229424829, 618890361, 206669801, 424615775, 841600166, 385835908, 21461738, 475482625, 326020957, 857394596, 170465839, 152567099, 517717931, 784178593, 464457282, 553957576, 150477934, 182112063, 345642578, 327106587, 796276774, 188550020, 693691894, 444653097, 777561804, 368938691, 198819318, 748900682, 696753889, 536968522, 3171371, 264809298, 81720998, 614553691, 600231193, 463612135, 38167018, 968353959, 232456202, 90415838, 229065072, 289278827, 759055886, 211529996, 375271671, 965935527, 627537191, 353796439, 281488168, 555351351, 339393495, 398301396, 856036615, 685055663, 167784737, 918656097, 666593296, 614389736, 981766483, 229547947, 463413601, 209215569, 221492539, 783023502, 990320509, 818326329, 698933761, 399922410, 328972818, 775064796, 962942258, 357134942, 691956190, 871377717, 384719553, 941642494, 957142119, 50789465, 932005556, 104468330, 762619696, 813214202, 929630355, 910115596, 964404296, 364942493, 379359960, 592680545, 765353516, 776481448, 454818553, 1693693, 68121420, 569285310, 584686473, 238130324, 641225996, 659331307, 318047800, 736307798, 451483828, 792092898, 183579100, 821910554, 323339841, 158332881, 624731134, 787278658, 588028193, 267282407, 985242650, 746438477, 22163878, 350252448, 687875536, 332477687, 106730526, 664195835, 946380565, 555601286, 230603600, 802555832, 115238479, 615694107, 507047911, 336606389, 186710339, 665010854, 773291431, 907861874, 530503444, 357752337, 179875869, 771964299, 243302588, 476775739, 432601831, 442401909, 753753229, 188656547, 375027241, 37618732, 303146602, 567408181, 379110836, 231911686, 987777006, 973993964, 79391883, 289074202, 913493099, 92141745, 37020861, 537830280, 68462765, 834580626, 670674326, 200873672, 383529171, 67536132, 857001357, 906635925, 634344048, 60820139, 271308802, 868745567, 638066838, 334518357, 795884749, 735066412, 586383994, 886473058, 81216335, 798055858, 414045633, 638698215, 108738824, 308519150, 767564635, 597061027, 570848142, 282590793, 239379957, 708943733, 865293648, 597201872, 210831871, 263565324, 968091330, 135678475, 587171395, 198379458, 201662209, 376541131, 303077448, 10585352, 810514450, 45682004, 852471166, 638701332, 60804534, 439540055, 286999937, 603093485, 202397968, 40817898, 906595098, 400648293, 900845143, 949636583, 373856862, 816670338, 361572864, 518377179, 164360509, 31959473, 439208326, 238644839, 516996621, 217338793, 956383417, 982002631, 143636485, 618913672, 862488070, 515909409, 5131695, 303569553, 176809930, 849175333, 530831900, 986009500, 763632004, 927618262, 811254514, 926803944, 89044139, 687746800, 767766469, 866476676, 383278498, 795211528, 894797999, 849752586, 676935332, 856534694, 338810978, 896987706, 791959046, 763297204, 112809822, 687507645, 76796040, 427098836, 436622673, 281775978, 579113426, 373161867, 932005530, 237859640, 963152701, 177775452, 867376596, 67683813, 524169237, 269091960, 95746444, 793947703, 226324464, 309635974, 782951108, 442434021, 402495730, 69842449, 230557755, 484742249, 16256796, 542184837, 598760870, 623472358, 623719852, 379902566, 706777935, 251367951, 49958029, 246663834, 723776479, 191409601, 881762733, 787258554, 328668403, 637270293, 106146944, 998412859, 793630461, 826903539, 168009781, 787934161, 847874055, 504195880, 465273012, 899860085, 986310414, 125540133, 64017435, 767989994, 447751259, 977300537, 877807774, 979316386, 508518089, 367528512, 361002272, 435629021, 689544223, 789157027, 99605740, 961200048, 716466237, 492639593, 663895721, 913510347, 432376871, 58102207, 379807021, 858136777, 789118819, 194838145, 80089414, 627248209, 777045194, 704118642, 920871448, 470938397, 467740375, 240050502, 547326040, 20528472, 556051737, 938116165, 991161247, 907416430, 183066442, 378542410, 391067085, 73139645, 28680119, 613448002, 794181830, 379575940, 847692736, 111038284, 992766997, 901860861, 842258656, 137648994, 419991527, 900799931, 281175798, 578369622, 640644539, 118453297, 417354323, 97491443, 846798208, 898905442, 523122321, 642917127, 211954755, 297864926, 970903789, 85581867, 910288084, 782853796, 781857893, 642258973, 829432105, 529969100, 131313624, 514406634, 140009341, 392028094, 656541178, 586224397, 917696665, 698509537, 443425120, 211869570, 20237242, 40617523, 495468562, 946573316, 479656855, 390578867, 587666000, 552859294, 644391269, 414043990, 658857481, 893708739, 494572090, 564767053, 515310259, 797047394, 67941121, 548759126, 352461506, 92328938, 328807297, 569999125, 302127753, 132262502, 680532960, 993074368, 67211881, 709408786, 752410917, 710748956, 799611538, 416697499, 805278149, 634454019, 531302224, 526340199, 456668693, 803256367, 73839364, 818554286, 823385770, 352623607, 570345467, 342579638, 256801225, 211828896, 523856704, 325486975, 97950367, 650504520, 775681796, 845157502, 934582406, 422394480, 401610993, 361908076, 455544799, 965363389, 193547024, 426052816, 465690036, 194901377, 4799247, 71118098, 632776177, 835963982, 872939627, 292428943, 588647845, 878151757, 322137876, 13990006, 593493019, 760225832, 729023768, 874887788, 684217489, 617705270, 158219313, 5345250, 971570190, 706111859, 240790451, 603949764, 606521466, 35501702, 277740662, 427500315, 970314981, 909415386, 692404892, 848582338, 496777811, 723374244, 497213486, 853523524, 353242793, 155512471, 560720034, 547366894, 930915213, 75426525, 934531372, 51666221, 228290701, 525940391, 790517577, 441753313, 926517354, 477604571, 513786587, 362448829, 849271865, 288652995, 233414725, 389453083, 677436711, 959472430, 842982084, 158294720, 882076588, 610434948, 514038817, 895081653, 755960476, 460096525, 687974573, 761363416, 244009194, 841934574, 346810206, 123804973, 364433354, 328331430, 569173897, 573054004, 695069019, 298346801, 253959615, 877691964, 156214243, 232648442, 176205986, 444938448, 570419581, 229162733, 55702414, 980107668, 864081439, 604157012, 325860400, 164877702, 908274603, 429677173, 929746842, 668624248, 905526184, 375120227, 286471385, 795104243, 73698536, 601421132, 667120677, 102897910, 18865608, 273263973, 936952149, 805676001, 453195782, 376314249, 928057944, 919947353, 855386040, 276985078, 404922651, 745652451, 132643007, 112950316, 912700197, 533828575, 910598796, 347822105, 887608850, 471691609, 399262176, 470858399, 407834567, 610550069, 425847387, 46550205, 323995742, 810451867, 998303027, 799392427, 100302820, 771304040, 185599565, 330640989, 598481303, 579196592, 652399528, 608538563, 336635510, 871492336, 545363149, 658370839, 1211189, 488528700, 396611471, 237223727, 53715330, 754754352, 11025842, 216055132, 27730430, 451717277, 988764922, 198479551, 969792007, 390331374, 72916078, 607995487, 312644647, 134277509, 724847352, 659621628, 399590925, 984017074, 972362739, 93218959, 878568674, 590531866, 933114613, 839185980, 914096474, 137513976, 239860383, 14510459, 363527699, 929000837, 602317026, 582222856, 655170658, 9359591, 817096291, 965169256, 699388455, 972458803, 824431651, 409224739, 476006990, 891467631, 659634300, 756074321, 628791583, 373928121, 33458279, 940901987, 155380211, 857689585, 673357101, 721017006, 125311268, 76248494, 54565945, 931118606, 407246816, 538281095, 179646884, 718415309, 188641016, 867149684, 654507743, 749563287, 27972267, 449554800, 888200624, 86927082, 514261541, 742448330, 254084492, 869708019, 644271436, 997890898, 443926258, 6380780, 456358586, 543174332, 94593673, 682691892, 505029770, 269554959, 587597383, 573645204, 777827805, 601416653, 295113815, 794435072, 412011104, 405448534, 757618166, 14629027, 319017917, 253067890, 211050090, 477069140, 155587396, 919373157, 68861853, 177564066, 604248889, 463746131, 927891807, 879240104, 821996368, 158876856, 158598789, 604951641, 577416544, 300581496, 766899262, 238203272, 476718167, 820582962, 933851816, 65272806, 22406092, 457736096, 587804038, 618386343, 271116798, 368741097, 359463101, 365675186, 635178390, 713206376, 757121958, 726483150, 28159712, 575854912, 266417874, 416414594, 887724826, 921977071, 293673826, 783066117, 270365073, 840936531, 422197430, 148758467, 502290497, 463843685, 559776579, 468885500, 413883445, 657854612, 409678907, 256902398, 364309189, 250936244, 831152214, 594864766, 951374189, 843746154, 545088276, 1690469, 872300493, 189420801, 201748886, 152774770, 925183469, 523818757, 742612929, 158186191, 507531280, 540188846, 71934809, 648328871, 106272166, 622424050, 985537724, 376326887, 462602593, 267871487, 261557248, 495743793, 132209430, 558508728, 966246858, 96432604, 120434295, 497520120, 39345499, 737550718, 331512223, 691456469, 548833835, 780533974, 634509870, 692406117, 887832594, 733692649, 958896561, 64311087, 848001316, 505223437, 788533933, 847238129, 241525142, 800725543, 247177700, 479183201, 342369911, 454024172, 898227015, 170653470, 774783378, 327561129, 353900929, 323042472, 415023821, 917072943, 350919215, 985984627, 793966950, 792303854, 337501469, 177554013, 756841723, 184826140, 223143188, 642242293, 543269752, 479613594, 985171565, 615305548, 165142360, 149434250, 385850884, 781618743, 665044080, 516157179, 125071751, 303863923, 594343837, 253836052, 994417324, 51212607, 538388027, 349006489, 248334109, 407874282, 382774971, 323400050, 697072162, 737989366, 501873255, 973336228, 180753668, 498875781, 358142566, 304604191, 80979110, 672634811, 979837914, 317179767, 360997419, 297801378, 487106164, 226103864, 551410714, 851793058, 354408188, 383042337, 160488032, 883571438, 913223011, 554123431, 760815592, 292252788, 871207232, 998447531, 509838846, 678787991, 89370819, 464952085, 309914609, 166876358, 925825164, 434152365, 372886861, 685196909, 568496984, 372729113, 616431418, 916035491, 220846729, 503395643, 327361865, 478998701, 793187797, 202610309, 358155397, 931467869, 760932440, 829263465, 740155293, 115586639, 443144983, 777047066, 447662880, 415035458, 726599900, 489138399, 491441266, 652517172, 315054692, 123148088, 545019819, 9780811, 175829637, 666578478, 420295221, 449925477, 63428657, 460060224, 406889758, 786878044, 468003255, 655917791, 594689275, 712556709, 442491944, 261914892, 125838440, 258689568, 498939233, 729890875, 649267813, 300602825, 972339362, 275319054, 897238433, 871258152, 735131127, 343864658, 57773100, 16841934, 497714268, 641665554, 964918635, 912863137, 519060542, 569769192, 333423551, 37107407, 307823114, 46004506, 353256790, 379262819, 719624909, 23784785, 265810219, 67599177, 951246098, 413208579, 686775203, 678874097, 724833874, 180754582, 355220433, 291555261, 66023637, 9186121, 218894720, 862388398, 463235559, 815550344, 397316119, 242608244, 177581571, 990168179, 253600255, 106919156, 265928770, 405698864, 417067109, 453518627, 106395477, 685791418, 259000136, 616767863, 623767363, 635371926, 605125672, 429270821, 812771592, 149032033, 989508656, 792165065, 937863381, 576563488, 248976293, 121690565, 589487175, 229235079, 29387927, 71268174, 607561639, 455418056, 899339402, 168322232, 181438012, 150892663, 599004987, 299349954, 73715713, 707931748, 382355264, 384420792, 838644157, 590537399, 896824993, 611874745, 145181241, 488365399, 338559012, 740205711, 666100085, 593640998, 767143357, 212136434, 1814308, 999284802, 590427979, 936068591, 754466206, 872752484, 123014441, 115881369, 803791256, 809471294, 665309939, 108993877, 843101415, 84924751, 668587639, 250757146, 240636649, 282499975, 626733561, 316006972, 990711411, 750229740, 689166385, 805827639, 777290730, 288785134, 801096947, 169900601, 497844761, 911338942, 460517949, 79473751, 876922934, 717014877, 748317315, 32826527, 69296855, 961809990, 919394942, 190228036, 410840598, 181083140, 196053104, 573195652, 937006893, 407117502, 31458442, 903207788, 498392116, 400592930, 961285464, 569333128, 735247099, 107415393, 448581837, 78299375, 898722314, 874803866, 128140295, 910459464, 346088048, 38808858, 344749273, 128621143, 14183920, 7423989, 319741401, 301962717, 658774683, 318884149, 558055713, 218933061, 663869780, 969115216, 467611009, 65493898, 494085698, 163977284, 423766786, 618682154, 226571058, 870941232, 563509258, 56680075, 382778153, 823513338, 672225420, 890158879, 784103320, 232120783, 321117652, 319289432, 934886778, 161236299, 445683150, 538599618, 452410093, 858326101, 46217490, 879876686, 945928400, 143660579, 506428587, 544925910, 401682024, 547125761, 266803370, 50206307, 445268790, 690010202, 292027404, 924114897, 714747456, 54929478, 809731808, 757911871, 524056039, 297784584, 632973367, 9330726, 96035856, 946536304, 409146424, 217489889, 699486249, 369359234, 636230672, 170656858, 637557045, 653599732, 965450154, 882858802, 95405466, 629779875, 416065314, 208044582, 346918679, 610764199, 485472196, 237709944, 50257068, 885685917, 443810531, 398592302, 71399288, 319338248, 398813754, 95832018, 967739198, 832014355, 878676398, 736941419, 449131703, 683564407, 110896102, 489888742, 715254532, 757728174, 4417856, 153208764, 200600222, 81068297, 27418446, 545525725, 833751661, 398968862, 583391134, 456944250, 639647442, 382382476, 305368549, 140576957, 547897152, 679122603, 446958768, 880896664, 76693180, 180457159, 325196732, 75502848, 596674775, 352070388, 562982316, 667320966, 334694298, 706545850, 719635637, 865481405, 215772343, 275048789, 110958514, 864550621, 857933457, 102035913, 819845289, 401833976, 369442738, 179127810, 870514835, 943052596, 206220357, 249301254, 179667103, 713634004, 879941822, 589336394, 228125298, 854287874, 306512534, 486191953, 953804982, 598014711, 802798728, 950178023, 225284858, 954399426, 8841055, 553442354, 639122821, 243153199, 519887362, 22146350, 427513827, 563918258, 558275509, 914945819, 424716626, 845784209, 825972934, 227523604, 704651468, 115054927, 732965979, 912338952, 452580030, 255775975, 580192279, 925665836, 205669728, 999468794, 471775294, 150927639, 956312081, 379766127, 37573146, 657566252, 201503525, 896670019, 275446098, 266381961, 787118845, 629209244, 88721336, 971469699, 180346408, 973330286, 100490471, 732709605, 914993701, 592745697, 883090561, 727470619, 612833969, 350545682, 462792848, 966062101, 778802172, 318716520, 848923517, 457392477, 502524829, 405596992, 546141037, 630059006, 616329368, 909575052, 74534767, 661372390, 977490730, 791991254, 464785238, 353287904, 219592471, 417403932, 133664842, 733274131, 626419214, 331524157, 750196654, 858868773, 649173193, 531009762, 58003698, 38146169, 128227607, 87122510, 725124907, 843655794, 302068847, 4353594, 983133517, 421933752, 662135060, 522562970, 852296006, 263614969, 296100764, 350217492, 271486805, 826443737, 230703863, 413962884, 897709618, 253740902, 33008148, 566695737, 952830535, 720355443, 190069704, 169643265, 910089547, 367446952, 948555100, 386860368, 563987955, 915974045, 814329516, 650771420, 130483695, 49210500, 636219783, 195111639, 580547962, 434978868, 526239235, 150628440, 981516581, 66962708, 619336344, 774333405, 458664384, 57686467, 408569867, 615201508, 904973031, 738571754, 953466055, 979591235, 159538209, 186979229, 508191819, 854440514, 485182706, 763581455, 460247075, 176036025, 62650871, 354414013, 205352417, 652984439, 85531039, 878357771, 359224502, 291371362, 16629397, 247632002, 625080814, 497315890, 399612607, 554519478, 470617243, 1742216, 530234507, 633211456, 318558003, 944248115, 264440539, 390191981, 709781101, 354179850, 915216196, 367252657, 433921414, 324155921, 407634479, 258567727, 864062356, 851861739, 564428005, 723489676, 399329061, 400502268, 482161600, 384997219, 453477409, 482221907, 176723348, 863293398, 851479041, 111614244, 990079610, 451263612, 108563143, 687918641, 411831729, 70338168, 237299058, 737402687, 848199419, 823733015, 762477516, 553495236, 501125783, 330373866, 219632719, 747559129, 7764523, 156670370, 235913215, 843577216, 240184499, 643444747, 360199667, 388525608, 314093175, 968290707, 765120778, 702479610, 655043670, 911944435, 849171989, 23747583, 81993429, 166430270, 941026678, 825724693, 872878911, 618051167, 617663391, 943972404, 682969389, 581950109, 93396844, 809458055, 898904227, 628842037, 398958331, 76808214, 341665993, 282316960, 249491072, 528825913, 669589184, 770347767, 189173398, 502618259, 856492826, 171116818, 16909531, 250210325, 388326955, 817410108, 982364723, 26504121, 210329353, 52103031, 846577534, 737882198, 281135670, 443553635, 843632611, 918359243, 711369894, 861854392, 73000444, 559395559, 698970773, 815714445, 884069562, 423940840, 672663168, 636833068, 563782076, 174412578, 323238520, 47870746, 723301919, 146424044, 382592276, 545026127, 902784403, 610663441, 869749489, 298762135, 388030113, 544667870, 176295266, 857832717, 845766373, 174326832, 145577291, 177197269, 891600112, 600151751, 388109345, 82847735, 961139363, 670832955, 247824271, 982453580, 522382840, 924785021, 327013402, 304029228, 379537507, 908776443, 634387372, 992016181, 533007155, 102586485, 222599686, 286368581, 447645876, 480296394, 662459043, 559707449, 902211516, 88252829, 953397406, 674304983, 404051818, 758885712, 480460228, 364483937, 322903648, 396310889, 257521906, 255343520, 860711129, 738483758, 143308611, 70753653, 165691059, 584236252, 605193739, 369882745, 266896305, 894303751, 117659501, 999212960, 76265004, 719697977, 518876330, 896884042, 686732679, 689814412, 44472611, 221669374, 718860650, 980202927, 521216263, 62414863, 308329334, 738161273, 631276380, 788152182, 787856307, 514655591, 889081767, 637388291, 303235604, 867649152, 272690077, 97262606, 281233246, 278331379, 883064143, 43034291, 155626803, 386292778, 268493850, 604642993, 65820695, 556488055, 17174734, 900128126, 619826562, 48087615, 246255997, 529384381, 65927269, 672815328, 371364907, 956720573, 693864225, 188887646, 19012313, 439949367, 423563783, 702642840, 162052019, 544595659, 196159058, 627036747, 410300899, 433258583, 854498499, 583554863, 606728866, 145768836, 638366831, 862634103, 110586261, 259776111, 501041787, 142400790, 628140217, 622228584, 331086154, 162469086, 964668929, 609546031, 11160184, 327034246, 738792666, 797001114, 252882140, 977967476, 733375085, 297543760, 397229093, 824255274, 956902128, 733631824, 869896347, 411275933, 675103315, 552414377, 639990071, 918849137, 592804665, 931141862, 477239234, 458438695, 765397638, 475324981, 499700885, 782828730, 272556330, 557336982, 220487471, 431426873, 607188378, 653692047, 898468625, 250219206, 466988660, 981833984, 235700793, 817628559, 789914965, 886972223, 490467549, 577241471, 885274491, 432245470, 898388372, 530517059, 775419767, 344039066, 268360083, 275075577, 462653292, 799467219, 204291413, 490788674, 292163227, 460595387, 857649264, 588484172, 755737146, 702609881, 164984845, 751042347, 20293826, 67209650, 635518796, 747968528, 927587198, 869801516, 176053870, 431118007, 70441204, 711621950, 673074267, 718812127, 417182435, 427650323, 734696430, 309726095, 562575811, 450737377, 337753535, 276390882, 681459582, 883101528, 196108190, 458209008, 995561220, 420337377, 594876014, 418398833, 820955881, 367398128, 423128447, 571265621, 923329513, 46233863, 601361063, 796685715, 640658046, 787508562, 352941170, 46812318, 498253639, 582549719, 293732110, 697327930, 196751215, 715791707, 642011715, 548997411, 589601654, 722593232, 1960878, 798221818, 210639269, 871745261, 328592678, 782882740, 993280638, 268918996, 228865891, 317786007, 219278786, 624921707, 455589852, 496742568, 695629262, 850839988, 403175349, 894248487, 111366858, 921053502, 355988269, 942312304, 219769922, 561101781, 975631166, 988360687, 242946166, 129729549, 839017100, 879887755, 511982176, 160121301, 118285940, 426760626, 240949067, 709877128, 924864613, 920018438, 19253312, 742077853, 47172232, 552907409, 839358914, 244685564, 692900789, 866800612, 911587721, 115700333, 879319431, 188119514, 158741291, 981382643, 602752983, 855622972, 694946280, 489646891, 950758270, 163130913, 417771415, 939064160, 63685834, 320716323, 783842565, 111988550, 191823970, 238537538, 753042380, 674314921, 444653484, 451837819, 145683023, 456402758, 524010382, 63794850, 467189553, 118177269, 634540257, 414740901, 174681471, 851725470, 340562110, 567056416, 151029047, 364354024, 471819720, 672360294, 848496962, 730811860, 158329364, 817038221, 528554042, 961279416, 681368192, 776043578, 120315914, 316816422, 253503149, 825762646, 461463608, 700215580, 253983203, 634868121, 297804382, 506951406, 952075291, 176521928, 800219343, 282963767, 38206866, 42262356, 767903944, 42720331, 623747198, 799707308, 773423582, 3545645, 982261742, 516816203, 206745473, 125164613, 825326982, 77637979, 870451302, 942658589, 926958004, 623040814, 232212467, 560860447, 918904555, 517556606, 12443239, 72237988, 410246095, 83546329, 596478325, 94369272, 268035891, 236290632, 950730126, 959532274, 995779015, 268788691, 932881681, 547717776, 132837490, 175371119, 850637675, 843052627, 974038297, 112737381, 637505688, 137738787, 137488048, 840442506, 121616461, 656918438, 14471588, 61646913, 929150144, 451279400, 771702971, 235503975, 555615668, 996273931, 588031473, 454667394, 551279965, 321825777, 607310028, 492433154, 263052442, 493859257, 826529825, 997809923, 124953479, 159327419, 749539662, 433669033, 433983070, 918060052, 592514121, 659905816, 345467947, 961789950, 738926472, 2560812, 541414184, 256002888, 326104088, 57944560, 451985774, 107384979, 837161589, 547927782, 9897605, 462604245, 244872671, 814766399, 711828070, 158138711, 780446315, 439220418, 340317891, 557733180, 822943149, 50669987, 804934760, 495470629, 299195869, 986563751, 78641382, 192129691, 54025755, 582950646, 982784741, 631215532, 254345941, 416280411, 213670687, 223906790, 993129008, 674355253, 465878372, 699492982, 390570938, 268513024, 516766667, 142527246, 645666736, 180621824, 344810960, 324634747, 263837143, 561224359, 820613095, 130304451, 181899593, 30013405, 883302419, 138637714, 474732463, 744611534, 322628723, 425167848, 993218656, 371943586, 703641227, 160411561, 856788120, 882237392, 127094184, 876834076, 592912601, 159820866, 559308950, 731489730, 429432735, 767554344, 672151292, 853644319, 4311831, 879519663, 134948031, 89618883, 710672866, 257083955, 283920155, 228767159, 833075446, 31414744, 459190895, 652650168, 692268178, 832271792, 463377347, 907249618, 800855781, 967847377, 195721140, 521084442, 408320715, 155801480, 752025233, 684095868, 374183478, 706994585, 933768547, 994844081, 268851665, 349622806, 472804969, 671216514, 611874981, 279573348, 64580160, 399092787, 666612853, 584209503, 839408680, 633747707, 455797489, 7721152, 231910704, 432849613, 160578748, 365398285, 450153958, 910344201, 102325992, 93903575, 168441093, 56853452, 477836328, 618629309, 510145410, 176046030, 313920739, 135366723, 826477615, 670925661, 858906141, 985952121, 85868694, 805978389, 149168541, 611839237, 45260352, 720825416, 369161352, 903070129, 113377020, 987704319, 378348459, 254571655, 967974243, 279917283, 14972158, 49134342, 49356574, 145215544, 338709742, 662355795, 687591547, 353852450, 955063265, 59797505, 900467424, 366011209, 315329291, 895850883, 361177069, 220678624, 850779393, 463218641, 304488686, 458964546, 31492601, 317941461, 74619025, 749892993, 117841161, 650575847, 130414347, 623182825, 874598874, 768083498, 645147684, 634096013, 414793449, 628340155, 27780834, 665156425, 378610135, 369274611, 485321135, 922964469, 922855121, 440461856, 75855746, 675595933, 204995594, 330316996, 666684524, 612414639, 922315552, 269912027, 135488921, 386560601, 999257514, 811268060, 858080045, 176211641, 65846471, 607240562, 945952076, 380360678, 284495008, 177052763, 982941892, 115155275, 847401000, 254565326, 54604425, 711280769, 179051910, 497462322, 727975544, 239534915, 3795145, 80270975, 390500180, 520719164, 175510220, 69572436, 1218067, 435966011, 563151634, 429670984, 671407177, 412638332, 463056757, 983516265, 113812136, 508405982, 880120768, 922239142, 510520380, 366950278, 237418695, 660483549, 720074248, 836754819, 120803706, 754637482, 219716358, 700252365, 325513005, 989023010, 880733549, 103608780, 598586323, 357158064, 661744579, 259384648, 7487957, 732061026, 224231487, 113318844, 845879788, 38681281, 530108671, 907744161, 206855195, 459220745, 887550647, 724295989, 196610275, 835350469, 218567529, 282740077, 946325257, 749100297, 918472401, 761227985, 418503791, 990476475, 715794421, 616565737, 530974503, 259851704, 585108152, 333927196, 967889716, 253999802, 228861960, 44639187, 11136811, 162159440, 413222235, 981448262, 621848242, 5143190, 932161140, 558518398, 725875799, 600993358, 966533747, 886806204, 844078563, 307247520, 544489087, 604601782, 447746915, 710286293, 410484600, 117810151, 618696529, 57482593, 238110722, 707885284, 814963846, 346953004, 109683639, 453699618, 891864642, 306471741, 54976703, 656271300, 804986476, 199336280, 266186924, 172646645, 471414780, 319628334, 515494061, 62685138, 71241731, 470219745, 318275632, 845139564, 799940841, 943141204, 374727217, 705368942, 983015826, 772359554, 619007236, 320348664, 39871388, 800329467, 71766343, 456733697, 178400207, 534841755, 146423016, 973228876, 985772405, 28931007, 758924831, 130749474, 968230994, 750743488, 536639720, 985565651, 268846761, 127241856, 621384062, 537308653, 19540782, 184113725, 790791706, 200950244, 350194530, 782919765, 111420652, 841860575, 917129331, 44793697, 345774501, 898022323, 409928187, 67386058, 144188482, 535763364, 483610312, 944446127, 378100465, 820230708, 709467357, 87476085, 941670819, 436153751, 740574827, 514698292, 243259871, 627935917, 660066671, 581694421, 39994042, 1495216, 80083043, 841586295, 507343989, 900568349, 759501264, 931935759, 176533223, 91914563, 301989486, 45932385, 891888749, 482201985, 197978946, 625328669, 140296721, 839059928, 264167930, 477702946, 198640750, 929167287, 812559220, 393254613, 7770332, 810630066, 68249761, 888996723, 983320337, 373939637, 104346272, 958303337, 650657072, 941738025, 679813020, 985621100, 440850783, 582174241, 219441112, 178838747, 326202819, 420868023, 604296112, 343854127, 779812750, 534631511, 583667779, 975159757, 117073470, 405230266, 468672077, 858520051, 100643824, 157380338, 14600176, 223918021, 519368370, 258129796, 647445059, 578699728, 514907378, 802265635, 537151655, 702397367, 226852146, 832588830, 812170556, 773514900, 282023320, 761829533, 309043515, 339504741, 761337843, 22872042, 796454098, 883667281, 348039795, 638119439, 824149334, 714584316, 341196383, 311886407, 379202231, 886193291, 220874532, 1975865, 372550559, 497928232, 356809026, 939139069, 412699629, 823951037, 566930810, 207524769, 787000465, 633206757, 483264028, 533621793, 80085782, 822596305, 953976136, 216007176, 522735090, 284168468, 485298506, 616885039, 350891097, 888667077, 273164949, 724284062, 445905986, 176993292, 441973465, 915463714, 430523625, 30711130, 927470385, 946469938, 487663401, 251677995, 67615394, 216422766, 778545527, 782834629, 997968974, 138524037, 268156411, 39517581, 528208407, 286016825, 585072199, 956423605, 664209959, 762912224, 981684506, 554672894, 770042700, 977107074, 82161431, 923883327, 312258421, 471826520, 994598797, 506801775, 628160529, 693495578, 819750952, 930214920, 354234736, 623833620, 211681204, 682701410, 716754917, 59807191, 294822723, 637993666, 538596261, 553307664, 270166628, 87155141, 331133521, 775680859, 293687956, 290550, 60136464, 405314976, 898520989, 422972191, 979881561, 861799329, 373325146, 322226270, 591969674, 367393276, 92162015, 749706445, 219346593, 630129914, 336699885, 164586908, 147666251, 207298066, 76653910, 560486483, 756689233, 522493884, 838175321, 983392528, 380336455, 543641418, 712086025, 174328329, 656040608, 46099242, 140190308, 650246104, 920722338, 620049243, 454473813, 703353582, 975105628, 664797860, 6635327, 391514984, 254718854, 220007455, 925146300, 577953911, 79805767, 704337267, 349079498, 869981618, 957150465, 85526609, 420070804, 80596124, 444178538, 207071084, 390210558, 844863913, 81130082, 910023414, 732468562, 780904496, 483719543, 640048214, 458257866, 114258227, 98399085, 361534701, 897883064, 654660001, 321912190, 342426912, 30077716, 463636641, 22300456, 337756452, 469075043, 954553763, 772566064, 11646210, 941056939, 471594572, 168123702, 202160874, 446765750, 227922361, 731426031, 179187005, 872542102, 685168471, 675842410, 30591892, 916523031, 457827252, 392567404, 268990526, 30147542, 64261762, 596008804, 199375580, 891203051, 539746669, 434944147, 617936152, 581521380, 265397205, 102640853, 211084453, 156703487, 656953108, 946347049, 543225627, 311870479, 419850536, 429763529, 475263521, 878238926, 744152505, 175673013, 899636748, 554898739, 614593152, 810736367, 393190796, 973267835, 342216326, 817810142, 984173144, 667912895, 106503415, 252310295, 961074184, 643808482, 540228869, 956568161, 579565759, 966213977, 238684763, 635090488, 558273585, 498832386, 865494049, 769175971, 121648566, 318216417, 611045117, 690850561, 729735712, 301137951, 932381210, 691833619, 19201231, 784327320, 641867719, 53930554, 175197082, 562971422, 47234778, 341964513, 853958520, 192969335, 108168467, 501490550, 725181685, 539080028, 134175060, 684937370, 775532386, 861334886, 181413897, 566057130, 7536596, 445889205, 139014934, 406527343, 750485474, 554547089, 858553499, 182571796, 519030032, 831007039, 18983331, 618593759, 749346495, 886112048, 449717283, 569544712, 580428594, 500491320, 947089924, 848742145, 777631074, 666140469, 510953567, 264047499, 481632485, 275360517, 847377529, 671302351, 48874819, 772190712, 939111380, 873694539, 664294393, 266642549, 394008094, 472740439, 852348564, 63930636, 792813273, 516702217, 978965146, 947793325, 501351995, 6756137, 133271621, 600278238, 715688143, 519141393, 181403467, 180583003, 543993515, 427329863, 520032524, 262782330, 512483006, 380592048, 591355551, 675456451, 571342377, 456106391, 21660104, 703087398, 676501091, 550292529, 624852860, 214789932, 587030794, 175658229, 104825452, 44600462, 285650320, 337801345, 946704647, 377269241, 234583891, 654793192, 866430048, 183414281, 116936786, 32423254, 232125598, 857243011, 281438961, 8399762, 652788925, 921042475, 266655922, 162157892, 345901197, 924048978, 480906082, 958685573, 363322538, 956297832, 666304921, 560446641, 63946169, 374198211, 694208943, 17157645, 521050566, 949444858, 598245743, 331657933, 141909838, 282498947, 342936364, 555032108, 857996842, 417820850, 688778480, 111258132, 202029921, 606776109, 391569463, 100172590, 307962319, 475370554, 223245003, 401064555, 550050536, 168256112, 351536411, 373956466, 660228657, 73250593, 494769043, 85743790, 708159646, 804303685, 769049469, 287491783, 727192144, 667423507, 415842395, 478750281, 715426369, 301111574, 447743972, 553019704, 548603520, 959293963, 862057396, 980426645, 187169551, 449483019, 562090712, 337761544, 240005901, 68095855, 547758306, 812274365, 39118985, 67935099, 130417370, 246578269, 214908139, 405862841, 871227704, 822274271, 412833673, 544509893, 67281577, 779298879, 738861329, 426951831, 376988162, 92372526, 985882018, 614524572, 777989311, 313815022, 412279917, 520708511, 869014808, 692069120, 251827635, 285586516, 343780668, 249577137, 878532230, 215208529, 992407270, 146364750, 109886231, 44385006, 380444069, 129543826, 760064785, 731082768, 880198706, 87425462, 749209863, 980775103, 988862491, 493440363, 987909172, 712480712, 697424324, 792239931, 97010308, 377123892, 114208823, 746358615, 930752483, 219354586, 121601165, 261148229, 554519778, 147056646, 82151136, 737846359, 693562983, 357420445, 9265284, 347310663, 107546139, 512590936, 324226860, 635096256, 322565168, 54473809, 232080945, 866133321, 964925364, 60301924, 418313045, 591057322, 331240070, 466537385, 316439075, 889648350, 585856517, 57899700, 4159351, 673798439, 692666083, 726042030, 496794431, 765535107, 293454727, 634891718, 621556739, 543964964, 812614064, 143170362, 837745457, 244777317, 585173998, 90427076, 95701231, 60041092, 851993851, 865425382, 41649103, 129897664, 622099458, 924764629, 49995501, 711124850, 747171302, 422509038, 977711310, 504833656, 945659081, 72483617, 205501138, 61837195, 313205267, 281384214, 477439368, 415200954, 790463260, 971137819, 81104958, 739522345, 368907613, 935154946, 142705922, 287742376, 795334991, 540419019, 510193349, 281880062, 352252826, 786778366, 482062059, 976346318, 331928080, 832962711, 16238497, 396506124, 782840636, 407797715, 294802653, 489611235, 474578348, 23904263, 210403762, 797600628, 525083609, 250136680, 239181821, 877234169, 622271543, 56953187, 824501705, 512668559, 375637864, 203855527, 383863042, 276804272, 584609320, 321815249, 992430726, 195000079, 464259390, 643152465, 190658434, 181106780, 507811004, 448781306, 540604182, 386755955, 400328788, 678032735, 944082870, 32733921, 519925571, 245651625, 902496616, 985648265, 324084731, 111356778, 366070455, 390679569, 676190814, 934888159, 298288964, 788734543, 932742908, 249812236, 414692019, 253688674, 277467272, 128145639, 796066676, 433344761, 595513805, 910666128, 266559191, 652906357, 58332523, 130738379, 330552550, 848856110, 647410102, 568997445, 999630627, 176562646, 256705427, 73773014, 881884947, 673098661, 302413318, 970181248, 308034489, 583556699, 589323882, 338657799, 403468007, 180073931, 552021956, 313162531, 590211925, 784498147, 372940711, 915626586, 658198532, 596031286, 959175328, 781387448, 180642014, 380710676, 979103354, 962231925, 404886703, 577025439, 511337522, 209193363, 897050417, 364730723, 304284072, 282739668, 434609211, 332604120, 577515316, 379840694, 541357563, 597178702, 162116318, 735228742, 685219015, 894001373, 843574562, 347990741, 768310103, 63453933, 859019475, 839197681, 799357085, 907725298, 667807083, 168257581, 253343062, 280090621, 403943448, 595066651, 337973076, 21669851, 965922119, 582943932, 34549426, 721951983, 344102711, 73191832, 345331877, 477402076, 581165349, 321437371, 965096938, 634788533, 805429883, 665101287, 785579747, 507925439, 625911223, 609812262, 422267804, 405136864, 77800537, 267183237, 39381513, 48931120, 919893156, 556782165, 749574878, 496038543, 259312810, 753560046, 337044591, 173194402, 874420624, 582807296, 750963400, 718075363, 281926164, 59019325, 178773546, 951282215, 833895398, 392008949, 384156000, 482934234, 109515207, 623803951, 786943790, 268326021, 915601477, 559182839, 209282893, 630796156, 328458981, 213389986, 758509184, 927685299, 322213650, 939277551, 702740967, 339949887, 464569804, 517006755, 703297857, 699693746, 701634684, 460758099, 122033894, 58724802, 28072973, 215463957, 915590361, 400815930, 883387430, 351657919, 335375527, 203880604, 135281207, 623716030, 624852069, 364718955, 849770676, 562433455, 738955509, 772661783, 36134578, 137195146, 389016468, 650374389, 429517264, 481772224, 41934223, 998379723, 647976132, 892515105, 158667964, 445659450, 499985595, 295499585, 602937767, 129133914, 901198388, 791785672, 622442908, 414318669, 332333540, 704319189, 487720007, 687305482, 948557145, 80057201, 288144759, 551638483, 990331542, 334988019, 307128467, 148585162, 96208648, 409316167, 518915475, 834119844, 286268982, 99091290, 593648083, 417792609, 821941487, 83116079, 52027181, 683609846, 174254128, 107535935, 786024165, 640311881, 887823244, 172503226, 92530567, 738736163, 801555088, 561039514, 231793626, 120463941, 851821403, 844766059, 865043303, 178865791, 398014332, 895990482, 878792481, 483945337, 567127372, 570809166, 936353452, 622569077, 266298443, 792128181, 976140437, 255912741, 316447352, 116191270, 526893629, 874905170, 883014814, 207091809, 199330182, 261729879, 633754722, 14176966, 884574855, 702004384, 189225094, 353294048, 651913440, 143353313, 925900021, 976565013, 104563461, 525686621, 40803783, 491424707, 160405573, 956758256, 965583666, 134325166, 875609473, 274953048, 844873013, 780136774, 457332492, 373218746, 699189724, 44661509, 649547255, 995330589, 77368243, 794182671, 979311449, 145131890, 511857839, 588232532, 792752488, 712354010, 809015821, 369551678, 525274762, 422456095, 364546116, 103356285, 982173092, 655709778, 278720681, 338397609, 559811290, 887943720, 539178244, 570078654, 970373234, 275142324, 160994335, 850482238, 354148405, 236798240, 70338924, 866627954, 791034545, 586947771, 642757036, 264236572, 283074437, 27637658, 458072803, 77586898, 433593494, 38235245, 536209981, 777645419, 203808859, 114518668, 549149893, 254660507, 435119896, 833816841, 104533974, 777284665, 984088804, 1519279, 84837524, 930926783, 562508567, 962370755, 77283348, 546405764, 75745865, 332035566, 492903141, 345864169, 661612572, 658262003, 904410422, 81488444, 263598111, 285677, 267701405, 949124219, 337855007, 267476394, 483562448, 760807038, 549486250, 919412115, 879905093, 470081468, 496129042, 517581984, 618180122, 601045290, 918028905, 833066978, 429219299, 268904171, 339906985, 383020466, 258036351, 552571954, 379876252, 635084433, 894698387, 102726522, 415620101, 627181866, 606300712, 348576335, 136698852, 957386692, 576548796, 878190164, 522390299, 818466525, 123266675, 423278160, 603183065, 676424944, 191818732, 512583904, 700814059, 788610332, 926299998, 90005767, 763892094, 551764932, 35430549, 131743641, 876004280, 777421996, 683564968, 35141647, 886990055, 445921338, 774892678, 150477045, 822622567, 761306329, 179136552, 81130510, 686327313, 874903557, 79714497, 599092755, 904343822, 116695158, 753313181, 466816797, 416604521, 440864541, 785561683, 162851132, 799146780, 699412478, 866728816, 951398480, 95675896, 579432337, 484008578, 519681335, 595698598, 334833516, 810152022, 883639452, 804146048, 392137312, 468721928, 263929374, 30164399, 654679103, 343514523, 896477594, 968919593, 787630638, 509179728, 464552539, 634690296, 144014363, 641660067, 266459788, 719105646, 887654474, 142318057, 403255941, 264987015, 478796893, 711843262, 176552306, 693322082, 351348391, 280634483, 737195489, 646582018, 105546769, 128616706, 927797243, 227819294, 278326586, 107760545, 364188068, 125414479, 75200421, 689051344, 549555412, 907701706, 147599516, 84418913, 627989667, 177786895, 151182663, 572900461, 13476643, 523301329, 322216220, 353301147, 663021048, 938588610, 787762860, 728767957, 522698309, 502279581, 553009417, 974008637, 482106269, 521827649, 146792183, 942927021, 599590441, 938496971, 566302926, 724123760, 99704943, 691118892, 527814191, 565446679, 245194763, 849735067, 809743634, 161371890, 805655516, 83014531, 352102517, 440885782, 959684073, 823039279, 738910039, 327682958, 508682673, 246903039, 582169201, 350381578, 118677829, 588489162, 292870413, 997577058, 9153038, 753585257, 406883127, 64539483, 229218253, 972695162, 871187795, 84835351, 42069808, 260813181, 311383292, 444183684, 672347543, 607850472, 595662835, 558472272, 525967377, 407623940, 404717218, 854752415, 199461370, 522098207, 939614120, 880594584, 979808744, 254313157, 776077507, 156058065, 917700303, 382728219, 550896758, 968391004, 824373366, 26130305, 758540859, 592751529, 414785432, 276052195, 722008830, 115094560, 153980832, 680899667, 456386382, 947305191, 2000327, 398203258, 168451357, 804970104, 374510804, 843293769, 880028193, 290364788, 906168531, 631333221, 981394818, 584090524, 864403252, 13857373, 947837487, 629036361, 981996572, 445390653, 254569346, 238218428, 602547370, 17049628, 660385309, 209599580, 136514221, 222754874, 429865885, 661724783, 308532734, 553116991, 2386769, 731715739, 701221211, 435597510, 378259647, 954793900, 723249189, 400009306, 392106689, 19168732, 513388218, 600098117, 951465010, 229569520, 746260902, 686461233, 567660929, 941295050, 23262917, 425461696, 256614702, 105875566, 412985891, 683273886, 786269443, 101449528, 168689765, 604315417, 25850370, 74594283, 999892379, 370860624, 657505214, 971244675, 773123524, 428858317, 102014614, 569847984, 664175058, 522041075, 782529529, 955533943, 151137261, 25212606, 40518142, 985360174, 51697258, 857356486, 905006068, 358228697, 137470111, 575968482, 791097522, 742094870, 925668262, 137379887, 595657546, 879286302, 977528799, 147505750, 277065299, 693422333, 172960215, 315243739, 190904300, 406064484, 268378106, 830153879, 699742326, 176201166, 375889230, 359209506, 952561566, 350813556, 918385629, 736160783, 8595137, 923230950, 547091500, 812419279, 710804407, 375648725, 872439523, 769586471, 925268154, 691058706, 114502681, 300734920, 469988263, 251555818, 681308069, 622454006, 469284793, 804883049, 912976725, 565999736, 510745694, 561263008, 136442665, 864594618, 719538713, 451258730, 736026437, 619385844, 33617961, 880739160, 294336645, 913301672, 580643899, 885053304, 594326818, 398149155, 463576029, 782836844, 599682817, 364522379, 717662457, 421669340, 847427448, 323591685, 171293750, 335454303, 562037770, 784853253, 578251116, 402880045, 529464360, 566739627, 643061518, 70238687, 112637758, 308131814, 52562485, 504078869, 704979589, 382132076, 262041526, 142364279, 705372856, 489723047, 461668774, 848381021, 30761810, 29630661, 494919029, 677767997, 601029237, 176277707, 612729122, 728108937, 800491226, 982657136, 322051018, 745092720, 876249190, 109342279, 443658347, 272884052, 706404502, 801029457, 23936677, 565429691, 938871139, 754137891, 928060037, 298655607, 754503458, 480967537, 715377420, 192503253, 432026666, 59991505, 190707037, 273530938, 229315273, 560378303, 584278309, 226637454, 142214910, 919085364, 578844912, 83370854, 354634941, 972544580, 839795370, 806300902, 700923521, 282966848, 427305000, 644264074, 626559036, 873993610, 912984185, 798523655, 906773726, 441885951, 980680732, 214147057, 576418724, 261628293, 123974374, 324043794, 572256899, 133008168, 357241849, 84048659, 388125791, 902012513, 329213916, 293406341, 192622742, 296274729, 501008471, 893085927, 649309521, 499170232, 732827634, 746609891, 99362424, 471827726, 769363505, 556005604, 146626568, 159285705, 750140306, 762416615, 705842696, 174771578, 188711546, 119599894, 746657658, 494656020, 877529704, 320566950, 918854073, 126129994, 170805795, 698307039, 650280501, 543941891, 366766453, 546680873, 995352835, 418242621, 80363812, 709652118, 669329362, 190768629, 62008608, 71442659, 928729779, 105429355, 767521527, 171489190, 714777441, 349412068, 476609092, 188749467, 399972203, 573140081, 981964848, 889261825, 895666172, 603962845, 596382938, 84241826, 867985172, 661575169, 579524170, 973227879, 546667281, 264162824, 809786194, 728624746, 820309498, 614946953, 893523420, 57968846, 920327569, 144566257, 550555197, 912074063, 992680285, 386258017, 369810981, 411647512, 677379332, 575924798, 616555416, 181908030, 13401903, 232316697, 581931027, 978889000, 988716698, 410941445, 259297092, 750500103, 132332419, 379971857, 153334982, 493740019, 134586098, 2803135, 113293607, 753799672, 469742010, 267953644, 289670434, 13781870, 356372255, 251124339, 712558740, 455728567, 969912776, 243710377, 833540655, 398176802, 295271657, 375851445, 740561028, 512950241, 497321430, 50623658, 447387116, 670420282, 345207120, 601287300, 456616317, 244376833, 928395865, 227348717, 310940119, 750104947, 556038170, 417998950, 969829709, 461267224, 3450221, 869006566, 333955747, 922860105, 848365072, 802816464, 148600063, 6650509, 676555029, 719370110, 559511300, 613749327, 885854042, 364774030, 487899678, 805947391, 400580721, 60714441, 586909258, 747457928, 46909738, 939983552, 663213280, 39699091, 264175344, 957688126, 332653175, 365071820, 761769716, 880237722, 341549677, 345726906, 910076339, 165307238, 737172007, 436024919, 104069303, 943953223, 690714658, 682392636, 991161774, 858117996, 783719113, 275164266, 243964200, 277118244, 305901450, 785040, 719571093, 554352704, 667348925, 144471291, 660515146, 4494262, 232304949, 578769866, 301081482, 895941150, 564159530, 942223374, 210167620, 450991741, 827360069, 416738332, 8536332, 734620524, 320190741, 688620094, 80243159, 587317005, 435610392, 410955166, 990052955, 320839268, 934601892, 175432712, 378677946, 771790840, 711837350, 75552234, 677593636, 922938277, 252448280, 890684687, 905745673, 358515784, 33692628, 626081402, 722763014, 604731264, 653339927, 561158978, 728420381, 465511347, 789754650, 611707632, 679210899, 747891779, 706220975, 674955408, 191249756, 140794926, 985749343, 468725288, 852867665, 735332236, 797965566, 592551630, 825620072, 787415655, 24018736, 192870467, 583886753, 332898148, 295253976, 953184150, 956986736, 561575690, 641835453, 594189217, 408750965, 944461267, 194391172, 168741938, 641274500, 825067526, 636501268, 994255703, 36940781, 516612168, 330165515, 106349921, 365410390, 682429673, 195350887, 815700209, 147814541, 524731315, 756236638, 356728538, 515005981, 342210289, 165649736, 356499803, 117557837, 363501312, 118039557, 448572311, 563775493, 91494289, 770689514, 709250345, 327888154, 379899598, 573316332, 312183983, 788097926, 325727290, 177090983, 17521037, 291708377, 122062056, 351829911, 911291498, 756533123, 571585091, 721268354, 348717662, 458396606, 474481309, 785279968, 211062113, 424742590, 575956104, 9742326, 716593863, 951090692, 382566506, 641299451, 254848435, 343900479, 325301514, 325054720, 300530722, 604050362, 710217929, 362214760, 413422217, 683641538, 841806896, 834352880, 975830163, 850665404, 3256037, 679313956, 494526638, 565967432, 906343137, 708886558, 606012384, 857186705, 578590070, 351708814, 469338686, 180021155, 569839025, 685624261, 924009035, 60855019, 27042166, 487616601, 863012662, 625282672, 69304994, 174672974, 246027154, 736558810, 701488197, 697937190, 169439350, 465140072, 370234238, 4172455, 729768831, 747600254, 389857791, 283290113, 131613296, 434039221, 460941628, 706417797, 83850744, 316727198, 555638935, 903697663, 408180409, 99087654, 774299108, 428617704, 428492429, 617911064, 307801923, 371531835, 112661695, 785756477, 255626792, 475649650, 651487572, 824062531, 402734125, 889102579, 313143546, 654593683, 150746583, 432433918, 903450951, 228348181, 623679077, 984257764, 223813996, 251979525, 77966882, 190956220, 42402969, 673509456, 420746960, 135562328, 756753820, 967081490, 633547815, 843267878, 948606779, 248194936, 431165720, 532231285, 325546827, 452858586, 931599632, 214864545, 476511539, 378799009, 972933454, 349168301, 307200439, 560630189, 272272093, 381571816, 201361586, 357846390, 166504306, 44217379, 937120340, 725459620, 190450279, 144648989, 771834858, 832453036, 707036088, 558500291, 679413729, 695834141, 388815203, 983171810, 996490525, 469954141, 716700490, 540363004, 418533889, 809703473, 872404605, 254451693, 790147928, 540419344, 226968996, 345205388, 959976174, 686715810, 943213330, 403597827, 624619241, 43682241, 416890748, 776613014, 796097027, 104365808, 512528165, 453168157, 267999170, 333998428, 67091758, 689665066, 694668368, 226408854, 345665784, 573097471, 874812881, 33898071, 776373008, 633017458, 824790878, 573833086, 382357107, 177806561, 382407924, 632045764, 182313618, 868400298, 915408337, 981848043, 37832694, 968642931, 907262287, 777346762, 845183128, 838630426, 560100956, 733275298, 661056337, 139879153, 466184992, 792969077, 427321149, 318532043, 969455404, 470035208, 119700452, 481321868, 74052424, 92538935, 840192866, 424385237, 608016831, 180389408, 478650350, 975290821, 403752231, 141021886, 195557624, 355608803, 948935987, 907520506, 163613616, 302037497, 60849374, 236161374, 405195899, 397717654, 519689603, 107989165, 839867046, 487848470, 770440049, 440779264, 461382940, 549112534, 244227204, 601928545, 426218462, 871449329, 802749118, 880484018, 541067480, 214769395, 157690021, 862955268, 169159661, 521501961, 566430285, 948814392, 681659888, 692505946, 22185495, 86121289, 915181683, 93336662, 723699478, 102705648, 341114585, 447482846, 660775520, 321108158, 888672130, 161776676, 507594037, 340013661, 656022817, 374752143, 922325722, 891886641, 551740372, 779772177, 981541215, 765862290, 244868904, 4142123, 404471087, 362926813, 303965699, 356204526, 920679602, 434444344, 866488703, 293773259, 772058205, 741232912, 818701, 509852226, 712255027, 546790214, 200812708, 958692279, 183341821, 909520758, 404134752, 518686791, 994332840, 813405827, 851513818, 895957094, 74784037, 390720056, 162186657, 761298888, 409259521, 701857028, 587032894, 155815871, 974540046, 106240271, 518058337, 401469320, 735052457, 961772920, 203052053, 773812966, 67255722, 249226251, 272279478, 937320592, 969081137, 606021020, 990637717, 232277544, 296565636, 963168544, 597478367, 437853358, 38489668, 417428361, 219281392, 41948028, 528556198, 961621031, 172511075, 96796416, 879363561, 777889349, 886602384, 18256231, 974835112, 86133900, 563680890, 838967784, 299036498, 213259211, 440748261, 451853645, 640683218, 243636673, 380951002, 592701182, 538025735, 981650242, 621166759, 881117280, 263644006, 994946735, 511228010, 668086587, 916187553, 231869832, 47178198, 490051167, 125009212, 72037008, 974149394, 963056646, 650332554, 857635578, 632016036, 282066530, 673283124, 191045046, 247833716, 943368319, 47527013, 419211630, 568921835, 686220017, 916667930, 34988168, 402605683, 966278504, 702405752, 650903742, 432201126, 534122698, 597358582, 708546673, 676587967, 773497177, 296669463, 724047090, 204811268, 465189650, 382011085, 177225957, 913297245, 450124828, 576823662, 855672476, 31674267, 752361023, 443250455, 811869139, 388443725, 678974045, 835052451, 584757206, 315553769, 728556789, 592538138, 916809100, 989801803, 255249489, 38321217, 166029931, 426697219, 66156907, 768986647, 41158003, 82790502, 285304538, 692075073, 654118704, 222014962, 412112526, 960292506, 194182153, 56609912, 639872116, 220842164, 994708995, 917230923, 486274112, 167415747, 539625961, 422994910, 456588355, 459039936, 515798815, 511004614, 640625147, 665809428, 681748433, 886042, 805802285, 552821602, 588070070, 842794799, 454663467, 139662180, 373975749, 259667301, 98815694, 553397534, 843053005, 410104163, 52965470, 719050253, 482628503, 583098022, 483754006, 561383950, 188621935, 928610695, 305006477, 304545076, 162333083, 610722713, 274574173, 649814748, 860914915, 210909457, 999050788, 421111377, 816685157, 603371307, 868537770, 165656849, 694409387, 792335875, 400145630, 557561880, 445176535, 541965999, 22608628, 917736124, 335484228, 782505588, 761366471, 970186089, 920245157, 848454212, 18118519, 216055574, 506619343, 515276595, 459261974, 692080225, 880620713, 753437223, 977101040, 723958537, 912664546, 370339891, 618401432, 452528178, 908828542, 768413894, 835964126, 250657502, 121948919, 255650867, 470573590, 669116088, 143673145, 192651816, 335190198, 60049540, 34490971, 947336996, 960844610, 573196408, 454931348, 491056514, 777312012, 142130409, 27766196, 827169474, 463576424, 452458086, 779577822, 325831768, 849001543, 906531926, 41722515, 620945017, 807873059, 818523477, 233509052, 676882051, 697211415, 904995798, 977356598, 293027406, 795032002, 588331427, 435115434, 705762464, 658486097, 713398525, 393595961, 464841232, 944808697, 204835086, 586112506, 606975508, 717274475, 649147068, 979825077, 375231218, 251760063, 408477620, 440715240, 85580855, 879353016, 485899070, 163668443, 685791655, 852397287, 862115848, 607886992, 53221801, 956431163, 246007798, 488558239, 198986751, 707021331, 725106420, 471522294, 402332976, 274276550, 831947595, 391273364, 166066757, 38878360, 222761927, 992901260, 670556525, 302742839, 104396136, 818718791, 801468809, 697566590, 290405190, 856870555, 812129461, 565025324, 323444284, 619992622, 414341932, 947720512, 857748404, 25775533, 186215356, 393387212, 595413529, 775221570, 147709179, 393150058, 74118911, 144432145, 344920461, 28197056, 176144191, 792591772, 111947027, 227058925, 713303210, 422868564, 746646842, 249646538, 734953625, 865737454, 599520744, 875381216, 211691120, 894642268, 8419822, 807837251, 814893510, 135173741, 981514730, 475509419, 166647493, 797736242, 554230614, 528181594, 305940682, 443759773, 180309267, 903989108, 455551516, 506984819, 997863142, 584367844, 347044095, 321983513, 380708384, 795905593, 225039467, 415770825, 129544551, 842625482, 757519428, 14461678, 278679404, 395124398, 747338498, 837380945, 764661473, 509563259, 495245021, 897272260, 790887340, 810081505, 730451367, 797813845, 357957275, 430268302, 774435857, 745977039, 647189000, 197970875, 678492086, 839181189, 414271291, 864628928, 662009079, 785254506, 497812387, 886793040, 578433154, 869364111, 324902422, 856095809, 555848049, 436489950, 17645732, 158207019, 234358134, 814091678, 418603290, 485092012, 140048580, 339090044, 213265862, 812494472, 478215221, 262642506, 908101175, 250520915, 224987832, 28342848, 896122204, 69030362, 381055799, 689719980, 757872799, 673560890, 992487121, 534942080, 525574773, 135091479, 35685397, 702251795, 567755147, 420729001, 377205640, 132842163, 479157153, 172238702, 300334591, 256474764, 652946968, 31447009, 346642349, 164609818, 797732525, 865690844, 789832735, 989822895, 616783816, 765164271, 214319609, 668856922, 613907423, 943617091, 22784649, 636860459, 731380397, 124276927, 582661265, 936729331, 867008844, 681685247, 924663573, 854546693, 667753415, 353016053, 248035566, 393432557, 603691968, 766410259, 628561476, 9008922, 654940211, 590413637, 849999718, 875582415, 204217798, 669850268, 336069915, 9331325, 757057268, 155761323, 113248523, 661048415, 23188139, 914728726, 871925877, 965407045, 218581439, 674787623, 594591402, 682128166, 574438243, 113534934, 937838629, 784454199, 288637384, 191486964, 412827203, 342123553, 479929464, 678595231, 203296884, 431977797, 907908534, 322440808, 797407612, 485696506, 159275669, 148104865, 133978555, 482168137, 645693184, 714943316, 396365992, 173193675, 711258504, 747554682, 961313971, 281623121, 585088626, 649045458, 716018813, 370657883, 704497574, 294429869, 892938986, 340093642, 101579113, 880907027, 111690234, 558821847, 529605280, 698245996, 3037145, 309973177, 240052954, 800855575, 619720198, 445306131, 230419315, 745435254, 744108890, 554794188, 291918372, 560308110, 165327512, 169435297, 702500081, 717329072, 335304529, 462660826, 739422976, 623355693, 910446386, 76452339, 558277003, 902080844, 509585960, 575553454, 261548955, 283950588, 265149236, 755675802, 240603020, 667730237, 159344409, 121565687, 244312309, 675350818, 823265416, 173451918, 85826893, 153541521, 49318564, 560399555, 46368459, 927028094, 232930779, 248625328, 811353525, 117397946, 706168479, 88235448, 816259307, 652113366, 124886432, 356235893, 146839725, 923069220, 685296974, 841299739, 311791250, 219922875, 704738160, 274850811, 738217593, 945370326, 821751533, 432956263, 113022218, 467723342, 319286812, 683696325, 619654547, 600769154, 659646425, 422142311, 485051389, 843097663, 106813450, 629174708, 484703763, 545046305, 472469497, 749823599, 514683531, 979353426, 83485683, 566920934, 166947616, 690157427, 105737130, 826854313, 690333500, 601325248, 350872631, 887965808, 288785622, 236205943, 816877781, 368100041, 281880204, 602546743, 247323342, 78880057, 916862829, 793019507, 927755741, 101745982, 169964644, 673588006, 922922763, 334872611, 224185658, 644445109, 123441352, 523053936, 905671092, 456697702, 764745650, 245599399, 733852588, 165146557, 635653522, 100887335, 121801280, 828662916, 531360075, 551549510, 557976379, 191494237, 486027392, 846816929, 326925161, 721858525, 501656798, 332416147, 533618873, 694835895, 334340686, 980873646, 502896772, 478113436, 39874155, 826817200, 432570206, 934201610, 142318673, 101786454, 399062263, 461041412, 530700651, 621092421, 352680438, 185106986, 967634927, 926962475, 265219793, 526012565, 167919053, 733231231, 77272908, 853050293, 62750666, 369601142, 349259899, 680097262, 739962404, 619049108, 46599289, 330720301, 365060313, 950805884, 668084111, 299785724, 478127505, 402246693, 441564451, 56284714, 377982327, 940518799, 511725413, 18056901, 588928233, 601964986, 510101320, 596208148, 612239281, 297213446, 294061383, 184239521, 184827262, 140412820, 992121259, 827093333, 151055041, 693317312, 631848353, 713686611, 172720514, 859789834, 302503640, 781032034, 47220988, 666896463, 147599272, 503087789, 855616509, 362935753, 438617375, 1559196, 86376438, 536278055, 474822412, 657285726, 767842484, 43418555, 991892436, 795535998, 883525745, 245550855, 281574401, 41687125, 303505307, 598300667, 956115533, 599855821, 89709533, 134641984, 313206839, 746595730, 79178609, 376816419, 510552032, 314660325, 922694169, 171849148, 581125576, 755628904, 242309929, 362173762, 276252711, 322431314, 929401111, 155368392, 5419202, 499099466, 32828307, 313308796, 289040499, 929693321, 639013562, 885060253, 56773958, 739166042, 593913683, 652311912, 934571556, 514122147, 161019080, 266434363, 163695282, 442900422, 191511110, 483686700, 575350555, 363499430, 736011917, 88328029, 236902044, 773606604, 290289313, 810949122, 211169580, 558597453, 986939349, 303583314, 201385932, 337412353, 296141846, 885040086, 446379533, 290717510, 457407776, 899324520, 672896194, 197136992, 488662150, 106092959, 218583024, 992485108, 912652378, 894930419, 703919450, 500815425, 529037224, 20794962, 526012282, 638287276, 836412489, 588610080, 696112302, 428670062, 560923329, 382652775, 27331698, 323395143, 628435921, 301278488, 867133560, 676379552, 359097060, 798463912, 913430092, 545809244, 605920555, 202811096, 630707512, 896782178, 30838425, 601755489, 114499004, 825641675, 381448284, 62113562, 234865802, 886000140, 907956961, 770019614, 46692764, 737078451, 792269767, 733426798, 333403826, 824300757, 130708542, 47359929, 859127231, 922081858, 135457422, 81372466, 925699034, 899263355, 114355229, 265513090, 698874262, 458876219, 53757496, 449830796, 34540124, 29196645, 641741646, 395363613, 71051537, 608565895, 180828024, 372817391, 47760241, 468201179, 83257977, 108986375, 644348274, 794934818, 66770032, 49697501, 352979636, 266878612, 813846815, 239928678, 775221118, 964857996, 311761352, 809588299, 185891573, 345454291, 642649968, 405500316, 400295682, 496741292, 355100589, 187982528, 185553884, 315195339, 118971132, 259140416, 571319533, 608986594, 45224617, 1553976, 672690126, 676146123, 36955258, 624347982, 932007789, 2780716, 117492160, 909418463, 459184757, 750304708, 497709955, 304814194, 921163862, 110473944, 350046128, 646076757, 409771496, 949755173, 192570457, 290090140, 715887385, 991594900, 352548207, 710947476, 821640273, 24351520, 13492087, 140434714, 427808149, 238051668, 914329451, 229013347, 216804793, 402276592, 91082561, 4939632, 304148861, 530216820, 594393235, 476107276, 264517754, 719099585, 96579629, 383052172, 527860544, 896336464, 281971681, 473035692, 640138846, 153188546, 983085307, 784567511, 941223127, 519922701, 333449373, 707326003, 295986148, 791357565, 867044629, 94202793, 35213436, 238603142, 82103543, 879234033, 791522134, 357205290, 599511760, 217321159, 160848890, 751226390, 659204129, 192498948, 588817103, 278384272, 465879656, 601924333, 831499922, 703445329, 767147542, 441838067, 352658370, 825505749, 525203376, 456162830, 520197532, 786506584, 54253169, 415531172, 23145706, 613901100, 808863899, 842109463, 581373533, 25913214, 28132224, 820676268, 361436372, 987068016, 873714347, 193287423, 438925722, 551681887, 21745777, 690464941, 912090278, 739619452, 915981714, 322085770, 267272812, 423555620, 400418400, 364644795, 894151937, 470753133, 461979518, 848083053, 192053657, 671977072, 381774902, 47046404, 303413704, 716109342, 958429887, 586384259, 32572764, 649310594, 955945171, 203605582, 931461815, 144471792, 928468503, 690371996, 531573020, 536392761, 397901714, 482719985, 212446597, 298764819, 103162036, 862085050, 830101362, 398162040, 236651298, 298286114, 450383936, 1627083, 372909835, 232934498, 327799734, 664968040, 593218190, 249827956, 230474445, 630217279, 952793075, 126681424, 348623139, 56258508, 459741538, 166903181, 801610382, 499793973, 610345375, 922995763, 839196855, 450936030, 807329369, 942163971, 788205684, 426636765, 875771008, 189797256, 496185780, 412263872, 151510694, 564856196, 607389442, 821670011, 819255698, 569964586, 709560161, 800821738, 179662452, 515490030, 770404414, 837671238, 267716521, 936051957, 793656316, 180321164, 575819823, 941613798, 61168422, 904396186, 13905486, 777072682, 703464823, 742318366, 86260022, 795038190, 272805726, 663632302, 632656131, 832763879, 217334928, 400713006, 326098492, 376991934, 451775974, 543447997, 543064160, 919208639, 640116408, 520009689, 573873073, 545370956, 553621912, 613221654, 684916209, 198858626, 303417256, 477515552, 296955841, 119448996, 1442134, 200264624, 280330480, 542138250, 595629783, 807913596, 653676376, 132156937, 121190122, 306142408, 831822720, 42263665, 924722092, 978765933, 677578440, 524945682, 527637316, 169779104, 397284586, 59120038, 448922350, 6636964, 291192613, 416136187, 337864497, 313171909, 889447563, 591231933, 920983921, 11894486, 277846834, 934925911, 450435692, 698776769, 623953140, 118187861, 155436514, 818627167, 260184589, 170238775, 67217545, 883908229, 598850306, 327778857, 179581609, 118242661, 216040309, 436933642, 884383645, 770806388, 847047105, 982937304, 395566947, 784207656, 384721666, 459533208, 451476145, 361404750, 169861275, 48976033, 579594665, 80222095, 241459513, 979121775, 843868748, 135617452, 789679015, 628720533, 898309134, 905969650, 39561906, 248291297, 221054603, 172308224, 362614646, 189603470, 275176873, 326539875, 253378461, 366523892, 657365094, 908291780, 809598609, 79916518, 2982403, 817948826, 513310468, 732749513, 550689883, 76272619, 812686131, 908586030, 237513700, 571441735, 549770661, 969149003, 250377375, 797570424, 172988378, 54901739, 283690499, 899364993, 36849932, 797234571, 353919619, 986923508, 932211565, 453975713, 538108766, 924476809, 888553624, 602079588, 123500210, 911742207, 367713951, 35216482, 674704295, 28185587, 549849345, 206729967, 695258092, 789101611, 181029197, 528288068, 489463589, 432443124, 332225598, 901153542, 774506724, 678801414, 160578657, 953205245, 815143514, 69618449, 523494361, 42290208, 251796149, 330350374, 983722586, 327879456, 625830980, 919948604, 5212670, 498045391, 836236837, 470469595, 232443973, 396785209, 949581806, 233584084, 112889577, 567667889, 163044027, 12685401, 23937631, 420250733, 916452397, 185912804, 146596530, 296908964, 850955498, 237729697, 527446330, 777025951, 327974544, 271109248, 502864624, 831621429, 485999830, 858386852, 786541533, 326427003, 191422491, 743805512, 625269665, 623633336, 141617378, 710490464, 285836583, 279756534, 380125056, 457087572, 124974526, 330078022, 472706283, 290602725, 499074290, 358978791, 694858173, 183086588, 597070380, 116057466, 882765872, 412272004, 414968524, 814734204, 388758675, 845653813, 707642426, 663524384, 297242172, 131129758, 313907501, 631175320, 438961402, 229023321, 514462766, 788454778, 600710477, 211794333, 527297561, 232278835, 944136083, 953437030, 420376174, 30824680, 910446356, 796159030, 573857241, 681289734, 843152153, 929046191, 643238425, 665344905, 633154019, 868239142, 792923804, 559651418, 492758654, 116617644, 939821464, 107041966, 582789836, 522015930, 722629921, 785089729, 678014046, 609824802, 66903805, 381350289, 308275700, 200154704, 227731657, 704777551, 224815208, 674198480, 486081280, 627840769, 632554846, 956511525, 705608202, 32051910, 491770339, 553922556, 860041321, 691997082, 730772962, 662676016, 857097921, 750348324, 531914306, 215647828, 230358133, 853953666, 725604756, 23015442, 193557020, 180381675, 672974677, 850203963, 677380632, 508609959, 272287330, 290987321, 500321016, 69356741, 767407518, 187067112, 739040165, 56924992, 19053861, 971703436, 763999594, 171083734, 356587710, 932951381, 599501153, 563612775, 919982600, 763995272, 876403686, 633818307, 170481557, 849771144, 417705859, 898134345, 622746686, 404499152, 952439856, 483698817, 133454814, 152992172, 745724650, 921655839, 215580173, 795124328, 260607579, 14745341, 536372854, 510440362, 499438541, 965940533, 77133744, 303905125, 756811135, 437760680, 585219381, 548845282, 191059957, 938051918, 25494884, 541192763, 914453872, 401643526, 419509258, 478965256, 880438451, 425831433, 629160599, 721659239, 579160957, 487401, 836146082, 291984704, 765393949, 884851331, 311977466, 304426843, 333201332, 688351112, 316339051, 182796655, 177552258, 181629910, 550720431, 81384823, 497209225, 823700474, 149389207, 282492210, 1599753, 647694740, 638335121, 895877250, 858492418, 585090517, 396923936, 490593616, 474722828, 958407669, 560302225, 751738885, 670147879, 428210089, 714171174, 251192398, 814177290, 975783286, 25150699, 189855884, 746674176, 285115395, 695648442, 460785824, 924945790, 191199272, 419499554, 963269173, 585989654, 286510820, 185917309, 461220884, 565117539, 589252590, 206357844, 931995790, 940866064, 659630978, 398100827, 289697212, 512625150, 621677657, 118713352, 895978499, 18358783, 171477529, 91196800, 373704975, 835029353, 740418984, 92484129, 703662444, 616482804, 672191076, 458404596, 962822158, 495511858, 180286437, 955874902, 322505295, 227003960, 262505259, 95702487, 866925830, 461073602, 118756459, 815880714, 957114713, 815326367, 943917718, 414768492, 143757398, 35523044, 730064885, 760839121, 596490170, 951874042, 249859597, 237433587, 896107144, 596204558, 151341290, 202510029, 646564619, 907762161, 974881553, 346275631, 2547624, 64747392, 374527079, 841181077, 285156397, 148447235, 377354976, 363880604, 521776241, 212427439, 545553403, 109006038, 121555940, 97621168, 421114706, 809785268, 331043255, 489297457, 583544453, 920508117, 176262254, 620669951, 902583464, 274591381, 997088166, 610960836, 443418346, 482330520, 234068550, 148448026, 319026069, 663131622, 626965846, 799947027, 356961466, 320192395, 832925909, 492326272, 431449396, 165274554, 198279089, 744943435, 938770724, 875501098, 898754388, 886563349, 232871245, 299537770, 509994795, 457363048, 299629020, 272455848, 310902877, 709596662, 169173070, 883950192, 474640948, 288294482, 28176841, 980084816, 990697733, 834342639, 932322162, 100109054, 810684325, 640259140, 55681924, 722350831, 517124764, 59400622, 109830053, 998028035, 770936209, 99301633, 337106374, 115117464, 382814518, 140981324, 541947656, 361088983, 671417600, 80026872, 494049898, 139493517, 567935814, 20995282, 981504041, 372690056, 536408448, 39316016, 663290441, 822428936, 701271902, 836542703, 467947451, 104701527, 431955393, 920919546, 645771042, 891471051, 808773571, 763942038, 604710261, 901607110, 402731180, 349088010, 694480368, 460251688, 725075577, 30576259, 521941060, 957884038, 736491626, 432447345, 98898023, 871239120, 499835559, 10929315, 338580697, 840629109, 618357527, 738359550, 872192550, 170759964, 59785781, 581682113, 862309130, 592634842, 531717029, 388087231, 829643611, 774362336, 36173494, 513060049, 699887254, 471055855, 286079048, 917394942, 738992144, 426291490, 342176629, 384553927, 670168629, 583881304, 428511251, 167299109, 837966714, 732669990, 217165419, 963339133, 239726277, 523662956, 532706462, 618591026, 560865045, 747439167, 408473347, 643438527, 466246819, 717885964, 23279830, 181589992, 662958257, 651773901, 454648237, 829190056, 223903059, 314044362, 722263547, 909671818, 123777652, 558796841, 647126105, 124396621, 886550405, 876822407, 298440387, 721251715, 932422624, 674731991, 940949406, 878709324, 164575852, 800567584, 873421647, 855368827, 903817677, 220119627, 904204701, 272937792, 988557683, 382587012, 715094684, 230785515, 260873217, 778497821, 697807346, 92122138, 621165450, 67591371, 771589328, 259763907, 971376539, 528300967, 866645822, 761835116, 723806649, 961512070, 456673876, 79185395, 879440918, 118568868, 860093767, 831820251, 309537396, 502026815, 931073432, 503420692, 186732317, 941247738, 563684454, 796307716, 300934573, 113553504, 931744894, 119936627, 793910937, 381573109, 825741021, 374838546, 862651391, 170774787, 18080263, 431880558, 495672908, 98452719, 977821687, 273169753, 355636888, 695101850, 483418760, 477920730, 647802546, 75827382, 499195375, 508996353, 968728611, 615926732, 908496225, 22567463, 738310240, 737294929, 602003323, 171502403, 244513720, 281330964, 842588568, 471436357, 660852936, 282410780, 255636043, 851230867, 728566054, 84509307, 822007295, 326267536, 558361513, 98898457, 881783407, 881010371, 868995172, 805674228, 53361354, 199386788, 793756639, 388192941, 992876930, 840636602, 111836211, 814818566, 616227101, 65111957, 937547565, 452986402, 613742923, 130581566, 288726307, 107781117, 766280042, 353409599, 178984349, 784962914, 627021049, 23019531, 134697095, 72091137, 845071642, 301771022, 97692530, 902846640, 548034019, 342995787, 584228673, 883817300, 951830044, 627726380, 384402697, 9396202, 836632912, 279081630, 466909783, 548166310, 479445136, 372589408, 915770037, 990686454, 885130634, 19273203, 275835109, 879549916, 825841561, 899002827, 81052207, 691618123, 448304015, 238349547, 398971143, 716093410, 844001094, 559995687, 989317688, 57220533, 946794063, 738613064, 666856116, 140198995, 189696398, 210312677, 851296788, 213647617, 365492647, 175215641, 942460366, 746108662, 486837129, 723825873, 163841261, 263222472, 841068327, 732176240, 749061063, 331234287, 145986801, 341497996, 521581676, 566990033, 670240036, 109111114, 170173325, 637951604, 21395141, 860792255, 301743800, 58128614, 131883035, 120756276, 99456497, 845665315, 816974383, 671187285, 241725459, 90771228, 516253043, 115487954, 317845278, 539190493, 427563796, 522462775, 188672576, 877921314, 632668599, 812340394, 423002861, 178245740, 173887687, 990710614, 264020304, 823737363, 600313713, 22530913, 744128325, 608801402, 14465999, 146023190, 478989916, 432367128, 75280835, 345642064, 890761873, 52739947, 760452771, 507797140, 174580928, 293869291, 959204286, 983747414, 489521380, 276017085, 892016851, 774664715, 971413976, 347561693, 735284858, 575687890, 833983567, 319547972, 383237241, 351815308, 639653128, 793287833, 257011803, 779726449, 183324798, 377814200, 716371369, 112616792, 663404965, 14419392, 506443733, 399575019, 219320312, 88962866, 596322486, 390446385, 541558287, 214033085, 862985928, 984829559, 40601810, 758034107, 342819984, 745042982, 139228390, 283906363, 515789810, 325076434, 636541809, 164905685, 669840711, 40200719, 931984870, 45792295, 928006273, 486102489, 110047445, 252838764, 666327377, 365268581, 296916102, 169427253, 990769716, 21121146, 736258911, 623250756, 608190133, 372741809, 924144028, 722367450, 4054965, 232528002, 21757797, 350402735, 82751232, 775455868, 851365067, 480537816, 937303942, 85918599, 215396901, 130170605, 294322971, 264844933, 566891618, 190084283, 247250147, 990827192, 711307258, 896469199, 468758494, 535980518, 649917260, 475657599, 591935226, 569916630, 152078167, 724177259, 267438311, 752968864, 142055404, 918535520, 1782734, 896166830, 248763230, 671775997, 89908404, 800442559, 949964317, 180328498, 262115639, 271469943, 469648218, 406291477, 799924251, 478643026, 37263245, 237948535, 17788413, 824337280, 124048020, 717103402, 455903385, 934876108, 616344633, 16669096, 440038228, 592687895, 138856379, 986453832, 356522365, 516301887, 140721319, 664356162, 480112931, 523788048, 798089573, 887671426, 27706729, 795127699, 462406761, 167906640, 725062370, 729165196, 529383496, 1792629, 86428135, 318113909, 359365549, 163780616, 749812511, 463139014, 645642592, 228263734, 611953454, 348542368, 578909035, 421572269, 797275366, 386835809, 906271995, 521947765, 249803895, 589053522, 415494680, 971970648, 778113273, 838299263, 452313244, 465551208, 660417648, 878651055, 794543315, 448443477, 918402368, 642213864, 92603150, 879846318, 549327837, 455612315, 972946769, 666894220, 471494303, 326115734, 25817993, 248407966, 13033526, 566826908, 527179467, 15750863, 845883272, 228120033, 169970257, 875650074, 406518327, 565422260, 206426666, 721565398, 737952353, 897081525, 941477878, 645866609, 819408663, 411353628, 117496398, 762156157, 980241961, 823036821, 49127357, 52011322, 872937429, 357394333, 684011688, 647258740, 594087901, 671974892, 874030897, 7987656, 412524712, 820406469, 177049483, 752539017, 939307825, 200737207, 414773328, 414533997, 823070467, 479617749, 489696130, 456856020, 107282352, 730378864, 484870823, 655633090, 169070607, 167889317, 406563181, 669357536, 88578434, 995100794, 833894354, 320938012, 700607552, 875046405, 852889398, 332453890, 799864709, 291389129, 407964806, 740263947, 597842487, 293537047, 242989344, 434586091, 831377481, 632647182, 744717195, 590905167, 900618992, 520715462, 708240395, 786441530, 752628479, 253364165, 457499376, 230969012, 669057775, 940302939, 397699975, 906160521, 793817064, 737431779, 18854449, 640964997, 188561191, 767715090, 416819121, 696505654, 537936604, 64910108, 679841654, 533506249, 952545311, 876541905, 475343322, 979249753, 358476316, 482741072, 984460683, 62498991, 565129569, 496448666, 628015565, 708283415, 988240084, 461227292, 703137205, 170194009, 79585357, 746684134, 28434093, 452972530, 607083838, 846428862, 517033099, 168228972, 852057239, 728397301, 543642616, 538687316, 591089468, 224532488, 818835623, 410468263, 194148356, 414579830, 593832727, 43705000, 210359843, 853064414, 672282350, 711491750, 722892582, 571920208, 350838365, 169269810, 350209242, 436220880, 239419764, 1768662, 442475202, 206211710, 753481242, 986373323, 497504199, 124053499, 895852622, 564173146, 488272853, 31822809, 34598830, 757544664, 555071533, 95935169, 798298266, 417763493, 69658115, 687320085, 55400323, 777068426, 667238513, 703933143, 727271991, 409271113, 490332463, 106826865, 994895073, 706410953, 145410208, 707373615, 64388987, 223519449, 825268355, 354979016, 221158360, 420228951, 320857419, 925040633, 270289367, 299676788, 757361933, 553491858, 715123879, 89050531, 23591166, 844914060, 173068937, 126439510, 579239786, 929373461, 739806007, 701296250, 545277041, 103632885, 32242467, 613793486, 666656547, 378383215, 356941401, 992741748, 589895198, 314122658, 622004707, 1762644, 92402792, 11163408, 300161818, 472508574, 791258712, 443632143, 417391816, 270529363, 670136179, 502849898, 954111882, 962113766, 582407189, 939919983, 929484003, 524101348, 128835834, 65791848, 754214859, 268034293, 967692988, 815728948, 13077681, 163787378, 581395652, 650727916, 543460549, 34594411, 7175303, 127730296, 987295025, 319994205, 757110450, 527353844, 72495341, 722341125, 714065377, 258084389, 684545573, 371024152, 688192773, 474425723, 928733204, 429034683, 328330187, 118008406, 228462630, 63673323, 270743199, 474022279, 568909186, 218358687, 462115607, 804197040, 417722366, 522261481, 970685270, 56573709, 816786133, 820271316, 257818122, 967010103, 834973634, 471182035, 218478335, 738473225, 778686381, 655455980, 870946746, 331019550, 214075278, 870587364, 486090669, 469980120, 1751880, 950592251, 581530207, 990047601, 465231002, 906964303, 528093077, 172509676, 225778515, 136750614, 308164650, 491901516, 370858854, 142476196, 950623738, 895598668, 904781500, 829259659, 683862353, 453513380, 758189724, 14861604, 444391618, 288785958, 890145618, 857177996, 367451220, 210968413, 87828312, 910092617, 917909163, 796670089, 739031092, 972218833, 849857686, 688830027, 419781570, 110684789, 5037096, 149450995, 865832339, 996235928, 469955235, 831501880, 137704152, 146373655, 409743503, 527806039, 494963551, 68465990, 750205660, 703671163, 365206070, 662350960, 157437894, 704435525, 990514927, 458479370, 695032679, 181304248, 261800843, 562273218, 139290904, 876798658, 559158194, 266893033, 776257620, 190029234, 60006945, 741479752, 195504603, 784050835, 109830606, 372412556, 961279644, 358256847, 711150, 911014025, 660734770, 281804636, 651410378, 287554951, 852973478, 269103420, 16926219, 733227281, 320858406, 538657521, 560495475, 664017823, 311014943, 90198721, 861779445, 533378158, 312218714, 310016220, 600028586, 396074833, 65185810, 996279548, 298031191, 694450935, 98135215, 765733224, 60870842, 946613126, 755434110, 326203609, 742898119, 771003686, 911995952, 183534781, 357671824, 484293340, 25430030, 911938228, 206136543, 564462816, 73185793, 334220891, 170608907, 580308599, 137947037, 578874786, 380558018, 882338919, 768495105, 984667061, 831011987, 736593010, 160267762, 337198073, 194195292, 963585256, 536822727, 606932533, 644759956, 780524179, 695093420, 437926519, 90339201, 772089136, 658565139, 359910638, 993814810, 82860312, 628766658, 800852242, 235400040, 618274833, 742240491, 597532563, 965386148, 239161030, 688220701, 570530475, 247710724, 150625211, 269096432, 483280598, 782618845, 89401859, 832418420, 229708061, 729813812, 999426028, 249578935, 177075149, 144934911, 488627940, 646430166, 183003655, 343907997, 214567001, 814219475, 893687073, 337012359, 78501418, 854285095, 732708048, 684639574, 360273800, 67425423, 433965984, 378994434, 929499391, 314461481, 2201616, 981716306, 749472442, 558957489, 253013933, 993704831, 481119128, 509232795, 115635506, 247396344, 332570464, 316262047, 727768389, 313349073, 80621300, 690931832, 526799984, 696757177, 693441518, 833478177, 591551105, 364359448, 417738766, 795167186, 983502795, 57648025, 959475747, 364214901, 552316752, 395022606, 285431237, 346979076, 602308293, 678677214, 336175143, 661563098, 468599438, 694270027, 203676328, 757980686, 679645148, 617156481, 516154879, 441088399, 459661825, 716902969, 979611033, 220336197, 525205079, 803886605, 212540901, 693253372, 446562923, 651948391, 598924977, 146816065, 584465358, 17703270, 921305650, 674243233, 681067369, 704561943, 545566348, 149192026, 652287822, 56494741, 961502575, 301679165, 804398171, 424305761, 872343105, 821547860, 437916265, 277710727, 781920898, 630729316, 592334975, 563814, 236002545, 1214095, 405561088, 753992195, 964359769, 997852597, 637395043, 453462360, 293439796, 118292575, 240823473, 207911893, 858571419, 645497708, 531682378, 807628865, 872476872, 951981544, 164660134, 866924291, 675648603, 388194110, 898496951, 968413551, 639558715, 943858667, 739912135, 736123248, 907768782, 973799784, 950050448, 110483833, 142610683, 452401664, 360301565, 668162437, 170126027, 59357498, 15698953, 355968215, 929549947, 115512145, 333439685, 35022427, 306825029, 606851775, 133259524, 559723856, 332514736, 405650763, 149064126, 588306124, 799152346, 133063861, 526855094, 339894490, 217216315, 215524621, 135869353, 239446807, 660754760, 302617792, 338602252, 806292062, 190323369, 400623106, 616011066, 259126257, 653220567, 222179786, 476375339, 651910701, 237672393, 555422997, 173409117, 179276834, 500521521, 308105176, 937717684, 345833174, 895044163, 343070237, 494369837, 722357883, 273740531, 438511437, 659531759, 405055479, 421312028, 852644319, 839356320, 342172552, 910750866, 604381727, 898982657, 536998667, 39667581, 987335729, 480705211, 831585156, 570490210, 171979006, 207879832, 559322531, 887323136, 969983156, 520332212, 9255811, 702003341, 220811094, 97346838, 113100290, 624392515, 204569952, 629099724, 84457577, 546468748, 219213132, 882019507, 555388495, 16484819, 905325431, 23279025, 230754435, 452864989, 189990649, 499666009, 601297635, 616969943, 195973770, 51667294, 323822690, 758301735, 361840530, 862959933, 183996606, 575186163, 680629710, 112753641, 852042916, 314770359, 797127048, 561517494, 313533238, 183447981, 71967787, 362738154, 975316060, 742112280, 842623607, 325396742, 493553508, 388704691, 963962757, 274112841, 321301639, 638208387, 372534652, 277901473, 308431045, 721279841, 481902911, 216607157, 841375071, 673746965, 748003561, 592910853, 746121279, 356837637, 40704730, 493022807, 399157371, 128225436, 104526697, 568579449, 751560156, 183847187, 351698397, 141287772, 824022551, 57592616, 949467479, 945409562, 301740207, 550456243, 677973965, 631096990, 789647078, 546994971, 874332423, 619758087, 305733124, 350372991, 222627150, 738023582, 137815145, 662383932, 447969523, 239257751, 847727077, 522043817, 57852076, 964317043, 759807342, 649907762, 495595905, 989952158, 474979506, 201803652, 830200708, 506111387, 570652101, 637224789, 913659710, 926720519, 593801848, 91728777, 137944689, 952165888, 983523447, 45266500, 749991798, 533580840, 585455793, 967424754, 786130712, 120234172, 821703091, 769705618, 640827969, 791042793, 703211729, 920741812, 963077600, 312929393, 638113037, 569630057, 271112802, 629135438, 24963259, 698191090, 117620382, 128416295, 477660239, 644643884, 227692883, 145385666, 335380594, 456463696, 181845536, 913441305, 711203475, 594302528, 979086203, 883887520, 145197445, 298385403, 135843549, 589590111, 739791340, 375568179, 456700374, 757972608, 839356760, 964521019, 793662824, 418388120, 214936918, 486016525, 157903508, 476425633, 707096105, 836402523, 909866464, 538995839, 168333457, 192085033, 580771867, 493338486, 134146025, 545983345, 861600263, 721388354, 51187093, 920580715, 151733234, 743038027, 641813331, 335721695, 661686663, 734020781, 407884468, 811917283, 387711823, 844738809, 818167171, 396341739, 811278042, 558732398, 312804025, 468740497, 319503751, 671297054, 551115577, 802033505, 634394626, 765087072, 901855060, 481534147, 354960411, 119644525, 10679267, 274410089, 860924949, 270862123, 171109103, 420227168, 77772537, 605251795, 281044685, 252902084, 759079873, 667323865, 895170126, 646381170, 4616811, 355893023, 837209418, 295482144, 705241568, 939612908, 940643026, 167787373, 352524756, 110556587, 436871748, 428606270, 861425478, 687134278, 373170288, 41153125, 913428512, 166389525, 354806187, 840930269, 844971189, 998965760, 377309300, 687100028, 57741627, 221210192, 963096049, 692609709, 593603869, 228943084, 124536373, 641626685, 320216905, 261771948, 929384453, 531824782, 91960941, 614247357, 184767245, 852524996, 938950782, 711178738, 686011981, 763979051, 529372804, 271792355, 135692699, 110190397, 757464948, 4382042, 175001026, 856987623, 635526629, 528552173, 333960027, 401629969, 631071611, 782847906, 718218510, 510386218, 645201490, 188280581, 707479230, 428625951, 340330413, 321734982, 806306944, 121493259, 6596485, 736170223, 205890990, 967499852, 267884026, 734042712, 724842991, 695405577, 630865479, 996020667, 789790284, 36408104, 295356362, 393067503, 718800962, 101050549, 670939247, 522263601, 713653442, 718418246, 956634990, 754890168, 42266862, 835636281, 693045110, 572950151, 639449598, 380606380, 709207621, 350572333, 65495452, 788993006, 962003080, 125972325, 28736338, 854539810, 466777789, 867521377, 672308602, 571365450, 912659693, 662830409, 219900867, 648872660, 217831586, 456185702, 503678527, 598549787, 368718463, 773936586, 936859954, 948839997, 72202772, 458894759, 592816383, 800023606, 424452804, 1023657, 417057299, 294338513, 768619037, 228433420, 547657189, 803879002, 769728776, 584644562, 7692668, 897527471, 229612621, 668332924, 345781350, 703469027, 372519779, 637608774, 837884890, 994837324, 197480600, 818296409, 344540429, 360647524, 417175447, 913950136, 390166398, 211466059, 366446377, 961092125, 135562494, 476544950, 60268731, 237880967, 943435985, 812927520, 140648172, 706585475, 799486421, 18088252, 712393878, 396192860, 288247379, 786735588, 869503848, 52126088, 390201126, 536586139, 667869960, 121594125, 759093602, 242882643, 685242866, 993050007, 127058490, 604965535, 779110601, 932035902, 355933683, 189493808, 149309033, 408987075, 977455300, 660451665, 469050253, 171031286, 989088395, 198328197, 672999329, 322809478, 558868554, 427118760, 958348878, 306059649, 114058556, 437400080, 941107066, 247004666, 88377266, 144319503, 549484839, 199156383, 310570043, 187793879, 523895495, 157930498, 962108767, 586784252, 315476553, 192380789, 602844815, 69999622, 658269781, 565229547, 65439485, 234602814, 136650336, 467339013, 432368914, 287141743, 245556409, 472770442, 120539, 521169038, 630523691, 500391598, 179516911, 736923369, 67738521, 958090717, 615260994, 436964783, 14806077, 860445733, 502881397, 303230477, 498185575, 28026146, 467616040, 381574587, 449463978, 302684729, 697095777, 443501357, 521567916, 402316192, 722353796, 269412068, 505073807, 217980351, 979762188, 916541824, 914929242, 515465770, 194821198, 319162342, 194947707, 481321820, 478766494, 101527986, 120936220, 884488040, 363006447, 863167391, 208061325, 513641972, 94616115, 625648866, 345402064, 92531911, 755894250, 324017745, 17777932, 752972519, 38968783, 434198351, 749238657, 584988230, 224209331, 256554735, 500085550, 607331282, 805772743, 424137194, 162556254, 961326571, 392542565, 313276456, 129221662, 82421899, 222361031, 290629057, 976638881, 156522438, 307860964, 517272480, 393584786, 774329059, 25078854, 589087392, 970095352, 213664510, 997286689, 986410915, 422222799, 299968646, 935877046, 317964860, 779697114, 169795444, 684940501, 513712867, 738933307, 703560672, 914737257, 16937499, 606353294, 743062229, 537408193, 64471652, 33425178, 678462740, 105969071, 501918222, 597349303, 12537138, 264962956, 877852396, 914819818, 388036784, 23330429, 397202998, 887604037, 892518701, 200150548, 115111348, 117622742, 805304937, 396684877, 701739212, 967998217, 418157225, 266738764, 922565491, 509173522, 791082226, 38050186, 941491678, 951435799, 296751711, 576251905, 88221469, 757370755, 773330625, 5600574, 226249596, 426055863, 998974873, 940062078, 540500795, 91965955, 314935518, 103531616, 304092987, 582949713, 867809735, 786526181, 219193248, 918900141, 133758538, 451223065, 288689649, 717133562, 321573357, 729660882, 731147142, 224278102, 670909724, 719891763, 81003265, 810503269, 23578488, 268070839, 454078577, 395476996, 194284059, 911605754, 49066969, 954278755, 757040415, 122499832, 255356832, 837095154, 735180194, 828893597, 232312376, 737938615, 130059489, 630160699, 487376362, 685554484, 959213084, 481245945, 85888584, 818627532, 584867022, 85237153, 80663176, 981087199, 976594700, 111146004, 631383351, 359418674, 244663034, 713881355, 457525847, 33614889, 37996533, 320173354, 156712219, 493927941, 76203496, 364792534, 373923036, 447494552, 364712333, 344922597, 384026424, 146621653, 213186191, 664023488, 650333166, 738565772, 735385234, 559577184, 994349995, 621912246, 876721269, 404807370, 319956128, 757488664, 577065943, 738971431, 477968029, 358999627, 719837060, 266486281, 949020804, 638951430, 879670916, 259059844, 303573498, 869103686, 335339476, 763371060, 564914536, 237891532, 668734427, 966381823, 106420370, 585515058, 40329102, 963569806, 697684146, 103321339, 970989143, 605041265, 788616690, 358028606, 373817733, 76357232, 428156808, 395734820, 290910166, 799833304, 839192454, 979566393, 390896945, 717210488, 636387434, 133624094, 720884729, 701305937, 282491140, 932673548, 781751159, 291553333, 633429827, 962017663, 589463654, 340397540, 182974776, 192634900, 924614414, 575112763, 98237345, 760526600, 391133074, 470688798, 551589733, 810074544, 828751426, 353343877, 798462834, 871125479, 714025262, 517018779, 875620871, 850717079, 748205652, 774596546, 838057563, 359505748, 44243398, 386083418, 483098625, 317760149, 713745776, 246941106, 668337827, 1968640, 920135242, 573059907, 331132180, 40359846, 499814569, 955696311, 493635224, 546074336, 728175447, 242022213, 937762868, 855405880, 490094122, 845289594, 508036926, 136879328, 215591874, 659363462, 18911231, 206882596, 993935975, 988971872, 660701914, 409673755, 131418083, 797835773, 518015978, 988320538, 167595680, 501365692, 839252327, 20589807, 683589876, 651564544, 895348380, 38120020, 121732485, 548165249, 826179058, 528996410, 338375903, 109590906, 446583698, 850971958, 596716754, 730689873, 366501950, 672340933, 984573294, 951268904, 546928298, 544263598, 416370284, 825689353, 160976948, 234262089, 216663596, 276662671, 450999250, 804907867, 880596889, 721970193, 320792203, 670855909, 529212547, 905498770, 961783610, 488320433, 652018003, 551672386, 956133249, 929824821, 890982718, 60957487, 713005966, 191570120, 9242333, 152212201, 715972856, 288103394, 805407879, 151947461, 956313512, 570962998, 662296523, 24725418, 902296464, 274296976, 893149923, 466813308, 209531932, 521004328, 845450787, 402281027, 309932646, 926811315, 895952661, 688231761, 155851501, 379721213, 590120080, 774145545, 700014046, 159488005, 92291444, 408227438, 749103681, 645161912, 423917324, 299767946, 16311395, 334146310, 861383071, 176956737, 56481488, 569966878, 597711857, 691253213, 889778686, 358403601, 483844272, 108583513, 813574778, 43379731, 571079313, 611333468, 823256968, 213781772, 655247512, 636406197, 895225858, 476977149, 488670648, 549687555, 588643353, 955413400, 43846358, 558338773, 908112238, 530336234, 885083501, 39511605, 24025383, 510028051, 277255208, 306349047, 390671803, 179788727, 90264588, 31011746, 572648431, 462855804, 483477721, 173616456, 888743204, 565065035, 803888223, 399961085, 560870692, 477738813, 487970465, 583513832, 169416153, 795296984, 215420297, 88329819, 266845311, 5204321, 855556860, 974858280, 354760044, 891111588, 191640575, 590778755, 955814432, 819954096, 450421110, 317779660, 443020881, 593280941, 703292695, 981708025, 818823641, 498002105, 384224408, 393179703, 662950224, 511592712, 576830002, 193700572, 917086300, 460396500, 393768147, 863444800, 404345152, 255253697, 171873161, 391563810, 856475134, 379687826, 241753170, 575222118, 860483462, 913071409, 242055066, 271821502, 896289997, 97744105, 507995729, 541932574, 355827760, 906855911, 346855399, 692456706, 654080350, 615111609, 676464673, 68630878, 526164776, 723655611, 62181876, 583010563, 488222559, 470901776, 182258147, 469721478, 996517666, 28361061, 438078330, 801474584, 994164079, 649105634, 951821061, 274304477, 680247109, 810821686, 169498339, 840045404, 383395374, 715835796, 604775288, 928933491, 212454423, 350818250, 82866722, 278945650, 540775081, 86233164, 441904804, 257939491, 510197361, 521493112, 288817470, 775051391, 436141873, 553348007, 792167849, 833462560, 608818039, 486605335, 230228569, 475230318, 303359207, 973093877, 838093006, 761471389, 949933569, 425215841, 568461361, 517442194, 316943068, 388596982, 423169084, 805573912, 429057748, 661749733, 821778948, 876098822, 200999607, 833876691, 784796811, 306520108, 541758119, 277498513, 265582660, 30626246, 819319730, 919676394, 848469629, 630905316, 137837207, 354436238, 819037845, 372954125, 560966010, 256177613, 310789806, 570414216, 208288954, 500736237, 320959917, 714680991, 391999698, 673521552, 497697989, 495114304, 839240445, 507336860, 959713229, 737351281, 213392706, 988364522, 826537413, 257332587, 750138310, 774050482, 706816977, 500627540, 432521582, 978785790, 552961431, 205805410, 15882944, 899197253, 746650745, 103240482, 541262307, 748889112, 354909451, 468051270, 13937192, 496475296, 816735417, 219655755, 18437522, 136990933, 441158297, 538991784, 534417655, 109769858, 842427818, 741689044, 806333971, 632064136, 446105238, 729307588, 93695505, 21524284, 321015982, 816535466, 144534948, 124632455, 32844099, 361118555, 595886380, 525672371, 892193804, 480864208, 597038993, 989802203, 820176332, 23662078, 467592973, 626559010, 431085927, 580130331, 541812222, 905765886, 180032287, 560184335, 432734260, 510032000, 579616298, 943333537, 133280629, 237331177, 212367268, 982683719, 647897508, 561190626, 813418050, 336038407, 95657299, 141276342, 984466738, 770219137, 610583448, 210429293, 923326482, 47298105, 626728456, 339246666, 233204349, 515448386, 572715680, 193879710, 357889078, 874182007, 458021754, 433100533, 650769040, 360986527, 640039307, 545452688, 909396104, 567956508, 250042395, 913700733, 236173340, 166504202, 105143974, 405377135, 349078546, 78259216, 393509976, 672367097, 898088841, 601546813, 371607889, 412605192, 535870483, 381320762, 210302272, 801766328, 527746546, 575803725, 389011654, 373710988, 496857797, 107036729, 63956126, 441428703, 493835393, 437123829, 670969886, 468727858, 175357021, 112233731, 481468526, 55706537, 255003650, 766866404, 710743510, 664494826, 326147110, 602745890, 290840972, 750986936, 594800315, 582265992, 57881711, 537540127, 442896915, 615316793, 200434280, 22235128, 21524645, 984684187, 659057602, 999997131, 727530658, 45086113, 941567161, 178265854, 999526035, 713118689, 771963630, 220379883, 581684012, 709670105, 891849112, 170372851, 551776074, 880332271, 222391881, 446001089, 137212048, 338551406, 490118157, 4024311, 599554812, 984067853, 990321954, 259243297, 292509558, 502911529, 194130406, 378834976, 618220992, 468275931, 164612831, 884054499, 526545592, 208635671, 76972893, 97860126, 833636155, 49769741, 386044954, 508664663, 754183988, 375666239, 369225099, 67920687, 836768849, 850911983, 439364706, 863526989, 494564714, 641774621, 850534284, 968933472, 354077657, 777724026, 112745133, 237651563, 542551452, 404821778, 242727196, 440869205, 508770723, 932595197, 871993703, 57389241, 154761232, 40062647, 989989776, 983638081, 79128293, 999742064, 766793664, 697634638, 713038116, 867065146, 514094420, 384650035, 668665787, 805674710, 461250285, 978232768, 675029478, 852453465, 905890353, 578088855, 364322009, 311325656, 290787183, 851606239, 127731009, 65084526, 308528647, 167903619, 651339409, 778854941, 903171965, 138647654, 325257325, 162234, 472284421, 421839764, 753718536, 374205911, 954554861, 656317179, 343021565, 95210701, 673491796, 686495382, 376488381, 333400134, 48150343, 267632772, 837355201, 330203742, 178082690, 400704626, 717506726, 633807309, 504062272, 550114448, 843352454, 253298327, 41254378, 724713693, 151361623, 467615186, 974997993, 716227955, 900262634, 950681017, 523416597, 535936560, 274457641, 972143970, 607217141, 271512991, 504991280, 411428424, 861102978, 315032612, 202826064, 931451991, 905546586, 765236212, 219205930, 614697967, 896548149, 585096164, 285592126, 730922038, 784066240, 876766202, 123127733, 876800094, 194998465, 932847135, 548483009, 623371576, 716940, 446227505, 811565176, 730717806, 839704190, 128048546, 165883259, 507381010, 644719567, 801018589, 573968299, 52812502, 503414683, 113642183, 868365948, 390099562, 280961513, 145366517, 65673259, 801644613, 479254965, 827716431, 87607572, 905295955, 971437072, 649594226, 114228076, 455003096, 826735210, 757938782, 23891135, 68254584, 965229155, 541653057, 124506546, 603527812, 995012594, 348618646, 517914199, 233008554, 423110546, 74647984, 152784172, 170350498, 369076808, 694878412, 419600654, 745591171, 725519878, 603776112, 249700653, 229222853, 141450304, 471956799, 185496049, 57257153, 680645005, 179246526, 158480369, 463332403, 277382752, 127287126, 272353840, 93249475, 163050858, 242742655, 143984549, 166737622, 949126171, 559939571, 960001693, 282513518, 521182450, 649166050, 585578140, 413856464, 209754046, 717405329, 270238915, 272904320, 197060961, 773834196, 973209493, 479650991, 69651550, 803302395, 315949313, 667394234, 676601952, 915516019, 442433605, 462693371, 362936667, 953435465, 237674673, 191790913, 452489372, 164908442, 877414226, 418479902, 178569749, 104935826, 721923287, 886600204, 586441443, 605534636, 753971762, 543581048, 739746019, 647674574, 483821193, 639461380, 257053673, 222980175, 989473312, 358607276, 118731248, 741462027, 286936829, 532668180, 543561756, 879984398, 521023587, 295168751, 517903489, 587950845, 66681816, 415508906, 438924045, 709146383, 898352706, 199257428, 434213400, 971010419, 645311451, 958324148, 699720152, 714147824, 525056353, 390832885, 590918705, 53373010, 170619176, 634766169, 236723934, 416488247, 842982688, 878054037, 499014079, 770280699, 947398686, 162845860, 526077831, 777690170, 878483734, 464366145, 805766913, 782035949, 215486123, 436607701, 857655573, 9420380, 545268029, 153631020, 150846769, 185552351, 953578473, 802232238, 781049553, 416180718, 388132958, 683504410, 205901466, 910234883, 946804491, 671521441, 593099458, 323571841, 100194730, 362736361, 563907262, 24857253, 343094521, 280430041, 636035259, 497717818, 352179157, 348913535, 829996275, 628900744, 310888192, 115045387, 863341750, 518445390, 593348253, 75089062, 496674360, 143849968, 364917079, 160694027, 71291444, 315506192, 929680592, 142953563, 694554849, 117663703, 689838612, 70374717, 38248589, 428778314, 141911251, 467644990, 301744983, 152859201, 450345223, 247819321, 340372705, 249066327, 125456964, 296085615, 153347741, 647890352, 453774369, 594370493, 697280746, 404476202, 727831257, 985129028, 684472241, 772337902, 180368199, 483473342, 477084982, 57066151, 792794072, 87290514, 916963600, 325108525, 718100144, 411084398, 76982792, 230750203, 632045286, 420043598, 991983099, 831956692, 425984318, 118753, 216229270, 789529601, 905588346, 171659988, 523455040, 743823820, 562131116, 721939654, 285189273, 732338363, 132575669, 318395834, 946516627, 415097457, 398994808, 480014363, 22337970, 295245988, 792521754, 184926784, 450560047, 873058125, 279047652, 928308748, 848748869, 17567282, 293519866, 700838879, 709120701, 696949765, 433086637, 180587429, 355523242, 582095401, 212982958, 392022386, 471449416, 884544969, 284385986, 320266500, 167122301, 345819963, 737846898, 585256661, 436717491, 432751158, 363564625, 898643084, 255244773, 767817534, 318403409, 337575602, 90751040, 492312546, 224315656, 920585446, 460026228, 225298571, 525924655, 544131085, 415905326, 253507631, 422268180, 704776330, 110782712, 492885503, 86436294, 364234189, 372490236, 12135238, 821082708, 416592290, 599424996, 711695627, 421884125, 329892489, 486310170, 742494825, 367554302, 594944348, 861317347, 789148724, 207131029, 201386139, 650952323, 504682841, 592999949, 362219718, 640222112, 209316863, 459671587, 712692104, 935812481, 95324660, 563420065, 836670629, 384095196, 670493282, 932879100, 163537757, 853351593, 113266479, 841506314, 517625320, 157287905, 130074829, 231358782, 547370685, 669910940, 143032300, 31293456, 338464393, 250173882, 965495187, 541628800, 43629692, 531069356, 82156675, 262577775, 834465463, 31846891, 246514216, 401806419, 708399375, 8958760, 210994807, 659153993, 148905426, 784091579, 357558419, 972964471, 418834648, 222326566, 978305076, 111304180, 63008909, 151047945, 659320122, 657657371, 437618402, 605237981, 397696589, 757769811, 602163127, 759851152, 679885024, 344343417, 276538781, 842790121, 209656764, 581817017, 89692875, 385514515, 437919877, 434474515, 941712438, 969934234, 878132384, 922794661, 41691356, 628067611, 459487465, 146579922, 768103536, 847158446, 57239202, 930482473, 444417238, 839203668, 24189460, 162852705, 206406678, 907894484, 208084695, 134926241, 42528515, 950757723, 302696454, 733119484, 890487631, 78283113, 922265780, 224843154, 277937422, 25322746, 660248389, 41954215, 490078396, 976491525, 503466233, 950307157, 517633177, 225551922, 866694894, 107732354, 938737597, 723184175, 623844246, 808855057, 193432219, 988535833, 116914082, 855879606, 154792745, 562614526, 486122518, 837692753, 943171914, 150965196, 885987119, 402130241, 437725868, 147560668, 800576536, 884773504, 475189783, 191733467, 114510676, 121363765, 380656135, 223093586, 842820372, 767399990, 310094134, 121968119, 677751709, 988827911, 126911713, 914573438, 619587185, 172690383, 283272680, 819248478, 804770713, 612196509, 103302507, 214889669, 120664609, 132051219, 686187413, 59476411, 760925432, 69703656, 58820612, 132835516, 994457130, 11949917, 743648580, 872616747, 848127865, 670496896, 150195706, 348151278, 363049427, 445451595, 27561470, 642354288, 121580656, 352780844, 390396950, 587246073, 280704179, 369373502, 553468140, 10495379, 858943550, 716366628, 979580314, 147802273, 410465985, 813354729, 747497749, 390580675, 225373919, 380871847, 315716953, 433715853, 947000595, 902245453, 243589903, 33686856, 165305932, 179077634, 845216196, 205071548, 128121397, 486292929, 183829880, 172284569, 105501883, 199985819, 463802947, 257915939, 589919852, 523048649, 491749604, 630198604, 832914090, 857903990, 455076382, 279478134, 213417265, 148823042, 369560266, 582548826, 575466954, 167702854, 593400481, 907976710, 637855721, 184460331, 117185412, 154911661, 587564874, 35321873, 700237431, 974961041, 216795881, 307409984, 34718747, 696766038, 7602795, 970878549, 816837280, 97438437, 736592476, 436417661, 726186038, 843032757, 43905669, 630025955, 769319336, 748374475, 981392608, 854515695, 55002451, 714269086, 937982967, 612397443, 309591846, 329719533, 30698047, 59043335, 667282477, 716036636, 579968707, 283316478, 571603599, 453974406, 550877066, 337865365, 925687892, 450333228, 386263143, 216121945, 331249305, 58471122, 936524200, 961700696, 313628902, 527467723, 755161815, 998302138, 585159671, 192802495, 242062528, 55253349, 916767607, 221861400, 32503404, 551014859, 172006066, 902799287, 999330706, 233757195, 525340657, 739761044, 834586999, 570832653, 887945422, 295489148, 910932595, 60952064, 446917215, 94339137, 638623546, 420125816, 413926585, 763212462, 590316766, 868124843, 525363200, 153636776, 114975516, 645698530, 61843833, 208670859, 422179252, 299842956, 282141480, 556248673, 261163029, 830001748, 963961096, 417267319, 586049156, 434514459, 95559856, 701675720, 742247485, 780100137, 553826560, 511777143, 810700922, 178562837, 278912413, 792562149, 830131617, 840319242, 656972706, 220353391, 209714305, 217506127, 171415288, 492445212, 316545283, 186418253, 495747258, 942996289, 716927572, 121516458, 324150206, 78870310, 242359396, 311285830, 347544074, 626900812, 96383529, 968026077, 817120855, 631192283, 267558585, 340962723, 299564572, 884333538, 729673123, 782449522, 128112276, 595918087, 881056590, 90970890, 53209985, 277776998, 349000459, 769255529, 474622569, 658206152, 860373168, 24342417, 172898995, 944311213, 366859326, 533597751, 44816602, 845415355, 566760319, 399180580, 896218905, 515963151, 429943422, 955524237, 847830211, 339492889, 3996687, 242228579, 45401951, 786715063, 876956038, 934322777, 334941329, 156647018, 68890932, 630391043, 417613438, 765323650, 393323632, 324604608, 683503233, 580675977, 937595006, 132823700, 649715565, 800420538, 557734457, 955864320, 17791558, 750307233, 98500991, 54844563, 625181640, 248232987, 420456810, 435375542, 382162044, 835818290, 944927674, 71835518, 625069479, 956907299, 420805115, 487286710, 25106991, 333016489, 32543676, 40221505, 821729148, 483410385, 750368272, 254124404, 970642779, 595925379, 923171861, 396301092, 704485755, 144873124, 685905722, 710495081, 994280253, 266804648, 155973779, 970585210, 519704820, 597521343, 214341514, 56125095, 50784357, 524744025, 49173433, 685449757, 875633125, 776006856, 952345901, 956774787, 770811711, 479605531, 934499616, 835556546, 311974249, 530110836, 991157691, 828635774, 402394100, 557627402, 468862455, 622384190, 259215079, 508020705, 250456354, 734071770, 116914617, 145341999, 438386009, 503212069, 407499498, 274364775, 401746300, 650741617, 273513159, 907806549, 471852223, 294924080, 641833337, 849869383, 453173406, 417885064, 773090429, 123329615, 957686031, 118920069, 890748066, 447563919, 843055845, 203478646, 699456062, 11438408, 965652008, 994041814, 269371787, 545906846, 759896176, 708130815, 840254284, 242256351, 670711536, 335706857, 627945847, 16673152, 85588594, 352511505, 6531853, 306396342, 465418776, 43610532, 391852435, 919405105, 443880721, 847427935, 102352864, 130624530, 683117801, 903898062, 973775344, 449648419, 530055586, 45280042, 492069199, 315576065, 480906281, 492118769, 332173926, 737954075, 787474701, 676685282, 536243140, 561333732, 238014942, 421863200, 552164528, 970306102, 856227710, 250149885, 299802776, 880589376, 394791564, 69677331, 427139059, 779244723, 579434808, 734910860, 40108094, 993460001, 908599905, 959668251, 314095143, 510981928, 394925613, 868406112, 689293047, 172660278, 688279797, 451992508, 730949205, 752305346, 524612531, 358198581, 86551598, 687365692, 744334655, 22965731, 501847291, 209629262, 411387243, 891523658, 544206063, 706607254, 512117598, 751450715, 499446903, 540093190, 54104618, 72915590, 911311812, 66368563, 548473866, 553771832, 43539551, 783102698, 427690359, 322343454, 901702241, 654968871, 863595857, 403121836, 928590219, 813886853, 970080693, 775018807, 371754456, 803811894, 283790149, 785538617, 750917099, 248507853, 372554311, 229827580, 488790446, 603464971, 994299886, 710846124, 332544588, 377714696, 38913820, 36179002, 270752293, 582565957, 991815042, 782967217, 38597981, 515705134, 845078653, 389475918, 885963128, 438876483, 266213523, 748856886, 767261334, 958597369, 711857355, 684856852, 506975199, 936610428, 675236770, 545696748, 434570912, 629680821, 313526701, 174506850, 632922028, 448121761, 344515039, 758519581, 325196304, 456000280, 673292961, 998603445, 965126684, 79244686, 826019091, 755292124, 575042139, 211564415, 305569990, 211626397, 191745652, 49042924, 886000551, 123073007, 211611981, 882708533, 577172357, 427152651, 379738271, 528307241, 544126283, 86676177, 838994082, 932759268, 30002058, 386774786, 402494386, 850740581, 818071747, 456928501, 263879951, 149088080, 219326998, 844418140, 818141253, 967843914, 773743088, 338090109, 634827754, 189930931, 349277181, 754504939, 813146059, 367298170, 147338033, 50223827, 568110642, 263128680, 302217743, 24822115, 994621681, 771530530, 938711204, 281550253, 781214019, 168653535, 375447126, 915283625, 807853722, 756526466, 209273582, 165290712, 527559723, 440214076, 545761137, 650236313, 772568659, 925805142, 383584462, 408011847, 476787161, 624802182, 951652505, 983369038, 791692223, 425228166, 302303296, 403043288, 959014457, 183818023, 896902619, 761120830, 644416660, 865556740, 350767252, 404903567, 200572534, 196408538, 9151832, 63842803, 524867946, 134208470, 523321373, 782119433, 228587101, 828740342, 321733373, 630294120, 22074130, 394153095, 341116287, 896595485, 971136681, 595878894, 546765053, 373640046, 587017126, 520959626, 719477325, 120831213, 169063961, 765104245, 584581009, 80777619, 265511042, 956882335, 516154219, 973045845, 44548581, 233167216, 884682184, 974291625, 105926972, 609690294, 568951617, 268404819, 723024363, 107799614, 130910198, 559802656, 910194586, 226535121, 963643925, 303402768, 766041012, 889106110, 371022242, 767588573, 989763844, 2320068, 570430245, 104394037, 692153365, 66680851, 175012319, 704784592, 499880967, 738028152, 745136771, 565916096, 493854091, 732517846, 263436867, 948669030, 205739002, 568140846, 963731342, 437900289, 401855736, 268797459, 544097504, 505845706, 768857490, 351953770, 223925194, 874930602, 488456580, 324108910, 296140285, 279405742, 943206901, 114431234, 404470924, 414761641, 953651619, 401913695, 423216516, 338476387, 205111441, 498683976, 791040868, 293903950, 501953463, 849492391, 764322779, 669513855, 330583707, 430829665, 603214066, 854780945, 744011539, 688159839, 854522664, 154798733, 851358981, 445126510, 763362365, 249104758, 468328251, 204805989, 491522680, 484521448, 748708206, 467108181, 301797674, 949966719, 495003448, 40078433, 946685043, 629013045, 147388809, 405547963, 928946540, 37947508, 987342133, 781501170, 176175770, 155578203, 63289188, 738280545, 69662058, 828942683, 776361246, 503489817, 565058364, 931681058, 479869950, 461855814, 771106600, 740435400, 294488394, 806855205, 747057514, 742467110, 269764810, 528324442, 218153989, 661698165, 215861410, 194908050, 398224779, 640581912, 119331136, 99673135, 172927068, 681676455, 707492279, 200592961, 782048606, 879824566, 497373364, 652907057, 477441994, 72366056, 731358927, 414942953, 138911887, 577302364, 262378080, 660258205, 128107564, 144632827, 713596346, 884205485, 883750073, 213998159, 430506416, 579744504, 465272555, 317855761, 58285403, 483903428, 42664093, 410217719, 272628784, 129544388, 381559287, 778418093, 457844075, 501863088, 614058326, 28129292, 86830512, 593075876, 960725025, 4408910, 330553076, 777818268, 217600722, 546321235, 420195264, 903445630, 182579901, 296829403, 975204590, 915566684, 395625563, 1905435, 139864595, 167101045, 485008887, 565062166, 973879326, 799009741, 77419807, 612101920, 811841691, 275111577, 387617673, 930313783, 49317442, 38114129, 397604711, 922313604, 31784350, 303564015, 308693636, 426474181, 391758039, 955983900, 963797303, 546558538, 537096289, 561741033, 879377195, 552996889, 143331521, 658962847, 745229358, 490191646, 513987265, 742023125, 720349103, 52328766, 684325674, 564264998, 521068225, 971773847, 663870656, 990633749, 239750798, 315924293, 85323861, 874406388, 158651459, 820008488, 597365122, 96486293, 140114255, 37962620, 35220549, 694248479, 297184539, 416777595, 513660798, 503202002, 827563165, 373687482, 620474279, 822453057, 330972193, 789202746, 645753041, 312741895, 499149723, 421158510, 185998837, 176919226, 875045219, 423325691, 316625763, 197942825, 893122655, 323150931, 599832130, 196822240, 568928407, 392422421, 81900196, 903805589, 894471170, 239182432, 26379398, 464908250, 450323952, 398271628, 262307707, 933766934, 848764146, 903463860, 358717977, 35164346, 881148451, 860000791, 567559157, 631149453, 466252628, 717292021, 22304220, 470970358, 997505935, 36894115, 782116582, 660809812, 552632601, 691582975, 237410403, 730995412, 258248487, 766304326, 485143256, 380227098, 293099114, 657259767, 586543905, 653381060, 346188766, 449945959, 877865071, 756049452, 737944770, 830842600, 343884407, 630226181, 25382247, 832978604, 695993082, 865830582, 718842225, 456466318, 837530700, 362267482, 627613401, 187935265, 413783223, 5466641, 612557019, 571838236, 83297040, 740800534, 567235724, 953116092, 770235531, 335449107, 996319095, 543204769, 543360324, 32538957, 102480990, 462445550, 457722096, 440736218, 126737056, 327372007, 106388905, 845515237, 697046199, 416967687, 293002775, 380025076, 62058084, 383139463, 874930300, 612543277, 922457663, 753711176, 157555384, 956227261, 277950190, 556784325, 296650514, 365419009, 132806707, 320282640, 20642142, 330994238, 43087977, 319656626, 114449747, 307108498, 138048136, 932231240, 657381358, 301511377, 438100808, 836597941, 915549713, 273753214, 554166929, 825252561, 750497714, 772124561, 527986897, 16066724, 975304407, 910537817, 817384643, 225186325, 402211903, 13006467, 61980649, 904188951, 885980611, 776962285, 372582191, 120914122, 672195962, 943555550, 310166401, 917852121, 683997266, 748576266, 466605795, 867528183, 741597650, 551677846, 688174192, 514761597, 536924773, 943648104, 597088886, 742870275, 437884076, 118866626, 878787365, 666739587, 183195560, 27805477, 775444002, 904490921, 165324451, 876287368, 526915990, 257116685, 808468431, 378328889, 878831667, 964826076, 378412432, 38538741, 979196045, 830962866, 936523304, 852613562, 885081707, 600459281, 267845902, 316484469, 504223130, 123797882, 305773650, 831943863, 83228176, 209181066, 632940520, 653357604, 441643872, 757051167, 708090399, 279654300, 335225220, 255765056, 48551268, 371398881, 407101534, 329723751, 112976096, 640285521, 609042771, 134584090, 357486981, 434517327, 914672406, 726037494, 719881430, 49662889, 646361056, 173100191, 866352991, 718211947, 307579192, 691793804, 974013312, 922199308, 895410380, 963095597, 824344285, 185860590, 818302384, 777478447, 883492737, 979126448, 28990147, 789437000, 257024826, 356405847, 141076781, 556789686, 266205070, 947442495, 545702335, 389843988, 46797555, 966523349, 664128266, 759595109, 41648338, 49904416, 187316250, 568629954, 397673850, 611492460, 457975089, 779834585, 896866250, 37313998, 966050845, 452061571, 122110682, 853623712, 458632336, 358441875, 988448472, 698089789, 26461337, 812075425, 609988311, 929183959, 249920277, 268745312, 156402744, 542062411, 653113472, 951018070, 829975059, 974437237, 82281838, 372887294, 413912636, 249136184, 269615761, 584944767, 1301038, 234540731, 458588722, 279692879, 782301322, 304346642, 114990406, 249264700, 292698490, 713510549, 970709628, 294319634, 799162390, 778080765, 88591797, 147420790, 545301382, 254615620, 555205083, 78787568, 711447495, 64255136, 319521738, 726691605, 619742881, 203418173, 769541281, 933476841, 638855723, 349988425, 696113503, 110815465, 2653882, 597499754, 696749915, 428641538, 512329879, 469344423, 373036857, 916179109, 574071693, 358043840, 581239431, 506481328, 130752475, 398179759, 6721036, 130315247, 591497229, 797143744, 569449786, 160936612, 46291642, 49380359, 624468377, 129766972, 388576159, 626745987, 877783364, 681095717, 116599597, 593152138, 571881454, 366144315, 891207353, 795467933, 863107302, 547959772, 238957274, 170986019, 592728691, 847072921, 72173187, 291222179, 173898244, 617177937, 880847585, 720097264, 938733867, 738025659, 450390020, 337915757, 207030467, 598223738, 802584822, 98977919, 756526124, 234433483, 28823140, 843224904, 357389175, 955929828, 769371203, 804164839, 589109162, 952996061, 531529265, 202866895, 942284996, 592763291, 96685445, 3514007, 717921048, 978301469, 428996796, 515339475, 561115859, 991968401, 163826310, 488589800, 565368753, 161780141, 341754354, 533093399, 319016830, 899031017, 100073474, 527856136, 66599932, 781121058, 315911177, 317073429, 116981097, 948937027, 516716052, 807783504, 207323279, 887590697, 611021988, 71434425, 229820440, 346805350, 674451489, 715527202, 495987187, 403776701, 314154537, 624814613, 339655888, 716154121, 832408760, 86181967, 10553789, 426176624, 581653120, 282808335, 682245651, 589630643, 793643487, 483579161, 145011632, 809556691, 416818945, 569669189, 809562900, 948255577, 280709222, 103619387, 482802814, 815384730, 466984119, 517154032, 367322724, 18995837, 222618695, 296988871, 325462697, 913047740, 523038748, 697851032, 821488826, 266953665, 443765054, 965770381, 142002164, 621143511, 69952074, 760404541, 147819309, 8705814, 787503717, 382038885, 380013948, 431203693, 955492305, 858187188, 955702326, 971778555, 162524227, 548741703, 221738583, 71715646, 910517556, 899019674, 766394707, 993151567, 663051575, 11804813, 561257085, 26955555, 724910469, 772796609, 410662428, 856301940, 875334292, 920554541, 883207814, 274585421, 186113272, 513068830, 962439740, 71396846, 61885920, 269081067, 610008220, 752177491, 872699743, 407275781, 355278293, 67575904, 925611207, 111020333, 183917550, 538128333, 359767675, 223488648, 226474912, 459496718, 783499020, 254765673, 441370888, 586894709, 113148608, 35995885, 165815443, 855821076, 341970009, 429443609, 220289183, 108018136, 51778001, 188704128, 92173615, 269799988, 944412496, 688783267, 774793109, 416618472, 878703604, 633228120, 181010721, 239289728, 116292352, 455386547, 373964028, 806360130, 462569001, 81531067, 583922150, 199316276, 259110970, 620935107, 47698152, 617797632, 641187303, 646664985, 604524349, 793404020, 806910225, 629824320, 341668801, 970186900, 500901893, 997162038, 42025058, 494987946, 137600822, 419534934, 636998689, 600446790, 153239149, 828959166, 704749926, 895971041, 872986662, 471499744, 109489178, 621636850, 120074057, 996514683, 834587381, 928293642, 240412161, 224985979, 498566247, 411940257, 439837518, 597121243, 429859694, 309471632, 506584595, 928967368, 988473165, 791091238, 989059, 896603326, 345876617, 538851983, 347371943, 606636620, 997384637, 739856604, 900598319, 211048440, 577403815, 146737727, 945453886, 91791860, 125010973, 631275781, 265393999, 308892368, 701925314, 454612378, 158699510, 939947486, 790667203, 203482297, 934307125, 613705538, 111041694, 827982708, 279610889, 619386540, 826528331, 202134737, 561525728, 18837052, 724137095, 766639649, 757667051, 338281837, 38401195, 624219978, 846521832, 567711635, 730760990, 220637279, 361917059, 141809196, 544328435, 85139590, 959810542, 233716291, 161295108, 838594825, 629333034, 275300372, 950658683, 421322357, 759891044, 70710522, 796667626, 670218805, 19547475, 670086197, 563070325, 585259968, 674926342, 958297660, 457161069, 782434867, 206889635, 921212590, 177069678, 59691086, 28771599, 576588441, 375683845, 566421082, 531627469, 513309913, 610068913, 168479894, 992687939, 978771664, 251305400, 22690677, 882098257, 11002299, 151193423, 988363369, 823774266, 32696858, 386823623, 986068993, 82572359, 271019625, 436982648, 834165061, 58985962, 496021652, 891454696, 126271594, 500931690, 610168345, 587004825, 896767753, 509445481, 661463290, 85876051, 95918868, 555347943, 346618082, 745145816, 355420469, 544423285, 880663016, 316609641, 122565166, 999718220, 604712346, 239397200, 664338416, 74892894, 481173111, 95378450, 561164894, 180776134, 814443382, 376080321, 478106708, 475850392, 593680426, 136657648, 862906286, 964999194, 984775026, 74133347, 610611612, 521200353, 950381187, 302587211, 647145063, 871964410, 530914544, 125370572, 344395743, 305851135, 167141694, 519050915, 665460693, 567581688, 763940223, 205387052, 557643721, 956629725, 529962983, 38737708, 205604687, 601374776, 59489256, 261496990, 166177063, 801577651, 788919453, 20302944, 534673542, 175859601, 506157506, 351380595, 361399822, 482916023, 230327520, 622413699, 185333335, 339900659, 11601443, 404719335, 494626561, 35187727, 546888612, 233615159, 980163661, 924660368, 983468837, 992406132, 984194402, 172603273, 837404966, 572148156, 923309756, 979248599, 901724648, 742093731, 815843952, 528713147, 690619895, 611562126, 954151553, 60046764, 212299709, 832879912, 273082988, 347096808, 484824496, 268322518, 272655731, 877981785, 644637594, 318112321, 455511269, 546290116, 626469936, 181941572, 557620083, 653597703, 800343331, 784764259, 179971842, 817343020, 753010231, 944444262, 863891983, 740253511, 535280330, 15132133, 952738691, 623589467, 555652345, 774169942, 527675626, 980680310, 986771315, 251810357, 741804418, 449508789, 487322974, 368665101, 555637957, 405754482, 718494453, 172133727, 270159798, 152118135, 349122050, 110141575, 341347836, 52945785, 926786934, 758082967, 748328844, 865906308, 545778528, 208146132, 683810325, 295469679, 187183511, 477841613, 752361279, 55684122, 414082615, 128732586, 52127123, 501911097, 754977028, 572325224, 45172843, 337530144, 752147861, 287765947, 878543852, 326547936, 550868154, 678572279, 620084249, 174267694, 161631550, 369717224, 271102302, 833709899, 511294014, 339375114, 972716010, 679616529, 315566241, 296176679, 564945112, 913800967, 951578591, 418865921, 577482385, 403903813, 323630224, 84409343, 308346387, 381724214, 930188324, 694766402, 75034437, 397204166, 462869753, 362015996, 743608007, 423327761, 734999686, 109211666, 494816750, 561026836, 765229896, 938115695, 11811949, 475703091, 740860728, 988292465, 860956077, 10182835, 336501348, 819705756, 278226746, 196634753, 274622519, 628868307, 804527610, 728902306, 931036594, 261219647, 233819574, 916827436, 109872709, 571336136, 813969057, 820168205, 711032183, 763567784, 83686505, 626300467, 538886881, 251955603, 78899445, 880811692, 465263541, 522637988, 505088151, 628714880, 514940408, 375329322, 349783287, 57636404, 123014092, 858965210, 168390106, 272301955, 151895971, 63723613, 592842219, 219047477, 907610130, 938291194, 741328259, 758695914, 546154398, 24442429, 558375523, 873639681, 462787815, 983407834, 329935398, 440167555, 824968184, 689903796, 810468365, 752397493, 940259694, 729729838, 347867114, 416167035, 703526335, 837075010, 508907732, 28944547, 261234093, 436359889, 743887999, 14550180, 149960359, 828613191, 768264123, 847761550, 503349966, 173329384, 17491470, 157621845, 26688306, 355852685, 348796642, 504312202, 983371856, 196606384, 615176714, 876919950, 882011862, 915098123, 637916469, 419379034, 894429865, 852150260, 148996859, 582375860, 196839431, 806607005, 418828421, 646743533, 557250806, 215127448, 792878137, 395401631, 459081754, 30358937, 779097719, 635961198, 708317367, 760457654, 38038483, 449836965, 767096526, 352944412, 623984223, 503910543, 457470836, 336805169, 874074733, 751520944, 241160749, 454555908, 817030168, 796741754, 373584005, 332346095, 569787855, 336098304, 653498365, 816611216, 736887606, 923413887, 522530168, 581853184, 778697463, 881843293, 126534564, 146159712, 198179320, 102168509, 60946545, 46811250, 822061276, 38150749, 930177964, 544088117, 575063602, 782122260, 978861786, 83913939, 181763621, 995703841, 474890509, 771982044, 919161856, 341523393, 239689402, 338477449, 170232297, 835753766, 812608263, 571810966, 420923818, 486526653, 396720816, 709781381, 942282561, 535854744, 139738683, 676760181, 333487727, 640066825, 593688925, 772770547, 613611424, 950283142, 847120511, 689184001, 171449858, 582827991, 715763875, 275839525, 359548645, 488662388, 577528369, 632631269, 730745025, 355919195, 937660827, 328345953, 563058556, 654481273, 773920165, 68292411, 513939449, 899214165, 745386543, 95465750, 314351331, 255060026, 601982263, 696701315, 875753492, 677639894, 482981078, 54360269, 68826446, 484310561, 45719174, 701064011, 41249599, 973529067, 710606659, 638792378, 443386494, 124447928, 779283692, 306636493, 219288264, 193668681, 225757005, 591044639, 129615929, 817593224, 647947264, 935668712, 749568443, 223834284, 180376274, 430959319, 301511550, 141448873, 380191025, 308667241, 269106093, 960653162, 957260340, 838090114, 605479768, 524516879, 381159653, 5384362, 292315642, 985057191, 315578994, 934959270, 323223327, 271994599, 813201575, 25421809, 157880703, 843880190, 263262553, 427206376, 720994055, 903169437, 635107582, 236662465, 42628804, 72406436, 73516202, 309103833, 878315055, 210999350, 317238462, 908524707, 484229503, 950195924, 795445657, 273601126, 798251354, 415048399, 823831674, 651335612, 607504284, 124800657, 278487233, 129069581, 282914086, 211373135, 668469335, 966578317, 301084385, 49926870, 876084577, 641702331, 58894966, 160266939, 889363566, 306743296, 349837669, 307243209, 228685418, 477260672, 290806821, 574313943, 33424464, 63478897, 456999241, 172293831, 615838329, 743695143, 191628471, 130469185, 777345990, 727084576, 243024089, 396381651, 563161255, 690593644, 590988749, 802301386, 212595762, 657634185, 340755448, 510066203, 842438281, 457199096, 657327193, 266539752, 452797960, 940784872, 372942853, 720372268, 834777623, 430303124, 846785123, 77516078, 816629519, 976730057, 542438987, 708657950, 730498985, 182318226, 815142119, 322689010, 61137427, 819910296, 347860751, 776873943, 328442438, 643097050, 748396127, 864004170, 634977217, 519994106, 428445405, 887216251, 307846089, 29333036, 316795753, 801120551, 773830157, 742228677, 12751902, 87812349, 100051701, 130480081, 594520608, 732361565, 351051394, 690670971, 262590570, 400898976, 107287935, 293300355, 910924361, 919378273, 338259855, 163241411, 228595150, 670300884, 163429449, 562036663, 493754322, 982888337, 466456681, 273013383, 308436038, 831269593, 681242827, 154792912, 350192812, 374332715, 464824557, 717232350, 786209347, 508688500, 52782002, 326832186, 285996481, 751715272, 302979245, 237880379, 238804882, 131460535, 386973916, 641553292, 782730462, 546316085, 272537169, 359481113, 707106570, 985586398, 499242128, 803165788, 369796661, 753868067, 868133840, 421271971, 82449246, 833064632, 191320016, 898516123, 59900361, 379221908, 893510409, 242691040, 122098101, 734134808, 990760257, 946719377, 499821949, 775360337, 492346064, 569974175, 912639196, 520224471, 962076799, 779327374, 749463344, 148849655, 402569666, 509053561, 12832618, 375707339, 434303503, 972985631, 90632173, 237922060, 753478355, 233422555, 19566844, 495345750, 912250128, 102168598, 32641546, 93644436, 953909276, 356633497, 326795452, 772907389, 299397730, 950934414, 891959296, 512529108, 903615738, 129776946, 8496954, 397365727, 140130856, 89277701, 857188967, 233962656, 983984201, 162291830, 596127729, 884988610, 769858367, 639410502, 80293853, 230368591, 14318624, 318342786, 356184602, 457224519, 758702206, 411699855, 445638955, 937274189, 189351017, 67172521, 712033969, 554156881, 277564397, 956075952, 300599971, 350989384, 746729263, 883538751, 683544045, 61196223, 473557386, 660880345, 212090126, 622021720, 224158410, 455390204, 709217321, 490648641, 614022473, 241836716, 820147677, 717010559, 164718496, 869954704, 671159607, 635705179, 327402030, 125383570, 408260869, 420557442, 12733586, 792774750, 163696477, 69448752, 95368536, 190620812, 636834552, 902628291, 874316003, 506747333, 466925542, 883805234, 140646343, 519776442, 877165800, 229654553, 116271213, 417445625, 776588756, 113801065, 902164090, 168690182, 512795841, 233407753, 328755834, 733379946, 2526874, 692714202, 982406327, 474919358, 978306128, 471213520, 34872159, 792228186, 11801266, 1147360, 888533258, 283382150, 57501877, 386955387, 845257226, 277035087, 378385659, 419728058, 358084270, 917032228, 543457803, 766895652, 717733167, 734940707, 70252335, 891227468, 2167790, 575224551, 143640824, 300664296, 969975751, 922847082, 760875228, 297492797, 155211728, 492403541, 816613050, 167727072, 719581300, 941625444, 949415458, 14428575, 356956262, 376489143, 48439444, 916301262, 595904695, 614798103, 341992179, 705304972, 497267429, 658788202, 559010237, 72682158, 138452782, 152198361, 287780089, 645045625, 716108486, 821197215, 508924900, 159009075, 224763712, 402903388, 231575246, 791548054, 750746925, 902006559, 922178662, 752542974, 628635186, 251846636, 933929515, 404337934, 58996910, 422072307, 425019033, 120663286, 296736584, 363973118, 941017736, 631994521, 300505, 599002682, 804833744, 182800919, 23587027, 123936292, 952200039, 955952138, 660476845, 871729107, 724438012, 374623945, 223225585, 84707331, 574628591, 665659880, 255605134, 484799202, 203031162, 230744379, 407729500, 843586684, 761595755, 5280705, 772468911, 517900460, 767212997, 57217087, 158877359, 457848541, 297779543, 143801027, 803316139, 20589887, 801219859, 604888816, 657260636, 409272810, 134144596, 129789687, 567553693, 557431389, 212375596, 415549186, 894937766, 322635750, 216218947, 508808721, 882939158, 602741177, 303046222, 201295532, 198319483, 239023044, 17456429, 159517136, 124869094, 727221066, 659691863, 140782770, 737763508, 667994750, 942747534, 511622025, 208383543, 517175998, 433416636, 560347149, 782892214, 937257046, 74976349, 871061430, 144474943, 457731681, 523433542, 360030963, 584006314, 402597107, 795889012, 547088958, 930555401, 862878860, 236886112, 360470358, 836850844, 187856202, 42793412, 96721278, 123938180, 339086279, 772420362, 749501522, 980661948, 68060440, 655164317, 491174423, 196885286, 781339930, 217140566, 32363900, 119373200, 181694078, 529868729, 394064327, 597325487, 89247140, 445247580, 105429215, 389816527, 182373189, 430430456, 144636832, 513022920, 711035795, 821600511, 194160501, 324562391, 629948703, 201947988, 90828480, 57085854, 470795273, 201907143, 424930106, 120502165, 109648213, 315713452, 94988410, 719829818, 771233105, 668548684, 831057168, 868435479, 332272912, 154267409, 90741702, 335523755, 308794457, 205089899, 233898038, 658957145, 332119097, 468076061, 471839478, 812962500, 585824384, 97300886, 31256506, 453622535, 885725014, 581295007, 956805519, 496168556, 999676011, 553459895, 524984711, 931722028, 332489479, 684668512, 905293309, 578240292, 690856300, 510448435, 281256329, 275454613, 523439728, 997344202, 393817989, 48127441, 440389512, 726984832, 318371220, 701239693, 706582674, 991662879, 400178650, 580445866, 766018698, 133354285, 91351983, 249115389, 947104681, 643642151, 495253636, 261967192, 74328008, 102786390, 790627566, 845571997, 923214189, 684831195, 845992705, 96792540, 79427987, 761840845, 948742103, 710310729, 287022348, 676124369, 393284545, 97805573, 593815060, 910908831, 27105527, 94715862, 998092039, 345655034, 685409222, 885940211, 642652684, 563921989, 169545780, 726632970, 8009433, 545962539, 8372569, 936612525, 687172902, 511114039, 763513134, 985646433, 758467293, 548509507, 788165729, 969606266, 429581379, 780458092, 6069038, 327163618, 6828051, 572827572, 800825315, 919359290, 970059031, 54367137, 913893846, 607571684, 33667867, 218684404, 48436888, 592234076, 849311274, 837548696, 15237107, 159896288, 158987384, 972330321, 860310576, 509556224, 931346399, 251697882, 523361223, 752182578, 368831958, 753409227, 614636786, 721993497, 979939731, 449106031, 75772780, 501486507, 625317308, 991815349, 994546430, 36659376, 874985823, 459981690, 147973841, 956913815, 123345392, 463973189, 405394123, 84290668, 237109464, 544798254, 517922917, 333464474, 4140155, 966531612, 646609304, 639175425, 437742187, 975045295, 317360008, 850624113, 534724392, 756004320, 370288904, 428431350, 233172048, 883701604, 943358034, 774551117, 645158835, 229088686, 551281260, 117007992, 769076927, 824951576, 987028479, 431695323, 323825183, 715619770, 658587018, 499875002, 44334913, 719623042, 381899088, 941352197, 822685668, 234200100, 375279902, 253369760, 417103496, 899737092, 61573967, 925138826, 409005291, 616164766, 361975023, 24483732, 472414687, 564236026, 297950980, 688541676, 274925637, 418859804, 862523834, 903276088, 34996310, 610366276, 198669623, 834797021, 110050687, 17585688, 93341032, 935923442, 726481640, 882903431, 468270962, 214810378, 137660162, 693464152, 419056919, 431421599, 606561685, 418450231, 747175108, 736077385, 525042411, 640044860, 211977335, 937605204, 171490402, 858321577, 760164894, 958247473, 865675880, 952204222, 490689708, 862654467, 811145110, 218886244, 577885276, 293671775, 37904631, 907072366, 451684532, 908974349, 506683329, 54490334, 472140785, 151319928, 548617084, 531621060, 815062063, 783372223, 582214836, 936506155, 972318507, 557919391, 505993398, 846899215, 475303366, 394559604, 482572394, 26184184, 371944584, 430950325, 67424337, 686943294, 412810147, 78157074, 216384190, 316113661, 357758382, 216898540, 597085606, 389526165, 657118484, 393068232, 784803861, 691877675, 903885910, 33575852, 594710673, 541449123, 230839105, 786829690, 786019545, 658144338, 581254247, 391350065, 370728228, 251691160, 393416851, 81779561, 371517515, 342008758, 600358933, 297801653, 244842197, 855223350, 543524382, 830120611, 875561833, 120053731, 716458049, 235131984, 231017392, 382753248, 754255512, 7097761, 391214239, 683624636, 24846569, 480228400, 131193191, 214159376, 771392918, 520494827, 708059368, 597683373, 823495719, 610580891, 876390088, 362138954, 768580062, 965112323, 193302645, 946312096, 616101752, 105761825, 828059195, 418606872, 333507468, 634930193, 975607907, 859919102, 210053844, 551160618, 47106146, 813801743, 363828454, 727494286, 498937579, 23273200, 866335846, 692466309, 902620384, 672045258, 143731586, 964220034, 918193764, 826995, 728049148, 447849111, 394253023, 464207222, 285802386, 555448289, 813501760, 182583910, 396414693, 968574881, 284168283, 522070878, 295783458, 529350563, 153044225, 805139219, 24703632, 593336400, 264198027, 873853187, 906999041, 700893384, 487473342, 274663352, 23272378, 66038415, 577545486, 100520842, 765881913, 450790822, 502523579, 93321990, 386109624, 482288591, 954008625, 106842956, 634588659, 24468402, 681909978, 232205846, 574675853, 639087757, 603401321, 559444617, 884852067, 500000446, 308066244, 466052532, 456532600, 50370637, 788563280, 567085476, 303665003, 505188520, 521826212, 665515551, 206372512, 291839966, 450289174, 867821749, 896623595, 21628669, 716516275, 743311546, 624182225, 320850494, 336181009, 445654542, 554444209, 122921414, 886389215, 493956758, 550394054, 695915462, 536560146, 222688980, 513153069, 331255868, 878233518, 75559661, 418414057, 980032374, 426983557, 48873343, 201647446, 945290065, 377842417, 63830358, 676615579, 127827313, 259664087, 966010865, 384919309, 184547221, 530917001, 531368793, 173047597, 898257059, 666674195, 422775712, 266424511, 373245676, 638515490, 912391099, 870949709, 183682961, 192994957, 814876462, 275601924, 200921556, 144417355, 417095474, 117198463, 262328176, 797517017, 372591867, 850139507, 729798062, 992639898, 406945413, 848675101, 207007723, 867595003, 596875324, 888168071, 133593768, 80493248, 537517374, 136534375, 191657949, 919636685, 318839435, 802601491, 143830307, 239779122, 587281543, 233466090, 600580797, 745762991, 749531628, 250043133, 358874992, 443043511, 401656847, 441438292, 306978235, 393155972, 668989929, 904761448, 465031661, 104173141, 516543481, 429816916, 369257908, 792381900, 233861393, 665232523, 244646540, 85242207, 168331241, 859408306, 134009024, 865923253, 335230871, 12932329, 924661919, 614243292, 607394714, 816269838, 70807574, 987353431, 463224856, 891740328, 824635658, 749090352, 253896619, 256036702, 673458646, 522140202, 262917860, 635145515, 683724570, 251621699, 553910199, 141532755, 546547148, 884620418, 313992412, 393490605, 294823326, 275869779, 175515586, 500824025, 331236207, 740986572, 398427929, 210174302, 943440157, 625096093, 549009095, 942994062, 484545199, 847661770, 950643669, 149061096, 940169579, 723718598, 730231841, 655924730, 227790544, 517723248, 604929491, 470839665, 259290834, 945417004, 306121549, 690177635, 616113903, 737718502, 304471083, 465273445, 935010001, 493955972, 689945569, 259900457, 279893786, 211650246, 127715865, 490493445, 485468948, 784454106, 553443603, 875521625, 316856477, 847077525, 956068094, 666877913, 821092213, 146093809, 342711361, 836461741, 459116021, 215693230, 155846006, 258160013, 69489692, 50663612, 961751750, 744693539, 934372815, 206186999, 901344168, 429748535, 237255458, 214300796, 994821683, 61260448, 609833424, 733599260, 283855095, 604098285, 809178204, 300040279, 912622648, 814075222, 446832870, 269811805, 155264516, 921304382, 759282402, 384905181, 13486994, 41034236, 344435001, 753639467, 12424038, 185702611, 446697392, 13227253, 905288864, 306882274, 631561936, 819713618, 570507152, 719567923, 862699981, 876991983, 994262142, 694458262, 846678839, 277536840, 482742997, 598290268, 220151319, 745263095, 551442745, 603422846, 440017155, 556719035, 27583635, 538316990, 586735066, 744188832, 754722665, 922442025, 901786631, 152108458, 214144084, 362451098, 707408117, 365969280, 848617603, 648525698, 921543016, 857992318, 119579055, 101853589, 104277776, 720308864, 217990591, 105143408, 337147514, 400187673, 950252975, 715454088, 361629862, 777042564, 398201460, 206749457, 687109566, 808056597, 842772876, 470885781, 977343072, 743790657, 919812953, 626709247, 229872560, 100446473, 595105155, 104318555, 694844076, 129531261, 792879859, 709139752, 75124571, 131386701, 169536427, 230828181, 800010675, 960673480, 870001475, 796527150, 767353718, 451049457, 476397614, 209019539, 784655615, 762120477, 351010762, 4186452, 805473830, 473310213, 119226656, 628320076, 354655728, 62959441, 886165785, 300041577, 215232337, 522745549, 614227251, 717911952, 256784284, 956610328, 9571976, 8127758, 147974612, 51273055, 74213768, 275186217, 844093286, 307739068, 642568433, 944517034, 396847714, 278247222, 762308637, 334233856, 176068553, 218878669, 81108452, 60198281, 236766054, 636394413, 224536365, 434303476, 320122792, 620776889, 237879739, 125334441, 496548442, 45593264, 719364527, 653775430, 677021071, 585105865, 287987028, 656961438, 669219323, 972816345, 108438575, 749141046, 456684885, 356271854, 812339855, 424889096, 637531277, 447707784, 596854750, 207956891, 330786435, 881084138, 634626867, 712959184, 114106732, 444681571, 305839242, 467342195, 300201444, 725050796, 361749080, 505661635, 500440201, 94002299, 633054180, 66414044, 245732025, 670206593, 557635504, 75710479, 501508662, 577019242, 649200362, 933858788, 732863988, 6238764, 817024220, 254069730, 287376383, 40867729, 698156510, 272236102, 591803590, 158951170, 723941529, 198269654, 196549150, 877696579, 326135637, 449444157, 416019985, 963029282, 9496639, 591337641, 451083624, 279525916, 317374639, 75954220, 939320328, 566846572, 740508683, 368618564, 827853419, 123075728, 739400401, 114693409, 202338624, 552672635, 283113443, 847065911, 926409379, 437240073, 454208730, 596839787, 845424337, 866232868, 972965192, 91110641, 35978447, 47155054, 331086521, 621959948, 886623893, 541493630, 672113071, 716322200, 114740281, 349614998, 110769949, 791103704, 744848771, 985328749, 16809038, 494093912, 360327031, 169707527, 767657997, 132414105, 364082276, 28118294, 564355830, 199828605, 736958426, 407242795, 435261784, 820504508, 530675477, 984407127, 601252645, 936757448, 492330428, 322026543, 599618008, 698248693, 914919443, 25051119, 342971159, 920513214, 303803806, 391261470, 3503413, 361703868, 631028815, 996076589, 568939939, 820203845, 159974926, 297052537, 423471400, 853399784, 464689270, 459257933, 610041016, 799637820, 735017114, 19498475, 192579349, 663488648, 734083037, 594264232, 736476154, 436286591, 450161711, 908554487, 907937870, 323670035, 165691835, 607684629, 441460802, 767883027, 865508983, 587702922, 84189748, 734996549, 186339757, 266624509, 330277035, 629695330, 147217105, 637922611, 31562021, 88506567, 56361322, 75102754, 141211866, 677713190, 945404145, 632596558, 634853118, 285929388, 876388886, 164309937, 113078608, 949112720, 352996140, 697638989, 468184730, 661686619, 77940835, 140325015, 339854515, 923842001, 554398481, 545103575, 437187851, 844541520, 994773783, 818664935, 724252822, 539231310, 2784672, 886114400, 823529403, 48958237, 334447143, 535378530, 654973826, 340594376, 132167129, 684541604, 571747315, 252198737, 303215727, 118771434, 81944422, 604235600, 835045826, 892514757, 325394861, 154909569, 615664661, 548276933, 513331437, 593363078, 329482780, 24613085, 562665109, 230411476, 575939781, 936900233, 15906236, 846506857, 295395594, 276275033, 613086726, 951635482, 887183154, 716992071, 304684364, 509337327, 432068318, 938147784, 498127366, 782396416, 802520712, 179594079, 588947061, 887013006, 575832111, 784931463, 969096564, 56118164, 425903649, 208252091, 629324838, 351392983, 757258095, 91382362, 307976741, 577827530, 728861747, 651914475, 400382821, 527219769, 614333754, 145020836, 907494007, 298786396, 88003618, 600186639, 112284869, 28505693, 407121067, 575119227, 221587096, 692419157, 379616117, 728319963, 13132704, 241266279, 949066491, 790387511, 56406161, 370370929, 86606514, 39006429, 928720990, 297706044, 205901254, 808360681, 578216961, 137252913, 985549456, 637307098, 759269588, 321259113, 41742701, 707975823, 148583395, 604696056, 607732845, 4434798, 831348204, 306217222, 353534632, 480849120, 719227465, 817160258, 921901383, 542815947, 264687491, 59613545, 288978804, 491324329, 616134108, 826351814, 585977184, 989747111, 761058494, 139418380, 197393419, 454425081, 883209170, 609418662, 336488857, 575420440, 370707246, 937579358, 563702071, 122541642, 189714729, 738901376, 606694523, 423889881, 529709512, 190385468, 687635442, 137668442, 109022913, 353482536, 877099331, 211227370, 597598355, 394586613, 202680403, 288819509, 692128955, 877186791, 231662814, 492458694, 873018654, 660355596, 420814250, 886464356, 856456144, 209738127, 977016290, 551153420, 970237676, 289428232, 495380040, 880406369, 171870087, 28908001, 38891814, 989764935, 780579718, 785382508, 660588792, 442977590, 487815046, 801586322, 919035124, 76321811, 489540291, 883528417, 774411360, 491757664, 56471680, 360665529, 503146173, 365436674, 251240275, 843152207, 593091810, 890613537, 443054327, 2196673, 120171714 ], 24944 ], "output": 10907454988577 }, { "input": [ [ 688263854, 42307608, 615339552, 955535160, 411496573, 85798758, 491655613, 470751212, 493060421, 613887396, 684731244, 695068205, 793290529, 649060860, 246706305, 543081175, 388978688, 8527206, 589603287, 661024460, 143077993, 583379837, 840588130, 628086744, 804574416, 454626534, 914815785, 618389247, 436148260, 328005575, 968581581, 828507731, 276950332, 815475068, 485240119, 37261863, 403199035, 920030519, 633456779, 794941587, 138165574, 23347297, 228297405, 757843929, 372780966, 524152922, 941949718, 772895166, 23591724, 559406179, 532301531, 158308883, 171223376, 988093785, 583999466, 136200282, 444977869, 51290647, 154204081, 420205813, 255028360, 312480930, 322439008, 319175566, 659970112, 510223972, 345190091, 430532758, 830042939, 430070365, 95410605, 899465380, 841955297, 250531149, 49890237, 224891103, 622386917, 86378506, 314764878, 899015478, 107883772, 443546412, 357996440, 882350805, 797392782, 477863261, 880516381, 17646181, 541752036, 842417878, 715176999, 898905785, 912396249, 439865851, 432418597, 413414041, 141077155, 846561586, 343492920, 938687337, 336070914, 947284629, 418673660, 764098484, 308128975, 99155114, 686500352, 75880543, 497382697, 914331545, 916186691, 231933257, 202782346, 276615852, 71614513, 821723459, 966420584, 227752813, 148528793, 113064030, 948322186, 657304273, 877572960, 40772036, 300841464, 850143157, 809570671, 710679331, 313580218, 351421080, 19499576, 432999644, 526585938, 586109883, 626036571, 330172815, 70095745, 345023658, 563234744, 245267863, 744371859, 915506011, 207433270, 136447651, 694884438, 629168353, 153662091, 750572566, 459669505, 748783210, 298924555, 116986502, 250698022, 66711992, 522889700, 33144005, 714650944, 444103773, 883398909, 842922446, 385925909, 687047197, 548913869, 350152449, 755337144, 319062363, 814246266, 773474696, 780113753, 594682323, 186352445, 437776629, 468104032, 76991014, 386780057, 210529717, 149578748, 97478186, 787066943, 833765057, 2337685, 782125836, 514198857, 774912650, 779709988, 477935902, 311619623, 144214361, 922746190, 773225233, 914259697, 277561520, 38413846, 603755445, 998784945, 685907723, 451732158, 270906254, 483187032, 771011010, 981522275, 40469499, 871012931, 260243525, 115236226, 775784669, 149294508, 294748308, 940086604, 542551297, 672034985, 498417442, 194649925, 467140255, 819009858, 765698823, 905566979, 392757314, 805237588, 891980356, 542086476, 697581044, 68905250, 68037927, 853254984, 731589444, 963713722, 898076595, 397762654, 569140984, 650022853, 582367922, 260994759, 94581342, 576962943, 509868983, 952465002, 225209645, 284832331, 716447514, 577438371, 588540073, 951417550, 36421486, 495805081, 433249981, 375408267, 447996238, 790035513, 431425059, 820525226, 681150250, 312235154, 850078288, 374101843, 158783071, 179543765, 91794413, 752886001, 246641567, 177756457, 822332755, 672532098, 308921067, 279408197, 415937781, 590090530, 703138753, 31472860, 867413916, 603853653, 464879251, 369882678, 273655307, 100031925, 491744776, 30277923, 981301152, 987884576, 138241468, 888158605, 683518189, 285066303, 398118107, 491339174, 801755751, 215823019, 21787503, 478935488, 364277891, 666950008, 197232931, 906052497, 176759162, 127273092, 660053208, 97525278, 683519481, 169378721, 797759280, 822771876, 865735373, 289416417, 841565643, 770641038, 989448271, 115954010, 760146378, 909404769, 16731371, 359517499, 526175408, 808675857, 951446717, 286335520, 490008784, 86136049, 237442648, 746267248, 259187079, 93657188, 519225361, 608817449, 515863423, 763007025, 317312105, 370616137, 728702679, 355287616, 974833975, 899799582, 689810727, 192015415, 28154302, 816380227, 623892182, 11410135, 893941489, 196957415, 369889913, 75741383, 787334291, 883839062, 842122446, 297459941, 871663268, 514859268, 64293814, 443823634, 865996299, 624186513, 909159848, 579814206, 460203056, 925892728, 820741984, 314359974, 735809104, 564115324, 770200363, 231046917, 590085161, 41442315, 917670906, 537342634, 727656452, 281258467, 56795213, 239114163, 668422265, 784876947, 735070356, 799084746, 642740605, 140627270, 62413742, 662774071, 154215339, 476613960, 9851415, 352079993, 799379924, 726852887, 669892149, 299924670, 748871655, 91040188, 396488714, 608514416, 310121346, 337054573, 718241932, 627735494, 417776562, 509073057, 462052116, 359277975, 465336130, 99527012, 936923819, 228303476, 687459968, 912493039, 969942352, 574137004, 732908140, 195133891, 832878322, 347141920, 317479152, 62098811, 340055066, 831670759, 739072414, 8630734, 390595218, 873903177, 926117061, 639531848, 405590184, 21841655, 860954364, 301181276, 203892951, 376595447, 79490546, 745471951, 333899527, 888736636, 177954922, 867474518, 846747448, 857367299, 952711699, 331047896, 132645841, 6436801, 491814155, 702451530, 162832876, 164519790, 139710652, 468981914, 260428924, 308821767, 476770643, 768451090, 300055232, 482360211, 682512813, 411241197, 901144157, 170240608, 808399420, 914290809, 136791906, 401643952, 959518451, 401701186, 482094416, 545252144, 211558842, 656786959, 810106733, 805587785, 565774924, 408873402, 804481541, 722130442, 744958461, 549976751, 781217099, 23656006, 78119648, 428277514, 48061003, 209622038, 75239943, 901362761, 562370919, 673340206, 141309926, 588481056, 156116176, 827422802, 33378856, 64130137, 367510205, 773033253, 532596310, 542115550, 402605918, 385447489, 938689984, 82254108, 116997167, 685920332, 617422345, 341287224, 698918081, 674817687, 928255522, 2154929, 302023924, 337306757, 107925317, 591024183, 344917428, 155565621, 548733421, 898810057, 883013870, 884919174, 211175312, 743117242, 22284192, 720526112, 614571148, 336421711, 667628083, 795135995, 577610710, 294541869, 963963172, 490159405, 121102311, 129183547, 636053760, 751312640, 991307588, 962068811, 117386886, 688591754, 195740837, 142533594, 941877586, 190881036, 96649355, 951004561, 522313291, 64909748, 237372189, 660340320, 182584486, 761186232, 820023486, 379735131, 359754674, 333885805, 370043567, 454590990, 735268360, 531949703, 931525045, 845566827, 715947935, 284549370, 388017950, 922728562, 908990047, 939198789, 545407763, 289612144, 714163208, 194788516, 835409754, 16779369, 205861249, 312797924, 269810350, 35218259, 803464170, 502246391, 445796972, 924325250, 6464873, 897656898, 173745681, 583450849, 663925324, 706546702, 317277005, 608384131, 747476729, 782136556, 692930951, 82705641, 3646543, 853369766, 123436530, 450441800, 782720936, 373222514, 279278327, 915891838, 143603542, 438940818, 138432724, 828908353, 209663398, 423358020, 555311949, 218982453, 601036563, 267320493, 549964525, 424380505, 166730495, 68931168, 198295904, 210649614, 163087300, 778194536, 474846990, 713208206, 525017344, 791733854, 69767300, 203923929, 867761802, 682436930, 971952180, 257974065, 525126021, 454096138, 126672152, 300470743, 608941872, 429846521, 325844982, 62965500, 298637124, 498872493, 520708377, 840176276, 89305253, 462875827, 38271586, 887024510, 681089216, 841554873, 260410050, 447185044, 960447087, 736383229, 718136288, 859478225, 602833300, 997255658, 970609258, 179418710, 999821602, 741087226, 252918236, 489160102, 199353996, 713215653, 221812409, 543935166, 759684217, 71881040, 545718773, 729762400, 467087215, 446716195, 361453670, 728826267, 380342235, 524333231, 785995661, 149454556, 38790585, 951903035, 470544015, 660326031, 624185714, 225964469, 346030146, 488591436, 49314079, 737326194, 379106337, 259469386, 259846017, 337103797, 431221434, 946194330, 120004404, 89904315, 409567585, 52245416, 906882456, 174471978, 929169679, 736770704, 20199921, 769398797, 650037320, 890760556, 390160420, 287130936, 175723441, 900174643, 422022860, 724524358, 767942030, 530958671, 873179143, 136352618, 24765331, 151061015, 296322279, 986938691, 333182973, 56315898, 630456227, 589101350, 185836265, 190192181, 229695404, 824350038, 191734901, 877390679, 614221516, 202181865, 824612440, 923854927, 587116851, 580824346, 125841099, 753528764, 695372593, 578466800, 997827583, 442223291, 678302715, 124794016, 517062493, 356819557, 71603583, 765899181, 293832664, 810414621, 303171900, 906887560, 276358933, 585530045, 477415667, 679276802, 431938488, 624147909, 676711425, 225422531, 599448178, 16009316, 637320607, 883540991, 857345443, 11643981, 377113029, 929894620, 131860543, 306768890, 511688327, 875997589, 333704348, 905896681, 901174140, 368367038, 400269901, 359226993, 761182394, 318751852, 546634008, 805170756, 780888002, 168409209, 165140155, 666224195, 425045686, 488471661, 121065985, 513784640, 725421182, 42673221, 245293521, 857411896, 110628090, 44310769, 44870922, 748089470, 574044611, 933318209, 643458475, 449618910, 323407447, 151787663, 330989618, 892802448, 478138453, 408380754, 663493344, 827083196, 623163309, 712452614, 201274286, 953228099, 109942537, 313039837, 216081568, 135091049, 82900885, 700321622, 335794320, 794514693, 605775669, 769698506, 830123573, 557803413, 502943400, 705928662, 438273872, 266267653, 524777009, 2314623, 702784352, 1284754, 169555524, 747873874, 753587074, 663342662, 162081015, 644377205, 241816568, 10882771, 460808854, 698448692, 134864193, 919004514, 380154733, 419182620, 470179741, 88587516, 778568571, 38050276, 104592383, 441221814, 249252550, 970489886, 415827686, 346614345, 944525534, 580899597, 475172120, 624642528, 247989946, 833692776, 631518282, 851791807, 105597321, 247754877, 168901946, 99964517, 549620639, 654194556, 787253665, 738472, 133318707, 141339506, 289474360, 652631472, 576233222, 253582807, 207950045, 609058322, 643840709, 198965839, 698161155, 598248962, 66611290, 363634139, 576884182, 464537537, 765591536, 199316832, 635309170, 106900697, 146315578, 568116102, 696979546, 217855427, 995036654, 434317487, 856998558, 341558747, 811005061, 225302120, 116722665, 609514100, 50244902, 545129529, 90043682, 938822023, 883355780, 617318093, 85501487, 752515550, 172134849, 1324996, 897478358, 922687676, 591889373, 729696308, 415867274, 270694144, 782339330, 627101894, 510268113, 893797836, 728583201, 673239330, 630008377, 885771346, 441027435, 921555384, 629118091, 756148749, 538280392, 730873000, 711348470, 288102615, 260290203, 44722653, 200818865, 500132164, 265279350, 871732745, 68158518, 184096422, 986236094, 865148397, 716807693, 329131311, 165010525, 912416530, 987264924, 838602363, 282835, 499866554, 737931452, 865518643, 563761332, 12600886, 557976813, 575703920, 287603566, 102725339, 80933030, 82428635, 500554287, 242759294, 88755893, 440152937, 612316874, 208193014, 852949866, 775430812, 312801337, 946680348, 223229551, 70804781, 351839864, 427647548, 902183144, 94892213, 282205597, 651577862, 320310430, 481503101, 955689780, 175144904, 781411359, 866993496, 33457500, 766639806, 864226379, 629074048, 889965731, 940234090, 145418033, 62353162, 122796560, 653792883, 736109397, 765426707, 836443713, 946788474, 454077724, 277770865, 864357678, 843151882, 761323921, 371932171, 65210103, 926671560, 151541559, 399660423, 18032031, 338004471, 367525145, 251907644, 239124397, 108649268, 994506313, 456406196, 320368181, 457537359, 77525231, 686153892, 339367167, 155659173, 753314525, 454864625, 661528929, 792701234, 81133214, 593442118, 990443600, 278738761, 643456943, 624122821, 956594740, 834690095, 62843140, 601426670, 474827516, 914731694, 255822172, 974760236, 213415585, 757809555, 850940134, 927444265, 145049957, 703379113, 260923039, 774144552, 299977442, 619519465, 131779427, 663612403, 311770573, 231412388, 381873748, 959744016, 880144292, 339922540, 421970382, 120506001, 270745159, 775636848, 578564909, 256044565, 261863961, 892571659, 837980650, 12430740, 641994837, 529973425, 661484537, 105429660, 582202137, 466415352, 763126277, 894217492, 835531518, 470899101, 391233590, 113408650, 438178130, 705991698, 984835926, 401418672, 243362160, 558246572, 373064094, 84797294, 595265271, 951431732, 903293278, 698549296, 36027355, 845873083, 730749216, 421975194, 940967794, 761271271, 139381183, 506108796, 942514463, 647245507, 599234168, 242117852, 919020269, 142890331, 565513051, 775431670, 652289318, 781764895, 783848133, 462611367, 604134579, 27824217, 493278090, 369589139, 622669901, 398664748, 334405239, 174862382, 515351963, 763193441, 843937580, 164115860, 594697491, 765274817, 954116476, 258615235, 517272297, 714652203, 507547875, 514386970, 570397021, 958409476, 529533628, 868278753, 834593041, 846404720, 128635929, 835593795, 664138086, 96017558, 590955906, 718379716, 443145124, 462493739, 17592255, 194850091, 973184177, 718282211, 513901710, 266295908, 841651802, 354867697, 105275065, 646670782, 625292771, 496984103, 668271901, 935511083, 34294248, 612406659, 5919137, 877761127, 577082744, 702831140, 36374940, 534854984, 798664180, 842251588, 478181965, 684703993, 404525475, 238007600, 911384875, 979192218, 780346156, 878197481, 617454129, 275959079, 147079639, 563674754, 682535600, 900565705, 514197020, 582701813, 444956195, 588119408, 45510493, 729009588, 451517424, 116818516, 348868814, 230746334, 891369989, 912163352, 247399973, 401124628, 192870349, 416870209, 683145130, 19438617, 654172276, 790288892, 442496072, 852500136, 400114805, 333552069, 998933798, 776485364, 450225758, 20771019, 211834896, 537492242, 561922413, 812307269, 342678043, 439137207, 809064858, 705525512, 546396745, 836270904, 188561625, 932405297, 603031472, 378353184, 872614889, 26030945, 221023674, 74202502, 579034546, 146205391, 849356468, 591395213, 352742136, 639891425, 863336843, 233123773, 841174616, 684062591, 623923792, 921663919, 978382056, 13624456, 826271334, 496749802, 608729137, 777297945, 944430920, 545627409, 863083308, 953484205, 740624416, 381633939, 662166339, 570142749, 501034060, 923134659, 263537035, 757596986, 210499997, 139692259, 925741769, 970509454, 133687127, 7524144, 613690276, 335193623, 838727833, 453045409, 491996672, 444850626, 946636337, 992917693, 707089079, 17865189, 963342643, 752250165, 377985500, 398311022, 405881240, 426819325, 671435077, 278280316, 652321809, 171789949, 710909992, 302569255, 328720885, 945095468, 594195376, 751762512, 998836813, 313272812, 799223516, 690612107, 772984649, 777163469, 529789535, 305954897, 993148887, 593507869, 928477706, 962218557, 722240973, 308505884, 468495462, 72913166, 585309570, 912620605, 147245153, 61685652, 85863671, 150869621, 199374364, 980030699, 395489166, 694102642, 519310353, 778401358, 332703785, 746871186, 865964563, 142641447, 295602668, 851530323, 676108148, 309824413, 796282537, 71721750, 983734119, 256732451, 47260420, 69083476, 804796021, 762414030, 857740571, 208882554, 962512836, 701907105, 52760971, 76761174, 274441857, 689828000, 73573563, 342946051, 638843235, 748632385, 313779214, 733007481, 829136050, 747621690, 432318113, 20745270, 233444302, 243110670, 18240285, 925412950, 559803526, 133792847, 377916937, 134868299, 917752111, 3049399, 725171055, 642978708, 300151608, 585406315, 979709231, 954417094, 322142849, 438366149, 250260821, 407998917, 256322298, 202361137, 126726442, 539903187, 618200494, 788120802, 622932590, 529962905, 882075124, 588744608, 953205552, 868312728, 272189603, 829734502, 165419067, 109578402, 710325888, 217657766, 594101769, 347685835, 283864410, 828184891, 988621663, 317093468, 959228468, 900007550, 959672752, 920542130, 652323608, 365254945, 643862067, 232274062, 670422925, 762827876, 835859156, 493674626, 297455498, 497487570, 146157759, 868550642, 89523888, 581415567, 913398647, 82880977, 135677551, 20643131, 764964730, 328653181, 91467072, 249591101, 272181327, 21341625, 394567665, 958406643, 230928679, 460109406, 962343912, 771400690, 986729996, 677281278, 701613997, 384961279, 428660238, 755593649, 953531797, 896865692, 990601778, 831067519, 883895542, 186756857, 703359232, 537161345, 123774143, 384899070, 422073900, 55854427, 923279431, 116457265, 487374177, 174026866, 54145158, 50321755, 588194884, 504488625, 691720694, 923139599, 722714599, 868148430, 411802078, 29826063, 240375383, 876803631, 63746304, 667007522, 776736827, 958877165, 828565489, 613021051, 438321080, 937687514, 746425267, 520240750, 549921761, 730518814, 643713552, 471070119, 205675381, 891417916, 702590828, 836545000, 460791234, 339012518, 528114472, 174682176, 463321090, 275706257, 490281127, 901363771, 308322694, 453484960, 603471253, 291930720, 376417424, 192028363, 166327188, 399401118, 515747174, 902890655, 989940062, 735567512, 523225006, 995902749, 503119210, 809374771, 839147161, 774882907, 373684231, 778441943, 515426934, 133142774, 160796303, 885593143, 747086374, 497204231, 780007567, 421662313, 164465406, 919211368, 933100185, 546261783, 150349134, 969201682, 378479811, 528866669, 197740062, 437836642, 33703201, 461660217, 228713090, 704393869, 658445808, 587358907, 951523328, 701233382, 412732343, 56425298, 733664796, 290494322, 80009176, 526792163, 379550730, 765850026, 824398920, 683925328, 525064564, 608583635, 620387361, 252296464, 87743796, 238725069, 118465458, 506234200, 441877458, 832985179, 552426146, 338220103, 411868220, 2874196, 235707972, 464443710, 498429608, 36975432, 724310455, 986032628, 969992780, 637501863, 585063912, 687108650, 716924347, 134880260, 45889341, 563023218, 745856453, 425816796, 786008518, 262828910, 66292776, 852782123, 686940430, 953810180, 145837340, 876046493, 652397340, 115853132, 182281809, 713595296, 757950694, 370183732, 434536848, 995115360, 531425572, 109099523, 825360638, 696476038, 871605322, 673191808, 453093281, 584481875, 893443586, 75793293, 375521710, 777166191, 985216932, 224510004, 608257246, 753221078, 473478710, 407883061, 188022878, 989597977, 963134094, 240404651, 323552342, 441078229, 967071580, 528828337, 198644293, 16830252, 764738965, 913081742, 992046325, 162847647, 891901736, 943364351, 594175715, 254731375, 672738267, 677364666, 488633502, 43722729, 687720295, 224249318, 695603786, 150694370, 540668879, 245599636, 114759381, 454250676, 377153645, 417703950, 611621224, 964381365, 113990128, 148238132, 230418470, 230950486, 231871803, 544935441, 302341566, 27165408, 984811039, 964106494, 204146070, 747922203, 821704596, 597479661, 59000671, 569102048, 991382871, 425162661, 553057288, 358475107, 625688879, 284714487, 512348997, 267668875, 892235852, 836371108, 72538999, 291634022, 874450652, 779938728, 747605351, 696901681, 304775869, 482876231, 573146363, 795040029, 358410563, 766334336, 180423446, 125993335, 642564542, 785799735, 701652598, 135630944, 785627063, 627311918, 888537741, 36139266, 213570930, 193253638, 134963645, 249176081, 593591006, 754183098, 667836151, 418269805, 232157447, 144102240, 215280438, 152308098, 265907743, 19965640, 962298257, 7675611, 632142033, 348046285, 181604158, 591029841, 406969895, 265179079, 430386953, 96633892, 656447246, 349493318, 820583618, 609599242, 657417863, 207926249, 715700631, 889719577, 483385119, 312688860, 22960673, 299194118, 937920284, 786484783, 578938929, 804535030, 135245135, 207183245, 783355891, 363145731, 78321415, 30351825, 785628484, 921410026, 537986782, 68814445, 837645978, 879684983, 480317624, 681770684, 830565229, 407813464, 870989149, 219239980, 779576720, 550393237, 852990075, 539599161, 307755240, 84624451, 829249107, 936625021, 830202384, 72876870, 863568785, 751778074, 363748545, 242762934, 586849340, 369900604, 619600161, 94209231, 372097610, 813228083, 479210397, 749291314, 851963243, 326544587, 365143842, 135046417, 211740553, 671353353, 335202336, 419193137, 470548864, 550952972, 527718595, 244691798, 950535706, 690445495, 411224733, 765498760, 261221365, 899115765, 332708125, 967735142, 968529315, 571886192, 928133880, 138534238, 593220862, 948360485, 115320973, 148157000, 406050488, 124096654, 497019499, 611084441, 860475275, 193637002, 947328115, 702418514, 749416519, 486063890, 348233536, 452983264, 872130637, 283401632, 803723963, 51928288, 811718123, 263402049, 126300724, 161178640, 481713144, 350695797, 490709175, 970563213, 530236035, 705416003, 605393088, 220974548, 110099223, 139589727, 6134302, 350139463, 116989021, 358985977, 485060446, 665166147, 798777700, 22693606, 518805865, 5688809, 246118911, 31787661, 141015493, 406779689, 978181952, 757515174, 776583367, 334928533, 110594180, 191135615, 213182651, 515977184, 6912816, 293271847, 194188984, 804438895, 824961316, 238804648, 896550644, 975269132, 680462192, 218757417, 178326278, 584333236, 252183047, 403390294, 396633077, 328900472, 8532803, 933017339, 100771470, 823852273, 479922399, 881605600, 76829436, 358998150, 294683167, 406602216, 601188555, 817555717, 605595765, 224799177, 543962067, 669816951, 641104714, 609368346, 66486455, 779475750, 195276031, 263075556, 404138048, 677659127, 531887312, 107364926, 752805852, 115822324, 366817446, 995123506, 499893121, 892814644, 275557688, 443762406, 586952498, 897487694, 21003639, 529251201, 48818176, 843978349, 899736192, 994712899, 669257875, 362577365, 778376130, 212868126, 418430658, 335424077, 228562025, 758502157, 598197059, 390451386, 145724526, 923238845, 603729799, 519339038, 739507017, 917213023, 561995791, 920999985, 135865891, 665124002, 913714452, 583090919, 502946074, 978777815, 277840781, 82056774, 461008022, 42698991, 106519200, 572586788, 559221480, 730060668, 40973235, 243077363, 869117735, 880118754, 564356489, 571551211, 814230367, 63037181, 874501655, 599703564, 737598844, 216430993, 708848667, 27219583, 621176351, 747827400, 881076323, 550678394, 994272185, 476527175, 6012539, 918807648, 695302313, 239557641, 716720522, 706009083, 309537015, 480888823, 68775170, 678258461, 578787088, 216111174, 965586346, 676783127, 315577237, 425485277, 373952902, 249204390, 367045948, 176178352, 355782273, 713931985, 633938269, 957246938, 280815254, 386256704, 969116195, 419696404, 88295577, 651213564, 815287107, 675937469, 911510789, 48740024, 911374692, 821382009, 978574717, 78425614, 33693299, 117098803, 153276219, 380555369, 68432637, 342686898, 270474168, 385257629, 713952339, 542116933, 538480137, 616970913, 160745080, 927676053, 534569763, 549396585, 302907991, 646406890, 464062074, 490825433, 179388341, 418578043, 205260659, 626649142, 762689503, 54105996, 837299720, 361823319, 328729633, 617504115, 392638584, 642726626, 523553288, 186885196, 777173213, 465757470, 609383850, 810664176, 103699060, 519750647, 960971419, 277518218, 217112684, 884884997, 681657795, 379446881, 567334605, 686424036, 611228909, 799284477, 170072819, 10187316, 74908137, 114404234, 547785378, 511716859, 718272065, 906896677, 907168448, 381270914, 361434625, 48409394, 537591245, 55502477, 367955420, 393490274, 643464896, 254939904, 933875938, 452193528, 618628222, 138041407, 322696442, 227668847, 996573071, 840510475, 608584327, 387910880, 180549542, 71618944, 477314385, 446990897, 338607902, 2520111, 139057817, 916929401, 685312178, 278136733, 666028182, 895769551, 702786779, 301045785, 919630698, 571680626, 537308099, 838853394, 211418568, 929111628, 971224024, 668884031, 901047809, 286288601, 722912912, 515993326, 939659462, 193518863, 244306336, 223647092, 67091622, 860420545, 313740640, 95827097, 104889982, 628458130, 395967810, 272754382, 367107982, 833164393, 909439584, 975707704, 313946551, 995099498, 810412592, 231006077, 952002592, 319558298, 959422886, 218648976, 736726522, 652500484, 588474075, 45120, 37232683, 697308949, 579593911, 259707553, 951604309, 869742588, 512716228, 337927574, 765304986, 311891291, 947567729, 566503039, 11527988, 891434655, 785675740, 756436651, 497874938, 332560243, 257053318, 544756980, 197568648, 224849609, 114410246, 506514135, 46006968, 261556954, 52179266, 805841247, 943273471, 429887879, 763542381, 815485036, 231062545, 592794789, 809887433, 694681176, 826688607, 788558484, 574388823, 478162497, 599453496, 495457186, 255967973, 815158416, 757960640, 193634532, 687841880, 609398720, 956485437, 629357132, 149453293, 758127301, 783439138, 526918472, 551752300, 561262054, 610553610, 395997691, 749413279, 683259566, 369683586, 159737070, 800624479, 134758758, 284621842, 526959267, 603505216, 262909570, 876089916, 743537423, 456510376, 720240263, 250486781, 190645401, 477049546, 290801952, 232472141, 69446296, 188154359, 404975475, 273471882, 345044002, 731200083, 822451229, 518106731, 281345186, 111589292, 503250025, 97752487, 196176574, 985707754, 463579702, 394902318, 870223856, 698108294, 958897776, 436058423, 767545692, 807113583, 183261927, 859638253, 895722124, 139319647, 176987815, 974888359, 59736751, 504749141, 327400511, 227336638, 223291906, 481875377, 907608981, 95310249, 565337606, 926431831, 164602817, 863106613, 46686994, 757032430, 458238016, 288381322, 596296823, 964556779, 315313746, 391200279, 302352989, 35039930, 410792208, 456869002, 626511801, 196442025, 237137050, 512924785, 206101276, 742486512, 170924741, 392335548, 905781079, 599899188, 298119071, 926727057, 269008478, 325256100, 42423747, 739880416, 309653831, 247988434, 5617485, 958040269, 482839308, 98587992, 142418655, 403196618, 274221688, 254350943, 954098881, 950356030, 407431083, 658800273, 160078515, 390257805, 841464943, 795425020, 367483129, 549094740, 40819984, 949382673, 38651793, 190207262, 140883362, 165879035, 825782720, 150907608, 163196395, 908415836, 135186049, 894167690, 3166838, 149314343, 601672408, 702413301, 557020306, 322867399, 494389562, 772308007, 145892186, 957810219, 803727024, 210646997, 959895068, 923934049, 282351807, 575093377, 614911880, 665792227, 398285705, 958074760, 60224387, 402316041, 263185426, 185245289, 450415938, 970928228, 635056261, 611763096, 910066025, 695641430, 9126688, 262332585, 908705181, 622803703, 783975738, 952040421, 922730599, 362211544, 35338427, 604993968, 800374911, 791488642, 785685722, 759314795, 809092928, 132712080, 165306992, 571633554, 825609258, 307233821, 466294736, 947414617, 978054490, 111569038, 350611343, 571376751, 392019066, 17769943, 623325772, 943241754, 677400075, 72396532, 170487124, 694500646, 491400376, 185448727, 132947792, 824622037, 509422976, 115607442, 219043988, 923580047, 875855195, 681068846, 516131247, 737702546, 732427359, 543838565, 748284308, 354427108, 542738646, 739520895, 498310310, 854472651, 431434274, 71072880, 338625493, 739290781, 59815580, 975751841, 90895460, 278005656, 163048304, 984687066, 480678622, 440897271, 28158969, 388478302, 328515437, 735717535, 654779330, 549196948, 927716602, 307124505, 847958379, 365011253, 364136715, 926561420, 809140045, 104248710, 430061379, 229759224, 405560564, 712489252, 31746054, 395650496, 33869329, 925309926, 793551562, 741539656, 442218226, 677310522, 773121559, 363981623, 223138588, 185855410, 987081592, 60176510, 156245507, 402291831, 499780083, 746793087, 424656207, 625156867, 165181575, 997536905, 461916121, 582614003, 910750295, 336365538, 741653962, 446554959, 948936985, 903989590, 103774620, 246107528, 867389638, 635189064, 109874160, 484567317, 257445172, 175840618, 304802240, 564006353, 97707777, 197451137, 60689015, 265197955, 469384367, 228241364, 517661538, 735980385, 224827067, 681117540, 188034426, 136408097, 779760613, 8932519, 627173025, 388342697, 620808874, 306148732, 285136671, 86331016, 464604386, 740891166, 144169828, 727525938, 914047687, 492732394, 673398289, 892145593, 855934278, 925548425, 453934395, 131601705, 136776185, 947971413, 644126303, 941895159, 793143666, 116410139, 162258487, 892654571, 280727790, 624422196, 4446209, 549715149, 308143462, 990577606, 9031734, 846763258, 49006793, 310117115, 34624098, 704756574, 510883198, 908070924, 156804757, 711284613, 663809527, 722321955, 747864817, 145009007, 710583195, 762552623, 142734259, 671100902, 855418363, 484149780, 598722701, 48654398, 59806228, 262035048, 781619061, 699695886, 656741623, 584494514, 726031373, 415780917, 653238874, 46906319, 596656959, 240472760, 263147280, 451565707, 422859529, 901941890, 65601724, 247029946, 414623276, 158749706, 8756983, 891741190, 321407888, 210975285, 269630522, 155588647, 395796247, 336896681, 323940777, 39093326, 758391551, 569337397, 388244199, 979471950, 692914784, 42863328, 591015237, 986397084, 185369943, 850081533, 230325122, 575673910, 995206052, 382335241, 173258531, 336031908, 779922117, 491897218, 309381028, 470916486, 586860899, 267453300, 238009149, 174658559, 113472970, 506259419, 472234845, 575548610, 755086315, 313622471, 277848525, 983966620, 77362921, 612934422, 190106708, 62424971, 191181499, 429646067, 20888040, 112547369, 179567735, 259876305, 859801715, 797777361, 747902745, 352490469, 327761767, 105214548, 516953757, 541232290, 588347426, 340840689, 727669112, 922385946, 67257028, 807259566, 741471739, 328569170, 191737230, 127789439, 774263096, 606866698, 896322101, 517971463, 318859301, 599709927, 976277827, 804167769, 378670871, 28197342, 903730856, 51605089, 867137242, 957552681, 902318303, 174505629, 52100352, 453175845, 239873743, 295048361, 333716997, 40166815, 806881299, 929593094, 398883271, 106736259, 556679112, 719206058, 151214800, 437965804, 801710648, 5832670, 641591001, 357459769, 806058374, 167542712, 27513690, 858974985, 163828438, 923752737, 584289335, 438647750, 777122418, 104023053, 424419061, 956468227, 731138250, 900569919, 894695684, 571217034, 838797442, 567820677, 558891108, 516887048, 861485426, 128301975, 299477142, 805462583, 142953011, 670664025, 7006519, 270433656, 27349356, 231551063, 175850200, 810180532, 297497803, 588848077, 783791104, 546144710, 508310198, 550605611, 540558635, 365248002, 281464638, 135083445, 146545416, 651097742, 76393925, 192699149, 234146224, 112965538, 859178038, 970877970, 446707516, 21922193, 896841498, 754249502, 231172614, 676236306, 69578469, 92625065, 914437581, 315045325, 787486760, 314731060, 546532122, 356913769, 490682064, 889989931, 774281586, 149825822, 760456311, 775414475, 254051699, 614128409, 743435180, 788987382, 797469193, 659300407, 931553672, 869993485, 309718308, 295461099, 186289859, 296627175, 781090078, 297097077, 314162233, 794198879, 755384237, 51868610, 776945409, 572740893, 224886043, 980912328, 152619304, 753511036, 127885734, 238797017, 212420451, 420238404, 502012300, 254013266, 566182278, 521113649, 570786300, 149280824, 388996795, 434826701, 312889608, 479400862, 314393967, 603858949, 427309171, 892125336, 513408943, 27715393, 797023948, 470671009, 162576132, 721533395, 613663422, 222547887, 959736740, 725269208, 920183058, 630008149, 554576606, 453643364, 700546801, 330516211, 784870136, 851230564, 988724871, 431519560, 901608536, 176822178, 987910011, 747572050, 921862128, 376103078, 496155777, 875786615, 215130053, 804390131, 112725219, 939662989, 494168786, 495880554, 238570077, 326278374, 442264020, 830300655, 852563483, 460035404, 989495437, 666548540, 630020720, 565575341, 789993640, 903545981, 818923477, 158860925, 524938403, 727736890, 534129471, 756204078, 748709535, 647579312, 248449551, 267718787, 588393091, 72015267, 389794103, 123720726, 462271616, 259905109, 74502678, 998478601, 467420702, 263879403, 709006569, 298976586, 474934138, 979984738, 310822279, 138825647, 515636566, 727504810, 196367000, 466015487, 776583184, 645583139, 353611480, 412178599, 238852688, 950984564, 580368082, 759721918, 966607031, 176209921, 261927400, 208408563, 520750407, 281785889, 897908958, 268686977, 377430726, 178407962, 749955824, 811380314, 322884751, 479791711, 976365751, 204071314, 332552889, 718323487, 466817628, 968955218, 343185149, 344252327, 963586065, 420388745, 180481157, 175403255, 652759721, 288310405, 772207214, 212482510, 418651339, 365821414, 897409612, 25174951, 471029303, 609970510, 228588656, 739913348, 842280221, 548987626, 571797618, 257259712, 580691457, 824428762, 276528993, 823604874, 223990100, 519667319, 161001722, 641041440, 370892943, 910424691, 516014989, 677044328, 540577242, 749340934, 529445067, 239389136, 746890690, 772098002, 548544326, 601658185, 778026121, 979863437, 959644223, 196358773, 87216407, 242418837, 406995746, 78412136, 708626056, 790149523, 24075611, 61277881, 261406486, 825563636, 990398656, 395148356, 865626403, 530205139, 99929906, 357159758, 613281190, 10126370, 268405050, 156596472, 801992669, 231214513, 104973518, 699416450, 493625977, 913940989, 339668512, 817954389, 226989470, 287648485, 883755486, 316490565, 405327409, 823361710, 959752413, 49477788, 879006549, 264259507, 82258002, 698787052, 336574286, 566161334, 803194521, 476212093, 877294572, 703221371, 938496548, 675654709, 520229845, 450726236, 692504816, 107924355, 271032464, 989864030, 344743338, 877544101, 739829027, 166578608, 726762546, 858504278, 923783736, 703703420, 905000040, 785996570, 457696016, 986538547, 554586614, 24680059, 385872018, 62855363, 482380469, 427051487, 773620243, 672695315, 500841811, 377609657, 432082445, 651168140, 708360117, 648380461, 377459054, 415610932, 686848223, 50209461, 867974485, 613434990, 446299536, 186405431, 902961238, 814719272, 366252226, 717301823, 552407123, 163732773, 388360807, 27744542, 848428189, 777931191, 327633177, 494929946, 314229002, 526097579, 627182807, 312038287, 198214678, 516559686, 398502153, 685739346, 73285736, 50272264, 669084751, 141198433, 66074823, 811866822, 69526337, 98010334, 882896076, 401573613, 849706890, 144123898, 747987618, 615411225, 180025124, 730533048, 724507706, 765628999, 810368367, 188083286, 126933525, 238402161, 616612656, 212403659, 317692488, 969733668, 300796568, 487800534, 834830012, 737672672, 163717938, 674953028, 642372950, 339315648, 490127658, 707032553, 694584782, 9873690, 208733267, 466078214, 370512675, 66870369, 63587091, 429605761, 777093939, 998007105, 214262325, 190809762, 376565509, 474309555, 891895157, 980457245, 803965250, 877398111, 472538362, 258074733, 30309278, 14614683, 992414973, 135239585, 353842287, 273956050, 178718736, 619639694, 616868164, 425949447, 360131970, 369176338, 424051704, 836752147, 79247079, 985428651, 600479655, 37729206, 440118032, 331345049, 883294694, 83389425, 316483181, 369190912, 249685363, 49686076, 661444456, 676855309, 736860269, 869516428, 187657080, 373928997, 182082917, 47374211, 219309346, 774910460, 325829376, 719939200, 138049045, 67648624, 897109198, 466660317, 153512321, 404545740, 249354993, 783794254, 995811918, 884639155, 108419940, 953359638, 221469173, 185261028, 857147448, 670489884, 915119652, 779327548, 878412943, 578563957, 471510827, 464109098, 640475853, 832705058, 995994696, 866492931, 102899508, 92397018, 358384134, 891025435, 213115653, 134210187, 449282924, 596153678, 997268062, 319774603, 642330477, 112246873, 123888462, 156508128, 29384182, 908613358, 626049611, 266210641, 580277880, 96855126, 462083351, 33725988, 293469704, 460150918, 351309019, 68128044, 703023296, 588735800, 509310431, 803505279, 613067425, 91632048, 217240212, 955210336, 506072879, 326474232, 457060121, 571322218, 92214083, 276370504, 319311741, 624027377, 71676019, 234075547, 906474313, 486119980, 280765003, 312195353, 277118813, 736183021, 626443040, 674741812, 891932924, 509191474, 957096861, 885484440, 813986742, 103032885, 425663727, 896039829, 893363199, 128714479, 647648049, 469842150, 599118887, 498081876, 273142593, 151407647, 605497903, 787812228, 798611087, 721845968, 28717823, 855354808, 595452218, 819739811, 773267321, 317521565, 812393361, 586491575, 258380023, 672268528, 813271503, 263066068, 365988428, 817178263, 36654621, 334533230, 518016763, 87766788, 495083379, 763326370, 368995044, 538260504, 597877275, 534489820, 820771750, 131421590, 877088458, 104950126, 503526296, 221574932, 938249907, 365444393, 361145231, 920099960, 45642035, 833446573, 569615679, 678916631, 307275604, 600000945, 91941171, 578143544, 238361868, 848349855, 458203351, 655902128, 223691348, 280948270, 300476820, 616727783, 98854316, 87774045, 185448696, 230212227, 368723133, 873677189, 245980276, 211838046, 652341367, 178979539, 321530287, 998975768, 488090910, 579368474, 913612185, 781411780, 903009575, 276150217, 146638818, 39123418, 883016275, 156027292, 136604471, 591288241, 68452311, 250356266, 60791787, 453413991, 746165297, 648474298, 143298014, 526019485, 367762550, 490856470, 96024571, 481894415, 265756027, 335928901, 199460025, 924710370, 507556889, 950365805, 256129864, 37906670, 56329492, 372262237, 11386468, 678579515, 25571984, 257779713, 117885289, 104540511, 221577551, 189764032, 156973074, 22507723, 169594928, 512991621, 26858580, 723194182, 429820288, 10814209, 31302935, 980861064, 894400645, 978754368, 112085290, 325694623, 702323056, 61239746, 4292145, 609510735, 894095518, 833216382, 113615541, 98958066, 60143615, 628931970, 901816794, 723602405, 64030759, 108304862, 447666588, 304642134, 305403771, 909847558, 837214421, 969686207, 646372943, 474384363, 507033190, 828838810, 647898247, 903983964, 776475423, 659716971, 821836958, 783938890, 172917095, 355100830, 100982951, 442166184, 808665930, 755262008, 94635618, 583444914, 581949943, 598246047, 365875147, 218182774, 336028047, 314683708, 77690370, 61448667, 163631110, 454305369, 181655796, 163393292, 987179295, 689331564, 518297808, 115897262, 997675952, 82436099, 995076001, 597501654, 340768502, 222769946, 408417297, 72207374, 894456241, 366881060, 286904385, 765154616, 77062971, 73791611, 166983363, 992381245, 785796771, 753232433, 132389439, 328012096, 894819477, 331541657, 261183799, 71626820, 76357473, 942020054, 667411999, 269358333, 862981502, 666252206, 506619800, 582218760, 729554815, 864884062, 716102206, 14894209, 170739995, 778227954, 924878634, 106884830, 522009062, 853078207, 39503690, 443773692, 322319990, 902397550, 345962801, 523909480, 362648273, 388937305, 668734610, 625625648, 500637448, 677184732, 725863982, 577339969, 874268860, 726647338, 961255169, 576181202, 165347207, 452529589, 2864401, 401921602, 597363914, 348986191, 711315530, 766723530, 689965178, 989742654, 454302559, 478076248, 147621274, 519311495, 293793980, 812857300, 538426997, 301350310, 442834533, 614046060, 417410367, 452083447, 343739981, 404168746, 902095641, 154544335, 803266929, 367037805, 262433531, 257503033, 548295622, 618379902, 327554224, 209185940, 567874845, 21792827, 575457213, 178898244, 331185486, 110761405, 49479310, 739576624, 126777348, 436226874, 424423106, 827616842, 470637114, 102367379, 205971339, 360770676, 84797432, 228769095, 936638704, 511955342, 306896071, 954174222, 638085197, 550802246, 660483789, 56703577, 715820154, 665497253, 323568477, 190036909, 490458300, 653945521, 198562676, 10156288, 356889831, 751774219, 789709903, 702380336, 731434643, 406846934, 913123714, 498394461, 956576786, 642674627, 621342391, 842582235, 206851796, 470646973, 501497166, 877310830, 597744507, 475995226, 233709759, 322627816, 338916716, 460125103, 761815391, 455701711, 418555991, 574524929, 893483898, 67055449, 701460673, 635126797, 112611706, 232154313, 802768026, 652441111, 187323456, 666826560, 724036212, 731791000, 613411494, 764736820, 475788385, 864224091, 447455200, 971967774, 185273125, 587889039, 933070393, 848669126, 766820846, 704200870, 237492496, 251325699, 15280119, 234909290, 318831682, 456316325, 725229530, 571555803, 29407857, 939398842, 694399052, 715676448, 813540762, 675669129, 933170890, 344879113, 917499165, 969288997, 653043304, 62232439, 664832991, 416343901, 324888347, 950282292, 596849486, 902009935, 259318515, 504727131, 484885218, 465275005, 143035318, 123375277, 895443722, 685370196, 458749768, 648408309, 839365646, 276162941, 801749066, 36550818, 625380194, 513577251, 641663079, 861144112, 27510087, 825362024, 776205174, 145136858, 97469398, 144983957, 475137458, 802842835, 295904239, 522671670, 736258479, 173614745, 655577834, 678052249, 430734575, 122121593, 870177315, 398704747, 217851657, 750784435, 496360985, 165565880, 943264953, 847237994, 563107439, 528189078, 244089685, 862481407, 971370300, 292040796, 205939525, 567315226, 545274583, 916583012, 323975714, 226816983, 512432979, 723512861, 765217494, 284064529, 995232122, 472381566, 835827875, 291702384, 693548659, 129945761, 437220684, 298025201, 476189900, 633867411, 954665313, 41895391, 877094887, 738747236, 355248500, 923900809, 328474038, 156416120, 433360469, 132684771, 225395022, 655183132, 377869843, 286784379, 306621264, 427067390, 415171888, 437927055, 27927085, 873768639, 691729134, 995016401, 529473226, 903257963, 732334589, 893105652, 278200259, 952064912, 323041723, 756921669, 784678208, 662398510, 33407467, 582597557, 10948534, 521835180, 465997596, 679806330, 300807548, 517548978, 867910884, 581022446, 13290833, 411394293, 796200880, 600962194, 493767685, 62119368, 142024400, 619042836, 177023506, 515578869, 999852735, 909670225, 720960221, 323605633, 725711014, 954080893, 979135963, 506767254, 177693122, 746743446, 833828701, 193111039, 586240909, 853017939, 864038050, 149555526, 546040219, 78957769, 515251961, 839642780, 887706691, 540425406, 31625940, 160604132, 458978412, 759442876, 494579935, 62954070, 27752979, 833952463, 617658500, 119006860, 914906519, 510840615, 534262896, 111235673, 6796077, 197628118, 595293905, 124807940, 476001602, 942748145, 869756221, 309959866, 389390060, 93062667, 781842362, 651355881, 903153754, 860386889, 70767651, 135316437, 374027512, 729082760, 77332608, 891658823, 17762577, 12639004, 927618435, 547082024, 559230446, 703254030, 369147581, 195616075, 523159353, 185334424, 413672161, 886665310, 315394877, 468430549, 991141182, 217597787, 137291934, 59906359, 381610184, 519806568, 624377427, 341298240, 282544819, 348491970, 841644038, 469078003, 348949326, 530030398, 318458994, 277279307, 865790508, 926726820, 522399194, 156966157, 667107230, 77052977, 473671177, 700625207, 744210726, 285569592, 464188800, 912589187, 244856881, 489708468, 876859992, 558059239, 443418559, 616300820, 382691800, 387590471, 848624508, 558029550, 297424092, 716402158, 914757581, 591395037, 990081904, 214690736, 482789255, 660822458, 602717225, 758500980, 74560282, 951666335, 900693497, 373782385, 547741479, 314722291, 181513735, 245364789, 612027397, 311024181, 929856040, 126303283, 322490376, 385970630, 429840180, 27385710, 26315905, 197537096, 914121231, 207655275, 936772032, 559027191, 211518720, 4644395, 523602176, 722155847, 708416263, 804780117, 788789246, 929089792, 806129487, 178404008, 554530271, 362974281, 458578219, 89069454, 724482059, 218127933, 198983097, 257787278, 84445743, 372863724, 527968854, 598496225, 730428342, 368068710, 118872258, 831362218, 342308136, 978749750, 182235334, 548515348, 622646164, 719274647, 938766528, 373855765, 386580823, 593014954, 199049275, 548242869, 669743394, 908394922, 42158909, 612706880, 411333164, 192664157, 11915471, 377213628, 579574667, 638559796, 377877822, 730957866, 453737401, 728950815, 348465968, 997784850, 243520800, 978539260, 676478921, 771502094, 504151708, 107574289, 53830418, 57601209, 767759088, 177650592, 520988123, 578319892, 439910248, 233670210, 933283555, 3926113, 836770894, 549301883, 637215658, 37361817, 18067082, 741791036, 513423367, 526116736, 706052070, 60262676, 483996788, 431041070, 889347675, 410918435, 542502083, 708449667, 589330310, 850565962, 869764839, 591918296, 220126601, 438464274, 532315934, 469845863, 513423600, 965988720, 701586834, 332368134, 167502629, 392926011, 592975691, 40265127, 397257662, 599718568, 517803565, 289519740, 705300728, 556229941, 224713077, 318624311, 539603055, 923874988, 427854630, 703750236, 577638518, 925599174, 678146243, 180849129, 842593924, 952185727, 567251815, 25616925, 795001107, 4534054, 883791674, 513789427, 595785325, 316143802, 471842773, 960873625, 389099562, 108527389, 976806665, 399611783, 928929379, 922903006, 182389380, 888583294, 808522313, 125828769, 197198840, 803053159, 737460069, 1622435, 521839135, 921442627, 868333809, 642804077, 657388378, 81909369, 89260919, 929436896, 500617222, 446166982, 297597510, 796304305, 987016659, 911582817, 107730085, 637130310, 254093683, 308579461, 715383006, 480542677, 421829928, 358867891, 742470427, 777682222, 387992247, 989748304, 297054279, 208556123, 300923012, 580331475, 727491817, 381995679, 554657928, 556781196, 247078228, 13093507, 955130859, 759786558, 861758920, 81323705, 496159814, 18905572, 378334413, 146403511, 902245365, 911372724, 863653059, 560617111, 484598771, 245036655, 549122282, 99394178, 568134779, 18161234, 972681462, 345606701, 701718812, 236307746, 438002342, 755529539, 218362919, 725386270, 792107060, 32775942, 755544576, 81849374, 388785240, 286699194, 282271668, 622144646, 212874868, 646824895, 259962482, 401458370, 983747536, 864502714, 384805253, 857413641, 602595915, 94693561, 367412841, 523548855, 543588395, 341770326, 806803492, 945684357, 511231015, 822084030, 113124271, 736838259, 1872828, 77659367, 632964170, 714534751, 539259597, 98471704, 447397709, 699818395, 223057476, 824662234, 825405041, 32437045, 925835156, 219555620, 71056633, 634187554, 193837996, 306957879, 216846174, 685303079, 271655669, 587986579, 874193642, 516222871, 258711441, 18212764, 519578699, 47726236, 851567439, 957413138, 278599994, 885226341, 19533298, 375604144, 437072782, 468113555, 951181740, 157577045, 345448831, 882242497, 9285878, 31468448, 815687596, 472289215, 277583524, 493734506, 588486778, 435602410, 16494851, 437435835, 522655267, 557625410, 380485430, 506470592, 903313472, 119496450, 997703424, 573131757, 868231096, 26042128, 343028310, 549657858, 700245615, 858421059, 765216779, 502699615, 882624719, 925958152, 624426961, 610992451, 541105401, 734537535, 269215385, 748678449, 584408536, 962526021, 170830745, 566579820, 416534903, 21588617, 698900013, 108173665, 460877284, 12377180, 594847823, 443129961, 716827477, 868238823, 83414455, 18842884, 475283934, 850686336, 511464158, 618797587, 81165974, 714298728, 681448782, 993068623, 499258272, 196812193, 194384598, 963635193, 205986467, 160228011, 137199840, 604204780, 615060214, 242100268, 642940159, 29498339, 801952866, 283359261, 308205413, 337748360, 608643431, 194416422, 627623327, 332485985, 191077914, 824619191, 207749621, 660293828, 224834970, 108350211, 31613666, 457093826, 938187801, 589496292, 471177643, 11241278, 958162419, 950933882, 697031596, 197517625, 56554203, 945632601, 785789607, 750410316, 819066523, 247466611, 928102627, 856392094, 690365388, 570901109, 833877185, 122415250, 368151898, 732162306, 743265546, 391275875, 821203729, 906236173, 228000970, 280160924, 431676290, 693750317, 333825452, 393186944, 575716079, 793362210, 318583773, 6435087, 84997747, 557753198, 4556969, 474732946, 329411396, 30123183, 808815005, 247949505, 7613448, 390590874, 787049562, 310759947, 174429498, 769252370, 565243559, 670168370, 10347784, 145836147, 630972955, 216451994, 195830106, 610238210, 462447190, 993522615, 854590415, 425075204, 212423178, 581238233, 278206301, 688046869, 277519099, 602162648, 261889455, 436982226, 209471542, 955307139, 893679494, 8358357, 993869901, 463136291, 152455138, 637871432, 475896521, 404755598, 273694844, 808554689, 478189701, 571584279, 822194995, 493466620, 963124059, 259419861, 446377980, 116553384, 339935088, 909235224, 143961320, 115029689, 619412294, 80887497, 877752333, 493897169, 514995416, 156675344, 458032393, 900501783, 475596148, 172827772, 646248232, 989015811, 311735957, 702228131, 501062737, 826346539, 783518861, 765085653, 331393015, 468881166, 249922785, 940707488, 549405095, 803924604, 86648367, 631314854, 71523390, 411218194, 289019545, 749911123, 355583471, 776159056, 412586388, 731960837, 723384169, 751942093, 180854977, 748737498, 705045442, 622205535, 758952411, 948588752, 292058938, 237512588, 419325931, 662431864, 151399299, 467820629, 877734775, 876354936, 269835924, 540127547, 991595246, 91231795, 114043570, 636596934, 554847961, 713410744, 186249580, 224084973, 655839122, 83722470, 717315759, 244277655, 618767211, 63773565, 273353660, 905249596, 48260680, 418484895, 873365631, 593863584, 781520297, 371238869, 129305844, 59980474, 589507873, 148568786, 875558319, 431907408, 482246837, 399195986, 115278202, 801769272, 696117907, 515095069, 949386783, 903503616, 391254389, 957410099, 533799477, 638732312, 885654486, 788030728, 619144354, 882080300, 629161275, 654332140, 605757159, 315744417, 10596014, 539471831, 242763645, 544544481, 544615813, 482632327, 754382256, 408034216, 520562748, 404963062, 239468116, 634568776, 179559758, 386764335, 231777821, 619698554, 804689449, 354377053, 738400543, 370768115, 290346719, 457356543, 17163290, 886299854, 940683932, 669684168, 95732487, 839334976, 323065755, 447996174, 953586728, 521502782, 473188027, 143442716, 851231660, 504821440, 231779817, 407221606, 255388479, 92018349, 594233781, 29311521, 345437616, 434375854, 445850829, 384737730, 807445154, 561757341, 25090374, 262895248, 822232592, 549033186, 167827814, 840903492, 278112296, 724442800, 432318537, 652263469, 712273047, 746495422, 850009784, 804438321, 125332350, 376065303, 530995596, 289583091, 693125381, 391091273, 573991986, 902517950, 193991884, 261343181, 64593247, 429141301, 505317535, 25430861, 255165983, 876348544, 533217190, 577512822, 673082555, 48033771, 133277220, 234053786, 437865351, 69806194, 121069084, 453823688, 456145616, 475518605, 82433894, 129972267, 999798627, 59937329, 603809052, 624963270, 713119286, 587811495, 631760918, 751448325, 731884894, 709175092, 561122902, 687660088, 377836314, 623413236, 677258684, 601314416, 782628049, 472363668, 141160063, 309559037, 138137346, 53192008, 596033055, 265521552, 530285897, 407783295, 400580860, 501561664, 58191211, 972730788, 951892194, 810182666, 448241594, 351536410, 506334245, 391401906, 438986072, 131820586, 431391995, 225489883, 797810936, 679559885, 444655688, 489607964, 502383361, 858708678, 858983825, 587020448, 815916952, 441943426, 199066194, 12650093, 114429398, 510354638, 718001479, 679342983, 332583861, 951701171, 751599265, 203924929, 318814740, 506942412, 172954064, 916053779, 678744599, 731082937, 160558635, 420062830, 666637852, 480754019, 909189306, 242196330, 252712212, 473670161, 609620056, 32281235, 344408878, 437526489, 635987452, 273391441, 872197832, 355531366, 856511614, 989731077, 299486043, 155698260, 835018426, 72606869, 827641615, 392071400, 174274412, 661059338, 170360704, 282190827, 464937647, 94073748, 525254701, 14420855, 596607619, 630020396, 41848163, 514441280, 479867396, 256430841, 124363331, 790401484, 885695188, 27021803, 292999685, 909940094, 392332915, 789072736, 556285325, 392948540, 988285520, 585440320, 247524893, 116816905, 206589753, 720761932, 942329670, 761257275, 864075433, 756189762, 293878457, 403660286, 610349609, 594864889, 682606127, 590369777, 417416297, 347568530, 2949328, 382175515, 956224409, 881219973, 546697944, 369015854, 659200143, 895538961, 275031242, 110289273, 530179475, 910162740, 928597386, 287301184, 352471913, 797874520, 435799390, 978194211, 577528452, 618834841, 950228931, 573364453, 639610042, 875152978, 482423062, 464420687, 778965924, 577459510, 562970739, 418350733, 551298106, 361463453, 223620655, 706694387, 527226874, 550629177, 690856399, 305635519, 644140883, 685889834, 304956385, 548391384, 308761721, 454113000, 572981071, 640692422, 896328818, 742312652, 188512633, 834848128, 961407867, 95388499, 458930711, 361257661, 322580106, 648801762, 415097068, 634159424, 867039453, 326411732, 933390851, 968556554, 70772284, 333118945, 524758179, 105951195, 932989669, 429886172, 343553503, 904078028, 1215262, 160953116, 232170873, 857892226, 10310618, 359582562, 428918101, 153640327, 531942952, 43185594, 218351884, 214762382, 951056809, 788881522, 82881473, 34480292, 175822942, 124626943, 500738152, 16215480, 124022176, 99602479, 62912107, 465234641, 809312423, 495386713, 401721934, 842679806, 233568160, 303056083, 73108019, 655961105, 873176928, 339559231, 474885933, 816549949, 888774087, 885025693, 876517028, 587774475, 39302027, 318992668, 84389255, 530852173, 103221633, 389759463, 709455481, 129342800, 292083916, 530067528, 220316929, 210224603, 923244699, 853537150, 325418871, 863835483, 971476239, 780137906, 381489025, 106775305, 99942765, 447757556, 651410525, 238271310, 381187157, 958070969, 100998117, 889343577, 796008059, 105530191, 781432837, 622144367, 718371661, 318615192, 717987563, 801688535, 186181953, 608331246, 71562249, 823130703, 814629929, 109165833, 82778872, 419688937, 831449600, 798014724, 551340224, 796166654, 841939755, 380994840, 401801787, 30232211, 651833214, 676673803, 379830921, 166855699, 58417192, 626106081, 328359111, 807491536, 263221683, 772472507, 624751623, 808837907, 434031769, 177384804, 131946915, 552623640, 752918047, 372865409, 51591058, 920404241, 274749584, 617472830, 68010554, 380202917, 158317519, 458862992, 597116275, 920078554, 332093428, 518672808, 140015339, 370663898, 138263196, 529449623, 104716550, 347656594, 242737142, 980631088, 462572047, 52251675, 339545270, 770629194, 22038198, 255538044, 790166035, 985540123, 282686696, 313635649, 14193641, 425271845, 519083879, 232937718, 761901423, 445096129, 7369475, 741404288, 304823411, 316258328, 188060591, 58156505, 477309139, 5250526, 478561973, 18921697, 221278280, 405875510, 585130441, 914497984, 333398903, 170777697, 30364047, 688146969, 460695442, 597619031, 664183903, 542655616, 612227299, 323646023, 318607401, 274940824, 817518998, 202887136, 894465405, 998947245, 232690375, 171937679, 985082640, 461458594, 807633495, 205095802, 456009148, 2102060, 494650401, 324276320, 285175663, 502489239, 861321356, 678472054, 492627198, 44581113, 68111401, 781632038, 28761484, 12090256, 688631898, 608024662, 372544587, 494709830, 774185380, 66075431, 192373375, 259245802, 896788280, 203508031, 127780773, 969330997, 322526420, 130229359, 664999997, 236473143, 483632094, 666006389, 531456153, 352722319, 78856733, 123959256, 271176361, 348445694, 845487433, 102685628, 365936879, 484620964, 816463059, 229895733, 406690615, 322834007, 101266578, 217442708, 769385401, 61330079, 869848300, 538695247, 837051137, 695923108, 174402510, 262417345, 851130681, 775004502, 624210953, 603775146, 629939062, 411704831, 364943923, 978507849, 765195554, 805689950, 876578598, 43468117, 813415210, 961387915, 596434927, 322906690, 72183653, 114057317, 29288751, 757420128, 613582437, 958417214, 626014458, 288924838, 724928824, 998542911, 748518699, 328984690, 622218746, 71371100, 257542231, 177425756, 91507509, 905012578, 899203946, 843989522, 270927598, 215074420, 303410447, 249187625, 359651405, 323764005, 165986221, 968021992, 474226418, 57111687, 350758278, 818416568, 961826810, 879270675, 943169971, 647992724, 237960878, 118582693, 751759942, 201701539, 176697967, 990756423, 77689890, 431036231, 271115215, 576609537, 447793852, 237455003, 824729256, 782445261, 103072863, 379664661, 260064928, 829347749, 977067260, 478281490, 254749195, 451356719, 152984895, 317581648, 786606207, 32137631, 76879457, 636416526, 685489106, 168548122, 421758715, 905047532, 559090766, 703923477, 810233866, 70401868, 318319125, 337644075, 101000558, 163711044, 723198859, 487207906, 449292841, 357548860, 108916736, 559286660, 762523686, 610586179, 631923220, 766328009, 715741062, 578081588, 272602302, 17907993, 759629010, 189607077, 757050457, 428346574, 682801004, 126037617, 607979388, 728252765, 482438340, 36674364, 829610587, 568879842, 83563376, 275010206, 727407232, 232082497, 436748272, 841430028, 985761761, 284805969, 663247006, 637899524, 203875489, 125301761, 991071142, 234981251, 109368279, 600744999, 75474586, 806175688, 567236427, 666198800, 295284031, 821642508, 132120699, 271451224, 426691395, 445703262, 73068389, 956580383, 765228003, 574621398, 523305484, 593840130, 853937248, 807823150, 533930894, 848477902, 455631074, 404743894, 664904744, 955706651, 722788224, 388975929, 186739099, 998836648, 622980939, 346986686, 154140826, 53033504, 310864962, 568293364, 639175983, 390083173, 482239321, 881862327, 977688425, 792290051, 161220442, 881971097, 309613783, 255431296, 375568109, 513060674, 631027744, 424226212, 157793312, 503779158, 299111777, 83081152, 394409092, 207328970, 132703580, 716764894, 498846353, 632647563, 280279556, 735419630, 433369644, 553141987, 301060721, 471243188, 295569546, 413555407, 393123346, 512119544, 206041812, 22119798, 407425790, 153563577, 115213416, 476287360, 470342754, 424910899, 662791324, 189954868, 439905404, 481232907, 585108160, 376250457, 405127926, 352640941, 785629817, 32040759, 359185684, 964492267, 436787225, 167690419, 578874621, 124948858, 611511766, 110238016, 199785733, 662834465, 369240914, 904352766, 911458546, 14859309, 40575529, 213136659, 412216417, 833013036, 900940571, 294375860, 604668251, 880878574, 641372302, 275943010, 895355302, 977965372, 606830854, 607748200, 441340304, 223817516, 414084573, 340641342, 516036339, 522578331, 703349631, 673961034, 975324978, 502970613, 248428865, 597752301, 767911406, 430324266, 474096621, 956242576, 969310446, 313935324, 191917188, 391278803, 799669763, 294029971, 656373053, 222024537, 441790157, 184123084, 199475916, 442797396, 810611964, 370701607, 791233429, 274613135, 585845677, 518751949, 364579645, 714326519, 586137857, 542000908, 889431249, 490987455, 935364778, 35072011, 159405784, 271155846, 160875825, 700205037, 887999833, 611526549, 71664833, 365461546, 92206726, 40743293, 818802395, 910763901, 256572080, 450593003, 601375192, 233612751, 969332989, 965311785, 437944956, 181544155, 298757913, 338261999, 456006617, 835443866, 73254412, 614595202, 615910439, 28628856, 833922734, 312562778, 398854685, 749774511, 565353547, 113804290, 826424837, 214601835, 916212915, 655725126, 352413864, 577658011, 696258906, 232757150, 641394431, 306636757, 63794873, 662139735, 162999785, 128870257, 814484256, 922739127, 884120383, 716262347, 673232429, 267164027, 629665547, 516576886, 360252452, 718748640, 447069744, 981731688, 319998809, 22645455, 105518192, 573141318, 336553038, 104520227, 189959325, 291433296, 525111651, 997012272, 131038760, 433253361, 783277455, 138427452, 388356363, 595341156, 794112327, 992157390, 908405231, 934191439, 231725248, 259709522, 457401674, 984496192, 251477074, 306019065, 10951281, 450400783, 809276046, 804337090, 605227258, 423277670, 187011374, 916757175, 324382574, 83617678, 222154781, 446013411, 419179828, 673167559, 925989117, 348456386, 749345304, 473557679, 735470586, 465316058, 779117470, 849846568, 289376296, 202084629, 509920059, 523622121, 841041070, 319019299, 174598106, 795562395, 589335484, 550665055, 486561149, 641289384, 736750362, 261944849, 78073494, 851234895, 704679211, 851792640, 380617961, 396034698, 616379146, 168126076, 611324374, 787511252, 935396128, 300796777, 208289949, 152115933, 418433576, 567765473, 999182212, 364156257, 824165777, 862937586, 270141623, 331297028, 592117497, 660312896, 985419031, 508993785, 947735391, 649345613, 382093272, 14630521, 139651937, 949107650, 881149, 933542457, 807912122, 871761971, 65403017, 654829398, 622317709, 545024259, 328098190, 783099840, 191284847, 739328360, 214568651, 157213012, 891353623, 805685699, 201321973, 695531553, 897767788, 960500479, 996870931, 580830839, 990865719, 691794460, 840343907, 374841186, 337358762, 123019660, 111879902, 821366239, 58546779, 615609392, 908827340, 752022736, 898722632, 373785857, 963795680, 801063746, 699303531, 353670709, 633430662, 564663991, 206309089, 460936495, 161048883, 137108080, 530232910, 779029345, 497440133, 350912773, 915095532, 272519153, 9044037, 823243009, 99932769, 401797777, 239858626, 994281390, 186766601, 880388556, 936408419, 265763865, 634563795, 706853262, 702552158, 961528769, 841721024, 395732020, 179732874, 61861409, 602724358, 927159065, 888991111, 839030131, 737431224, 465127845, 928051681, 700477649, 362882971, 790396498, 150755449, 133332974, 831925304, 773709871, 888197492, 189354615, 572614318, 950058906, 510848802, 494407869, 644317870, 190055593, 138769805, 953212596, 832610660, 76605043, 73705657, 946800256, 717923752, 997330302, 139473629, 854246876, 542451789, 194067349, 462201777, 386928403, 32333602, 251923600, 671314338, 912886088, 853837265, 423791735, 85207929, 533749558, 47311489, 402653582, 783711490, 991895366, 452877979, 492728694, 554666756, 299864723, 229515102, 466257310, 767052549, 801704356, 311598138, 206188672, 716483280, 268490077, 53351698, 872608897, 995079175, 528875065, 258968883, 618977621, 757451243, 386484726, 98098166, 854616280, 152871083, 732475712, 173421088, 304582974, 581780777, 424692824, 476332514, 479114963, 189690527, 721516322, 376442611, 881590934, 592228828, 952942546, 519222362, 929862635, 341987508, 122629058, 12849813, 177388691, 733768183, 981436967, 644910065, 730724668, 130572324, 334286571, 591284966, 427158010, 247183180, 813746665, 96654997, 996945317, 302316167, 127979657, 440340726, 374336605, 910044018, 159859662, 524264594, 4129153, 624645186, 633314565, 126009794, 363622287, 423214978, 877094032, 346624766, 108804743, 415706265, 228697225, 238131621, 151858559, 416506193, 881842082, 875775437, 784955211, 274582955, 679995682, 356799394, 704315563, 388891120, 180342996, 45260721, 436767633, 709859179, 942318249, 173113714, 373763528, 939282191, 812651322, 606243050, 706372445, 512080940, 371759574, 333771558, 399440102, 503011172, 843717860, 468789496, 985172947, 535277128, 848288541, 670847083, 222027625, 171988705, 788303630, 919408970, 345473286, 139978731, 633365990, 987854977, 516552299, 779546789, 35945827, 904953365, 711490427, 851676431, 884169152, 977308125, 220548531, 867763795, 300080692, 69844252, 249728310, 617824456, 820065473, 936925348, 475148397, 382699070, 907754603, 976318333, 222387163, 69120799, 900356079, 261038866, 829212118, 346675076, 578581548, 207822780, 364338679, 967377547, 382562706, 292324280, 525390094, 131969929, 53071431, 256616967, 580080325, 732442279, 226102360, 117135653, 990204952, 843322798, 146148407, 305406578, 378606069, 337035277, 820751504, 88344931, 869449195, 372263691, 726975871, 809933805, 153504086, 224849539, 810551137, 411208295, 161025227, 634162217, 288337885, 371887420, 990055259, 540374650, 632565211, 517079798, 634413776, 862541550, 233126767, 185351290, 837648964, 603585656, 449755081, 943674420, 189457632, 935938720, 363852993, 373470256, 252193475, 461830340, 565504267, 335234657, 4440465, 772696860, 213321211, 298843339, 203044672, 610269750, 386644542, 872413466, 776027757, 113534486, 528779325, 508859191, 819688278, 500052811, 332969657, 603475110, 756239564, 732699064, 440970659, 800225334, 549740189, 989514047, 866109367, 248400179, 951532991, 957436619, 45166768, 424232794, 60661489, 391375923, 455723306, 636307710, 428102537, 244288291, 391881837, 753565838, 410928584, 399165182, 654354924, 21543922, 77552448, 719088576, 67343010, 482187411, 990281014, 428004560, 840687324, 827655083, 52839659, 716312244, 526137626, 968535105, 607672499, 810480695, 379397714, 168604225, 729460710, 689583515, 184920401, 240066118, 991781942, 49778200, 892603600, 168105371, 311653821, 948239552, 172974315, 402456455, 922550470, 91271484, 249164920, 784869770, 125461634, 603129569, 680190296, 528032118, 544461710, 78425626, 718974607, 341285029, 752123628, 724592844, 162463358, 114602143, 438460294, 670203066, 659058080, 15570696, 903836176, 824857478, 971880828, 408929188, 3674131, 852894493, 614546450, 434579903, 422959800, 314005212, 615048911, 821070616, 519958159, 176398981, 188146989, 596308892, 168911723, 382959045, 251913407, 334762156, 240829858, 574596907, 330777410, 656839996, 728221522, 163106709, 444568984, 44929604, 915707911, 640467881, 751224962, 587683458, 839179294, 972529928, 220986006, 315063678, 473718117, 141083824, 729732472, 768009263, 775010588, 83783084, 817658656, 335648238, 206824995, 814918731, 464058694, 6826464, 101850685, 184282437, 189866845, 438209764, 47409061, 250359846, 610831476, 767822891, 860555113, 642431806, 353040053, 337881111, 855705485, 919594815, 70695414, 609289839, 712149113, 44559828, 773502813, 324337613, 782043088, 260547247, 920015904, 667478659, 399591398, 868236709, 148961593, 237489169, 587348671, 478716790, 436429541, 600189594, 477973461, 208361766, 193091441, 796573843, 336971046, 614405485, 488768189, 332437721, 69700564, 745803646, 519737692, 535502769, 169723300, 655170685, 114095042, 236458159, 427638299, 894381408, 230991500, 160352223, 739766782, 81660490, 315325623, 990862056, 255953598, 216868052, 950425707, 814782099, 321271388, 448632283, 719778286, 432657065, 845683106, 197099665, 271806371, 137485039, 527796937, 524771700, 436331620, 720214694, 512740259, 315170490, 130138700, 888220038, 226005549, 602926237, 348082229, 241381707, 524415811, 218470643, 490483255, 301925884, 319391623, 586087288, 979160709, 220118769, 513826041, 586073766, 745113023, 969433465, 662453238, 266996831, 294817110, 997204406, 252686349, 961886005, 794919529, 692750466, 119254925, 197986491, 259560900, 453619518, 888852203, 828194633, 104970299, 343102427, 543918160, 947499184, 952539965, 198933955, 276598451, 730629232, 361035182, 175134847, 808324893, 57030630, 588841811, 657667845, 460446360, 204789803, 214455234, 631639596, 960495960, 57373786, 640060107, 867297852, 168683451, 401345221, 618786869, 808566908, 175986354, 456842101, 455129016, 381052416, 33261759, 352429587, 456838422, 682133962, 501926067, 865538549, 511173213, 342911328, 232958584, 54912413, 372478244, 21699284, 165073037, 540446001, 595784707, 864051059, 569395905, 990796378, 785354752, 208061511, 394702690, 326325925, 390226397, 738108376, 327672129, 174446077, 49150270, 378021603, 314987726, 542775839, 28431328, 591293103, 170549723, 137591247, 388108253, 410273029, 507495578, 359144528, 130389291, 729921311, 774383022, 743871935, 946579287, 54893118, 249460064, 341082850, 747730889, 234793045, 343015763, 806844002, 795981733, 190656320, 485736316, 696766396, 553788102, 745913869, 362695749, 713788007, 865181708, 817574132, 77960324, 555197975, 626628669, 721813922, 673341268, 861708464, 104242347, 725835526, 938490556, 269968328, 119736424, 91081020, 509984069, 546121526, 452455307, 350420139, 496723858, 813378515, 849023763, 451138582, 712856987, 207750404, 137587310, 770605689, 978865439, 63749894, 259799697, 449468400, 816249870, 13166215, 523990513, 981191154, 280679115, 437348591, 248340132, 214483766, 571368009, 909646106, 906394920, 198338681, 726166001, 113891650, 629347532, 361112347, 560901928, 419576014, 393388089, 851210481, 673997150, 905862470, 714075726, 447113303, 880056018, 938624521, 748302510, 580289670, 775275143, 671934612, 98573997, 68153030, 880039916, 250982570, 140876527, 436943975, 627093997, 277396511, 918716330, 99089716, 310191715, 168817521, 92573897, 57196426, 139261454, 135951640, 597179732, 29585290, 271765636, 532775340, 263394242, 739886285, 639814964, 587198176, 472192472, 255312550, 445881043, 508181600, 153072369, 328731606, 418132042, 421016178, 259060555, 554915729, 318428029, 695334199, 957255143, 531878592, 625144677, 302707464, 899600124, 781799118, 408661025, 128200698, 506504824, 621967099, 927275891, 522457183, 356972595, 770917991, 280605496, 6543221, 655288474, 117827738, 2362284, 519871726, 527280987, 253492246, 780098215, 795724017, 750799968, 432197555, 771087800, 917497774, 169160470, 440507361, 261655349, 316241548, 996032677, 521934824, 521181494, 64816407, 90686810, 807938400, 685104248, 460248, 189286934, 584216717, 230272359, 494462583, 946162274, 642290568, 603516994, 502639490, 572425075, 967252331, 127630566, 384983080, 343987702, 900447647, 405301163, 172398760, 921585944, 419453682, 623358077, 929062411, 32597375, 334590002, 578851983, 122071066, 554865180, 475090486, 309280849, 812763257, 721682002, 671562916, 142235225, 183438029, 544208298, 376105324, 632603178, 369516866, 827268659, 972368334, 12562816, 307089507, 618207355, 646367807, 276745144, 130842684, 765314906, 120201467, 48605095, 722688247, 394895520, 123422734, 121171866, 836736959, 414905222, 136806164, 374042375, 898079193, 474954012, 667383373, 314689853, 315150448, 99552326, 94626480, 84611182, 101561208, 392338865, 538579768, 724759032, 817169490, 113992658, 534334621, 196389730, 24974931, 952190518, 573156914, 475894623, 63348338, 977622531, 664359290, 92157489, 89664802, 63322770, 120211804, 94759662, 588832825, 591631723, 471778983, 29429771, 206345141, 431136215, 264506475, 347571699, 324184646, 360553645, 391039889, 460390868, 988619133, 359587508, 276768815, 908052384, 540026526, 136360494, 733074754, 849351151, 553465182, 763277928, 559832824, 405437178, 223875926, 332001037, 355394303, 464331810, 941722882, 702147057, 634753635, 735556315, 119159254, 815671265, 202273652, 643623302, 388928089, 280746060, 289962131, 852719956, 918170937, 303671257, 211023174, 783585905, 31007844, 569995194, 501660701, 255609820, 739076928, 597261513, 286196827, 855426948, 149010275, 763961713, 408529825, 202025502, 262853663, 758120682, 712709982, 71789712, 894237523, 964018208, 675464985, 934595131, 278113769, 835891579, 487399989, 617712175, 655515833, 60192796, 569577977, 650180512, 273081282, 947251472, 111191259, 842044791, 465012789, 317283079, 310816241, 454328206, 189890086, 746555117, 424413966, 483407967, 389054433, 963128907, 767037638, 7963160, 287366765, 730474753, 67472845, 325716900, 212985779, 449737181, 872767104, 713316073, 524225748, 695457145, 135455508, 33771378, 400824499, 148226286, 796205633, 303886859, 355751041, 681091150, 827399094, 455011248, 973673970, 422621301, 266800559, 957213029, 228408355, 298186472, 887678491, 390458345, 656473704, 157760502, 429157380, 361443278, 867965847, 107659941, 445773398, 163645695, 411611174, 357122187, 96748899, 522828403, 339240388, 416024562, 432779304, 815835766, 175198195, 732635844, 235713721, 550429934, 877363123, 268858016, 699814234, 15352189, 549046386, 816819300, 185850827, 942603419, 168535285, 918472380, 603096035, 134860320, 159038253, 271602722, 577122007, 447790415, 133567452, 410947808, 875625403, 83715270, 170638089, 87269861, 188292662, 239653180, 771163650, 258005248, 735578227, 297990298, 746312502, 268566088, 865833411, 818690952, 758877556, 648630255, 708962966, 580537727, 201005795, 997029468, 363624716, 249201095, 983592197, 300544747, 518357678, 799471846, 548329135, 137510381, 999782534, 8107414, 445089913, 428000115, 120193056, 575719709, 274905927, 466327145, 128791367, 135882782, 505281496, 533090766, 776180919, 577554662, 87927189, 700287884, 626975514, 94870247, 96906255, 640382452, 168511608, 459229615, 952636316, 692076804, 773547957, 201208985, 541501556, 650895143, 25200999, 570502610, 364150925, 276673401, 666164454, 120717902, 475739836, 244523442, 221784444, 272306944, 431241812, 83155087, 900044139, 849910884, 600797624, 817832818, 20897584, 358218312, 99963162, 966317657, 116473754, 873008541, 211566443, 638909521, 510281558, 475115619, 164174659, 923690, 988105395, 812264893, 612040584, 997212891, 83641594, 980538079, 401697087, 207133256, 266235774, 214600599, 459435800, 268704809, 775053943, 148906663, 104871821, 282723682, 916026755, 131718095, 767256618, 867515236, 585883334, 481580120, 278331138, 854970677, 184553642, 271944391, 87703529, 816349687, 401026397, 889231717, 560176366, 11094760, 289884914, 889802710, 992090026, 189862280, 289408668, 664888652, 374532178, 717159877, 324250380, 197170309, 148349504, 547917711, 703157354, 474199359, 553454118, 922826014, 988011496, 981571956, 468327587, 265491681, 272241930, 860317149, 11212956, 275910997, 206475901, 908943100, 493433862, 257366968, 198093100, 992655193, 470420982, 574590214, 693080345, 44975958, 420275352, 651680895, 522127389, 632267957, 60178950, 756833365, 813365666, 539382999, 152516292, 456553338, 324368082, 683192155, 35603187, 826647772, 607894164, 17961960, 464429407, 882220571, 797161977, 101496808, 518639047, 119957240, 603175509, 260162774, 383290730, 388303787, 906928546, 944330675, 369042679, 793312477, 902709294, 729440151, 725833274, 622343063, 25616222, 184132246, 430300261, 754960481, 805327735, 839504249, 285929489, 123666550, 900318536, 376148223, 808920950, 619329056, 761783543, 93667136, 454485497, 814560792, 577839657, 98295854, 945135124, 190907068, 821353956, 585073176, 611998630, 358748799, 697559745, 805874895, 989699054, 592303594, 499326308, 685537585, 168104943, 953923330, 258828542, 815392852, 983826199, 834775820, 875310520, 983424711, 504545340, 361758913, 801296116, 331215205, 13707076, 567678707, 221346226, 61043174, 330627642, 863217540, 526771995, 908146563, 953387789, 411961341, 90264221, 56418582, 47858512, 321765709, 265528669, 224912534, 119756371, 146000564, 983677820, 722863020, 423952564, 177248205, 219305064, 96708269, 853067125, 762645103, 448351328, 77200180, 355836977, 760941029, 399221592, 459592702, 500701881, 785839597, 266824477, 104428075, 551119030, 873992024, 367542324, 375658541, 667807829, 339876351, 253177108, 523940326, 520684617, 303324178, 669061586, 465187961, 182725208, 288179540, 739342294, 14318055, 973242241, 821209586, 292602542, 315411076, 20662101, 610910915, 971658289, 702485018, 172658898, 983686453, 484065749, 408352835, 259923186, 401970928, 837067139, 749464641, 66428418, 215820582, 702612762, 513447027, 856588386, 460819159, 962123158, 202620983, 179795057, 41711220, 454444417, 505301763, 12196157, 654498603, 331310398, 244827378, 436040733, 793176846, 325991691, 340607992, 471843557, 150292200, 859884168, 146110557, 923597115, 6764162, 701964312, 987867218, 737854060, 609086970, 709535625, 48969241, 583593276, 987306938, 551510840, 455014646, 520464832, 623876172, 918172579, 812304062, 482147778, 86275489, 977087375, 331009367, 914907980, 833156363, 661936977, 907410876, 573397887, 925478301, 187350778, 257750548, 63079594, 590371481, 344368478, 811160764, 168578560, 14380439, 323002876, 630382612, 193319982, 376297902, 875039952, 126648046, 458853147, 148514866, 812545506, 572076634, 881345835, 207050854, 56728323, 604013021, 338905390, 68961864, 242936211, 330802972, 799216093, 972143912, 452111199, 743488316, 683610351, 337673692, 587235831, 978785770, 340613038, 518223615, 942241740, 176797365, 101003275, 137800793, 765107007, 657583865, 35675757, 530118181, 706716519, 121382800, 574824022, 492501425, 361278392, 59557974, 458220918, 165850780, 691892751, 796316411, 68303916, 546474034, 647056234, 782965841, 476085451, 993683907, 566664430, 127173850, 24809657, 188357207, 604453598, 321455810, 982212771, 237704548, 648928308, 474843702, 449079392, 452281505, 974751086, 995331906, 719106330, 793951319, 874091102, 669758688, 960429633, 199794937, 948764751, 446740133, 905129310, 32021333, 165212199, 589728599, 299214773, 442673591, 790725125, 315016163, 736144373, 752176490, 564984444, 723724253, 975022284, 73727410, 536961031, 931145193, 717732338, 166465836, 818191504, 710331410, 826650274, 909312634, 782860914, 381651458, 256255285, 979254912, 196783496, 385613087, 296708885, 69917455, 272442423, 266909323, 46333035, 39018305, 224392950, 937600029, 769025865, 156488901, 672814705, 946315826, 763121437, 718808396, 504960395, 650945504, 482385805, 511300679, 205137105, 936468298, 997106792, 686610979, 706707954, 94016252, 404741482, 510996141, 892511994, 281396959, 217875241, 686473901, 257071629, 348585840, 175979068, 990098651, 857482498, 58971662, 694027265, 666983208, 798915759, 345618517, 608153279, 443755191, 592084941, 590579919, 702671942, 863190216, 872063875, 755230594, 2273146, 797995150, 872181941, 769569454, 610418089, 341592121, 843850907, 208162856, 11038991, 370104345, 988985911, 57478250, 408757515, 722376677, 833091445, 485016769, 400595265, 315495845, 778262867, 259048189, 207987726, 950847722, 207507491, 454804215, 847551185, 638017709, 463317553, 19177330, 860473645, 747876106, 749209217, 742584424, 201520472, 308370595, 621863872, 140452389, 570253678, 682589328, 436766759, 267413634, 86479620, 641207042, 831083667, 916271632, 532691532, 602216124, 776772464, 996407278, 968091849, 971322483, 892623896, 799555523, 671899063, 782449570, 22959179, 773491583, 553756559, 315074608, 610632472, 190694097, 610278793, 264945781, 367825644, 919079717, 970278622, 963451957, 127510039, 108633438, 151922849, 615822424, 423589074, 58530697, 796182105, 849190611, 320700463, 211753547, 227250540, 813631557, 5108747, 558236376, 669870211, 367346498, 548207562, 669239117, 92043560, 628237087, 224726764, 687514923, 393797834, 203816299, 872111164, 466920801, 497983011, 779773028, 690077922, 250109603, 229970808, 73845290, 81492866, 504220850, 557463414, 311961225, 134229720, 908115791, 457282810, 134460619, 103349412, 535736380, 18326255, 439197359, 779180236, 95906763, 78059027, 343262234, 276480324, 781772899, 714557492, 843214561, 605261678, 248801712, 996928357, 220032156, 527200488, 506038953, 277379443, 912398121, 829251433, 287737914, 377299201, 891552500, 489185021, 743040493, 818009561, 923220650, 145589596, 936080931, 724180931, 481063882, 812864637, 486104870, 981211456, 134300087, 115218544, 319316400, 387097838, 433316572, 906988824, 583589939, 526917646, 658911820, 305084804, 357450626, 425822041, 590976647, 644642137, 839966584, 805513338, 62623696, 898175802, 240031757, 96612462, 222256677, 485122646, 650877817, 444953663, 34476509, 927370650, 436755490, 236286624, 462699733, 392698339, 579505082, 592934726, 659753856, 555578538, 532084828, 962356493, 210689758, 420590108, 648306708, 428768804, 222674563, 755453767, 579085135, 939862191, 405226517, 538394162, 912337619, 996279995, 220871921, 947242860, 720095925, 966535022, 582277199, 279502098, 563279562, 317800938, 457057873, 617414733, 438604940, 852310652, 493647762, 749085151, 50682839, 765533045, 132587121, 95615640, 163704351, 807045168, 890913184, 226091311, 35580747, 63714159, 865176294, 263809867, 560705949, 514595026, 56841162, 488574845, 933628896, 416738561, 196448127, 836506096, 55905238, 66710283, 532877178, 777507167, 924321734, 914202397, 40620462, 766843334, 331600345, 117234202, 608842131, 275851589, 943136886, 435212586, 48075046, 38061695, 782726292, 151152453, 947479039, 640050689, 223147848, 76670697, 199598118, 817298880, 78573578, 544344017, 485030529, 496713956, 953307564, 999540061, 730651917, 247135798, 572166335, 921892774, 779316759, 112037035, 61144078, 761491442, 272823767, 174847593, 789101009, 145541507, 261402558, 46397017, 91858774, 535837880, 587592057, 368806682, 75165393, 85210571, 663924121, 159298861, 376041101, 813778198, 508270709, 761789703, 599223190, 315198181, 194262668, 266784955, 985831647, 582502838, 198173830, 617577541, 575901856, 175897251, 393355400, 645476232, 257899255, 773858412, 6870608, 834024099, 639225891, 219130954, 473999705, 279546382, 553462513, 716216809, 88037286, 170143859, 841189968, 732772322, 111654206, 455170743, 70567377, 37734636, 547887854, 265277202, 729306692, 967655391, 382408864, 522719062, 736449377, 65816197, 625499619, 462035745, 526798595, 382350544, 581273645, 182346478, 665203560, 123597515, 442685657, 947258865, 893301239, 365824300, 969506158, 42757083, 568003577, 320480529, 886564352, 28652122, 947189045, 256275286, 9781974, 488143334, 510969822, 158151079, 126959245, 516915117, 230221559, 991036420, 37962062, 454695080, 698095723, 462635764, 393463261, 491854335, 207299855, 219679199, 110954153, 812184131, 375992581, 386855962, 726179209, 220228974, 431124410, 771624001, 553821195, 936883316, 190219862, 459293792, 192791518, 86209095, 570331129, 849650202, 181180834, 779309877, 293208444, 786333682, 588527806, 784311803, 752966695, 760940364, 36772589, 451154443, 996255110, 778117318, 472806684, 543725762, 813723736, 447674123, 773835782, 181752964, 924331419, 890240726, 857129328, 192841055, 171375644, 417894793, 69297311, 173808230, 908500731, 153082958, 669636308, 438568960, 307490679, 968940034, 25521569, 163264534, 855174362, 48686360, 69094544, 153683919, 237499266, 872290691, 232625679, 355220347, 24108452, 850816835, 949072310, 465930007, 736202075, 165898338, 346029582, 596674193, 925171444, 338136316, 144374336, 573079000, 681520631, 969815129, 189345145, 235691348, 164911316, 510583304, 28810031, 548171444, 592004329, 118013558, 296890991, 809353152, 108601681, 714646737, 555237764, 124720135, 552945993, 685804671, 269012151, 461802946, 253109754, 892246683, 349936490, 609845513, 113850807, 563540687, 402615248, 959677962, 354539268, 962510171, 776780465, 108180480, 600346090, 944143850, 769173940, 305045530, 206800933, 155271359, 472388518, 847534731, 359095815, 263899621, 116921797, 231402723, 920990057, 690483373, 313885813, 831707250, 522299118, 651512736, 132626551, 240822726, 320794409, 663192199, 40940700, 379463634, 709217716, 453682273, 539817006, 126953601, 566095149, 194297237, 374758865, 555855651, 376307184, 445407763, 737886173, 125703733, 936572949, 413829546, 218702042, 688398850, 555197476, 507199154, 713928219, 497436728, 717428356, 486403660, 536493220, 43167957, 584831155, 195785223, 16677076, 503649841, 180560500, 152442021, 331325394, 264518612, 999390234, 54000207, 959874661, 274619366, 585766261, 555983984, 663974798, 227069753, 680372447, 854486930, 882688824, 775455679, 52308667, 772512688, 513114487, 510998268, 141963052, 691311215, 421141599, 117797999, 410749262, 358074074, 125289659, 489823817, 288051597, 539637071, 816907881, 750749650, 767447113, 398603333, 141657704, 809391139, 19248620, 377510811, 594581916, 222322507, 37200648, 476215452, 12569682, 535431135, 285744347, 596093879, 204340023, 564214491, 43128070, 10852072, 594142906, 593693157, 80902922, 862460913, 613221210, 271190367, 879739387, 480909621, 812894635, 21359010, 433368831, 236174244, 526866611, 587446089, 583086692, 307819423, 889438845, 186454192, 863936925, 148612962, 716585855, 550081022, 995478931, 812695915, 723432594, 773507652, 542086393, 19307815, 731064025, 667289634, 186712375, 240855817, 725410178, 382771680, 453841046, 272720519, 971944573, 921630161, 631057291, 837680074, 607564068, 362852973, 835651620, 623358487, 204146772, 275118016, 339567709, 895268191, 11760652, 764270157, 940613662, 625170148, 869464286, 223412734, 839090960, 698595205, 327018804, 603699277, 871337652, 958885655, 35297783, 219813601, 999143834, 203660431, 96081258, 30111042, 377627855, 289206118, 128871425, 112536386, 333819960, 979413643, 645635387, 108425096, 827248852, 394219199, 460416705, 127442719, 811091967, 417823652, 107487316, 378734672, 156795774, 394332041, 31224043, 877288306, 139849772, 868762509, 838524304, 64514480, 184911828, 916527426, 500052000, 211855720, 666600850, 750613666, 840298210, 224637036, 183156672, 62814382, 165299119, 368095939, 930219429, 122928778, 878520479, 941776846, 81371289, 286880622, 147185117, 463234160, 739032991, 900963499, 704394734, 803042344, 699524849, 603029982, 542366782, 779295291, 996910054, 946140015, 447233952, 795431566, 742955764, 708457584, 377341972, 848490717, 890559349, 596876804, 264859357, 785021343, 239413398, 483033007, 171695719, 379640617, 257857039, 230546003, 360463023, 209146884, 428753584, 360036739, 958738538, 849505366, 992247727, 743670190, 417036011, 93821209, 702923639, 623769350, 448698746, 936710567, 387396224, 537912396, 276713639, 883426896, 907908212, 264318266, 793778665, 634126985, 220783179, 681000310, 227318802, 138429147, 690350881, 174790355, 12810277, 806940209, 35106533, 753728550, 768574596, 392726935, 44306136, 649208641, 540243549, 78156513, 292806080, 454229793, 101533903, 599651902, 111792439, 667195514, 679029353, 100750204, 923171854, 87148871, 493977480, 866731711, 256842706, 164468401, 481068250, 262751561, 12464385, 11787082, 188963865, 280529271, 92887039, 177651503, 574077338, 114911390, 139319916, 604746848, 493608108, 613911930, 982752404, 135066118, 694228466, 373404383, 985805688, 141929905, 136662554, 753124674, 94105913, 851820865, 155256568, 892069327, 448693346, 340227342, 612748244, 542189572, 683871567, 328034560, 135860266, 318979819, 248557439, 359124999, 893766959, 987849904, 952482851, 104710537, 734562197, 438667391, 676747854, 164431395, 382576533, 719109006, 189762453, 397880752, 590682946, 381474270, 581938267, 342916219, 941014180, 743877679, 472459015, 580429135, 248685874, 198698888, 137376068, 253707511, 873809397, 228116860, 654519751, 853509380, 874903234, 656366113, 307344111, 334747910, 161076086, 764673793, 672938774, 72565339, 689255782, 131803389, 47999221, 414569502, 511798632, 348522403, 526855743, 946417419, 379367264, 8916021, 797191315, 68064197, 569125436, 209014034, 843913150, 48235697, 968149705, 234397644, 700973525, 305931606, 263523460, 931708936, 498761353, 363209372, 138377207, 65884855, 825597401, 45842383, 991620421, 314645573, 983684517, 225110878, 620684340, 133350081, 658123781, 837723165, 271154719, 383540417, 626019537, 632292167, 857343404, 108777360, 680673391, 581800459, 41841196, 216648963, 883785111, 285562382, 289644423, 764089545, 1173690, 370760209, 831728599, 383091164, 838582099, 435610608, 633965708, 802563054, 514765926, 54557488, 594561555, 761325493, 329965990, 304479698, 420289767, 239521681, 969331695, 471928506, 44958732, 693924187, 453825199, 560157989, 56163764, 931513618, 277404577, 258601173, 879101985, 948101324, 263100203, 131848013, 756301850, 640432758, 310934582, 655533607, 374156541, 139024364, 301969451, 798073869, 242753973, 936193961, 121353354, 109161945, 951209152, 509769000, 472272547, 535265811, 669671746, 230607950, 81626022, 690241949, 936898014, 715470073, 60751132, 994250180, 28736466, 894833507, 289959298, 819448467, 754105699, 382073072, 266601940, 386420494, 372524632, 417435340, 3943883, 984232604, 432550328, 579529908, 13311776, 49715871, 261177470, 692812750, 990314358, 276151253, 728416807, 653420272, 436674869, 403130737, 670566437, 950601548, 730836856, 165462596, 145563386, 42695601, 73795248, 55456503, 997650834, 792653987, 912985969, 805064144, 483795575, 204005709, 87086360, 112143289, 182313787, 469184164, 593134458, 668129077, 19515468, 523625683, 781180928, 800245175, 928836715, 232632105, 571743748, 257665617, 141123910, 544455007, 307443205, 260978623, 500064146, 350396792, 856021791, 712272597, 655400755, 635329031, 349054897, 123737785, 461608489, 620829699, 675392518, 46925094, 197785706, 433590565, 405313210, 32587220, 612370522, 739129906, 581511799, 311517702, 240276014, 960969323, 319392942, 278037812, 956017917, 428116956, 84368791, 441578662, 896105976, 550264430, 503808087, 933023762, 275680899, 577621877, 256628307, 502833216, 736680564, 965018422, 271657789, 270068544, 227087091, 278684366, 15920351, 119503320, 799979043, 826807159, 779262077, 822073519, 182241465, 286936189, 510041958, 732397030, 5957714, 542780375, 841945616, 666283960, 927385136, 684767916, 766382945, 934030339, 786176997, 927131033, 332885740, 82019339, 373021631, 314921431, 33112717, 982613474, 722967782, 782603231, 82261433, 130157889, 305347953, 89164882, 151407270, 241827516, 623869964, 415871492, 468555240, 893017683, 560346097, 250528354, 113024897, 196116500, 147003562, 14894883, 797781046, 940708627, 818772967, 775737947, 789348400, 502188445, 141799319, 619156024, 978729521, 749224247, 759380929, 325401638, 474817287, 452106508, 938937390, 72330783, 630751129, 918336856, 515955903, 982451845, 494035269, 183708244, 504265034, 582967472, 115805086, 75276336, 15347508, 809985269, 182334475, 736589918, 660052148, 640968104, 682057688, 707703055, 772345845, 493281757, 456248026, 876608045, 555829327, 879707591, 418121393, 857973923, 540447599, 823185149, 232090677, 116186791, 902796653, 379964277, 107524802, 650935274, 715595714, 678119748, 495848805, 141658926, 55109201, 554413770, 567456761, 881622719, 523905402, 506280684, 612831908, 371603347, 577653799, 714338389, 50168378, 277715393, 80874634, 85319351, 899466289, 687466036, 148219603, 453450616, 618664200, 41107367, 141872089, 533256918, 471100410, 603508076, 375806659, 998961624, 414968497, 153360306, 805440289, 163123509, 637285707, 288407583, 105513798, 482890228, 26131444, 586766889, 40147070, 566892028, 786648498, 444358133, 749407294, 814186311, 688055952, 405867091, 562831402, 302364944, 99233940, 761342400, 700497666, 356187878, 180044792, 768502632, 456053033, 556995697, 713814495, 208784456, 932982481, 352124581, 941346896, 679973934, 734619984, 10325397, 217580434, 239897583, 588419351, 15260964, 53631442, 394955309, 862201873, 444828220, 355727928, 873413908, 549931202, 707318840, 308941431, 29306235, 398484481, 438309476, 866149062, 25960391, 720844112, 981798258, 360660508, 195056409, 877935613, 259630498, 665581338, 13912155, 281429813, 488444540, 290427244, 902770270, 727704745, 142797487, 927698793, 668767189, 399521626, 174323773, 143347911, 672958010, 245577465, 405445007, 621325809, 610222944, 123489768, 265347454, 659333544, 505730046, 543189, 513521769, 362813088, 235041274, 970459712, 340144257, 860338016, 316892575, 491585322, 977758462, 781125511, 449361184, 759248097, 59555467, 661456659, 594363183, 760975834, 31585554, 61928192, 643796187, 375747914, 433113495, 350733365, 115098763, 76325178, 686388965, 773077106, 785759945, 218637466, 40808479, 984777567, 251430699, 712887593, 487202389, 930165941, 59867793, 345015299, 812954268, 664677514, 783990246, 709796163, 457175769, 798041868, 75059840, 652250649, 406588336, 923729379, 713222102, 215699774, 923857767, 946929368, 947966839, 12583597, 685254656, 232618318, 540553799, 781184628, 187526092, 621723903, 270353891, 361106293, 126687838, 283595753, 112121120, 41001279, 125240441, 597998535, 347649161, 362920134, 344362196, 210106398, 683884684, 774120046, 994191373, 791913204, 489844774, 401466166, 942809669, 508010978, 243541334, 623888149, 717842730, 121301846, 813491838, 26393093, 955413878, 490670204, 766733001, 337712236, 33662973, 555487243, 375721820, 987155284, 513248626, 355305160, 67794037, 102899982, 114250416, 210698526, 920592020, 181495805, 37757246, 617685183, 575176384, 390441481, 741779043, 83620618, 863731664, 798733310, 653622639, 653778970, 75693213, 301977613, 406056400, 823191280, 141472834, 633604217, 743092598, 518141952, 923042949, 782326112, 293281716, 46179192, 695102880, 224007905, 605995872, 565869455, 569161563, 801316687, 978793072, 447358523, 755530227, 840350122, 848216036, 60730613, 498968025, 471006278, 860199352, 716151163, 680980364, 743609996, 555456733, 754289579, 754302284, 292018100, 774626513, 203689721, 830875733, 310862134, 145192222, 187054616, 923861168, 49394661, 829663321, 574404975, 403280586, 197611636, 818652898, 531347394, 326623450, 405167932, 528046983, 808393605, 21273663, 668577565, 249286840, 108079351, 114352682, 128671821, 234399756, 389199902, 530431033, 950297236, 671378403, 777393989, 28218116, 324601022, 829917455, 357977953, 117069816, 231533527, 391649913, 417658875, 473524120, 572080814, 736170955, 193281304, 375532923, 421249915, 147447570, 769344717, 861324709, 353618361, 381875249, 572068491, 338136644, 272003017, 694824983, 647011704, 21534419, 164517079, 823300215, 465377128, 775948231, 444401293, 761981289, 732673461, 616412913, 567820550, 308139557, 15325622, 966521313, 536425584, 228320095, 45035573, 894027791, 622196095, 714027684, 386685295, 995510870, 970170375, 160344803, 301701798, 5327438, 563319075, 410637062, 188176003, 149436215, 510981373, 230101371, 520079930, 22911720, 182239233, 566338293, 737810263, 52604762, 714206861, 39429995, 606084679, 468650182, 177780156, 878324074, 799158156, 798736243, 414434934, 82895226, 526976234, 527971229, 146083486, 98015937, 849985724, 975531820, 855435908, 297645471, 507289302, 340302708, 333392908, 96993948, 26724901, 573128525, 905583752, 802152067, 199932317, 785148030, 386624172, 32427454, 809579491, 902362722, 342417101, 362158587, 862037558, 960141716, 293304222, 530806367, 492486186, 253360104, 838117882, 314101732, 645557650, 970909818, 401618769, 502868379, 328952322, 716379852, 660713832, 367651500, 440255778, 622086960, 465690140, 180034653, 435990276, 895581017, 591841551, 306945011, 891352094, 67245109, 23685777, 490163692, 861855787, 639973016, 70019985, 814368962, 766589604, 267920277, 642193709, 280147482, 236389739, 410323881, 368264164, 876996921, 335130867, 106287983, 55063599, 835789569, 687334161, 603182031, 479902612, 25032138, 638865151, 605280696, 235199723, 635148582, 147794767, 306716285, 338241417, 619878315, 410204710, 625268108, 590601301, 969016293, 480636147, 621037311, 413356172, 644015860, 242834557, 816620051, 550105843, 481863459, 850156611, 862761809, 459615576, 236919599, 567458645, 486549742, 438326993, 11119571, 64358625, 228806447, 276617217, 446492939, 885494474, 535640003, 791231964, 81431846, 991723749, 876609177, 309799222, 103267575, 246586299, 993995703, 933331448, 20448761, 234026290, 314048137, 993282353, 76268313, 200896616, 616736109, 666324174, 869082593, 21522208, 692420766, 565068530, 655746130, 548377453, 514443235, 41366885, 478962715, 403842244, 747545852, 219494681, 323666, 809658047, 687991538, 114139390, 434077798, 287139068, 263573262, 334031665, 231671115, 240828291, 492806584, 263037860, 97166537, 33684320, 562597157, 262724722, 185051998, 430843945, 203296305, 851104766, 426944510, 649974710, 66290318, 268832149, 529140073, 945842857, 547916979, 604875463, 480805767, 289716577, 292286929, 230354456, 939246113, 670904962, 771132549, 42562720, 90767451, 639278053, 334675511, 551216289, 311436243, 535076582, 810815007, 636951159, 352419344, 914500943, 522156369, 457455686, 66983790, 248514553, 148977394, 742299165, 400878455, 474238707, 473016881, 345813245, 436232866, 144225052, 636812798, 989920104, 663608094, 87035117, 536868205, 476817059, 418207963, 999929463, 569537141, 754123827, 913580752, 778603734, 987429755, 291365220, 241629089, 360492279, 217019510, 288865645, 691431480, 668745383, 711445870, 5193485, 663956036, 88940875, 28037433, 201294252, 758838000, 736722843, 713589253, 215157802, 262648819, 419737766, 217166764, 980956999, 481252853, 485236201, 569654987, 244963364, 695194317, 694626066, 954664085, 949466770, 130531664, 979628463, 644499543, 570436605, 678115283, 636769819, 586624210, 344424685, 456622270, 849287659, 973317375, 663967160, 631097226, 971467364, 917731376, 791595662, 528996836, 836879612, 834695441, 488219551, 189058962, 806104802, 898274880, 64463462, 920420881, 437783584, 110508086, 100190340, 701292144, 821564404, 931482386, 436543265, 465599388, 421351258, 277261947, 745842746, 504571905, 33366968, 928605247, 886085198, 95156886, 736768789, 958066895, 219953524, 26255895, 197710715, 582625740, 955227131, 669763860, 305819365, 207386018, 855504262, 349594068, 483612482, 197095333, 505061013, 996694916, 868473202, 661910953, 702047293, 65456792, 328477154, 940120230, 874684205, 688290895, 332843943, 818003931, 920973546, 199442945, 212980116, 200228507, 345828867, 471576263, 782230201, 302997267, 385725344, 499515013, 58552434, 144960114, 678560957, 549538196, 729397491, 951987599, 54457345, 266779701, 991815624, 262737422, 123307093, 667452570, 579773643, 878464025, 459847442, 83851771, 670091370, 507647493, 906429918, 912959610, 677505027, 654569641, 401626054, 965695686, 224904563, 620101272, 536099245, 851962287, 508062916, 64369980, 986931347, 628961737, 848487310, 311163197, 866161517, 683904517, 312959341, 299631952, 978652512, 120808937, 555637445, 847745903, 695789129, 622349934, 712632367, 749649974, 564265840, 757270462, 652541272, 949135652, 959354665, 587580131, 394964847, 293895690, 208654507, 406388650, 633645453, 103326632, 456928069, 206148440, 569964738, 644210343, 741328287, 218854213, 553285911, 993273925, 667432383, 310246116, 196434877, 682093881, 782598358, 280569628, 681451181, 524506977, 492644653, 630512878, 58472922, 934373316, 165345174, 478033299, 296617740, 545092217, 291705142, 699496889, 666414896, 285264133, 16362462, 118979998, 602607851, 732284690, 589819356, 314634062, 414571534, 583402642, 296963406, 953030454, 234133946, 559896730, 369027066, 876414950, 910558338, 638664406, 702365238, 929554551, 510668681, 401793892, 80303956, 459393125, 54223151, 931341061, 585274878, 722718786, 886786555, 904494744, 251554161, 130548298, 972413964, 642183360, 296528600, 185762910, 674426818, 595988674, 648469130, 463458154, 25339458, 254011791, 995096942, 364421892, 825998311, 546685781, 434893094, 573177265, 525470010, 891611255, 260243499, 316739380, 658248397, 901418753, 122759043, 566977918, 184905645, 397211553, 884950757, 237642977, 301936094, 642158800, 428041634, 147621053, 862545766, 59353879, 981032436, 518631943, 833394722, 432871380, 377264490, 705828021, 797603749, 290148236, 719329697, 21912137, 682104188, 522050467, 592664702, 380640255, 833955031, 596558511, 75065575, 644206129, 919613201, 938409080, 803245653, 444043936, 522757627, 321743264, 338633218, 737006116, 18782784, 355342639, 788647158, 720108132, 763420255, 118230632, 464469297, 873543405, 17319086, 809142478, 122491108, 476464051, 935489280, 990473493, 858914822, 348191741, 720826527, 628472251, 598029331, 615134325, 28026354, 492171058, 703584779, 218504796, 21674479, 324345387, 626188503, 50194661, 97688961, 557689928, 364370691, 495390884, 300340855, 281443691, 976905198, 172677230, 306214398, 860766299, 366562978, 167373628, 490013914, 769987105, 999314341, 835460930, 961596848, 985157933, 275008968, 676383739, 921459889, 35126581, 248045225, 159395890, 542138108, 953165519, 719125724, 165427809, 949793388, 168951235, 140282908, 274496809, 911281124, 192617793, 15454296, 318777464, 775128415, 938064528, 400499999, 422814104, 65342965, 985535684, 639356670, 912608652, 682893769, 823048509, 165995619, 688712744, 585147741, 631175765, 135247707, 54483430, 569182697, 790704162, 424989290, 103249066, 331118874, 568223299, 31632897, 93822734, 570363532, 290467570, 301903609, 489387468, 877211063, 366279847, 566844374, 90333203, 576983726, 298909219, 717163217, 906033647, 294847882, 301070068, 193963609, 275860436, 248679031, 626470407, 572484023, 740452809, 570502644, 927303851, 808740917, 202332208, 870010656, 35748145, 36455958, 750142867, 20789280, 929549785, 300271775, 475627599, 837251659, 829757143, 547517974, 792409802, 727928702, 393693115, 196265265, 681597025, 2428894, 395061724, 30711498, 640727065, 893998067, 9469788, 653488314, 155269561, 314456888, 330434716, 512997276, 988974210, 547590870, 222143209, 865120085, 713697105, 602310508, 526584864, 696932863, 880940237, 357393681, 484490252, 719569160, 621224587, 905369502, 117762510, 513798767, 902249272, 386669589, 723945767, 279175309, 697083544, 394967750, 606365250, 901992411, 617059633, 921092251, 924548783, 997779720, 828783173, 885852755, 607832869, 749430256, 229328283, 10558205, 698622644, 581796373, 941430885, 617083986, 399311683, 331209079, 849419540, 330745807, 93736192, 347293895, 809773482, 831041889, 103144664, 752599503, 347539343, 396403188, 160528673, 263346522, 794920254, 935085254, 688772548, 739991126, 942711225, 284880999, 485796951, 952814246, 848275744, 199810280, 569141973, 84439885, 749479806, 731251395, 625577802, 400532221, 986707463, 241558732, 624454852, 831854746, 223821350, 832545082, 137202095, 923084080, 190268609, 536934610, 763173200, 937875931, 684554329, 851284237, 885502185, 322578786, 773508929, 803929141, 947817883, 120405896, 576930007, 597643422, 942727523, 347651313, 650961686, 191473192, 493402606, 273135999, 270873488, 702114323, 389298309, 451185694, 979799756, 350575242, 366895314, 238809503, 339121277, 479843982, 829400172, 11534711, 123569749, 397347441, 233906122, 694793675, 83034766, 243643776, 440962669, 687051940, 652984559, 152581387, 968286700, 91275455, 354079950, 51763480, 851239827, 850639045, 230305385, 766809468, 107230353, 642023748, 186905922, 828991626, 293434487, 772671640, 285961486, 925982970, 722781119, 170714681, 509322732, 670005427, 530844844, 380981734, 679446841, 315821349, 304901256, 450308947, 777956587, 607227904, 514369363, 800804100, 619172364, 267963925, 621728696, 690628866, 336196158, 749120455, 972845320, 329468993, 861764368, 697874111, 147223185, 449611869, 738066536, 29711595, 113318304, 443601602, 922014338, 381908376, 631776982, 538532427, 286117058, 323562071, 485513195, 956320605, 248340818, 889339294, 794704504, 903168103, 821366435, 291000691, 850064883, 139834085, 50542186, 852054024, 51918570, 314023998, 907720114, 922111165, 296274011, 948257888, 316289525, 392021933, 326844176, 687103134, 183938681, 642159231, 318025554, 783336131, 336400532, 679805052, 289574235, 116981127, 71612271, 531812312, 989308265, 82314147, 825646734, 548187011, 210880132, 214708784, 678616426, 255592010, 801954258, 667992928, 593701004, 652782180, 156115425, 351248575, 325282272, 69521021, 327745550, 424732212, 172994442, 82359843, 315359006, 946301688, 442646435, 191288407, 353831154, 341800242, 717539124, 344283556, 31829311, 708252611, 982582646, 396428421, 911961346, 109013095, 458658509, 570741814, 106417959, 125527946, 480799819, 213784921, 323317892, 174203785, 375377496, 65517599, 566751350, 995793278, 645316211, 144040978, 532526085, 911034584, 611433998, 152741266, 864149965, 258039339, 824029584, 851249350, 564519202, 482999470, 620972229, 228749267, 319755184, 454763149, 643836208, 655202746, 535352122, 186882659, 552203950, 875742391, 155735796, 383793938, 271865416, 811727032, 523897073, 583619625, 93435023, 27551812, 579691262, 364683192, 93855963, 676630813, 195731041, 59242952, 238701090, 914036840, 499793714, 416593808, 429590058, 995838532, 666464249, 751093786, 265174952, 759607762, 515424605, 570111512, 317495327, 704937064, 851421885, 435061227, 850444930, 896059169, 520152044, 357362729, 74548291, 632243591, 928146628, 104749461, 29401023, 748242245, 286100294, 78549517, 544532808, 486536031, 812998358, 322727881, 53039244, 595489884, 431177504, 757816911, 425879425, 267987002, 431868236, 175136628, 859828077, 243385927, 60409327, 275279091, 970606983, 200836789, 580538717, 362452704, 750868265, 629329621, 275261703, 789418144, 24410239, 379231330, 6340112, 774666775, 368546901, 570362880, 463657745, 293472137, 61789652, 824856574, 74770597, 284650315, 597367598, 410931119, 876865666, 195794972, 217634530, 306220315, 82291272, 579130594, 795247953, 8060712, 373016349, 296830124, 914772415, 704582483, 169653230, 629883437, 373948321, 131366761, 75093740, 391105696, 1641172, 624092780, 280686321, 790886088, 972578973, 988412720, 868346466, 755389548, 455256420, 917960483, 214760269, 281961050, 607394717, 743359148, 91462798, 767115910, 298945757, 981192367, 51058269, 670646955, 105856335, 860103076, 532522284, 989030962, 320323761, 763266809, 98290820, 255356068, 791012444, 26564697, 48786572, 445084272, 506449999, 36898152, 38860856, 730392573, 540657847, 901337932, 790020005, 289029333, 156902270, 70337016, 567639159, 658724902, 179183444, 173064438, 616067820, 943059113, 261337370, 392459203, 804891650, 37562318, 961151971, 500582875, 460711297, 106975284, 45581782, 703198915, 926380053, 942879018, 730189684, 17889771, 8185487, 698076574, 311351718, 891134655, 109275216, 763763911, 705407780, 658794235, 331060141, 857101505, 46038485, 205423320, 768989909, 687266982, 608642646, 174842307, 782039306, 902483387, 542073581, 822273088, 673739003, 590153284, 900063676, 319059722, 68150513, 150847119, 152534118, 936811619, 88394432, 626663729, 827995219, 547629276, 529268519, 7177295, 597579586, 964472896, 468218948, 669453752, 372685330, 917179602, 953500757, 536530597, 184237798, 551443267, 419217734, 327789576, 777154375, 816844616, 198612777, 404279376, 908707668, 898724551, 321060448, 413383739, 128789375, 551329127, 503818784, 779431864, 451859327, 721453671, 97972775, 650366301, 394666401, 220265582, 527220753, 419030802, 362394494, 579656785, 119212196, 648988856, 596621644, 737290236, 591402324, 567259241, 606872350, 74752782, 816561374, 414102597, 657486969, 205024877, 929828334, 292495861, 500783870, 441928465, 30526421, 972749953, 74340594, 620491067, 455511719, 991008639, 551742847, 126912891, 316149015, 91632563, 284485269, 400769592, 790313743, 126808729, 544137979, 407938058, 908999633, 540841016, 716491572, 974930254, 171114508, 645616282, 248435215, 310086462, 202499708, 599043447, 981681358, 942918087, 448621263, 50035546, 644739878, 483885244, 581175417, 572502455, 703915399, 373873699, 902004601, 479461115, 771196441, 614190110, 14432285, 9024630, 349407198, 947931533, 721916579, 612471582, 244460414, 247021913, 815749372, 52860931, 253074783, 940213984, 881406892, 726141251, 975544753, 67813551, 801896920, 36640203, 717609904, 579734270, 858628126, 373166804, 64206376, 809305677, 676162536, 914677063, 659354490, 506062277, 742903977, 648047948, 687751047, 51601967, 319519808, 872659379, 994950822, 61524913, 850386575, 349831041, 246043516, 576425974, 683319078, 969328669, 46443487, 261115877, 261298870, 880126293, 603766508, 669270563, 441611825, 966241939, 77111943, 258834557, 489589237, 686624488, 278446274, 630251290, 559071207, 44933764, 754678104, 800264263, 749217752, 493007287, 945896976, 679378021, 182574269, 531214413, 553077259, 113660754, 67002915, 818365500, 826692406, 908946122, 149213127, 791417026, 331139620, 969121796, 56866777, 981558260, 502339543, 364800313, 460272065, 366931080, 333090034, 504224727, 580379555, 746940478, 579813095, 881081348, 826605312, 919127672, 323742457, 342494715, 344949642, 935414360, 851327892, 407263554, 86232581, 332977757, 845665275, 873078342, 506993064, 645500223, 923900974, 254536773, 147230210, 21439805, 817853302, 774739038, 90449601, 217380381, 589203086, 854215215, 166767304, 716088413, 140791764, 80576821, 611551884, 67279041, 466672113, 466764225, 696654824, 827255963, 463603658, 578352535, 473117986, 785165745, 687717252, 589607982, 885351258, 50982132, 902800884, 124999359, 19838543, 763567001, 758858206, 111789113, 421664070, 358285962, 116937412, 653189639, 786784771, 182702007, 601768602, 126785121, 580396265, 656672615, 841827303, 965517586, 778346296, 93837326, 823478413, 571935150, 472667219, 86561990, 309169179, 134238187, 777486169, 387107324, 380348589, 100220212, 50491483, 40061198, 172377593, 545238551, 853674721, 24588885, 665597076, 384697673, 187970765, 199525822, 664618189, 190255569, 959632233, 330962594, 465750228, 633725166, 309035110, 991099536, 674558936, 928909744, 396504829, 760434621, 989604830, 956652383, 763179313, 347400013, 208318468, 883602107, 22764244, 904740314, 821191270, 267044780, 934053482, 994194225, 337537017, 20295234, 580571455, 788943580, 753423732, 898059055, 425088489, 397953586, 781278984, 110756997, 427006436, 919052650, 703240457, 153024089, 77239562, 659826615, 881877269, 183918125, 157133251, 100331982, 122553477, 3075984, 825209199, 835416036, 51892647, 782319220, 332301117, 487829339, 652226989, 369284399, 952648023, 307228044, 659531606, 912037578, 37248207, 449081102, 865655208, 578659556, 423453486, 758118843, 614308049, 26818404, 921551571, 227034883, 844042303, 244241386, 545033678, 656238138, 691580142, 875693840, 428970542, 526440783, 429013758, 594779458, 113178813, 608466342, 140053909, 55984624, 409568652, 336887699, 805456245, 691210029, 190249962, 430455685, 392757841, 750787958, 737212681, 913946492, 453145240, 287648911, 332736129, 24428782, 609409582, 354953738, 284067099, 27202630, 800177623, 155782055, 459152945, 437701875, 711450492, 603086686, 504808903, 107894996, 477017036, 631367723, 846754220, 467781722, 527805728, 419683276, 452988876, 550467183, 948184650, 226321106, 504556581, 411065119, 336239040, 606238154, 460241398, 808431857, 71412313, 740289908, 714855047, 412768034, 971526851, 12344110, 348645478, 314921375, 486389465, 96008714, 492236957, 300257359, 740879994, 49346361, 748829503, 146675233, 810852148, 133099328, 877232623, 864967936, 573059805, 510866246, 598633410, 633346615, 876609511, 665056995, 144788383, 708902203, 362396889, 675558690, 31447413, 326728789, 542203124, 704540055, 650894345, 196811533, 783848093, 374250382, 204024534, 235338736, 624943616, 70307074, 113954187, 314037241, 359375996, 84038401, 767260540, 863707550, 241820300, 262348277, 199611286, 348365943, 985427923, 614594388, 19177464, 790468020, 54789113, 944849356, 854952762, 350743073, 624578899, 9985703, 68331400, 387163220, 287423125, 640368553, 641668147, 723008352, 448736608, 481264848, 756819849, 290967579, 907214314, 554658913, 849340805, 161096419, 607493784, 625039351, 265298682, 840957255, 201503794, 604274864, 423260554, 134773970, 527547626, 791491940, 616815633, 252373493, 143084329, 546233787, 53251166, 308555505, 675282890, 941949549, 354927162, 923467325, 362709820, 584583168, 725971451, 980845947, 414838519, 615672129, 264068645, 936873430, 683357498, 27466350, 711904652, 582515530, 558936097, 95981929, 384844599, 945770780, 802683795, 64400687, 656725554, 872454735, 844189349, 697865236, 700484770, 626172445, 978106002, 5596829, 167832673, 572221734, 912687123, 316197660, 223341049, 526891063, 570960926, 453485176, 189384790, 924501942, 415658568, 368318276, 507823597, 214017484, 140871591, 996493785, 839609924, 287692729, 967357280, 178329115, 69683714, 974005406, 85609671, 876948253, 828811323, 87056546, 301724975, 847340286, 225169529, 75425945, 527706425, 434816588, 319425768, 441419344, 469726432, 470221347, 55634975, 819532523, 639081818, 689372724, 846203841, 621998588, 428121459, 867294551, 374215653, 123937931, 4055689, 496837359, 531212597, 644197720, 254137164, 785842862, 209356710, 680068018, 616481199, 155443579, 356847354, 824209928, 753176856, 749589681, 270038220, 381579560, 508605463, 234731370, 50473923, 909884976, 97973847, 330567994, 789653988, 760068016, 749985909, 808472197, 454230757, 743310961, 156806147, 164777865, 507606998, 941403101, 1959178, 152428008, 714780049, 961821282, 518882573, 247520854, 99293365, 700723915, 961577104, 448827316, 266943262, 433881702, 59801277, 928574408, 632733217, 123829409, 770028005, 140603950, 109232824, 776359986, 504359598, 705293295, 622067208, 801725243, 968183639, 929505404, 950166883, 823836024, 983817906, 229102638, 697713842, 654868649, 995861901, 784090771, 808445886, 200117103, 67850997, 529793431, 276873807, 519103292, 543167434, 14381193, 780876305, 789453631, 728611589, 424008991, 113549817, 866704457, 856535073, 19109550, 768057841, 913445647, 774156232, 409918418, 164826322, 664293898, 177627142, 987039594, 883086078, 766145636, 524594496, 135220304, 937185085, 859830130, 181534149, 670622630, 116844964, 727559131, 954952372, 456661706, 734398288, 830070156, 997299940, 738444778, 350231213, 731724623, 230623341, 58655159, 436220480, 208589447, 12131113, 205649584, 460182942, 720477492, 367200214, 27860061, 56393096, 692745515, 409696573, 38696853, 705709938, 380090733, 686776990, 968879226, 40724875, 754640123, 451852424, 734734876, 401155075, 786100650, 260938127, 662449263, 149490881, 102888235, 665456064, 90266269, 366503342, 390982201, 601481717, 427257622, 330303361, 214592578, 844933090, 656651928, 48036012, 204345912, 226470693, 120163124, 955041674, 393509748, 959879170, 791615480, 152119305, 610772975, 584718843, 285649993, 837335306, 572708551, 108720215, 186336593, 691897898, 889702150, 723077786, 745181473, 838976764, 155810649, 960377168, 20998497, 906442618, 163650230, 178753954, 47131754, 501479868, 613806676, 518518844, 932038742, 302199289, 577034961, 972684349, 914126384, 494768848, 450153925, 827852934, 798132935, 481078909, 160527006, 893043071, 471997287, 690813590, 704487348, 892660502, 677900910, 149062315, 817235780, 448223104, 811293215, 427121574, 397873324, 897020463, 550980383, 91412822, 630597928, 343420659, 570614872, 609354078, 630410602, 651554708, 336535857, 61564264, 686913273, 651709737, 558782797, 69949494, 3623943, 345421773, 716785034, 841994017, 460083892, 377227119, 177044027, 496395036, 618138543, 558831151, 483991910, 807378812, 831813570, 312346595, 842722328, 526981031, 978620763, 292754111, 529152606, 659168068, 764744974, 439292236, 577545075, 787293842, 408306219, 813671197, 274194735, 50958681, 597396771, 602130942, 442230109, 201011818, 733280797, 9284518, 819716334, 956581498, 515775743, 577023507, 730066940, 863409261, 297393612, 577674357, 60592639, 893551532, 238594242, 60124334, 571825387, 132969521, 223709894, 787196680, 840531145, 240103334, 912347178, 853704118, 852453520, 806759894, 602489721, 106758730, 71213260, 432890570, 80384999, 816296282, 80367281, 358754901, 383772953, 962908907, 918366228, 772302837, 929482144, 70974966, 913955904, 122911902, 218540933, 431390629, 972723360, 599045084, 584998632, 178600984, 137758113, 588163352, 352562498, 684352161, 558282727, 657810125, 881970926, 639954491, 311779866, 232240750, 690625564, 210325368, 979613922, 134905987, 239896393, 619904214, 819497041, 281417090, 857544217, 328421675, 463783649, 182388335, 588091439, 750936784, 834283403, 518696529, 897320342, 78510426, 430913341, 373384685, 351500519, 393922368, 765717405, 105851131, 181109720, 201767806, 680977017, 168124383, 471429785, 255508962, 771678520, 671358601, 31022916, 582122046, 973846237, 663099319, 198315709, 626496087, 10812512, 165303270, 615634935, 828284130, 570992374, 389273848, 168960665, 540463932, 288358020, 329250132, 483031292, 679526461, 150283110, 687678756, 911353047, 706520297, 891714628, 220411422, 248278819, 940365833, 509399252, 206131609, 236417762, 911451048, 488690879, 39646231, 320899479, 116921161, 180241944, 132614147, 660160959, 649973885, 593723539, 617718814, 486037104, 181240164, 146853737, 378668983, 915967633, 843628739, 126488892, 887566060, 143681502, 980199946, 58245046, 694418178, 678086345, 727455975, 327731652, 831495089, 681063576, 343285701, 112608038, 87410169, 306422014, 421275661, 961185877, 178650362, 520496209, 85554229, 27089084, 585616852, 675315262, 369531115, 494608992, 114638253, 143147924, 696388033, 827870465, 963320028, 203055426, 522717196, 131245173, 560151637, 917436940, 278784286, 461494421, 769488034, 243484716, 899195557, 1504024, 782762115, 325500644, 430436019, 675162097, 145615364, 1696868, 798502945, 131047203, 277837744, 644455039, 369039572, 641118710, 706673109, 660774217, 585189867, 902435226, 79252799, 898861087, 232233532, 64969074, 27585811, 619169552, 257116570, 831860961, 38530825, 202789169, 527428889, 774623158, 826752912, 289636090, 763075492, 825199891, 928380158, 654908556, 174495618, 266162725, 773156425, 328588165, 781558668, 192395703, 369969318, 880493371, 629798952, 945444041, 855386240, 67390315, 605133522, 569008055, 600898156, 892005926, 207278042, 816147990, 456810031, 638746313, 160806222, 176465104, 746448877, 652484919, 768821173, 87182942, 212072060, 882916215, 940593669, 949875944, 555385464, 217920704, 127101235, 250123772, 171075309, 54016577, 916959918, 244933653, 674255664, 772319063, 292334129, 33891770, 516369585, 334095942, 205953287, 199062741, 52389907, 204204786, 453303958, 489277846, 368514069, 342153697, 389612706, 643264247, 128795400, 750566622, 73656178, 581112538, 849386800, 556815265, 38406492, 881648045, 515137350, 161179432, 163185792, 955984957, 711686971, 847143806, 84450123, 756627228, 819134699, 306173021, 758649612, 618668099, 588811559, 878111977, 231179289, 586488118, 376172681, 641313628, 427550819, 275423834, 181972268, 995125521, 195460454, 427834258, 526019492, 371159745, 963131307, 387414127, 147426672, 394167995, 943278796, 728123870, 80112937, 532882830, 407065406, 36912931, 776037477, 712206300, 949636221, 494472033, 599395807, 968923469, 734714512, 921886641, 97043273, 711892670, 895085918, 454553614, 809939927, 364329975, 940549629, 143855365, 812096417, 402488760, 170568376, 129615181, 117680457, 13851294, 528777085, 247375447, 729412828, 580406516, 942364467, 621076446, 526885951, 495520782, 705156173, 395175364, 641468618, 908933586, 677175085, 676940088, 412649278, 318957266, 892592741, 964938518, 90705706, 631400159, 136996682, 452435294, 139089900, 880544337, 138022136, 191345039, 278280456, 19254246, 172389636, 329727385, 795901060, 692664035, 2961237, 33574447, 556706101, 2487587, 861419203, 270781710, 833457093, 114142293, 758226906, 710105404, 819335070, 261952297, 636847911, 106052418, 951912716, 553956102, 892727235, 858766414, 293141212, 428979092, 730913448, 505259447, 554628240, 96828820, 672353829, 834346388, 668164065, 827241777, 98537861, 84698285, 399772361, 734100490, 478064617, 143642168, 282594066, 23892644, 174770469, 668678730, 387526651, 794903949, 43520256, 826730077, 182798606, 904527122, 816449345, 575949014, 74553329, 271313014, 465301271, 966651155, 508589706, 389582346, 803811475, 567721100, 578528342, 985437605, 65275406, 261722471, 156218456, 217247036, 29177641, 411503470, 255470732, 787159430, 611208926, 182650695, 42283411, 416949073, 333509261, 195620899, 37860596, 815725447, 324065766, 419566799, 125603294, 607675318, 608193353, 963523330, 82628925, 719862164, 445747128, 36141787, 295614886, 10915521, 269401440, 459730843, 819722940, 84869692, 842020519, 788891126, 744468491, 43493090, 951930672, 862354750, 65002565, 17448989, 477813404, 916130278, 9825454, 451232646, 429536271, 714501124, 942200478, 150732127, 177805946, 476197979, 560928445, 451891232, 152246328, 240845853, 193002604, 406874565, 61319862, 519235540, 737599082, 331702832, 294648759, 954091118, 911404924, 957214227, 230053197, 19555342, 88595690, 704317998, 612170224, 418879137, 993613794, 500223961, 682722333, 66695846, 926537794, 652288959, 396140648, 998527435, 194640001, 751681737, 124215587, 830678055, 6817815, 305444968, 397204409, 421605307, 85362960, 192887258, 729615541, 619260358, 812066120, 508393203, 297433103, 314797522, 290153516, 758896882, 56850303, 969152818, 852295449, 749976366, 282341332, 352928488, 770712147, 727375372, 463519280, 990978801, 405807565, 762157959, 42354264, 130134042, 341041531, 90938702, 981832975, 66049337, 853020776, 304862056, 974575450, 438771843, 284910082, 953995566, 20084813, 795499990, 725136588, 928955148, 967441876, 369638395, 950216443, 656438714, 207506424, 407865892, 630990296, 88634057, 920195104, 291891718, 331057790, 762294603, 423214372, 832530100, 928212014, 491230387, 689457188, 132873446, 191361949, 526716627, 682650549, 537772905, 852853574, 959281369, 462876628, 647837082, 169371799, 148694638, 256504091, 689374441, 314501524, 880223760, 760327331, 371677840, 258743837, 174028952, 616143087, 940870609, 797612735, 194146688, 472960530, 807683500, 629388032, 960453437, 157967790, 918068135, 633525886, 717340979, 909582893, 599513485, 156947780, 276781486, 94673656, 249414687, 206710658, 506089033, 843086987, 577106666, 702616991, 196743137, 644526194, 194662628, 111518054, 96479549, 59362061, 781284409, 1331664, 193933008, 817687541, 361098947, 412062989, 836321277, 209237259, 625573824, 55932921, 928563292, 25569442, 98695952, 70982204, 161841134, 829170240, 920881350, 279257339, 657360200, 466616842, 795954942, 904819945, 107633849, 655453188, 538884819, 691133377, 294544810, 813646374, 396550110, 843764379, 173473286, 31526794, 273264733, 2274885, 724063516, 5565985, 136014709, 247033772, 299709687, 484860336, 870055248, 868193703, 549955719, 519714666, 151002504, 976978677, 906956245, 925427308, 491215065, 5406889, 746666590, 113863277, 663913345, 764086242, 205539381, 944512955, 384612091, 764773386, 878122122, 293191466, 495753067, 856530051, 237491386, 666540381, 220278617, 647946129, 368460068, 765818440, 301093102, 694499421, 933863264, 111248755, 154594679, 380114803, 793154502, 446043875, 57551728, 366913132, 986291914, 900314659, 753147356, 413841822, 213659283, 677256391, 315320586, 673044705, 755543551, 182699316, 650876725, 168246874, 771143677, 676246042, 335648157, 713391061, 716794869, 314562596, 501170805, 619889311, 989955387, 476890321, 964323841, 307309170, 39297475, 431190451, 987683740, 955132252, 501073113, 492551846, 195443775, 637328732, 795276111, 46738823, 694190691, 939780493, 355466663, 521367373, 400105329, 638428792, 59106552, 781361512, 101673595, 323729084, 572961789, 897810650, 741682932, 81457519, 462287390, 21509789, 279150107, 664779868, 670527139, 793737511, 500601513, 859768663, 131784008, 764761572, 227577725, 220227666, 376648111, 160696217, 730470558, 188028888, 887009173, 395235120, 15072024, 54624586, 68550173, 66792469, 945458828, 981543574, 898210221, 231683884, 364758719, 110779299, 515090625, 102110763, 732180997, 411771349, 472113121, 355035491, 17891395, 241549309, 652403580, 344800153, 530984706, 928068743, 123937042, 863697459, 678680133, 55486189, 788717175, 100185938, 222466219, 488596822, 62723714, 382038648, 403151783, 520393690, 423748760, 116769169, 894010128, 882397550, 53990846, 182816016, 584198725, 101257261, 373464999, 918835361, 756930200, 913083034, 961991613, 392160585, 626761668, 837633380, 730006899, 30163367, 102941441, 264870867, 831533269, 447338079, 884424104, 351167193, 249522035, 660602547, 575492985, 610170249, 857020015, 221085402, 934619188, 619496461, 982662340, 432688848, 193157354, 560263809, 586171412, 544996218, 805937234, 866131029, 121695823, 23187707, 478097652, 258624859, 11699646, 360889440, 592094496, 813886631, 259309468, 687893996, 464081653, 18388623, 767590673, 862683972, 609757539, 250549217, 619908155, 775858560, 183396110, 838183438, 569755957, 489470854, 682090215, 296792960, 839943774, 609678941, 246708162, 32237765, 31574075, 711074367, 138042504, 502053527, 368960585, 655696846, 374875111, 598984675, 700331814, 908626784, 306377562, 96089083, 689427476, 16143942, 400251820, 405663525, 834534855, 315457354, 120046793, 631349552, 948627215, 359989253, 550414098, 427676597, 701636157, 713784912, 245233229, 819738398, 400843332, 953733276, 477375124, 412081132, 107685498, 981731545, 860245057, 83636917, 427896735, 861894538, 621212995, 355318337, 542868342, 398970710, 357041040, 552994339, 91468691, 18939901, 808685750, 468659449, 689476774, 889294805, 629600327, 156467184, 949171454, 61146184, 413195763, 413963260, 155176376, 509984767, 201371977, 954092105, 920252107, 721843314, 784935205, 460104171, 918640465, 483397559, 199822137, 880718569, 998260081, 411251194, 506483467, 651857132, 888437669, 226487660, 325662550, 865250437, 538789824, 111866228, 368140618, 157360562, 856635810, 966969142, 849837219, 596126435, 105004334, 826874206, 830175212, 205911091, 146019673, 710382938, 519269862, 525045425, 211799307, 308648472, 118996865, 811463218, 496275897, 587147084, 734382085, 154649862, 637193655, 491457317, 653028816, 905235442, 921707591, 408586597, 6679716, 757810465, 668179405, 851025206, 351847188, 458667324, 588450859, 596357260, 451201960, 32508088, 848900634, 399072063, 422814420, 258330617, 232171306, 751527587, 950367996, 416006902, 658948256, 885833469, 773498689, 635454740, 9820509, 834203543, 3792288, 174068210, 581704648, 962214147, 391294392, 586991338, 503028604, 175078420, 245631985, 212842540, 472187474, 462448532, 619121117, 244526587, 692069841, 579914031, 507298179, 610747273, 6691528, 704401825, 212701957, 91488991, 118846292, 773531027, 382339762, 500133089, 536726047, 283488533, 549114674, 239480346, 636225523, 509239466, 745901944, 180740531, 616589282, 229647493, 758433168, 310526762, 416668279, 493796389, 283937900, 369561692, 374457207, 365676509, 946855467, 124161107, 202446849, 63792889, 334485036, 589065766, 5573196, 829792109, 631369366, 368783652, 28387991, 754631681, 743595680, 41220454, 412312634, 425917766, 368311652, 913843759, 801152597, 577122410, 793548193, 764852768, 69905498, 452757521, 803311107, 281502221, 797589958, 652051053, 743625769, 179096444, 52031475, 20365425, 537357229, 719252408, 250391345, 66540496, 671615469, 188202476, 641496754, 234619055, 510803568, 6450377, 18793367, 634835584, 457077667, 243653294, 300046930, 558870174, 799861165, 829431764, 984107463, 206486170, 350782276, 895467479, 970947297, 536134728, 512626260, 136836887, 974606605, 548782009, 323271994, 233558510, 372807503, 760576926, 603665651, 546188237, 247361116, 754361979, 627215014, 873537063, 983398434, 652462287, 317638566, 342521249, 407242183, 485371187, 764322801, 73846762, 584871555, 543756522, 815827036, 854301208, 857572924, 451468999, 362669381, 783262221, 970074453, 886507725, 980480683, 664783400, 221662835, 235541338, 245519130, 943087657, 709853833, 748099590, 860948108, 182307087, 510398949, 870464713, 624099072, 128366124, 852374289, 573361307, 202293524, 387356156, 768687766, 940279530, 240950656, 125730587, 48230672, 90886554, 363797331, 469649207, 994766136, 258020264, 797464615, 366701221, 72686417, 488214401, 876011175, 368429521, 293496033, 19287014, 251650594, 387578861, 792244300, 881130704, 240676941, 795577745, 346085007, 367067965, 199497134, 364671495, 991947224, 373774112, 559331388, 522829226, 589731264, 260372874, 247732106, 299363036, 826133240, 577697790, 88430670, 78815420, 878078453, 103449577, 516950206, 812115524, 452749737, 974806473, 250497860, 34577942, 886831769, 264150954, 557487198, 242714247, 7368262, 380790900, 211070427, 485288646, 28645768, 683877735, 887015919, 574376104, 116150455, 607217293, 218712080, 775859202, 930076366, 390076375, 686066775, 192498014, 887883743, 625827462, 718200577, 387562156, 811078281, 176910910, 564567808, 931007688, 253804423, 603406547, 219976444, 268458193, 647519715, 962967189, 2850308, 228845958, 967901985, 382150376, 751089088, 626007079, 166321704, 318543328, 831315728, 913688149, 260691574, 440745127, 845640061, 986573341, 159829247, 700408715, 189286077, 194925455, 849187593, 809075552, 311740504, 613901279, 73042400, 237108175, 550685595, 363365989, 538139630, 706632537, 239736720, 594410934, 433169399, 255875079, 877654991, 830050801, 549084257, 460072539, 701844839, 543435238, 195520325, 202072925, 358070010, 271648034, 681472002, 752378337, 587397530, 285434912, 232829459, 341191083, 177165626, 621790266, 663320806, 786359842, 1435795, 828974225, 682125358, 669685649, 759680006, 661109980, 109673531, 370392004, 175482649, 218216036, 201751629, 338892658, 740281189, 190803681, 892627145, 626813274, 628784048, 732744828, 789835370, 994490103, 361398465, 616209737, 66321918, 197553084, 304375981, 272048113, 85147925, 506943734, 723831869, 747460425, 75947174, 762117934, 976181028, 326007842, 506035908, 245488249, 546714657, 846228114, 527456008, 998382907, 808913195, 453659622, 5624463, 550034820, 195285842, 751216232, 329678349, 393311027, 268906517, 954506001, 208349800, 117722762, 866591991, 374914012, 982191756, 638254111, 748621572, 191538511, 940747877, 928559430, 691637848, 96878635, 200055574, 749851024, 558638917, 799745504, 678247913, 192590878, 820445495, 164317003, 215289780, 123372536, 214960736, 701282142, 312437047, 29624718, 508263509, 849168666, 394006613, 610210882, 680158486, 295494968, 396163277, 933418052, 92743278, 275427961, 218676701, 401267651, 259071684, 696845038, 301241322, 386561895, 613157883, 195663391, 922064706, 155432433, 794807673, 111001685, 385808736, 89662738, 386236763, 176171864, 797332985, 666796312, 387793685, 310024948, 43643348, 352088475, 216245539, 299981571, 666613963, 357846918, 322516277, 268877718, 9899488, 413081114, 191703995, 294812993, 792805297, 146010269, 669258425, 792186301, 226885755, 526554499, 302390687, 620703558, 916877511, 318789543, 884987779, 199068307, 281601485, 834058954, 734454136, 312610255, 901306969, 148054293, 877805156, 301716984, 833437748, 638429743, 720948199, 141116794, 570834152, 367111609, 449959968, 668791729, 199134335, 539562396, 579931354, 14201166, 22204514, 562182957, 574139458, 616463688, 451230977, 260365246, 958239324, 608548321, 722889474, 410223778, 533013861, 708414058, 59590914, 541612214, 185485370, 648832955, 346030754, 26703805, 219368470, 755219488, 121872614, 619054594, 226543269, 736679471, 153562398, 705521409, 781116043, 553049124, 240799965, 634593912, 339213830, 277705350, 48714354, 788348339, 885660082, 576555739, 836145046, 972097663, 188147396, 412162062, 250491996, 10377098, 504093218, 453498836, 548612622, 698070300, 20767893, 414632955, 903193409, 96173382, 73399072, 777923415, 7856886, 969151116, 629961412, 734708022, 314590011, 936499383, 407477794, 750821130, 692904399, 911933279, 823080473, 978003239, 479541819, 40859518, 975633586, 221517832, 840923595, 693222316, 378806301, 104128962, 302515265, 633694394, 248565856, 782636963, 992572037, 408723056, 858036361, 765126800, 543674749, 530375553, 129680026, 843572711, 226616008, 961948747, 631115458, 81292290, 139994940, 793600508, 261310496, 77811987, 885111096, 183925857, 520369908, 253150178, 634664709, 959167752, 782057246, 287892247, 281512005, 692636359, 696840224, 36570681, 242722534, 615051094, 384708200, 491664150, 562047884, 172015002, 481119125, 441041113, 742440370, 752124877, 343222586, 471533275, 496984111, 71976269, 26019552, 316046995, 793194604, 569288946, 582251847, 263392052, 463290313, 433196178, 30866909, 300299851, 618352548, 892358512, 763639207, 928031029, 971488222, 267115234, 110042933, 759522051, 773199413, 857419068, 684770116, 408595065, 27479980, 712652237, 885621368, 186645221, 73058320, 773237353, 29750297, 24725379, 587011629, 528755233, 892639238, 343057758, 954250331, 789758235, 181547341, 71534561, 944038465, 912533005, 980251357, 610746063, 279175436, 422023609, 131687159, 440702295, 827462181, 18644334, 455014908, 84859264, 910633085, 274936336, 434031591, 949894975, 573113215, 910740412, 703839370, 292047268, 481381133, 643540673, 655145070, 876552953, 865550249, 39609891, 370812265, 14823449, 378471499, 94066724, 220737620, 329697184, 920546999, 524360735, 837977718, 265389202, 111003388, 715175914, 683374629, 85014167, 895799411, 538262825, 542695108, 416922402, 137374778, 938297201, 30467567, 88566992, 224928735, 490072402, 766734338, 960592964, 104070988, 974155215, 201236604, 726014143, 329811369, 995777397, 428762561, 325229102, 892455161, 63878619, 968232397, 504351046, 184839402, 472786789, 196295357, 187285224, 798329753, 267776503, 698307348, 92628694, 777662581, 283327981, 559771219, 868390346, 523894897, 971383652, 648397513, 761248773, 288047090, 560318376, 327290495, 464776993, 178557308, 94299835, 294033952, 225821893, 422379851, 102474756, 27231352, 42076074, 769571637, 594884853, 127438970, 278771393, 341662083, 36350614, 126031215, 941524017, 449435854, 425235499, 43969234, 823932984, 250736120, 912463333, 362727170, 6455444, 776291130, 202455290, 287875605, 988169788, 897005973, 684462883, 102771675, 67555822, 263899324, 368334833, 495772435, 896013831, 966148757, 115519875, 243366003, 404932507, 72297520, 378503544, 622584845, 420789330, 960934198, 803609504, 154505494, 640884641, 776987099, 725449896, 457752858, 840375214, 421720856, 126853808, 130015266, 826941704, 394153601, 883524674, 126666749, 572693674, 579115103, 380256007, 804523675, 629993320, 587249275, 732258633, 361130340, 242542848, 881764304, 376482337, 283613392, 162735427, 661782931, 248552149, 565349735, 306000469, 494557585, 790833252, 271310353, 670785658, 302115637, 966564656, 645939127, 129537705, 991395913, 559859428, 818861467, 649426109, 180050456, 343531069, 327412524, 324565621, 980457050, 592382082, 422590806, 178081108, 685768405, 509387260, 387919317, 765202900, 241724063, 924528158, 972984559, 712075521, 430124129, 210482403, 602155870, 258215790, 974380030, 33239793, 928820745, 982193971, 379844369, 236981200, 19232499, 917803523, 637237571, 298686837, 587270309, 71502210, 441525959, 329749569, 86579473, 742656599, 499718692, 533295271, 257727148, 185412380, 740274460, 644861363, 109008090, 635473085, 108930370, 248687164, 900652364, 877311338, 22887132, 152378244, 352199328, 455783537, 658500058, 263152313, 939373823, 188974576, 222355676, 195755464, 905597811, 502962575, 108239567, 56981149, 456529944, 786258350, 837995962, 857939690, 999215294, 119755261, 554444868, 258051579, 798225102, 899854517, 669140090, 176222896, 253322506, 334894269, 507996738, 431681088, 793712850, 566592594, 613185303, 729078526, 804383145, 633705802, 513165196, 827864699, 949935629, 152602212, 457905074, 797725247, 450125561, 820177175, 814117039, 48105000, 972155086, 966910905, 122976825, 613903589, 905233933, 711863557, 161552629, 380441463, 219743357, 898969539, 634467472, 526796224, 135111284, 532378624, 421195393, 236492587, 130165393, 529493836, 855012756, 847961564, 731160496, 900065754, 653276630, 245079257, 273745732, 761483010, 888318367, 449449987, 793994231, 758092134, 487335117, 285474889, 942602415, 24815430, 130957849, 583338490, 404246437, 779071351, 433097666, 476176648, 222020494, 551468744, 973377389, 66217030, 394893392, 225319567, 415503603, 420199271, 784028266, 527105768, 980856694, 689241623, 31207221, 974938565, 573623563, 149952894, 869421597, 804418413, 793890084, 806889524, 129306685, 726073461, 998124820, 736993289, 723830463, 459796784, 725033519, 884721593, 971991655, 738746380, 394866016, 548870368, 97118148, 139622602, 853392869, 733243182, 750834677, 852149055, 634210557, 688371712, 814881277, 820936845, 899016631, 190323664, 849685331, 443843139, 780882860, 335810413, 77748793, 62883934, 148599489, 689123743, 204503027, 463337944, 257150382, 606881472, 441115798, 897282171, 44375592, 71529187, 908147995, 374128118, 716027292, 960752693, 412455815, 280625123, 509980623, 41730268, 319725981, 334622163, 178523689, 209733681, 463989103, 252806045, 537569396, 925734864, 612289205, 86545818, 422380584, 756929775, 262546720, 928580547, 885597056, 268437246, 649248503, 650759692, 999894260, 427564873, 614672062, 756866400, 352462447, 594569193, 213337452, 160742836, 396552828, 476744988, 209510957, 134976551, 204094061, 300211376, 212955744, 858958814, 384261561, 554643494, 583667465, 441138842, 744620985, 314545349, 191100503, 32369148, 305743596, 722640541, 294123216, 804783827, 803297596, 970162799, 550608458, 502187185, 842165960, 745945004, 213003805, 782975367, 788674513, 811865491, 98437261, 518244968, 884013522, 75733474, 916781087, 499602079, 841898462, 470722046, 447635127, 878573455, 108282559, 882233398, 117435542, 297798691, 260057866, 495630752, 210860945, 302512391, 347436755, 637155893, 785233236, 90210306, 651316680, 665260550, 277109087, 194099753, 29213190, 84929025, 366405226, 977649931, 663562922, 527419199, 836535180, 225865143, 508134159, 190314161, 957475255, 864105116, 611557872, 279714715, 841318608, 70100825, 654807255, 25304978, 724053674, 673441512, 974029205, 369139644, 346958950, 551467452, 321028044, 10984494, 104431912, 881779835, 460376409, 273180272, 989923906, 640358622, 228645471, 120538708, 171740260, 141527776, 371175574, 941903315, 77803952, 674990079, 687288053, 540329873, 323894116, 366559941, 629224107, 705625455, 439645725, 215383644, 302347800, 624428817, 65770380, 152921271, 507168976, 151189044, 807812976, 346532445, 955146588, 29151686, 279850665, 819617963, 500680218, 964461746, 633536778, 957483997, 264973767, 918997861, 286498790, 406046209, 265371595, 405067895, 180448467, 727720418, 667729334, 232405260, 632072901, 76419108, 421202708, 808899570, 119365422, 506579283, 890530150, 824729845, 331609400, 910351040, 2011341, 546085729, 798505832, 411216300, 996214785, 213099692, 258936179, 106782380, 620150496, 284036879, 327485530, 311609004, 855797748, 252472517, 279896981, 741160551, 441969017, 880967678, 609990920, 26275367, 828129467, 950663405, 998863715, 556286160, 472328951, 632087313, 793151982, 876426773, 154361671, 198962920, 381875639, 819628155, 398014314, 874382386, 45433600, 672356168, 314255297, 887878645, 485932514, 175868885, 558276919, 129925889, 59271961, 20201643, 709841413, 159234600, 549087816, 221565032, 444545599, 152272423, 197992837, 710082259, 105176271, 785899372, 871770657, 805249949, 5131251, 426651683, 519405963, 336765046, 398396955, 921676739, 406922155, 246474438, 170287733, 627794906, 491612532, 843751530, 289349046, 127324159, 874605041, 289149909, 964311689, 761855679, 933373878, 285921224, 894745865, 992749427, 360342419, 754373600, 287619896, 986163903, 689619256, 728281359, 83622463, 918810023, 783883847, 333617052, 473167206, 571810797, 286648970, 32776562, 30442315, 363092444, 555203084, 906920329, 932610160, 615722590, 761761636, 879670349, 872244113, 613647647, 33309982, 283349501, 818782501, 145375982, 116466015, 867860843, 468932428, 826604027, 620281337, 288021544, 746912337, 871806262, 740529492, 712650706, 440053795, 580009176, 902976374, 452932997, 872717528, 366838674, 309938383, 215546849, 271500044, 333891601, 496584008, 545444637, 161923642, 478729681, 522248185, 913303612, 211020437, 528521481, 547976146, 464475371, 229593942, 772474021, 180391427, 209592793, 753283830, 505489603, 571086770, 898457371, 505689231, 653672025, 217783960, 965891166, 8082249, 742862490, 747033422, 604785085, 433775159, 66746378, 197401152, 209292791, 953495517, 812375040, 856476919, 917694683, 472416737, 528980952, 230095140, 942946095, 880169057, 311257853, 838325622, 57703591, 743719723, 889217715, 890768496, 950882905, 903654312, 884509342, 939225024, 998369793, 623813029, 102648682, 55398209, 814337617, 18309479, 573945636, 292556478, 374346625, 812750092, 483406465, 429407819, 123434318, 614413191, 363850563, 923164174, 359097309, 936732371, 169361996, 757901000, 358332727, 769525487, 133324805, 919165897, 421557521, 778356841, 697320755, 392639919, 704856438, 879261567, 309786794, 854210506, 402106694, 800332343, 550531482, 65921655, 98170385, 599059941, 857405420, 545856231, 723512906, 918882733, 196195032, 167529398, 499008965, 638792629, 202581551, 690360984, 673976455, 165515925, 301886578, 965055634, 381945482, 802484633, 551589084, 329524293, 905692883, 386664761, 410386690, 170612756, 521546105, 119398453, 661622538, 22986745, 328012034, 533811359, 654781898, 517954884, 829865491, 679823574, 164776251, 14379616, 488235695, 896496901, 571845552, 681909526, 654576794, 798071935, 135257239, 100842975, 15281299, 56913488, 362385564, 114010845, 868588631, 606163777, 782339093, 692740389, 770224683, 174979433, 983370180, 693999512, 497102057, 294812784, 795979104, 691172133, 240005969, 224334507, 867381995, 967783409, 131981929, 458522330, 441398847, 748764674, 3124578, 371579476, 93535526, 722531183, 937198373, 587181584, 65986057, 267605600, 539122859, 319360815, 779787075, 694093909, 589633021, 687440026, 701470563, 693538537, 191687603, 499793746, 697188001, 844755391, 770950345, 42762415, 30847046, 477766250, 307399828, 270241335, 328155237, 667945105, 349354722, 13329480, 393471126, 233503277, 482746182, 572669416, 513543239, 425398532, 819052381, 928582869, 761661595, 56012090, 853634500, 381070420, 465311375, 290614884, 543651592, 179752476, 151942980, 97243743, 2263143, 70170377, 651882140, 340456549, 658201348, 62835410, 355194352, 560005880, 49430987, 22927648, 49145077, 334996527, 1732651, 225835513, 311876355, 387910740, 29893416, 722707607, 297322514, 529722915, 637885543, 340692050, 267455097, 197210007, 142898268, 398230039, 167579920, 456397598, 826794519, 235215973, 809516265, 542522609, 353460783, 172521474, 261090340, 412633723, 487787329, 965643103, 280910956, 302472588, 132492452, 30964070, 849432954, 646424170, 612580446, 520258789, 692983200, 755601151, 655866858, 647458944, 825052959, 579874832, 805496372, 642002288, 366170758, 770529263, 97787218, 67930911, 291810596, 425401476, 765790790, 261697710, 497892821, 552618905, 653897996, 744842785, 430264340, 649717338, 957996882, 21262114, 364677403, 369547526, 861671707, 644718090, 236172739, 607028772, 455144597, 359416813, 618912531, 231058465, 585991253, 118978935, 653851161, 58561847, 359433750, 777106323, 623134363, 10286761, 893571438, 216936817, 44571340, 870562692, 382126412, 579674403, 313332115, 405771696, 976288768, 30663976, 839234333, 433040392, 44443688, 194749869, 168939828, 877927094, 204325257, 735161904, 738011501, 289788990, 569293501, 283447642, 153382880, 943670677, 556594463, 912151478, 650545924, 194695775, 587326534, 317479508, 378687951, 321704388, 962517943, 605533949, 227986915, 792491487, 28150543, 197680304, 292462402, 5894385, 679468052, 314406016, 693659397, 748809676, 112958634, 422359170, 379580729, 810378645, 714645189, 333668668, 251873796, 860528313, 176762335, 776746543, 682486927, 66420646, 512856773, 48814954, 418198451, 387871489, 736860954, 797669853, 100893593, 869302757, 27784129, 395014720, 991088708, 178833386, 935742224, 665366496, 186710496, 842434083, 823546406, 286044777, 262769896, 927409622, 31164432, 488355522, 639777287, 9869454, 599217286, 193680731, 945720555, 573688842, 537103839, 818472363, 795779517, 574137223, 133864699, 338606868, 373327496, 204840816, 496464570, 970034213, 824925804, 271429313, 878812329, 636265347, 622933839, 929141413, 156627690, 660653390, 482269022, 864076247, 78913466, 665387253, 547765054, 34706551, 805094122, 641488769, 67158615, 734481476, 180268197, 24588541, 70057478, 866135555, 632599012, 437314004, 832498021, 550655630, 929394879, 892685276, 249259836, 680011039, 341362163, 968461370, 72837488, 570122369, 68159305, 931514846, 780505613, 188556004, 916302797, 626077512, 473893573, 754978345, 766145943, 410104405, 314524392, 826048011, 253106882, 828002278, 143058751, 905529832, 516225189, 911302001, 931544154, 331734480, 594967289, 932506371, 257804265, 50096247, 462501774, 913353426, 101774907, 75748593, 998018735, 184943750, 760227819, 373238719, 912829066, 476371409, 96667755, 666616900, 674334840, 325611339, 20219692, 182254636, 858408725, 81043094, 672286194, 572297103, 776991866, 792854174, 951664090, 494876926, 715600995, 866105204, 139894342, 982653833, 886958064, 99582959, 285489569, 821662761, 482138879, 953061924, 692588578, 969535998, 124986435, 689494110, 205539508, 588939763, 364355301, 85411196, 666689273, 584194047, 684265450, 239641357, 353004978, 894401243, 177774100, 280702461, 698577856, 186722761, 946706436, 925211730, 114959717, 22642203, 714971604, 885509781, 521471182, 50161730, 874911130, 772223480, 803565728, 687041015, 468879596, 621606059, 201447316, 99282344, 687904541, 642076939, 447812578, 684280292, 315256506, 216806148, 494710659, 44669137, 812982982, 30508298, 367369206, 288422298, 248778954, 102640270, 647543835, 566594450, 630805453, 47048603, 549450277, 16380403, 300290009, 621470728, 569936095, 287970825, 545022446, 492589726, 246799878, 771957902, 847031948, 329297120, 630601863, 38455276, 77169067, 267480779, 68586471, 378421761, 506013858, 288474380, 799202321, 213393857, 836868245, 724852410, 615684469, 203120639, 851092062, 913683389, 375185344, 776792315, 256268735, 93502460, 930978202, 212445485, 260895961, 94211929, 502227138, 865850611, 383889377, 918238382, 350132774, 338514958, 310259338, 371487760, 240155888, 383836032, 6992094, 28228790, 510510521, 450329826, 435897971, 529431899, 653953386, 145975008, 122203374, 192923675, 309155393, 436278130, 41435745, 721321879, 835135025, 8593530, 968062360, 961960404, 188384513, 533163947, 716441440, 360576188, 276500197, 573378743, 524927618, 589315675, 516196711, 167312868, 775684704, 945577628, 377147497, 400467674, 780403367, 956829520, 896214440, 342761281, 721317243, 713036527, 12868667, 497401843, 419095894, 588503116, 34338835, 616861223, 777515953, 420814502, 759182424, 373372008, 880932214, 56303505, 256565052, 804372701, 608511039, 434184173, 286485530, 719638511, 916828404, 120003168, 989560168, 79243358, 861337535, 137369964, 97272621, 103579346, 345182012, 297035748, 336971066, 604057220, 987484547, 712751852, 191012334, 127012322, 120311812, 702597348, 397017456, 369324948, 543796744, 394687318, 592096625, 406124561, 338263277, 895752529, 516989692, 924605759, 898280233, 920918431, 658520355, 428925050, 887041451, 657624995, 449423469, 836930273, 308568284, 31768593, 56382799, 754610389, 930001590, 519548486, 396061214, 274845283, 30519371, 916477280, 361220664, 270991217, 246587412, 385396900, 232125417, 569415191, 948587584, 716103990, 252303462, 979847704, 409229465, 716323224, 600841948, 682271720, 850685491, 907131021, 210861563, 901065026, 185736170, 952229439, 287402292, 970701397, 669527056, 256855560, 300503938, 343731950, 34987876, 46144232, 944241313, 367933533, 828219694, 984770377, 135023196, 372151885, 798851196, 836908681, 795066770, 340090467, 812009212, 490947049, 474560401, 744390250, 583575790, 554492798, 728398532, 334899628, 23271272, 129103181, 225860482, 770276633, 388724990, 755386746, 443947276, 420099772, 919373320, 824969684, 837868567, 913498791, 106875194, 254456937, 175429969, 474495954, 221220459, 823856103, 90746322, 545759780, 388422297, 651915301, 529789875, 330203724, 219558025, 75241008, 698549653, 895714526, 282400687, 449930853, 551303522, 387289878, 978268701, 730236864, 699585715, 79006558, 735902940, 154322229, 817586820, 888784534, 159254267, 619327698, 55866937, 195387848, 54666243, 726353434, 758167433, 989343124, 894802565, 384036148, 323339763, 696382594, 136512239, 734465265, 88324120, 86687755, 234885489, 769557316, 728809534, 740238876, 413776262, 434112980, 89784015, 10063047, 808906055, 124258873, 965797215, 472731855, 123048169, 237109944, 437565657, 692491377, 205760651, 256696269, 200077512, 189274665, 5665998, 948762635, 867687625, 467261768, 817892518, 267906758, 577236870, 304554017, 576601803, 556368041, 739157106, 375780992, 762744896, 641113470, 254171406, 580080391, 442784222, 457454287, 551317480, 349719691, 287613730, 582161938, 532928097, 958483548, 823501531, 614787371, 928301238, 522196010, 10207376, 774457677, 907251807, 736344728, 571188931, 251569569, 901203112, 938920921, 312600429, 799312948, 609186540, 446678330, 959929887, 190994393, 264798058, 710597038, 496321135, 243660101, 827494883, 689164518, 390486293, 860189734, 682861907, 143625557, 440506113, 270274250, 438644446, 326747504, 901921448, 358296023, 78866109, 653035795, 22199721, 124803065, 343380975, 706783884, 15344672, 604426474, 252269174, 653057835, 996519278, 962468844, 280458828, 321400571, 499829839, 682276908, 501721836, 266128044, 701853708, 200820907, 821679597, 229447834, 573050505, 342886796, 611736464, 505931372, 600923821, 269473600, 220666107, 755375981, 957377034, 704386768, 68422780, 625622307, 331162779, 905823694, 677263176, 368076522, 301358050, 980397258, 89426183, 840430772, 80742730, 142761195, 697885141, 935797212, 391287944, 984533343, 329823463, 558475190, 309233589, 791957180, 800541645, 637225901, 532984316, 357446703, 463142618, 211534228, 854458142, 537018214, 266758166, 738874832, 431631372, 633846870, 162403420, 585872334, 449975749, 388849006, 98714394, 878879661, 32137647, 737230818, 472735240, 373888896, 150359568, 758110505, 945127059, 286276515, 574200646, 348293809, 609539888, 508696580, 613392996, 480481425, 335286683, 166334334, 615570018, 503649474, 793989966, 570221782, 577051848, 508970605, 242590855, 139195365, 198479983, 169155515, 877325152, 880189840, 509116115, 155835037, 805675586, 539862558, 187842713, 184401395, 783429412, 239260330, 319767121, 226361278, 859058831, 838511365, 737951759, 15492629, 68710917, 433948188, 134097340, 640960431, 51460359, 45540459, 428847878, 526686183, 442034469, 268231148, 976126403, 183884533, 659920678, 264579697, 538969720, 838496025, 849833848, 334926474, 68387118, 974170282, 433571784, 777496253, 93138913, 746111720, 788298398, 340830762, 260855726, 70735756, 746476524, 59943266, 256909075, 314506665, 307724498, 859163322, 554182827, 815702751, 114311148, 940664235, 85987602, 732893334, 6545459, 525127419, 953004615, 891557725, 102604347, 203976170, 129426135, 909642554, 109780701, 528448568, 76947352, 51357161, 467478884, 64622592, 22242783, 816219298, 458209613, 561579091, 601793330, 255798346, 949631062, 293998272, 159946569, 294844901, 369591552, 557256737, 971343013, 335881315, 256338005, 854310103, 752806508, 411512570, 139855252, 64362276, 994101432, 27128315, 834105281, 270223513, 171106586, 399580193, 707690508, 657095063, 820682099, 210527420, 960153024, 384042972, 395867259, 707879351, 696290168, 561805433, 682727704, 537437730, 851695964, 676989828, 892684369, 893604082, 475445041, 990168911, 26780736, 762283361, 350683292, 614952068, 675582652, 930136301, 897251392, 548031787, 173667050, 950202412, 786323174, 2473675, 813796173, 584835040, 284945330, 891084942, 199655054, 241853680, 749251897, 622799817, 393050310, 973864830, 688922867, 974159788, 297555179, 343148466, 250848185, 642186723, 665251413, 162690782, 608250124, 938266548, 847274515, 805066089, 468164831, 779186714, 32368557, 756944836, 650204513, 687060599, 461207382, 365608436, 614083505, 211274975, 300992280, 20651186, 930248828, 269705798, 584665945, 47595082, 16775350, 388985823, 229967687, 701944893, 973460590, 387417058, 764436516, 480409290, 263983279, 343235020, 450032392, 41785991, 991544714, 998505203, 522802106, 806401153, 78926495, 429080804, 155826603, 472842643, 667882144, 926414225, 132366863, 612244382, 795248501, 612448858, 731459966, 346664518, 994704030, 498613511, 167124471, 177857920, 986645932, 22814501, 749548952, 848452167, 206997614, 5965673, 727790003, 377222706, 30073511, 527240863, 799693161, 158077920, 875389230, 315998562, 328277025, 845690480, 795696090, 938120362, 1373432, 899114426, 722232048, 10536372, 49486236, 905808389, 482977580, 377200651, 955108167, 815018804, 217543587, 946422834, 875340818, 688835169, 4984623, 89621185, 647406772, 867698204, 765522316, 244611490, 443669528, 409045480, 536742441, 148409448, 21108021, 247101475, 914305145, 707713859, 829787354, 565239385, 544735124, 55394389, 706198086, 497879053, 868209663, 503147313, 518828507, 392881287, 935982363, 514309769, 295528387, 796311044, 614556724, 626040875, 759358576, 457636472, 194450544, 950029216, 429719299, 699535580, 391783972, 557054571, 652970185, 190916340, 399554938, 386036259, 336611672, 589613829, 543841630, 374332873, 996986630, 217228070, 191984435, 22338855, 233071824, 964363479, 857843125, 120231441, 502946039, 274126010, 495090526, 416632222, 405172388, 726945211, 94067596, 605983440, 183988241, 221697710, 676474530, 866135296, 875872436, 134062753, 601677725, 727442616, 226397658, 247573667, 995592456, 521596888, 339456282, 305759576, 681996249, 764090907, 268362392, 496623747, 496946177, 478829746, 721812879, 441266128, 869460520, 396262452, 380512368, 131171299, 843270375, 425503439, 632392713, 209352919, 336810417, 186830327, 451432362, 791674000, 757973690, 591257850, 348605282, 9597044, 66412752, 910894242, 689341501, 164580622, 123507268, 681314939, 580461176, 670160575, 372387565, 365870591, 661003602, 23906043, 381167019, 652560819, 110695294, 397679024, 806044628, 147416414, 956707199, 949539265, 140861347, 112902775, 530473924, 662133420, 796079858, 495265409, 227233016, 40653868, 353546221, 13105187, 759747867, 499189211, 894217746, 530088232, 348711734, 433645328, 120678904, 910893407, 165688818, 778314901, 960099173, 208720060, 846741882, 336389821, 309293036, 466983654, 190575033, 47822064, 962973395, 15009988, 176084844, 652270594, 2697656, 933865760, 818676958, 806929257, 225314725, 718859010, 526250792, 213024948, 212743973, 153834479, 589056554, 161195776, 296788184, 56910567, 610809850, 288027231, 358950157, 372729839, 562303169, 565313647, 177712154, 839634415, 933494003, 994085493, 407094869, 527996156, 863728865, 950036497, 342389768, 484482935, 139424524, 896048915, 28219155, 154427728, 396120975, 815323904, 250586266, 311737267, 135903626, 566488427, 481108788, 332498580, 481558664, 303880694, 34499484, 457494619, 949206749, 358128323, 875916294, 742290019, 545220435, 583867215, 548357244, 322276705, 766355385, 120251610, 561272182, 72369590, 475523112, 257057343, 320438948, 891522386, 842860342, 741251496, 205544741, 604245806, 81478356, 75770690, 566670628, 458939616, 80182387, 461026906, 841398177, 874100158, 527341601, 761830844, 992649652, 152874514, 791710383, 777479822, 686869754, 153599837, 318459841, 183985537, 171117081, 64601771, 372544920, 367533818, 762033411, 88184659, 520948760, 844379241, 167544565, 119883245, 310159838, 653251277, 251301909, 901484547, 840356772, 437554149, 786188574, 551113475, 491043964, 52288244, 938430269, 448331634, 478471300, 932139630, 414421470, 320637520, 484350907, 883047935, 969128370, 427163938, 503836352, 165785692, 192120843, 690280397, 230731877, 136651069, 324357673, 350821254, 207550813, 43737006, 438111392, 470383255, 916545039, 986409923, 211827704, 259785093, 373792737, 172698319, 512218377, 341886297, 815390196, 574459364, 3874397, 660535181, 715010731, 383323372, 941503539, 277726471, 249948147, 733972370, 235964047, 262877576, 322872739, 197501458, 6628194, 135803386, 553495875, 417505346, 983782211, 747979484, 836017794, 502194655, 676187829, 742868222, 368086335, 459545252, 476947734, 928837670, 30498302, 843830696, 843891151, 527738989, 267446895, 217584966, 814944761, 960623090, 455016452, 292078442, 808379242, 716338693, 129048125, 400989127, 113435894, 482803840, 805005185, 804354614, 302174193, 38828508, 823918652, 528820818, 411044889, 441459110, 324618426, 375639834, 190723507, 751582801, 857087830, 230702384, 826257851, 94317479, 196981985, 719899269, 770463748, 646736295, 669407617, 727212071, 183306668, 584872783, 904511658, 26287180, 965962229, 893526041, 838674157, 73178047, 534874429, 343335227, 166274651, 718434769, 740228701, 125649950, 621378630, 996865187, 166915488, 800474932, 289409169, 992891686, 653243139, 730535899, 86081254, 798385385, 100194525, 716732524, 107018141, 860333362, 49998355, 311362059, 445799475, 995864333, 314486751, 414690432, 541828469, 617484585, 244723716, 239380499, 285557042, 683412485, 285936715, 413886122, 296028918, 28756006, 917918772, 95446965, 887273038, 619484991, 289968391, 765230321, 42667914, 110825582, 413966877, 46314541, 580977657, 564991354, 954410902, 423507868, 532631573, 174871925, 289022832, 601000165, 130867244, 388222548, 79611446, 46511109, 418559720, 86983306, 946905473, 667971510, 552444232, 770493358, 112596557, 641474352, 336282530, 168908237, 946333945, 12893500, 633938992, 49006344, 421317442, 187687236, 613507749, 932220745, 767678309, 718724588, 342297557, 108248497, 95823616, 536720057, 548379135, 338625946, 110560004, 860534042, 121553788, 429249521, 634988923, 143047948, 981713531, 188627851, 647538352, 775955507, 471048469, 302456924, 414842064, 166558265, 54053008, 268051369, 465280115, 763633402, 913860286, 796334721, 815848644, 343893055, 466301719, 753140778, 540333476, 269177559, 200422985, 720815703, 295759046, 232012339, 919380740, 468359255, 124086557, 312810214, 576948396, 817629386, 431393663, 787033655, 551632613, 744350506, 246006640, 924574427, 321433808, 148309003, 367402921, 814057686, 396829634, 213315879, 244002690, 444184400, 809903187, 978133249, 641408742, 894671116, 275975238, 368791127, 120808102, 204872507, 157283098, 963842047, 282491116, 843098974, 327505889, 463094757, 761780576, 803150042, 38548087, 436660544, 502130787, 337195537, 12665104, 597526624, 299254875, 796999500, 950099414, 958067031, 235726938, 181766322, 618211152, 159787232, 365220309, 348770673, 10700020, 392103598, 497079144, 861934515, 276271002, 473955571, 667578248, 438251290, 967952734, 265014979, 828396571, 69981998, 701103808, 121883794, 193412060, 338957319, 475400239, 542050670, 466919533, 535277770, 909677406, 309135786, 297485920, 316176608, 164514260, 86280759, 212928484, 887782927, 485505302, 807144196, 2626276, 549271281, 9909535, 473358047, 133737590, 196681494, 612175153, 568044247, 362332910, 432489522, 474501016, 705693423, 443114921, 692669220, 712143838, 539194118, 985529861, 320975079, 271812120, 891009814, 692614878, 131837018, 863001560, 856960274, 937345401, 972889622, 242209881, 995296155, 49091190, 839420981, 609884006, 23488556, 205473165, 981818437, 56937190, 775954756, 564018147, 146725679, 70492388, 842530495, 816140572, 572309882, 57129602, 389943385, 581605386, 651911991, 429119278, 421649381, 817046059, 243358354, 562192060, 804371958, 29811643, 160543807, 917123995, 973306719, 401923851, 571480930, 859382056, 534020240, 541187566, 555597716, 394040854, 376974284, 242208892, 249179118, 381556171, 500398405, 74415060, 524417889, 445879203, 878530335, 569227674, 254266560, 249760047, 760988218, 154514350, 258590317, 229611759, 61375366, 746563545, 35843119, 140260345, 372834083, 727085569, 547565871, 76216058, 242906487, 86981771, 685665020, 913110322, 163664375, 902853166, 568298051, 807638649, 200718367, 919957121, 801334454, 279139231, 582177672, 37979982, 550786078, 852803497, 693286133, 643685386, 478062856, 813399291, 207572360, 121179836, 114153840, 885296835, 191748577, 915574600, 680688429, 653353860, 120704999, 900216048, 487869441, 538849396, 677055455, 284513132, 419103878, 270475411, 214799262, 301094324, 648643611, 548719916, 789864109, 29846333, 605201921, 489435377, 557886071, 176160014, 293045564, 190803329, 702293952, 615224519, 311358864, 474686899, 2248028, 227630099, 660965693, 318016506, 330739109, 634704287, 428481765, 867489571, 283936141, 549316125, 671802457, 918671118, 113464688, 411212162, 374431957, 8079730, 956018241, 814286969, 307170885, 323924381, 92082544, 734149673, 372590513, 771069613, 27435, 870641577, 250294515, 703786163, 915182135, 62013025, 807260003, 610754703, 580517430, 569061665, 658313607, 15639803, 645657327, 791867814, 249408926, 502243736, 50639038, 286306164, 456912763, 487522590, 681768398, 63103000, 657516855, 917798935, 600480580, 374241989, 37864655, 818936772, 21428036, 172634321, 878696791, 853033998, 540653176, 702675574, 824117203, 901297307, 801102559, 719733962, 619297290, 371723364, 978389866, 277073698, 792432046, 458151843, 272267754, 375050631, 436568501, 782006684, 951467825, 297639379, 905575237, 34347532, 881357435, 651246259, 751661102, 969170003, 51038627, 289900513, 724750915, 510270141, 116016102, 989380442, 734576016, 873341882, 565449715, 549787071, 541073411, 7332575, 657861683, 626371068, 638827073, 917755502, 377359243, 658805742, 571970721, 784781634, 582982236, 750359346, 123261913, 406540649, 84680043, 182635534, 777180338, 281132671, 776443761, 175163455, 658785392, 424960915, 296236552, 67197252, 663567784, 157451520, 669644812, 688460925, 560108043, 130516173, 587765355, 744811189, 318213543, 16153082, 917412495, 417282328, 274370411, 743097780, 722605443, 650028565, 75198439, 107373436, 683549683, 981796650, 922129987, 902544929, 297297067, 341960228, 498810848, 594849706, 533070091, 477797957, 699880889, 818105567, 676306864, 348970204, 274398412, 900930792, 170265741, 568321488, 619797015, 815205624, 524444674, 403010920, 302339733, 211111366, 163180208, 202053054, 757980856, 35001858, 169925772, 210070944, 111829138, 637671496, 602551251, 980619038, 955965921, 383941092, 903467439, 293445200, 628127859, 324481115, 891284637, 893156460, 29867866, 515703677, 345442466, 745003604, 813238970, 252877233, 772195639, 952955941, 666709598, 711237592, 795991268, 617712969, 608032732, 664603492, 905758474, 918961872, 400122912, 196689935, 949473172, 268570217, 690893235, 287654951, 536943052, 811544453, 346973935, 231747834, 394237349, 495332227, 626709598, 787282312, 674823897, 958118037, 628397837, 30774174, 874864916, 585232648, 36680370, 392643726, 447327447, 310568943, 216036132, 387032871, 283873883, 59401870, 673973521, 426544337, 474036783, 219745411, 871203658, 468839478, 863733076, 410067198, 576861134, 538844315, 430552259, 860535019, 829194550, 391132687, 380813386, 168293908, 553753547, 472127999, 634516268, 165054404, 766310957, 193152556, 63276070, 362573738, 569207550, 880789443, 929985187, 517453817, 202143123, 988696035, 930909835, 681962407, 872088693, 599489691, 340155465, 983590548, 931916927, 446867632, 461831037, 225910661, 470499429, 230480587, 438657073, 731994589, 464164804, 703314923, 19219368, 805238188, 460548190, 678047001, 614172030, 850871475, 624603256, 871387745, 926513864, 295938548, 198276678, 208209703, 90607732, 838756690, 668693632, 997149182, 791192062, 233148064, 789567374, 351992896, 178761225, 730162131, 740224803, 777881246, 73259406, 920643989, 148397870, 395488368, 334709141, 72652060, 134322218, 618316695, 561926139, 625621083, 433372414, 40894629, 921262622, 161052966, 622262153, 897583625, 999311700, 39101991, 601980816, 921640365, 188963683, 772858603, 796063695, 627904752, 333641687, 673002996, 623208364, 771660144, 74391537, 378114899, 136580577, 72293189, 831721029, 627079928, 864445727, 351034518, 941267767, 574123703, 32766663, 240255713, 754072828, 526837304, 606899862, 531223540, 820915976, 783219419, 706383062, 493711723, 9795558, 386413961, 727454011, 197527053, 516824889, 961325533, 208387412, 863099701, 364374715, 436530621, 281275264, 46702052, 713820651, 939123205, 279063848, 411295356, 134558162, 293486038, 173024314, 639058516, 776944980, 728604072, 659362146, 103975722, 539820615, 839271880, 999929790, 834112521, 363926959, 310927453, 571708365, 690631274, 872864435, 260585486, 589223866, 889582580, 344272772, 824023620, 890844509, 691244302, 532464699, 457777122, 161026552, 324616172, 268757892, 489948285, 738857221, 682790746, 223867713, 10784281, 477299195, 55493479, 827710708, 75318943, 401041267, 126097101, 324306229, 719842738, 266084345, 60239197, 618984476, 559873964, 584871697, 516731068, 844234775, 406268780, 804456341, 620295520, 289771462, 445648438, 768569302, 365702236, 588222936, 314622653, 242218968, 491020537, 412306259, 463575701, 944012827, 676790819, 82229130, 803073443, 81366830, 362505826, 219413885, 726753115, 137750716, 578295244, 649924290, 204186793, 127048049, 207610355, 831678147, 823289292, 834214207, 56680787, 279350185, 605545725, 442011048, 594301972, 341980657, 348623152, 596703851, 271522216, 897320263, 561584487, 770494321, 630425212, 188953081, 123744977, 656941151, 844127351, 242145881, 934457385, 378205965, 808841666, 193945053, 780350902, 685576639, 139445385, 619892153, 689409662, 385291834, 791773956, 231872470, 860569901, 571904039, 692880537, 939609914, 381668222, 934404615, 398504873, 853806741, 204405926, 428234874, 651328170, 721708561, 622274199, 978173966, 629203049, 452877382, 167443935, 82379674, 523698178, 65767663, 337698058, 604094584, 419294272, 534741521, 26721495, 415412473, 169442923, 818774621, 375232894, 517645791, 343960801, 141789318, 888095862, 833631190, 908604437, 887794807, 205106149, 378999212, 52375882, 856026197, 893960202, 93877033, 545492962, 478325767, 396291647, 894506255, 490693120, 947766612, 822541060, 100375715, 327484404, 436441781, 411362117, 846579668, 935545373, 526239674, 449008923, 541081043, 422129880, 660799013, 179658638, 872120136, 652245658, 166978392, 533825270, 156144344, 370716392, 67236818, 143702355, 851693127, 710817437, 34393313, 843597201, 354809045, 626088457, 781416150, 161194721, 413254177, 393730926, 465769507, 60879864, 460053180, 960979169, 459663814, 610333769, 211490801, 952761920, 340411811, 868278148, 269547053, 281891693, 917514158, 738960105, 211771784, 861523529, 296845179, 781724807, 43938928, 330067123, 568408349, 649163174, 200701262, 149703143, 294133712, 812084529, 742682607, 885316705, 513108392, 418577440, 119772172, 675236457, 141755453, 779044518, 747974664, 87251291, 359281944, 478456054, 611219648, 220294880, 475931110, 709330465, 87890616, 663259407, 99685824, 220134574, 351059657, 137599440, 919389643, 505343693, 515997010, 375951808, 780179504, 974452917, 362441499, 223482846, 948705150, 112235950, 900701383, 890626163, 895302716, 553614199, 432200479, 965605298, 910874983, 429360316, 964118709, 407154938, 885400907, 811716871, 68860884, 915960466, 590811043, 776628326, 531778418, 89246901, 231077957, 37043497, 889238841, 130014164, 857083879, 248439216, 376621406, 386688190, 430493777, 341356212, 757529534, 159676920, 119794189, 908177624, 289020473, 500366013, 962117661, 398523453, 776499335, 456003314, 284516544, 310074316, 294154182, 540518185, 772761297, 782260229, 431937760, 281257600, 132983464, 824688927, 31498288, 83797712, 28351029, 546943836, 589079307, 949583647, 874959843, 423084502, 892101824, 705829331, 987121121, 247154025, 559632324, 380111611, 415044671, 297054226, 513110768, 837108793, 475130985, 100376746, 907310826, 506132479, 539880958, 433242461, 72662062, 854323932, 164121798, 531702958, 283795871, 728484620, 339015695, 278611923, 902209803, 387075054, 962490471, 896795026, 535859719, 408502551, 304588717, 995193382, 990886621, 967031445, 445392439, 76121324, 463169179, 203968888, 734064085, 347563182, 586805085, 694037589, 320661313, 109435012, 892973690, 911380710, 973003347, 97172991, 460364912, 556928045, 600223287, 454168788, 349738614, 518015915, 745340435, 288862178, 517281761, 432172477, 626510809, 543673405, 865846503, 856254848, 896817973, 717898030, 38725747, 345950080, 108035723, 368782361, 150561980, 680608239, 218493926, 516477072, 329698185, 275285185, 803941546, 545250775, 660041000, 455473521, 756520638, 513612480, 790535457, 543770081, 103436961, 141628744, 208712038, 935107456, 738385820, 885171966, 998017839, 882109538, 803539987, 570081243, 207263479, 508306536, 516397616, 255118087, 613335062, 788372520, 757606960, 989998281, 703309884, 127223312, 438032558, 226358454, 646315963, 331111645, 129047435, 649868360, 635369787, 752502138, 718017844, 983175163, 165094680, 796553824, 324987410, 745024905, 459624369, 169960834, 262395650, 586034633, 874732069, 434082288, 943850981, 24132568, 736761964, 255308267, 641840372, 562273482, 371275255, 995504537, 652212803, 238332073, 258017963, 779405877, 493277538, 10128556, 889637177, 499091101, 143065571, 923490369, 854744325, 138170796, 847422461, 970737948, 253398593, 643720629, 365111279, 710383034, 922034635, 342956437, 971660756, 441918068, 901700721, 702138512, 564610097, 570453068, 779618937, 540962923, 996920475, 861286557, 836593096, 584160276, 995686956, 652787241, 313151894, 943805051, 632500598, 798588681, 316537690, 530586882, 424485098, 491401358, 440516058, 805231152, 746037189, 843873448, 527548345, 340318220, 518043957, 615639301, 814099926, 901837617, 786019533, 385467141, 351896307, 804048222, 427260908, 11671455, 613943149, 870340167, 424724956, 810844128, 376033422, 900857179, 90600167, 577548361, 771868653, 105903857, 478107016, 401450308, 288291792, 678930104, 23011106, 844430670, 655323406, 492630832, 168058179, 74700849, 496800661, 477552122, 417717101, 281694048, 652440928, 672347300, 976486081, 738002131, 67824120, 387495246, 998107871, 365903657, 640746447, 970990354, 334417934, 542838627, 281552125, 172122317, 536742593, 492099124, 808534701, 135056258, 54961655, 88532924, 318885918, 836123576, 447186520, 463292672, 274440212, 329252523, 250467383, 319916675, 33865333, 458514459, 577125841, 595062971, 547107512, 986922832, 874190503, 461664527, 409187410, 555680737, 773780009, 781417342, 336828744, 8429835, 536733218, 219421344, 40139876, 238369776, 604122763, 63554240, 238954285, 813296347, 978941161, 172352360, 747889226, 428750114, 270978258, 686469410, 19791471, 855312645, 850409187, 316215132, 237970099, 714960283, 30796314, 592970816, 530273321, 736288198, 825060408, 700738090, 682998400, 497055056, 38776225, 442943736, 822855067, 60354809, 992029713, 76162859, 450559034, 561754615, 324373080, 826529318, 761350943, 383559142, 543211853, 237940159, 366616217, 790196282, 662625892, 87055259, 472374784, 291625513, 522392359, 578525821, 845358219, 233087916, 619083354, 901556758, 534872839, 924627510, 412323824, 543550530, 628424181, 335741784, 554718733, 265522542, 637137709, 837061108, 844862434, 259498689, 477850172, 219231323, 96159719, 825080535, 717315347, 665141140, 464669287, 535214486, 646809427, 640505116, 402384653, 197754718, 482725596, 287538653, 853550692, 426322521, 709348025, 185602037, 136671916, 622936241, 148035485, 372758764, 47025754, 775163382, 399817097, 458165927, 828957277, 650145503, 443662876, 398191385, 382579126, 347870629, 78435147, 368385504, 154805336, 222584992, 999522215, 521549277, 220022684, 222491851, 619459998, 987597266, 722008244, 819821150, 294206861, 506170522, 476702902, 218386495, 417408662, 453317329, 286763506, 944266112, 260835397, 607627459, 866452239, 428546959, 413689716, 988012956, 478346613, 837050512, 648040056, 409588287, 27607531, 977595934, 259119460, 767620501, 433343440, 359254602, 813093048, 514134968, 427846179, 169891899, 288227622, 162107763, 697956595, 38550046, 845998452, 855143784, 590889339, 902310708, 869724039, 857351229, 124675565, 228343253, 282516024, 103327815, 596409229, 519701282, 944385600, 582641964, 730335821, 478646495, 210792008, 628821384, 270707145, 722077523, 801671116, 894987759, 817933454, 887000402, 725046532, 571143956, 505893638, 90915661, 818942665, 861306152, 986722474, 835502066, 100271065, 867832451, 266572761, 257408241, 363501756, 852955465, 523825383, 220872266, 548986063, 39823954, 746255594, 587936106, 638538405, 114046241, 926664330, 735454585, 875423346, 498625176, 194772773, 466255757, 376007552, 178190464, 528300287, 930727360, 111268693, 215592678, 256650310, 858658145, 782757243, 926057719, 392892944, 422861268, 883126219, 242812923, 28922501, 913129513, 358711570, 216921568, 844587150, 478616258, 217845183, 373633288, 454546448, 804889930, 552438668, 687905448, 614453676, 790174173, 86265832, 326431868, 785859315, 572314369, 481697702, 604544423, 467495378, 40034469, 450943910, 952240556, 78071817, 160527172, 485656845, 769803913, 418146671, 893232614, 389416656, 833275319, 749263450, 297248045, 634054674, 839461893, 345698337, 468276764, 92938378, 262002451, 685938274, 597687658, 297433777, 446925656, 196913799, 516874766, 286950397, 427386713, 831782472, 276927635, 115892045, 150529110, 50986005, 214945710, 382468521, 692559913, 671743108, 845004417, 289767901, 518012378, 909185450, 206937217, 77793212, 178389522, 395652555, 711555447, 973618116, 715023409, 619836347, 479294745, 164994617, 64765960, 417668024, 242524844, 313625064, 174998250, 677735652, 479434951, 406288452, 649392929, 387564562, 147779477, 858622137, 161421058, 208254228, 548753811, 234479755, 8298380, 91831301, 56604257, 176656411, 673992902, 322931669, 479991742, 662219273, 491171283, 969476893, 686660193, 916017308, 319958726, 458064763, 585610820, 995842610, 836263691, 427922765, 254324790, 385918404, 726747377, 993926757, 154175890, 444372912, 913091238, 170145254, 64113402, 915397469, 304859429, 137554834, 29057659, 961147788, 767641304, 92825142, 147607000, 866117349, 227282771, 409137648, 980037124, 906481985, 225751268, 933735085, 635861581, 13183290, 972466843, 961548531, 30015723, 888297589, 446748354, 360561145, 916466107, 122501276, 907379735, 327748653, 46141123, 127767824, 145732910, 90416470, 560741476, 876068219, 705117444, 472907444, 984271307, 670537547, 937666482, 264220692, 689441064, 403011024, 954670366, 257099507, 86516686, 288249363, 689687682, 527510334, 967831584, 37035467, 23286761, 525507232, 975150002, 948415131, 614626023, 641138961, 809348367, 545139811, 68956436, 709370796, 354520537, 150889919, 415430433, 161459151, 235098646, 412081110, 466718646, 582403688, 835116371, 358294147, 65064888, 783572946, 919388213, 289688396, 242820555, 943045762, 547442358, 772870060, 706939177, 631467173, 715815404, 213735200, 828648627, 846313660, 798799933, 391334349, 423034630, 153918262, 103944240, 67139873, 610164555, 42349884, 446990953, 129895774, 659267363, 352006336, 442005818, 339272335, 823794857, 557626291, 685682225, 570104573, 631817323, 519179075, 910162891, 760160789, 842371236, 168455303, 503928541, 917374129, 9359861, 783151276, 343460080, 471950508, 278273542, 918304146, 172088313, 732167445, 289684425, 148314673, 993792280, 593516935, 822473640, 41876458, 771213731, 521839702, 858006377, 281294938, 37711431, 698291310, 793821946, 651011525, 951358307, 368231952, 990706211, 808290431, 364423148, 345666332, 894010460, 799217540, 871872161, 527628818, 204369386, 923472976, 840097540, 918811421, 633768932, 624914464, 162510119, 102602048, 794484916, 709072484, 496840521, 953184094, 854926007, 24557330, 292483609, 660523489, 951169919, 568938420, 517876672, 816472445, 955821967, 849671100, 553330093, 392391322, 158030473, 826690422, 168531607, 740213616, 649282736, 976718798, 393694156, 716946553, 462127801, 837088063, 51586596, 343409994, 915815706, 488704473, 263348151, 143517768, 604870781, 747672578, 116911824, 706950103, 355332207, 838175520, 481091887, 654587138, 784159816, 287503361, 44610305, 587207896, 355365753, 866798422, 439094686, 161374216, 533996178, 675250662, 325256610, 940570900, 78136677, 314721030, 460804801, 444131960, 792294136, 3770472, 327842546, 78837810, 785702896, 364317447, 967571904, 424532457, 898968302, 434888255, 273106936, 507028043, 913976878, 4696501, 499753855, 755179335, 751916122, 283220019, 882013699, 257554766, 264390323, 127360219, 430065753, 865321696, 705591564, 9322410, 582708743, 495036229, 412520090, 759926041, 868077361, 674247516, 625862600, 431299920, 562410794, 854153946, 155120302, 718699311, 703636370, 931847165, 967093547, 623819337, 952335666, 56767414, 134798877, 3157599, 54906052, 372391995, 508845015, 560735064, 617315970, 136560699, 662110614, 470590375, 520749357, 211805659, 540690430, 20763247, 282072690, 710020192, 724604966, 467656948, 505422912, 341869475, 766018772, 737808709, 858172541, 558439335, 860763975, 249219170, 503646967, 929498625, 653783624, 989904635, 56017711, 464652129, 828160331, 569129764, 643918789, 824946921, 11779579, 484202109, 996763105, 605937630, 214602347, 12827193, 55519430, 199827576, 360823578, 43836821, 627336588, 357776828, 41497293, 52679192, 592281602, 848189482, 862586018, 72623185, 336243168, 644340762, 833908149, 358754980, 484087080, 352666114, 718456122, 639816368, 843262457, 379144236, 2968787, 795114494, 643277750, 90633777, 142393140, 465033767, 802717498, 15479770, 98896595, 192426725, 434166813, 620113329, 731762261, 524040941, 518852581, 277006985, 503690701, 458124732, 483315303, 874318839, 472855314, 601100941, 869984363, 541679386, 497174091, 904344495, 853219457, 961404083, 177232962, 287177304, 167392760, 584286200, 95901999, 355002131, 590384293, 88862047, 603810364, 767968211, 52733492, 241542608, 775856666, 518665337, 661391769, 340367986, 229745487, 892980963, 99366784, 434015978, 715409903, 85815153, 276776591, 268179390, 770204813, 166127410, 140810043, 842712193, 541011455, 936026450, 221274554, 258640943, 95463025, 734670395, 183741323, 908766809, 426518621, 399055942, 496045751, 896622267, 51875702, 957311770, 477599491, 309219059, 425825379, 288758668, 436610833, 382766056, 877729672, 866871282, 790941895, 457411602, 912163751, 499653411, 898227345, 931420944, 743225467, 268249863, 149573090, 153551876, 445740759, 228696623, 239812295, 261105461, 791776885, 535446343, 994480094, 130953512, 158782051, 314673650, 117007133, 777756618, 190533297, 28025917, 553268707, 234797808, 525289298, 937725890, 711251404, 556135357, 203085585, 210711349, 676927408, 889091798, 619245336, 53843572, 689823128, 422311073, 618805492, 67206328, 521615088, 286100192, 228909635, 320005093, 653772357, 801919092, 291783631, 320955909, 695942594, 407501449, 293176022, 915553478, 94717600, 799495365, 645601460, 955373152, 686817379, 891362812, 868190663, 835955376, 936996891, 139748769, 836434556, 418091319, 836622667, 527101441, 146374599, 624425579, 466969115, 953313759, 977134551, 376606157, 29117716, 739100570, 980786088, 609396225, 189548226, 981515989, 134297670, 806826154, 789810993, 366424548, 544089690, 167575380, 488262774, 660439582, 901968193, 618387695, 803134553, 729122294, 424784238, 849563674, 218240705, 372671159, 18079506, 917751434, 807970195, 212782178, 363972553, 335970231, 348642484, 133322040, 135487732, 18596212, 302766950, 417377418, 539645473, 28575189, 829909975, 325498648, 278148270, 389290239, 183577836, 324367939, 337629788, 208070972, 223380647, 597062402, 892981610, 134099244, 63201638, 674734002, 738923212, 879240187, 960266450, 543387971, 324248316, 491090420, 269887805, 475851790, 669427932, 8073560, 84904139, 36157408, 91470125, 898894632, 769258921, 49239683, 338820237, 451758787, 817752166, 469743365, 371349391, 248231813, 626168975, 657612837, 191756411, 633995407, 219694090, 542391699, 664483989, 882922042, 981501771, 62674537, 216315909, 428266546, 509533982, 875428151, 158176977, 788907820, 767120023, 632929388, 38328448, 450349604, 24465048, 906704307, 737444961, 928246452, 601454255, 4175417, 762673352, 934882077, 420353003, 292370921, 527189109, 369173816, 823405305, 275917492, 298783350, 554287818, 280430354, 175834296, 798497253, 517866650, 675982095, 61198435, 307835790, 332050552, 475875420, 14292979, 665608763, 630429770, 203905111, 362960708, 172885882, 392180841, 389104412, 816343942, 209666287, 86948087, 194767730, 10596347, 462844857, 810895768, 888799829, 40769091, 342942045, 893519658, 911257505, 163241018, 260646893, 228740555, 392075865, 388672626, 922227177, 312076056, 233382403, 178823938, 526946708, 634293934, 538659379, 30615331, 589073139, 288544099, 579816765, 973103154, 230795157, 114079709, 389631859, 781892510, 925787871, 970416005, 829228251, 52223723, 944885496, 371978759, 66882523, 125942873, 905531647, 359615068, 16104580, 924784470, 451385597, 790677859, 358812175, 438139161, 771226774, 513783126, 899529225, 602719469, 447891025, 522924813, 937251262, 814180800, 226640541, 755040127, 459034013, 92751967, 241549489, 347872333, 691351203, 675505437, 289735827, 823394759, 94741308, 34178113, 109330098, 644659731, 840265361, 906516908, 431835016, 224332831, 603557279, 253915651, 907876326, 291251774, 713790799, 403032927, 438476081, 806662247, 649447186, 631463694, 740568914, 288108967, 818156296, 491968480, 870058200, 488141825, 238340888, 711111750, 545089129, 838657660, 864606425, 166180842, 320195150, 847585363, 571280957, 262770074, 797413964, 449597493, 371793838, 310072952, 265262565, 256748139, 906681040, 414616919, 80122497, 272588157, 621992839, 64387313, 568076373, 118428046, 808771152, 361737546, 84485575, 286284205, 456058775, 598188123, 548101019, 684386612, 327358927, 124870395, 876043639, 293031294, 599032076, 806204900, 758143716, 309473721, 440722125, 801053746, 98577189, 46997123, 824936529, 101376151, 523534226, 76030623, 862523050, 790293143, 822036240, 350031873, 370876923, 36919723, 195680834, 586818967, 749142505, 320232558, 108590822, 244241700, 246642037, 333188422, 99419310, 42632925, 936514393, 40732579, 452994802, 85186546, 254893386, 461215166, 975363881, 666862346, 410668658, 612983135, 572237884, 491680050, 308656892, 913787641, 183189440, 652996274, 354932511, 256511254, 233534805, 190679410, 493570001, 794365443, 257681232, 671532018, 460921639, 458133459, 22456224, 16055069, 178554204, 826339082, 834247547, 926311885, 221008997, 444666171, 774371570, 414326226, 318371199, 430414311, 672465464, 277741313, 579890844, 516772345, 361201574, 779745961, 570096312, 329015629, 908526146, 319937028, 634819900, 96216804, 813053854, 453712723, 851909657, 166522068, 581946127, 645068784, 507534843, 154521339, 451909990, 667246795, 734285971, 684576119, 995838704, 712285726, 274838773, 512252454, 301788656, 315610717, 389198605, 980036503, 764225016, 540401800, 599771263, 294782713, 822727525, 691476878, 567079616, 648436803, 52874706, 914614842, 167345881, 338553819, 748276252, 241187750, 879451575, 633908750, 275046193, 889366992, 307571339, 624153147, 68257047, 897000632, 437147865, 631699980, 706380316, 383452125, 384594647, 375382101, 20175752, 199102536, 465108938, 547853417, 643195947, 835843401, 307048882, 156200527, 71797375, 729767577, 870194920, 254786615, 917855388, 44147222, 447741591, 767670218, 434757556, 362594824, 967174644, 225345873, 157787165, 77582157, 985873522, 210094182, 752229511, 154048119, 336760173, 41779973, 620927603, 930278719, 355258336, 516270315, 881217866, 911735289, 615690694, 891437655, 194608811, 316926592, 310001702, 567643196, 936668094, 274297065, 684203176, 369235749, 973338736, 646695903, 30726901, 130627922, 938683337, 751537818, 641487162, 946773505, 349191974, 285453774, 212320616, 595653882, 171106247, 539105773, 560228063, 709260602, 81833013, 417225516, 244025887, 18482370, 84941110, 547026300, 429629884, 485591835, 960328521, 455486239, 835099415, 701956371, 142435738, 27791212, 352075554, 237544595, 327230879, 360764515, 51130020, 584007126, 607227201, 212366549, 299088121, 7256847, 592437500, 722761122, 621559066, 292715876, 251380804, 231611947, 949381953, 713750799, 115487542, 256330604, 449935318, 674481514, 734860085, 976701498, 585426330, 457879612, 857201204, 538122195, 121681914, 668558091, 910082822, 246663823, 140259183, 429291298, 973470143, 986841520, 833178122, 331755091, 271922483, 803596349, 280306243, 64799783, 740265916, 160125833, 384391434, 623369527, 647871399, 110568074, 631961099, 481819402, 486544578, 62391973, 441019841, 646040009, 353851401, 347093411, 364007985, 987243010, 438116077, 599523221, 111596373, 587368906, 721582557, 907011907, 54786207, 865416308, 955070975, 329701528, 137630528, 769467438, 749144419, 671407380, 971203359, 925392998, 553671546, 79484399, 327680082, 76357756, 523632933, 370090873, 124649696, 528846050, 98810657, 78750366, 684244464, 619258079, 398231726, 589051633, 998466506, 483539582, 523466156, 469130795, 786453350, 947846167, 936793687, 83342797, 431546512, 581842585, 552680404, 621924101, 590606664, 156915024, 632020337, 936210113, 867062027, 715541066, 18712557, 575251819, 103214095, 647130308, 227649491, 163698335, 773086530, 641420951, 951320122, 487839874, 251624330, 760622694, 492973097, 122148026, 606629265, 38273015, 136831167, 748008070, 652484218, 205584271, 847407169, 238478535, 73243202, 970826963, 270166134, 483786602, 464612316, 830982914, 127026354, 414739636, 438779604, 529643503, 711886688, 225611760, 872124636, 150494394, 739121850, 922926887, 503763835, 125605698, 895514182, 875117530, 167639734, 152249342, 870917417, 945497528, 597466953, 841280170, 339145713, 432145355, 762600903, 549165886, 815901254, 720245346, 175952386, 953463356, 482379351, 588024163, 284318680, 300568488, 267374607, 984634008, 710355218, 755912240, 84877310, 104651441, 78911443, 1274230, 219594680, 288768484, 79428225, 776216618, 77349997, 493493425, 391645594, 414402145, 912346480, 920094614, 661258115, 657373165, 397973508, 308002972, 935749694, 522585332, 611493409, 743258785, 455415464, 203544091, 471725617, 820102150, 872389543, 19226025, 263978560, 519211319, 153075436, 567665247, 865440801, 999752544, 302987750, 479385746, 896726243, 899990343, 397220302, 671127513, 887972584, 851343006, 262810840, 345517408, 261382172, 297384413, 392557276, 753886221, 770946214, 539872482, 510379611, 478634902, 722341315, 760586336, 854861485, 604262388, 273037768, 13981129, 156038631, 211710392, 118171494, 320479016, 198992649, 425101414, 726788773, 247259557, 949469533, 511836241, 880689363, 307277224, 138327830, 496363020, 571223548, 16000547, 80975324, 437045938, 444436892, 874066942, 846895464, 169979252, 368356393, 451364218, 193855250, 945436829, 365502506, 661980713, 625516560, 904911107, 117820945, 644678178, 774464352, 752446667, 532196442, 484933950, 744347714, 551680585, 782654612, 492403750, 315101525, 107549168, 841370716, 717405579, 187922738, 793343557, 882625761, 946780827, 478482420, 649851371, 774283218, 530027211, 288354162, 269187019, 479518161, 619864327, 565134503, 518119549, 779344629, 231821331, 959486048, 669475238, 713391095, 439499091, 406911578, 650042480, 459356532, 24939203, 987688695, 396632731, 460089803, 57045648, 789424402, 410391576, 443085033, 423722284, 243908437, 61629596, 120831683, 572598491, 367627477, 631668379, 153639732, 89979088, 529656291, 119999833, 30812473, 99447599, 400078065, 299674947, 905025931, 368360308, 664379281, 605805181, 552046997, 592391215, 915681316, 690144283, 332263157, 293576073, 688092040, 504507975, 551458517, 848340780, 619125100, 385312540, 340753288, 793052202, 266816935, 5891432, 752388631, 910801876, 154405379, 874185356, 702029029, 747443463, 341628872, 833889364, 829472633, 453249520, 53070972, 110390855, 627975764, 646248435, 835126408, 70438229, 999960484, 418469169, 477828012, 641423235, 26406847, 696778177, 759990835, 701678079, 268446608, 272827402, 339555752, 85628483, 382990681, 880493275, 425525112, 219061690, 603976709, 262157769, 269534253, 466806544, 394855258, 364435297, 99699085, 730943978, 455095401, 36007597, 886545011, 560781768, 531630796, 421508439, 298404671, 329940837, 695545089, 46142039, 566011696, 688822242, 137487726, 995643923, 341967660, 911200853, 108296281, 813797905, 593549042, 19912467, 300508121, 276457204, 718098598, 765640506, 30851115, 945726249, 646560267, 506173036, 721928634, 260605568, 238555626, 489087545, 100557758, 931222688, 837710056, 212635615, 390691783, 849339460, 619957534, 119076642, 350661729, 805545157, 731216978, 656499364, 54833578, 762931667, 719615172, 388836615, 776409096, 782586652, 472977893, 425086813, 885499895, 747333764, 835963746, 715661663, 575018254, 433347910, 562792701, 355209496, 878274474, 273027720, 588968949, 68755052, 220857386, 218515229, 254341193, 665447093, 638534919, 718544476, 611634850, 842385220, 177638765, 33260833, 15218400, 801582806, 769956402, 202905556, 607943186, 963399922, 893682763, 166981710, 759575553, 588162815, 925825201, 871508464, 863539918, 534905447, 917434480, 741479733, 628587054, 494682846, 837619230, 727216915, 534169484, 966127759, 214543448, 92476870, 50442433, 988761869, 220432833, 522871496, 801029085, 520220846, 975392110, 485170233, 876343486, 631640685, 160881252, 652303184, 146378524, 154888165, 141055645, 311805096, 983248851, 85097886, 325007752, 446217205, 630966538, 556796774, 651487022, 754602010, 612961251, 478209979, 924242716, 125293106, 476745780, 628824827, 368524397, 436038519, 842589037, 451414698, 18484144, 819365055, 613248176, 582305577, 681042814, 679851410, 289504508, 205599959, 332623130, 704399498, 672627728, 3777523, 604239410, 57473532, 879184688, 681926556, 19392621, 916789392, 170036846, 539202353, 70159462, 681208133, 483859252, 592890608, 617370227, 102629017, 953312093, 164382609, 921401453, 480747519, 916976636, 609435923, 180925286, 480849064, 385095589, 944092030, 223619886, 147084658, 736042706, 629574826, 189053284, 924125831, 347868159, 913297134, 868171599, 594598892, 427345059, 213038472, 253148012, 674270825, 279683071, 568261732, 627137705, 257733724, 275059710, 29944715, 536363201, 887872262, 266486104, 842756438, 406267851, 383463857, 669953199, 552627841, 875679804, 921608281, 192178119, 526765693, 301807477, 83343580, 610869189, 131286644, 627474436, 416911262, 475684540, 363686384, 911536712, 321715577, 924077013, 10160028, 112928279, 466376725, 711346376, 587385138, 543144566, 320240501, 310569322, 735130373, 856268533, 261830322, 972157174, 184228128, 435154815, 312761774, 67643916, 323158482, 408705677, 705499480, 415098860, 779103930, 361372210, 83052903, 751806825, 749875028, 534268887, 410003701, 646933186, 445364562, 681215111, 1223017, 203804604, 128105607, 134030406, 673740015, 484580311, 855238091, 768755603, 945646118, 513051519, 895465088, 666479347, 103345910, 880600878, 143120585, 782099944, 104090729, 497921326, 92214094, 391215431, 45223585, 637393175, 982442798, 824222183, 75695898, 867895881, 590210484, 493470893, 582257297, 643502659, 960493028, 478679866, 353822699, 977811377, 120524700, 261682763, 817121536, 68858151, 326412115, 445199268, 503172443, 763534999, 859692732, 852750476, 2755, 443162801, 8181686, 46781867, 309991890, 666807925, 650176153, 75988914, 187457609, 560049445, 934506080, 534001966, 96575511, 706584635, 854296164, 222216483, 586274010, 555300180, 48953812, 970043196, 703515480, 670260370, 569984139, 597740613, 962737332, 628654203, 433359847, 511039544, 956034173, 679122233, 58619813, 916010474, 44345028, 78977523, 432487062, 240236365, 819254758, 455226960, 965547489, 149848947, 78714260, 967467232, 457354284, 796644893, 783784330, 955927406, 670580321, 428819093, 174683790, 162982451, 538593960, 900931488, 498203051, 49151623, 268797382, 216432737, 299968084, 960693078, 875172535, 191847968, 232580323, 170360139, 346833326, 759755004, 580611832, 445911273, 404447208, 802857825, 974901938, 3800957, 262804625, 473803539, 899352655, 464380775, 7764429, 665023968, 593748682, 639188980, 793527895, 961098123, 322675243, 926877775, 604917970, 31335882, 947426921, 160061010, 197657022, 40034898, 371026048, 561380909, 910189669, 790769671, 860631579, 851062027, 302729829, 391792442, 750715193, 619731791, 4157677, 311818808, 445342942, 725315375, 572055111, 22308833, 832241336, 837239065, 250242464, 630689793, 749671529, 1013119, 667071838, 937100811, 470134114, 362415515, 193206170, 788271964, 43249309, 45967925, 3230355, 839523078, 735272621, 894154456, 18475080, 289925668, 708486300, 831837128, 573510835, 964125087, 396228715, 945306965, 733543000, 387897105, 883381852, 163506547, 128977649, 526404716, 129518684, 608173328, 150432874, 272467942, 705711696, 319058861, 626479655, 836859299, 737689530, 148433602, 122327237, 428549034, 428015136, 557900338, 323788331, 584439035, 19686186, 256903052, 368316702, 926694944, 982390109, 765684288, 721400204, 869051548, 964692814, 289719112, 519662946, 215921983, 316427910, 314817112, 775267097, 149784315, 872253070, 61308388, 753642393, 416273632, 170411442, 690057747, 75749314, 130815424, 625108935, 294483500, 603818698, 47479391, 371151746, 876902942, 397288337, 562078032, 180119086, 121924180, 182033358, 183240644, 863997019, 939935422, 42444759, 116947854, 678750784, 799067294, 734516859, 202961135, 895252654, 963122584, 652258699, 438856557, 802254011, 753985704, 999191457, 849896509, 13909896, 589628306, 240563355, 849464453, 460318758, 66910972, 126169640, 852033739, 727938476, 747934199, 535189957, 905901866, 494747260, 499023276, 31168109, 160910473, 530578783, 920889565, 923906628, 352903520, 213929749, 599991000, 909300029, 501970820, 454978114, 165507221, 815445172, 935273953, 367260509, 808208130, 109510245, 331900776, 465603865, 198122601, 410482117, 223710355, 599487333, 148415833, 577029431, 676499139, 475985651, 16615102, 175686323, 184169046, 257515724, 517952645, 566327052, 299872990, 816675309, 453366193, 135352464, 145799704, 258420569, 980643756, 247924340, 594132944, 416326453, 97029654, 501786536, 413570110, 18416893, 758563271, 859699489, 788806845, 177458269, 924758223, 915285189, 833315658, 433346645, 935668432, 911954122, 340295948, 902980438, 661901280, 349160273, 251699124, 505696845, 520287242, 248771319, 699349398, 303992665, 108261148, 261991440, 726205006, 539468886, 251343915, 288915390, 646990518, 686734602, 100652795, 918242422, 413874644, 597533116, 472657438, 429809766, 668293860, 393776564, 535042801, 196536698, 489655926, 891183811, 330033379, 742794213, 381377537, 880048058, 313520721, 967403448, 540489954, 482300850, 313379865, 769652689, 604139008, 342521322, 474178559, 392702159, 231994680, 150209645, 661530062, 976418849, 865021348, 775188775, 211230346, 696802519, 948997538, 512177717, 223315112, 173253227, 103702683, 861376297, 394362148, 742468974, 615816056, 817977845, 727458002, 530867431, 655546145, 685102518, 585758991, 781096199, 489158906, 152526682, 488016794, 329864306, 112485001, 904210288, 106293659, 68451175, 137553764, 909925458, 164047949, 486437495, 264557182, 543264337, 405638494, 809121939, 406919810, 246268806, 125857219, 658963407, 470746868, 134980467, 492867750, 111495, 898798797, 193832884, 839895202, 684669843, 414351473, 127311640, 315712678, 261363037, 810432534, 349583446, 568179433, 657185008, 323082252, 459494100, 429369063, 154114577, 746418990, 845831180, 697589852, 829586133, 19172142, 395122689, 589481093, 237799607, 446285561, 47189543, 491295907, 552553502, 58152712, 397433638, 674604724, 456273334, 224874860, 600836575, 770082649, 642646733, 850264481, 334792906, 699007782, 469992599, 299865262, 990008524, 336517749, 16398206, 749426387, 664825407, 847998283, 245467174, 956369354, 94917401, 595250948, 523816056, 535676096, 961415300, 86627662, 547660031, 240692957, 770801077, 558071249, 105742424, 46588135, 169540473, 591090236, 982426609, 504834881, 471073289, 162917422, 840660880, 313474391, 401622850, 252960719, 913965162, 415458983, 329565831, 98219215, 239441966, 37885818, 728527374, 267942405, 407209292, 127785682, 530077836, 611972217, 166865792, 337626657, 452744556, 332255317, 962858870, 267470411, 908170035, 39124755, 160345337, 759791791, 411969042, 535935851, 957204533, 979589883, 738044460, 572552889, 303136338, 238839997, 631022624, 698077108, 376656344, 974107291, 977220267, 884135229, 835581885, 57753457, 753829370, 358248726, 199086749, 507322881, 932260065, 349888979, 824310803, 225737516, 920800871, 1232306, 167537650, 18868784, 764306089, 348813184, 731393224, 540096421, 630368067, 54636353, 167422328, 920889152, 994313663, 267099227, 536377017, 90111027, 529060666, 608613110, 331660045, 849431326, 431551506, 761305028, 349569707, 378559001, 50340183, 381554474, 932316822, 524740493, 777004137, 444023868, 795727894, 312882622, 201532593, 627236809, 594950529, 756075259, 342407776, 39924549, 184817079, 97882628, 866787069, 2608997, 693179396, 852681272, 549698025, 246216036, 941248710, 613946863, 928707602, 166131620, 560084012, 56729147, 411701960, 188313130, 7150384, 332578571, 143499969, 664947589, 991383410, 12739260, 678103043, 208194024, 217458720, 748283662, 65210593, 108385962, 266300914, 327259456, 545042172, 486360320, 984340282, 235601518, 143316892, 751185769, 969273077, 17013861, 671334555, 118396216, 411305807, 213451754, 532531960, 100546684, 893408981, 709443294, 150890635, 67818469, 724461453, 674493532, 826093662, 627479716, 187966624, 625773634, 268383884, 657639009, 432549542, 774557418, 716068797, 752866132, 269587351, 726350998, 688325280, 742124338, 550553793, 674592393, 738385495, 866248960, 863513949, 9622666, 416260746, 676356137, 321605448, 424878959, 567293165, 284253347, 231616597, 585584387, 13833678, 5550208, 64029427, 636166609, 188209904, 459631477, 688972926, 824945230, 574867170, 541116346, 600664352, 924565967, 8075619, 162487649, 260998607, 249608465, 832040008, 157196200, 41122731, 701154258, 572313667, 131687508, 947161734, 356017151, 238420766, 439159442, 679341358, 848859591, 498639135, 61917565, 311695959, 26992449, 27179524, 555322188, 535200655, 849160670, 769589259, 488655649, 616431924, 505829840, 114964185, 160400806, 555733723, 701241969, 459813284, 892929200, 517207562, 456503767, 798501844, 899224086, 501871265, 240472514, 464376300, 82986057, 64518360, 369022064, 184918071, 674216379, 256549143, 32023740, 32998714, 399129001, 921035102, 826895351, 157294468, 395739328, 740645638, 907904165, 892571550, 630152690, 283995878, 276872049, 369066350, 796024916, 464546177, 257170869, 309639023, 989956317, 951327269, 952349592, 731123645, 775086693, 854052219, 851945420, 997211524, 626061368, 570801947, 389824219, 397653325, 929782919, 406049871, 847995429, 949851593, 71852332, 282903429, 676148124, 259620843, 658767850, 850095388, 859176618, 667276388, 53137112, 820821058, 241587002, 183780187, 6684658, 377658280, 621855843, 846443078, 735780056, 748047456, 98975768, 849351849, 284738422, 760347430, 623430738, 988015885, 158304828, 638018949, 868691131, 264514838, 15586774, 913593642, 414933797, 67254896, 973305732, 546834062, 236021246, 103542867, 647306807, 448664763, 678658932, 887714868, 991236322, 330097679, 52114318, 728496031, 820465309, 211800016, 503975147, 378416731, 295431477, 451588695, 5316370, 198075482, 795305800, 917859766, 524444228, 461343521, 666892041, 15419912, 361693721, 620463327, 845954178, 380523649, 662753572, 820187481, 765708035, 588897086, 264934060, 930241121, 4150606, 866915989, 589039795, 792666127, 462202265, 70420277, 743699718, 578634706, 734338769, 356538844, 625872453, 415241485, 392913048, 615886056, 502470364, 19513344, 654101860, 82843036, 967318683, 242479956, 135008656, 745323628, 996775636, 430245328, 29151060, 459431010, 869365745, 43205492, 695561290, 295478287, 177261673, 962779967, 616014081, 927806238, 262894631, 389555937, 6856055, 563425995, 790800091, 176166005, 887425776, 726081086, 509217148, 566889946, 968948567, 569255982, 860043909, 176106841, 446914886, 358899552, 177296422, 455981068, 202664985, 657622203, 786241924, 817331131, 115198601, 304682506, 305626463, 324207446, 611756225, 144300813, 267231409, 198446683, 152298462, 482540035, 444530551, 707230976, 292805562, 7971925, 180140952, 197148209, 580688639, 587225513, 966958162, 721066648, 322079698, 116559023, 826504991, 214128738, 178845634, 385776972, 238107589, 894545983, 362331924, 208014132, 859082387, 166766743, 117343630, 430092729, 226331793, 163514171, 344640926, 189330189, 922170970, 43970633, 393872164, 845112752, 924904431, 88537386, 811433774, 928220120, 384142416, 976333642, 578652964, 267500802, 247961446, 711983532, 523503822, 961883648, 460118657, 389987528, 764138641, 594349495, 736130519, 365734572, 192718959, 745225928, 429018892, 887338308, 378085696, 296720305, 92051996, 377758443, 721589607, 849354071, 670794977, 166104998, 579594416, 760351420, 468253973, 474461293, 296453258, 6327936, 828252613, 389776058, 526062867, 368141059, 407829699, 899335288, 684897408, 549046256, 53643402, 736051600, 443946599, 723591276, 258277230, 964491810, 849995982, 817093865, 463177181, 312827976, 898851042, 242252986, 251340759, 703880501, 95097508, 792189333, 38662107, 434634273, 391084692, 770198422, 119620487, 986678322, 863581824, 436170781, 982235202, 523978181, 74460513, 961907806, 291427551, 636043174, 350777220, 174634864, 459585383, 509411139, 350512649, 216406767, 500440661, 926918451, 625068753, 472769454, 818949358, 643958217, 599935741, 257044961, 879458997, 155788832, 148986000, 271799546, 598208987, 202437639, 858121633, 590347187, 330381745, 69037731, 510125285, 287884920, 949325551, 364745252, 86409087, 35205526, 251344493, 261756261, 121450114, 222076506, 935669769, 578595280, 232004916, 21273781, 4013216, 502863254, 414818516, 622567878, 634773375, 164835474, 132293263, 988931571, 453138624, 238985611, 338123377, 379265997, 501791684, 884859405, 518160845, 561559247, 783593162, 946683026, 683795202, 547304128, 732582411, 603057032, 576350419, 35791501, 656516085, 129916924, 867713253, 941340641, 654170115, 248006736, 858397436, 883745565, 197905962, 771222279, 556564362, 667799849, 477320873, 7504764, 899758928, 536098841, 173971338, 693816398, 393081556, 882191018, 40152326, 636974510, 733701654, 438444767, 637560671, 259783556, 607137713, 349651471, 353999504, 620845836, 90088360, 465256522, 518931691, 157486947, 468119601, 686546769, 768487356, 124103762, 676244497, 823595892, 916766902, 83044179, 465802393, 735357581, 344341433, 768275657, 815800421, 823766104, 178825690, 998922138, 825796383, 804045235, 232234834, 935303435, 450951213, 529160114, 84012796, 516183794, 143528969, 470983942, 775151500, 635309111, 355236768, 755683021, 365444293, 779788475, 306276792, 328291873, 712617901, 869177103, 867674751, 12836927, 520479293, 894673176, 936963861, 443079225, 995323671, 47457532, 75396960, 468057993, 674340296, 356948076, 618758743, 590233006, 502865793, 260463547, 149826179, 985918945, 54507834, 258057202, 93259021, 149993308, 701357013, 797194477, 822471482, 617392277, 399650565, 527464002, 817561935, 691752078, 817000097, 137774461, 159502801, 568004898, 228093288, 453656152, 468386309, 460908531, 456163363, 137545726, 811764101, 388214443, 482154669, 320533163, 570495762, 477769033, 149185518, 276462476, 286782332, 566486104, 735369194, 823830916, 480666851, 149080904, 783688681, 264979129, 910568263, 222647238, 794939664, 204645629, 801803075, 295392917, 837623773, 912262207, 115814194, 147149557, 777439852, 625944468, 266219549, 173893958, 921731304, 346200959, 45891334, 191050407, 190803164, 475895569, 592536390, 483160544, 13032913, 59918341, 530903531, 269277930, 402366107, 146959511, 925407417, 737002644, 227795374, 364912161, 813919562, 16742097, 219156226, 251937617, 513041472, 534694208, 655564082, 2996852, 731262175, 717544069, 715955505, 136143076, 780020689, 779240142, 647672223, 432946899, 62358096, 361299564, 653035085, 332584033, 40202380, 794836803, 758985980, 835394343, 577077661, 468666468, 604015514, 482997284, 485422082, 133777574, 220164563, 400504660, 855215718, 816218257, 385312529, 706595008, 788840610, 433319107, 32429652, 60119336, 634474004, 522314819, 827923976, 954551086, 582032667, 891809082, 68545867, 671762152, 473600013, 478558736, 213107646, 450346058, 759248150, 686868662, 210695290, 943466654, 810895569, 412946738, 92950733, 748689761, 736424380, 121063698, 73051589, 665307392, 728610585, 237230070, 769733852, 134843042, 905617846, 301969928, 828822324, 517622004, 1848519, 787358518, 402923395, 698311633, 384288438, 56437862, 66329427, 690667809, 169348351, 151247262, 411908995, 440467935, 602801469, 357333526, 536475022, 593293775, 366105181, 434316154, 996469931, 967544804, 539921444, 866754204, 205334333, 444282831, 370056508, 783373006, 846266641, 621535887, 477877280, 517108415, 970353053, 477258025, 435529051, 223639902, 647682085, 539118386, 838469167, 268535088, 458624773, 269375039, 422484332, 485186857, 670861037, 499030080, 255910861, 96753455, 331757908, 368020897, 972121578, 996031969, 136154133, 57538467, 446202751, 644054741, 199461593, 958256983, 703146123, 84809002, 760285344, 733190526, 3470982, 999395201, 332473758, 683464920, 745989966, 357071577, 264483255, 50392635, 354946719, 223454879, 890318453, 817657701, 441857548, 589506817, 335432115, 679514722, 763043962, 536260345, 735033503, 998306633, 156638488, 29376350, 894131184, 926155729, 623248399, 877996344, 642794840, 535321202, 253769642, 268162284, 31180058, 721035593, 743484263, 40485524, 284629457, 106828313, 903344324, 584652069, 905557427, 757291875, 867290025, 590639594, 567336135, 40070991, 873419701, 880777875, 458169936, 644163794, 4405826, 84300917, 737438719, 484837554, 470940105, 59053155, 392860449, 253093708, 841218738, 889964048, 232210162, 865759007, 206408997, 834962021, 520955251, 525616081, 862585649, 651231653, 780759773, 985837388, 634180952, 647337238, 232989320, 227688765, 938722902, 138982395, 264043231, 539300037, 637680010, 29365600, 46485942, 606473131, 907564560, 885278152, 819917435, 120780173, 449245722, 272442067, 317449680, 695190246, 983472059, 277276584, 802417337, 50858419, 914440810, 195150942, 697222185, 258495874, 801141439, 180246114, 565698325, 902541414, 601148239, 963684780, 399147784, 937107147, 758293582, 961498177, 167653324, 704602307, 74813763, 363353160, 926190574, 553570558, 875008332, 3631707, 389668785, 208140198, 831128917, 46189182, 901876146, 98645505, 152237374, 413113711, 75193373, 826180645, 899934835, 176721682, 500674560, 551996568, 221561385, 470635588, 678866865, 12168027, 145878499, 653329255, 654462705, 168810679, 30441125, 201802876, 957928808, 508436291, 427892625, 69940625, 295951544, 871791984, 113424761, 4694686, 951680617, 698140104, 381690096, 943927345, 126303437, 379414018, 606661981, 491455308, 107706615, 915643015, 320315610, 440569153, 142885865, 781526319, 824082154, 919970632, 369682789, 39739933, 519841419, 315810885, 36836381, 454416113, 332050625, 591578354, 939338151, 35182960, 43268126, 267253466, 147427624, 93951106, 983290245, 499070200, 164366441, 574212713, 643264137, 79297144, 812187844, 301327880, 202558344, 319636730, 209149608, 740184714, 45016813, 712859717, 429583687, 804394993, 680905610, 314410163, 411849219, 502470961, 155553007, 980572266, 879783104, 887332293, 96971517, 220286937, 467345038, 587436952, 478778477, 583047354, 253993183, 698607435, 556751082, 476406630, 488676051, 390747794, 440151992, 912587889, 104771131, 451028307, 872223335, 167075587, 234249899, 138927717, 593799868, 238791197, 523865730, 530327117, 536560843, 850482754, 86945873, 680529578, 152559336, 526417684, 458113852, 262134732, 60482430, 193878189, 684913062, 778766580, 566452464, 557811393, 58926486, 525563273, 450956582, 319723296, 22598487, 804923075, 552336032, 375880199, 749635096, 274278464, 292238302, 70071667, 90602868, 776942691, 359840889, 139067593, 827291698, 544194263, 949148521, 303224759, 261994014, 397715375, 650341156, 527764778, 740157090, 259007608, 159540152, 36780, 53698039, 88796082, 46390437, 48910377, 862552685, 178401687, 329707391, 808791758, 382580070, 722254887, 249390281, 195219301, 783063233, 471343203, 391440512, 655856558, 34135996, 849237041, 653419610, 867437645, 718273964, 881129330, 99232600, 77067562, 484602582, 782051955, 76492816, 771884676, 634950386, 631952852, 373982548, 605746945, 126030267, 147853435, 614449648, 438634426, 534499218, 109096047, 597177992, 579617040, 4967756, 3460271, 115851765, 857425108, 543951319, 402616816, 227285080, 35641269, 420547610, 827628612, 212409288, 610641668, 491917203, 930432395, 545742499, 10286890, 141610202, 390019262, 399885285, 276286297, 165919561, 820809009, 80907468, 997405153, 32439907, 272189184, 41686246, 561745792, 983499043, 125049438, 628596290, 742288799, 893440224, 288697651, 427301346, 620070091, 219119374, 173973515, 543343575, 157142492, 323920218, 718475191, 653256746, 383329075, 289911485, 108340173, 545331147, 735459637, 858804291, 195746740, 613658529, 713557097, 914703981, 721258840, 677524476, 933336826, 343847100, 965145489, 231645426, 24675923, 671847313, 773584444, 648422481, 922320500, 383560440, 361594855, 904915288, 159689156, 605353155, 566528505, 397676210, 759076027, 276858859, 261468660, 602357977, 272033001, 275021581, 4868131, 918972761, 445725561, 155554582, 780758446, 917500683, 975965890, 521988174, 989627314, 996167897, 74500861, 561731805, 966375453, 480313219, 177298077, 214945534, 343745032, 624176400, 512048050, 282471986, 789564670, 376088038, 623678585, 778077505, 683489947, 372297251, 75900245, 980471763, 13752636, 254223335, 133961906, 107501679, 533421618, 824514326, 768819347, 723542124, 534106328, 418278101, 377479775, 959318954, 111241923, 514212414, 756411633, 8471002, 662366605, 83693965, 490293728, 61107630, 26188381, 917203158, 718563549, 637853825, 869302361, 297977294, 122469350, 282385510, 495433995, 309054355, 543421812, 937267332, 481202393, 644264243, 499018748, 931765994, 660566806, 342395578, 946626594, 675010998, 165550467, 178762216, 522732133, 808610438, 936598619, 850158041, 2199264, 93483960, 763779035, 180766686, 568748762, 383493034, 762483633, 544708340, 577199984, 440284633, 26916178, 558008663, 864850007, 39935379, 276494686, 461243878, 485046110, 144773497, 99466953, 188005933, 419524189, 985096302, 638768209, 597544443, 476758172, 260082778, 709662701, 215361170, 812081773, 855112260, 965397739, 860917706, 847813697, 633880100, 423739810, 803569043, 69716995, 337515972, 168642549, 996322272, 161340813, 792623910, 282267865, 531937639, 237341499, 624272888, 160323174, 315741908, 125786804, 837736800, 598190238, 240447281, 713104825, 904752512, 722904506, 106781572, 971149528, 401295859, 584177796, 789733632, 716585465, 640178062, 814750083, 934226450, 714154573, 567902922, 699826298, 760765355, 616921920, 606223669, 118337541, 738332009, 413935188, 531688117, 348741067, 460829034, 763013421, 876872613, 866429115, 951342149, 808584379, 839607453, 323633784, 767040362, 367256805, 465050915, 706682870, 158354904, 792878299, 194592704, 921846523, 164513712, 303800455, 255335098, 793668411, 870002898, 307443729, 748814118, 908344204, 233810005, 512573852, 24486184, 769099584, 879900812, 316015780, 613573833, 475963706, 34840018, 321682417, 37233138, 101567526, 422748593, 454886842, 115044522, 791589314, 799782450, 821546648, 887424184, 684214836, 582818991, 786112493, 608417775, 792131496, 344841571, 451370844, 724621504, 704021932, 127188833, 916632607, 577154660, 715970696, 282657475, 585864010, 615994230, 799634217, 132402135, 708018290, 752403927, 449842840, 192057193, 393436569, 762359696, 699434122, 718202518, 635182659, 141857298, 219607966, 17187362, 277781249, 951010172, 80590112, 501710422, 445594713, 23061550, 750995479, 256083792, 510592680, 657951049, 631329864, 714527948, 396115268, 188405150, 361453587, 830309662, 441208279, 125539569, 642431455, 785162189, 364798876, 289365914, 537072188, 802178526, 847456215, 969957926, 428246567, 70082583, 15599748, 903729908, 26011587, 74355907, 47613940, 705306769, 245901813, 734817414, 824653122, 719283986, 811102404, 159221456, 488260158, 598240131, 609724617, 496338133, 543105880, 961973022, 658169048, 609246186, 704545391, 373280279, 531470006, 404499661, 615340678, 827893169, 247910016, 570973640, 888023526, 735570359, 916179286, 437005020, 394717002, 783210888, 499450432, 355574063, 911774120, 859524983, 529856281, 635809437, 636941488, 169663709, 183885408, 930297593, 769147534, 531767079, 843106101, 355313321, 862806072, 62152739, 479517434, 596106169, 464405959, 452869864, 686916857, 339969054, 686425264, 686146389, 664335559, 767145411, 274477767, 551676633, 293961639, 393886512, 434701690, 639453126, 615799067, 695765234, 857533741, 252764307, 278842937, 350077806, 98748710, 908546723, 233707012, 378552327, 476470667, 888992748, 192856930, 101911764, 107045223, 881727926, 884172039, 730361685, 668975655, 2221709, 637289983, 582764277, 713771456, 17746500, 500943931, 46764628, 303828498, 619721434, 928530829, 885465192, 830802926, 728046267, 769224958, 670414408, 117402817, 153079229, 484097433, 987913267, 783224661, 725704317, 931751452, 810826836, 17727812, 916834458, 46860968, 920366548, 652100684, 130138817, 496086537, 578330769, 510131902, 787527172, 651934956, 661907605, 58378019, 252367987, 96150185, 750409466, 135311248, 654167423, 397812827, 492621929, 812206741, 620439127, 688580523, 408466366, 923985871, 593809819, 463317643, 567645436, 241330610, 511246570, 835181989, 296621580, 913928968, 226018530, 185285252, 758014911, 141002071, 146683333, 673597650, 978927209, 5300783, 799675940, 194801841, 882190856, 104455, 290871931, 648374604, 196289662, 70799829, 774484063, 615311960, 549317195, 232065471, 344356098, 436664942, 526868518, 6325086, 975088319, 69505596, 9974871, 792356346, 501571900, 387649456, 230812441, 131734919, 356882312, 892986663, 47355074, 120859973, 490075392, 221886630, 766502543, 185690737, 196247792, 725667940, 921929701, 609399556, 619921482, 68757390, 203811024, 974566597, 185171914, 882765847, 74042223, 28707286, 663135939, 863017862, 669999327, 234404494, 628300355, 910538985, 676764905, 588156875, 118270185, 886547640, 358686181, 461729362, 193854283, 684899141, 117005151, 148274864, 828917985, 601876620, 273772950, 474953152, 364191040, 580883505, 735027571, 993246232, 104291109, 812529555, 42297819, 284721105, 402216259, 901038983, 611002301, 98904041, 112962960, 547251346, 575912570, 450385365, 385729309, 665329496, 801415465, 88856136, 658727862, 672270116, 524402668, 47900235, 341103581, 313147835, 892516626, 528416790, 955587689, 849210726, 84310128, 340552893, 478973679, 910852605, 460224425, 43760926, 501388491, 922288791, 909678394, 104276387, 504275628, 44140256, 91426113, 789127435, 448665520, 507033650, 109522763, 536727100, 67337374, 498601754, 591547761, 165604396, 651896927, 297352475, 189935142, 890921077, 164962149, 445923667, 73356504, 868833623, 413860407, 707793718, 794902042, 757225915, 577672108, 464715690, 96251400, 148660401, 827928343, 625659081, 791446805, 963125716, 224549519, 609258906, 327177242, 163303742, 876673556, 523289141, 455641877, 811089070, 659196747, 295071707, 696716050, 780308629, 273573895, 355581221, 483089164, 723077582, 742163560, 382851854, 273654289, 156577205, 739445294, 708079950, 134796046, 993239119, 586326423, 629298563, 268324344, 216454691, 480341849, 816101544, 493581598, 221567184, 163988494, 599626464, 59103028, 154156103, 756764435, 808157551, 339811826, 664382216, 249831850, 765547219, 434900765, 670951898, 24078741, 75610598, 493828986, 725241941, 607691299, 593432562, 76601831, 560304835, 227158213, 547561785, 667259738, 79306227, 302654281, 959923189, 467730015, 732339879, 936072281, 843086033, 797283996, 620205123, 519389771, 787843105, 487359480, 586591603, 962804977, 768296858, 878420482, 887359628, 78100259, 904384638, 133320716, 51278660, 409959309, 480293132, 166415331, 220093008, 735236293, 521844929, 597264370, 389684132, 448368459, 810720923, 580082469, 734782688, 48449746, 212903844, 806773749, 732721014, 325755346, 709796030, 938150033, 593746002, 39720899, 848098621, 825533337, 466378152, 13588592, 479769822, 892596703, 869167644, 111886935, 161447765, 545705073, 59157563, 9351244, 419917663, 815886376, 734347378, 209324277, 549416057, 573836274, 677927101, 865915967, 56784250, 720970466, 636922393, 756039627, 325652279, 707679234, 757527903, 268116969, 260921819, 895993936, 285592544, 615457847, 401149397, 815558205, 99842044, 496345919, 481552767, 977789685, 558229735, 185566097, 661910252, 422213362, 373165354, 307585710, 375730470, 668950506, 31374241, 485244351, 522730378, 270332785, 255693783, 797578824, 758344014, 629095184, 176979944, 864500118, 250655254, 296207400, 741182666, 268992046, 500699321, 653565224, 887223300, 398036837, 550959980, 287557233, 976866287, 989588793, 82936963, 648425571, 533183789, 638205399, 751031464, 658951654, 627612781, 247323884, 50196306, 468626015, 143897820, 464220763, 826395650, 549488712, 240891919, 405900564, 522008917, 821332298, 411390149, 828827159, 840574398, 515709811, 325491107, 389933871, 106495789, 841630465, 213653111, 600324532, 541513736, 329597272, 595408808, 101038223, 939729981, 316360526, 647596889, 21669362, 497326296, 427840716, 613289786, 215346870, 139360672, 725555567, 433973238, 581568034, 37040420, 869005549, 871483930, 702059292, 740014152, 42232986, 422664402, 930541982, 482167579, 725494464, 97539039, 680869566, 166421336, 107854427, 865846060, 426556441, 163330530, 991804341, 362116235, 716465380, 980938574, 239414518, 614800824, 208194329, 88619480, 217280084, 150818012, 466050957, 222872050, 731675731, 93702113, 351777636, 97578692, 903010715, 830925340, 644256325, 816655939, 943510814, 75000366, 59147139, 351700686, 840772500, 186504809, 343223748, 310460086, 599148603, 36882837, 623657321, 371870784, 557100364, 587204274, 595496573, 419776997, 277866530, 460449185, 705233822, 75543171, 223351727, 394927565, 346713869, 617941124, 149268470, 158704231, 311625432, 667079955, 154391752, 132331931, 230864616, 813453549, 973543157, 851110718, 933772366, 515402197, 393772398, 532395892, 695958110, 283184954, 584284979, 124529670, 483606100, 409748286, 443388090, 980107811, 212937605, 682053494, 491367311, 152720374, 353847376, 67719686, 225937127, 234283583, 593686495, 895624295, 816954979, 967888769, 969613889, 207147205, 894841310, 341966371, 706866451, 617233765, 974141685, 656451005, 570378749, 157193130, 861131262, 120479512, 14262441, 771350438, 327646054, 207804423, 406166640, 173636810, 299747455, 517903667, 729916635, 582768248, 948701521, 266043578, 320471798, 560691998, 759992530, 701334205, 895278685, 486128432, 980659126, 519322403, 884625885, 687877882, 297008647, 5787806, 541545117, 490566045, 779997428, 978786874, 246160174, 249142823, 771473078, 710012248, 965404211, 409173033, 113021127, 996099355, 550036626, 540364884, 152842814, 232677906, 465898177, 103002336, 240346002, 587084001, 153117186, 477073069, 188351613, 310705626, 144690161, 301661002, 459395627, 999535088, 207072835, 664431105, 825547541, 633062138, 241070820, 39339025, 113011271, 871968553, 816833467, 116227341, 704119731, 60942986, 394992273, 766244919, 862811042, 606850904, 361522370, 902954668, 345398490, 3364985, 109412448, 396515329, 776197010, 953718711, 658466283, 439204981, 372191226, 907981007, 192927666, 173260190, 500839769, 733052607, 70164274, 457785095, 979806101, 82518805, 244327258, 619190408, 99664171, 249887315, 383445359, 713990918, 960973616, 959866066, 12605442, 922339099, 575808614, 946165020, 760099937, 287428069, 981908535, 985363939, 771319354, 841587446, 950663263, 946795615, 383439809, 761266091, 601637068, 873297306, 42142162, 717042557, 69614781, 20448457, 943446942, 130046270, 122751374, 166407335, 890459229, 146390010, 407724664, 810284730, 698589399, 3001461, 813750593, 776885472, 299992195, 498126270, 600647851, 765231452, 685000878, 796627389, 817765968, 707216094, 114348215, 490454265, 361812709, 387169628, 739174801, 913539308, 587529576, 808078040, 121014756, 760878343, 503184489, 590391122, 328393349, 750137446, 456595420, 336254599, 456930260, 992712815, 471229500, 741254413, 377267057, 787664051, 104946587, 34891827, 427074529, 920461777, 918708506, 497686258, 495735997, 13437644, 740924082, 33601976, 333659603, 141584036, 852709507, 294651929, 258764124, 808934832, 889903727, 425692366, 234501010, 564747846, 272858871, 35439843, 339110895, 161843480, 480122441, 348730068, 923773386, 699737552, 883528926, 775154595, 445747337, 960789878, 914548165, 610821578, 817262971, 182941140, 685546993, 353769111, 326438128, 397065422, 787269517, 5906729, 774645941, 116277296, 724165079, 681645056, 66696386, 937321406, 467699118, 208882810, 830542588, 114750330, 47834821, 599455795, 855006024, 304780435, 380806252, 477042748, 429451899, 928116384, 192550224, 665397727, 613760371, 698527999, 717272296, 76457189, 755765641, 533130598, 647374473, 86833027, 589206940, 985341793, 792673564, 715809587, 208195140, 306955876, 423383905, 803527008, 886736607, 74976234, 937517315, 745563323, 539278675, 10628397, 977650903, 134517721, 756267272, 920369263, 418797179, 951301725, 747916522, 700071087, 517132713, 806107820, 497715624, 128150053, 924875270, 26987470, 678539739, 177044574, 749030832, 760280386, 848441638, 392717426, 369067663, 196446825, 505848268, 817965899, 565764246, 493607908, 156677129, 934079125, 411246054, 78709656, 666975702, 758731487, 747541968, 124739083, 589356270, 83494944, 309816019, 801795238, 581865966, 965551486, 872368950, 404337539, 772780104, 615400720, 32006852, 13994500, 486308685, 870023616, 678006185, 394236754, 814517773, 132980006, 182776725, 892281184, 363444158, 402153793, 668596669, 691209647, 47168896, 536151748, 794589120, 75008258, 819233288, 311411689, 263980234, 7946307, 504200913, 746378841, 908057877, 603468711, 704683871, 163177755, 374438570, 158627296, 528751805, 465146842, 956756980, 205124977, 989082353, 519864699, 306286899, 92755321, 359432123, 356360122, 832667964, 879505429, 493177600, 298170554, 457507575, 286295166, 504138202, 928476336, 387838045, 87819360, 687515151, 965772658, 35987773, 872366312, 411988733, 499458570, 489674568, 244806195, 568108761, 751731602, 851416599, 528023163, 566878138, 869999666, 19232006, 505952034, 683124473, 529516210, 601655116, 399911990, 109812398, 287030126, 10369573, 755716796, 529925617, 770560956, 204089300, 742901873, 699195713, 742657329, 929184161, 410356627, 888565024, 615559659, 685055464, 429796472, 584920044, 83347649, 23211806, 317741273, 985543200, 84054231, 617744198, 541605814, 380476500, 337998928, 279741937, 175424946, 817199955, 674345643, 223168829, 685283175, 879364733, 964990988, 616027039, 128043615, 892258573, 522167950, 466646216, 214684537, 664983164, 984647211, 71870904, 80646860, 755339629, 572356651, 145946378, 411444221, 44307684, 830689552, 190839502, 969651885, 624295979, 237855838, 563074015, 606298423, 638753933, 144686042, 167114610, 526805672, 527701441, 861448162, 569953570, 291412568, 28028062, 527812371, 575341758, 672528013, 220839626, 907998799, 171847889, 764486244, 209066040, 502266027, 149720685, 539564138, 662393455, 538879411, 356580569, 363852153, 640370850, 623931572, 254143339, 474402591, 742243947, 82294876, 819204778, 2520353, 74129613, 338344843, 998777937, 537627762, 357211248, 558194610, 11831715, 501544296, 253757297, 237202290, 442382681, 177785504, 421044066, 509398845, 121396907, 981197818, 28284350, 690219165, 193323974, 621679045, 536334983, 852487857, 84033069, 989808485, 948445845, 244596263, 289665639, 193636180, 996080917, 221494075, 537902499, 235858733, 685301600, 60720774, 141838254, 708656923, 12199738, 819917827, 366872377, 226044774, 828634273, 49207241, 899448493, 461610794, 107029382, 589323617, 200947576, 829409239, 165676441, 885848021, 299406060, 127381367, 807538720, 777829967, 13746440, 981331007, 164257741, 124555411, 873466462, 369746099, 132174228, 84372261, 111893509, 347110606, 986990105, 142413081, 64229060, 347077620, 999302548, 535329702, 450154900, 346707420, 511994212, 70110038, 652449133, 855274342, 473165569, 212856043, 253423401, 21815609, 423162979, 520386495, 948151177, 140947104, 545195203, 203958627, 474790901, 79583273, 910165074, 352940174, 423189510, 289169938, 646824305, 411364254, 396137824, 979080212, 953673280, 93058649, 681988410, 650058402, 407671608, 350893822, 363499656, 210859617, 736818874, 50968819, 157958217, 246681233, 394067700, 279072738, 383302112, 223987484, 217128616, 928177208, 290213206, 431197025, 367117008, 802777492, 101698812, 662224349, 600613252, 95027467, 408463288, 115016376, 230752834, 394749022, 30953905, 181059078, 978139170, 59703104, 444544874, 945398801, 724153431, 983898092, 289108006, 163804419, 756838010, 799030294, 183705263, 413293767, 106360850, 893424510, 376909536, 857112226, 731211588, 965441646, 627798604, 526357520, 800533370, 408704459, 933856405, 353942342, 239140504, 49998417, 681932671, 596301227, 894264592, 722764106, 564588935, 958358383, 638794378, 361621544, 98060873, 66105415, 866384585, 847894548, 894407625, 623553790, 533802035, 844805122, 253044376, 410093729, 509577577, 628524412, 103208257, 359671231, 25177540, 951628438, 28802012, 618230258, 313617891, 945922617, 308218772, 653647460, 416201064, 817428611, 433263385, 53443280, 720766394, 657516673, 136104222, 393443086, 94172554, 468436233, 713655543, 896734506, 544767457, 401724230, 447306580, 356928081, 985061974, 948114633, 507846693, 97802520, 951461811, 35218959, 747011328, 305485386, 730196658, 83825632, 81031032, 607621303, 228565049, 603147148, 461614686, 701921186, 65145681, 128382151, 117803455, 512188172, 460035481, 775244493, 370520133, 595067597, 484498897, 939220455, 690711352, 685911208, 39975751, 179271063, 657744707, 425064994, 242835493, 21130299, 121853970, 987374051, 361769858, 580813742, 884283657, 927670688, 158098495, 921504456, 345389394, 977933193, 899224007, 274477804, 935817915, 20829029, 635915290, 821228784, 204946253, 784955946, 965358206, 569993127, 401439774, 299172653, 682409447, 548463808, 604636861, 252140475, 472715310, 961805992, 728048092, 778626077, 853377418, 546298323, 302600886, 557022942, 616835441, 878344722, 317181600, 841533477, 417517300, 930076806, 328553226, 123410787, 195475535, 815838305, 458475443, 400667752, 988600524, 308636424, 451575442, 956959167, 754666511, 133268509, 581433611, 106828650, 538013158, 347990742, 637277015, 191261974, 538205961, 296068460, 274496006, 959349716, 721707697, 366619450, 371118135, 373832703, 612302848, 227926067, 465339810, 857897544, 482701431, 341245247, 692845825, 865590228, 946445613, 507933419, 183355857, 612575464, 719820430, 23829530, 280183505, 431856877, 286003998, 292575406, 626976458, 208601822, 391404307, 458756690, 152031142, 755812414, 481351097, 61526590, 641200625, 497756969, 915618752, 623536882, 368674123, 874736073, 595405094, 545266920, 427313788, 824094714, 959622469, 351080501, 744172611, 560316020, 493104315, 515947480, 965680049, 985723459, 815671301, 606393491, 802983311, 331626818, 279005250, 634528792, 353428508, 709502529, 80148266, 156308923, 64839612, 385702018, 24964677, 968861583, 776993629, 538302884, 739009046, 14550347, 492028991, 928764342, 344421526, 118400162, 134126220, 902393018, 806565958, 906736570, 506197214, 577337708, 740318504, 25072214, 61219118, 646836316, 755943640, 286332721, 747965075, 867749321, 967948150, 432152434, 997368490, 100959869, 802701814, 810479943, 674161561, 266965983, 436710231, 642915893, 6939884, 609006570, 295286195, 33040640, 674402578, 468346004, 129883953, 548756042, 946610832, 629175522, 415633304, 706956417, 183341729, 22380346, 465027468, 600039712, 634531629, 715497107, 621400132, 899911492, 455679007, 676356918, 477655839, 437138784, 283267094, 342455867, 669290997, 167994188, 299004230, 62270097, 555728223, 131297174, 669006459, 863020941, 555368743, 857172547, 219078712, 811412794, 210384748, 723400939, 673860038, 987591152, 947265294, 895587159, 798291696, 260726724, 967675704, 490950789, 229318298, 207350139, 346892271, 563563789, 620809430, 198838663, 406235190, 260078872, 285268165, 771453600, 96309792, 214201631, 855725260, 694803616, 786056404, 414469323, 382802752, 762989218, 639100688, 549294831, 344999539, 498813788, 237899984, 963601733, 402313917, 947665934, 137549314, 506303233, 536568715, 522717114, 169092773, 115170384, 8488652, 404302295, 792594958, 673549136, 52642834, 793162462, 818861260, 723631991, 357037512, 166722403, 790820292, 573117205, 180837151, 357314401, 888070047, 951455856, 58232474, 509200437, 720105042, 735473001, 78073210, 197467954, 665176058, 774127207, 938769549, 3680237, 382954718, 170957313, 183103453, 278487830, 154696963, 708788039, 875327300, 576967341, 150002645, 191555998, 524949740, 605592441, 152495669, 827560174, 890513218, 302251514, 828221192, 256677411, 852748950, 512422815, 847385947, 158444737, 278746114, 571845818, 477801461, 858322981, 244465502, 108586313, 133685896, 225074411, 696793517, 918621025, 719872018, 296438435, 909341194, 765827514, 285469686, 190677582, 116132446, 399526242, 47270770, 861261743, 481742014, 938524919, 854266047, 905091622, 169992913, 281422039, 765932046, 895657357, 489544333, 919190252, 212008239, 430005443, 610334924, 418539134, 220418519, 146721742, 295113936, 120725449, 58660548, 621509158, 727343469, 133086045, 956371527, 484807669, 535174914, 866492158, 775129483, 724961088, 892822456, 192268447, 682107625, 893651413, 91650835, 567180422, 567606773, 615636490, 329665104, 431605872, 852289010, 34414839, 582997976, 160415674, 825090508, 943337195, 276031458, 638009977, 394995196, 9265002, 27111033, 875820470, 887140988, 363766194, 146105881, 321790308, 864021066, 76542803, 904082545, 401605017, 779805870, 895634084, 284905359, 67269279, 950592910, 518765596, 362591506, 382641600, 147936804, 80945986, 729570742, 525796159, 878380392, 281995353, 969668754, 733500533, 74871243, 739579074, 299158674, 388621084, 18995920, 210070482, 498745584, 931243080, 939260867, 168739914, 442530032, 794060078, 960535197, 412910200, 651084687, 771119002, 299539069, 987788324, 603200880, 680577913, 554362248, 929131457, 30645281, 867844106, 993276216, 28322262, 778998220, 899837416, 850693549, 424947950, 766106861, 153612552, 674998548, 945872945, 807725732, 906195879, 431956961, 818318931, 936824299, 844476481, 835440556, 459082950, 210933057, 265450275, 451295728, 808450722, 725670795, 591330442, 845684507, 49611711, 336758468, 248185552, 432298457, 98111039, 353569472, 655935928, 485835514, 426541122, 742923886, 263059877, 168618597, 226083344, 196012786, 451631254, 277749491, 178164666, 913585038, 790162161, 258655799, 587333463, 386755137, 504522670, 751331614, 700021583, 902093962, 61779949, 225469168, 399830179, 888916638, 860294612, 641727198, 358219450, 460127397, 677554417, 750752286, 856626754, 245101729, 302700375, 756365129, 314893705, 898009577, 177891542, 424731992, 906055913, 418043947, 270087352, 523311525, 895495838, 749625143, 637048708, 179995605, 131885539, 109302968, 101770808, 390040691, 233601068, 244758643, 323928077, 711605031, 362863245, 152786087, 394997549, 431464698, 458783706, 337537046, 162443531, 806037612, 610119455, 397419571, 663548436, 250164044, 883991083, 366420533, 112239125, 843365761, 588773143, 588852211, 895611744, 607038710, 150244969, 492672050, 331158846, 565051517, 413803552, 31874531, 562088616, 383262010, 739297635, 701552208, 251443370, 869798962, 34044834, 226791619, 187453314, 798330766, 573878359, 63598405, 114127789, 837748591, 223273662, 870295840, 729235475, 827889506, 979775908, 295366413, 270310287, 223357617, 955649037, 340329085, 336224997, 525925508, 350340588, 236252300, 889938408, 681436231, 968319831, 257489519, 605738303, 950032748, 979730338, 691081246, 659597998, 190621288, 774727283, 551495719, 714830157, 500062670, 211390361, 694502183, 519333691, 829093614, 435573989, 349863789, 404563603, 924473461, 807566617, 500181786, 662533022, 235595876, 751075049, 952259077, 883320241, 724151476, 193456225, 110150864, 294158505, 363813125, 177586263, 20372967, 267594477, 622215256, 67817319, 94097521, 839442700, 130844921, 724800117, 571195377, 240776783, 844639095, 109502070, 454969513, 700635259, 545515137, 636501970, 79000904, 482879085, 934524908, 262968255, 510211932, 987453033, 151820544, 616562022, 668265004, 257180504, 368875571, 369966739, 256240808, 450443766, 640649295, 402803063, 185309172, 69336324, 120004207, 970772247, 895817276, 446145342, 159658030, 707688583, 966009769, 864259914, 844754110, 143785088, 781558476, 453511538, 625816378, 958621336, 454846396, 160216873, 349520935, 49638090, 26610678, 663476759, 974768846, 368780985, 137288195, 413146017, 370667113, 341558801, 283755575, 73293689, 427217833, 464416493, 281950497, 534687495, 428630279, 485926438, 641528316, 916046597, 616509013, 24382639, 44938623, 110882098, 804246005, 596670052, 52556658, 970759801, 379124173, 396293704, 572737118, 557835639, 372400514, 334756623, 899076221, 458345559, 987981384, 302876138, 452453890, 234490351, 709495613, 865761990, 22310385, 411578543, 460265822, 259061096, 617727173, 734215872, 226173652, 899420225, 55743014, 622565876, 695562908, 770221255, 675261438, 775411729, 425807293, 113351723, 207271416, 999406161, 563941938, 805064715, 857240594, 518993854, 822911986, 222612942, 608631068, 919641998, 865384443, 142360242, 504920307, 504663432, 734162021, 530756704, 316815848, 265055395, 421980839, 903119108, 994029584, 705533022, 70598858, 448560124, 86741721, 766360216, 871719886, 688485660, 852572606, 359603335, 829397734, 385432538, 46862260, 955392129, 264618817, 724139112, 452556747, 546577564, 156246102, 831764247, 493463459, 165788519, 495040661, 407189861, 703883289, 78262051, 436344614, 879732788, 408157429, 377139909, 636623900, 843068227, 745327688, 390055874, 855403555, 250079134, 919276137, 879501849, 925975379, 529152297, 159299292, 344386839, 674529241, 370104758, 728918943, 296525705, 972332853, 388094693, 418447298, 877191634, 241071900, 500236369, 830310223, 265442993, 387908129, 646079207, 203722809, 625957862, 804827895, 649600588, 683316070, 371565998, 328865201, 367538330, 325940667, 344136996, 800582276, 804307942, 328320138, 134417652, 71298142, 313858852, 762311569, 767209430, 742857979, 993455029, 598784430, 229312053, 359945015, 716024718, 766787308, 827015442, 87390129, 730632068, 872353734, 629922466, 515413344, 805401747, 61525985, 893933402, 719378256, 392143990, 557994517, 165638367, 597267352, 708833182, 99771334, 631568541, 356170939, 625544924, 6536721, 800427634, 621747860, 195552466, 896831707, 661058161, 238522677, 778633365, 624155636, 337267801, 594548133, 254815531, 465945803, 522780419, 443247957, 370909610, 424406749, 920625990, 888656884, 579880184, 185780233, 158230225, 999980332, 500894546, 221453492, 370320218, 603721371, 951092188, 705197820, 644582315, 427818947, 679640977, 228544484, 8651583, 655196725, 272125087, 282236298, 171023680, 878118608, 841764039, 105525594, 141746861, 438624374, 829623549, 701321255, 24843841, 581758225, 710690580, 598995616, 243982769, 922399347, 655232490, 475249475, 424711999, 465186711, 945929660, 828119024, 856026220, 148233564, 956365239, 594878113, 468570826, 824500157, 836516990, 566136119, 916558038, 745870885, 13467029, 228959300, 227551587, 155356194, 550662574, 444443618, 714745224, 977087663, 498169770, 87925740, 951018565, 172005749, 377444909, 790702987, 767197838, 675097199, 614645914, 378344988, 267565364, 250882745, 70297752, 831078087, 121375578, 843650748, 655679662, 294416480, 308603657, 546430018, 906878149, 495630365, 494831026, 101873005, 892886354, 769086485, 140616409, 344903109, 461336427, 820794822, 554279546, 902273043, 229590993, 519221983, 673599988, 898963498, 462658615, 55617300, 579836664, 749243456, 10984998, 415339191, 72209139, 305954952, 268767206, 326654700, 165572585, 38223727, 632938574, 353962220, 640176270, 28095780, 215809843, 971775948, 814688592, 616319616, 803548540, 222038033, 390082896, 317228536, 751227585, 471065714, 209875837, 125911527, 291757543, 90881543, 600065877, 54157939, 548940776, 241994993, 213822994, 485582101, 885997795, 44511598, 219649228, 832643231, 145488441, 388745171, 925121653, 278307391, 600565658, 18352775, 416485741, 445837525, 721129768, 719113710, 677728787, 483405156, 137523557, 947765896, 423803196, 174115384, 378708609, 889465126, 733774524, 835778473, 882097103, 969859634, 684639910, 179258842, 49298539, 191396582, 760025464, 46154696, 895598934, 862985670, 135382953, 13622660, 66313119, 77752247, 560108461, 465884292, 287428626, 956488188, 512092007, 892294413, 927230527, 2515332, 165241136, 969792191, 710882774, 916874681, 539514855, 703720004, 156100731, 841029402, 140756974, 886408810, 778256015, 421404985, 373777262, 241963205, 233601304, 617133648, 92553124, 159974143, 284101252, 541593089, 148141685, 552235002, 500190795, 46278139, 413526388, 915958530, 775691725, 898901516, 309598081, 724644037, 680036458, 866938526, 501844834, 943205679, 239932153, 528800012, 473363138, 631310745, 995915968, 801796356, 679619522, 864539903, 228917683, 343894865, 203265359, 128128050, 339290059, 555414285, 589997055, 931738266, 653119138, 188391530, 382401453, 318667009, 643991532, 355176778, 40226114, 697733245, 36064948, 659463721, 423576436, 829569256, 198452211, 742820418, 201890100, 108857030, 684602397, 802900398, 151329259, 876255524, 32327602, 56268335, 167735968, 995990214, 885872473, 37146629, 778284798, 815319059, 93956709, 331958253, 430869243, 207206745, 541751636, 354263335, 757531612, 716395237, 418528429, 480619875, 738328956, 602743922, 392126588, 350819263, 906194811, 290266125, 52552123, 219229497, 253923375, 448171983, 815471091, 695273723, 355249602, 769990664, 390933448, 225331461, 21359645, 209211249, 797223085, 522148577, 550422535, 744942926, 483861587, 150074428, 513198632, 735832069, 425950212, 467593285, 804974742, 529063309, 848730683, 272207160, 149715680, 722636603, 630899001, 620722618, 123422588, 71375872, 607897066, 252777832, 362480197, 390187342, 696479902, 509129532, 97047049, 653173430, 261212081, 975269520, 708895253, 56286555, 646109404, 40657017, 607652802, 20851932, 920046530, 347953384, 971156514, 276057139, 600931893, 114173227, 133038115, 646566507, 145361970, 835123517, 403515974, 701808541, 57877131, 323082428, 384119389, 610554018, 832394778, 717899541, 453864827, 830065795, 665453716, 194213885, 353683447, 631520589, 606345616, 395981742, 883001062, 163591117, 717306531, 225873753, 315225938, 174277815, 817494217, 49685037, 909111912, 93234924, 557775214, 477925285, 317548854, 723929105, 824685436, 226361458, 440043699, 54697765, 996131393, 17519851, 470294700, 203044827, 934538939, 462129091, 685882269, 618361592, 643717350, 270717340, 198871609, 108721033, 409457485, 20892343, 743001479, 467198377, 858434115, 17394799, 212258187, 778657594, 385762519, 551154782, 14450761, 351088018, 939325542, 942150521, 866186384, 463678382, 650378784, 538623156, 859802407, 921290018, 509442766, 498325034, 827897579, 5202198, 659638656, 52468513, 65919323, 543387940, 256320988, 327895801, 649261265, 131762231, 288471683, 157413902, 718601182, 112814157, 111787236, 920976559, 495406594, 819327506, 202609712, 334917025, 205254295, 652789972, 195770370, 554767745, 181920667, 533965715, 178510841, 997969720, 779401677, 253936017, 303650980, 353723224, 155288978, 904870662, 924990408, 956316561, 428409147, 782449692, 126125180, 706212943, 280693722, 274804160, 600890579, 356949416, 854755112, 897513544, 167075458, 319094154, 402599813, 80719956, 103632662, 658548668, 631313144, 519538908, 837384294, 445092389, 930371709, 512631884, 455568332, 125434891, 190902688, 46235859, 186472225, 11398243, 216848458, 203950367, 307925136, 975472759, 636455063, 378117133, 621839505, 271640898, 879323041, 925542150, 231285601, 401295640, 797449674, 998341505, 255640713, 228109622, 624415428, 809534721, 818703585, 478181617, 819352377, 69444434, 123184452, 506542367, 634563293, 154169035, 109930659, 783384079, 467447954, 468287189, 835303215, 399304299, 744766389, 124073278, 841343257, 839262953, 821416047, 591158153, 782189360, 435001385, 781577184, 472474668, 54941895, 778397048, 294104666, 625748813, 66703759, 851167885, 44536626, 198232687, 717092999, 6335136, 914468392, 60246288, 521096228, 347966058, 90487679, 455683992, 661493696, 704531758, 240155661, 517017407, 963465470, 79502965, 59219101, 451396375, 420314224, 488625833, 419638471, 732039853, 539813029, 928893530, 539116184, 76396731, 131238684, 687285969, 522344136, 249098889, 895310150, 742009980, 255915736, 252445387, 979321073, 28248696, 512636951, 996363761, 812686872, 793557943, 781807300, 291677968, 783966306, 608904447, 821015330, 44268709, 445443216, 378293009, 548204332, 351762505, 618488470, 258201706, 944872466, 183750042, 711642533, 335783088, 798127620, 215811300, 857321909, 627932895, 387069943, 941342295, 861503689, 900170306, 583038606, 331900497, 507988992, 626104426, 352698547, 663394147, 813361356, 803345745, 808662721, 988940259, 679566026, 924640405, 657929959, 955237337, 985802140, 99213262, 269877677, 135603132, 169361348, 200232197, 487937567, 411639482, 963400533, 427389999, 112454205, 743298178, 972285933, 767322815, 865954810, 388276602, 817723021, 873016834, 465269761, 329748425, 924058633, 413842337, 941898663, 14314370, 781994861, 389679343, 525982397, 929989611, 500544708, 443445082, 382296900, 474935095, 412058208, 953674533, 763030164, 952209924, 302221309, 63066862, 872511130, 133432017, 644897192, 315466747, 313413174, 194411162, 573472873, 511996888, 171572858, 684248923, 61162681, 69699912, 874663618, 17900541, 545908144, 601219999, 662755305, 784878583, 640171995, 300012123, 690725948, 788058657, 422137562, 991553646, 49938302, 113580746, 753718649, 935655609, 757443818, 866291364, 872704939, 863074736, 860559195, 614032313, 52292337, 313717527, 771418157, 239012241, 487363015, 54909938, 703682398, 30648702, 576256845, 511913410, 207953396, 28878126, 444662511, 441044507, 111254168, 660683709, 793902803, 905034018, 665440826, 681362024, 921968071, 45400139, 925958138, 553077769, 828041271, 542828240, 751785509, 263095366, 92677883, 940232213, 100673368, 544951336, 93692789, 109262158, 244654822, 87804844, 388393521, 283298691, 985522878, 81262008, 708486607, 472312330, 256485410, 521177303, 892119559, 402657292, 874355598, 492256581, 974777448, 461729349, 92863071, 971751898, 532881340, 569707484, 639388929, 155155802, 264262670, 863759315, 125559554, 319958430, 169520025, 186830591, 892424348, 168632382, 555731651, 560772721, 28878509, 440813278, 919624151, 433778529, 522334761, 11972356, 115476152, 590076422, 47549618, 305010899, 468501405, 712123902, 245379298, 623985601, 211110601, 520668510, 666639226, 179089765, 96713041, 244395054, 226399245, 449298025, 802361347, 888789488, 207919156, 126493760, 645202128, 781624325, 667585600, 347945660, 48584293, 272213217, 714809422, 825830736, 878778016, 260348636, 629066253, 378318392, 29495087, 460740216, 471848351, 343142678, 167714050, 377212080, 860822835, 699796981, 605418525, 505838159, 76299072, 429291709, 364034120, 442116597, 612471758, 991078996, 348817129, 937821895, 85638924, 91031276, 983502902, 417391454, 721887451, 390592800, 846352488, 480485966, 972301212, 189823528, 121510212, 312787326, 949341396, 123256470, 335639188, 545264084, 259366786, 416247132, 962126807, 381865423, 957412058, 360285438, 518944170, 849475072, 119339918, 459648661, 497945384, 143788124, 650879072, 776754014, 203929, 984131529, 415568043, 11863246, 388638679, 817523997, 147451717, 971936428, 508348566, 588061825, 841335887, 532390123, 734737228, 489040159, 962259562, 780946249, 109459965, 88424685, 319336938, 62830825, 57419188, 606752936, 327514477, 659387309, 168686067, 309495675, 9132034, 290389417, 388961656, 542378663, 656670869, 194229574, 74407196, 639189667, 791173370, 95451129, 207374729, 175331048, 599575983, 757066245, 528922433, 71209813, 311159198, 836813714, 428954970, 194343556, 385629619, 464902565, 87446954, 851566614, 642239945, 681097058, 937417736, 776058061, 67637278, 80113396, 601842822, 267047511, 876724814, 197173602, 975847127, 711507820, 653013460, 529084629, 808759709, 374898707, 159967936, 342348088, 214069441, 437984815, 669266556, 402305480, 864335351, 205781750, 574166951, 280665485, 627799930, 434464689, 996187892, 366718232, 532013809, 665185776, 599160368, 951094235, 111946258, 538984479, 94126663, 133662316, 955501613, 680324298, 624217654, 974835468, 103471784, 148815796, 13271928, 748803307, 343278356, 617722521, 581817517, 610316822, 256077882, 253727440, 508001581, 516653543, 668554440, 110804622, 806997302, 779534986, 475635549, 399730180, 443649933, 514348257, 247336695, 9427485, 47033105, 917941842, 261738702, 682560257, 969625003, 266292198, 185902250, 899095937, 877623508, 566310112, 404745449, 535502918, 488801597, 254489400, 557021339, 878645617, 322394173, 821544674, 937823245, 550931902, 552396697, 463427610, 630539078, 890543365, 512953364, 44447391, 9514532, 169440938, 356442961, 569150000, 794526607, 444229275, 830084716, 86852991, 332370666, 287395225, 867587476, 755788991, 669270476, 886951014, 505206690, 90028857, 179916932, 111487830, 497430463, 545661993, 294138327, 232764436, 942025537, 11206949, 766623542, 405980793, 644676224, 940963425, 151667985, 991208343, 316869070, 873763597, 387700420, 108024356, 255940511, 850587404, 567653653, 372377019, 595127507, 909465976, 365404594, 617425723, 410389044, 602541538, 575144181, 418384131, 349884033, 84085646, 171080479, 427430154, 305624917, 687134971, 641350375, 771166356, 913850154, 312176598, 895341981, 39900936, 722679737, 206863224, 168702121, 686064311, 533199185, 763649367, 247528002, 720175594, 930398621, 394799401, 930448023, 422472166, 688085485, 917287693, 993228487, 328968004, 119791157, 575193709, 226624198, 474519592, 851300690, 553037785, 943364361, 361194545, 630742455, 857756270, 93079695, 762033260, 977118482, 191178049, 317574226, 145675088, 620319256, 813978817, 695379329, 907999853, 674502488, 198109840, 577849329, 127266281, 770851555, 723278584, 800413245, 384831784, 862204016, 501210988, 412978865, 531547502, 387291983, 973825371, 489227860, 224359844, 292287227, 480575215, 738011080, 348921185, 88869733, 938262732, 540307125, 697498276, 688539902, 539641131, 855377804, 58399956, 887594006, 741618118, 156447708, 920558926, 286447086, 74717085, 700274967, 300712701, 515760591, 910370416, 255156374, 429290606, 174283933, 845965017, 119463366, 199073766, 669640620, 829270031, 918173536, 423499201, 687214953, 263994660, 956420305, 513292445, 641169008, 455873732, 241036405, 296092787, 424833760, 689576113, 475163299, 155657174, 691521022, 270872802, 631660094, 532157713, 630046524, 6294743, 430606204, 22853781, 328380787, 444870849, 918669084, 501243501, 40466109, 907614102, 667344061, 294094150, 477386307, 176681817, 600786300, 106968802, 150218562, 249489374, 403359406, 476316436, 72067959, 981549778, 866980037, 522893627, 987451007, 114946127, 778664431, 432189588, 195546236, 644666190, 33705043, 509948685, 243015693, 263706059, 993550065, 275047034, 539306375, 610615649, 136931670, 965803256, 177338032, 773418653, 500671449, 632700039, 573473472, 458098056, 263363506, 66370156, 573763919, 491534866, 620553479, 276045056, 243040551, 764833837, 352073247, 469291888, 470644424, 11325280, 663787492, 506271620, 523947006, 929106695, 837146834, 123949415, 244570209, 70145703, 954551335, 704600287, 478224777, 215536383, 120245704, 421352583, 461329998, 52746335, 644212196, 391928156, 127522897, 488591569, 795168190, 61938837, 840272775, 37528142, 512904978, 943070715, 214309825, 252892656, 584888607, 572287496, 483764245, 885042387, 678870501, 507456940, 997199162, 438407511, 164649482, 796722348, 682392229, 165770118, 970032728, 336515132, 383689250, 473397346, 956899532, 483559138, 569843536, 825098398, 22661004, 617765553, 656585933, 825794950, 601938742, 540032102, 215508207, 484571893, 297167197, 723164367, 316357900, 92815477, 145480728, 543869002, 683442902, 106716689, 406415229, 742811275, 261304582, 810081598, 963209689, 233831988, 400800291, 546654001, 467888571, 712223062, 489719300, 742696459, 333958019, 357928469, 352682318, 249558563, 46556932, 844917400, 629486183, 256091074, 547115053, 727426735, 192261089, 444054930, 642908727, 137216619, 968212580, 675662713, 343429889, 177203609, 325039106, 625126526, 762220790, 693308425, 910432849, 383891365, 799402262, 379069932, 616440068, 246452903, 173055767, 466682738, 898275310, 791126912, 896782266, 149652010, 329339620, 296512131, 453692541, 403490664, 809369909, 256426180, 55293969, 120827446, 24437829, 980834494, 124341122, 235669381, 136108427, 394207026, 132526761, 58454745, 94706022, 396617847, 12559018, 125205261, 786158682, 176408002, 49488676, 763402887, 725736148, 284718508, 849066145, 188126639, 558350177, 20863669, 439234172, 475420639, 707674365, 74986655, 573847796, 899187733, 373456350, 185431001, 409799245, 894582776, 827673156, 232801526, 942044123, 510960353, 515031773, 485235255, 382769720, 47063163, 865236367, 636706271, 422032540, 254115051, 688552993, 548332911, 610648391, 804389270, 590541474, 388631083, 784030805, 414160218, 762392987, 215231624, 695900475, 189145391, 819366165, 860393538, 947585976, 91989349, 177982259, 406962654, 517328775, 68185912, 380040467, 999133319, 446561691, 585349831, 213936137, 134935755, 791707243, 657558130, 393739078, 402497513, 334028754, 824370805, 670761451, 712718911, 482114339, 940442407, 4995836, 754845623, 316696753, 604275987, 545020735, 576402458, 442231139, 371730388, 79639276, 772331968, 690878967, 163346143, 105170076, 196736190, 953164942, 874524444, 767563785, 228561038, 411420130, 530145570, 820764645, 605040209, 154316260, 742314852, 193776168, 776011003, 476777967, 538446649, 596330366, 528950832, 375153692, 118992002, 530210438, 627385579, 604153633, 818954082, 781388546, 190816115, 440911433, 168973811, 962047708, 137737013, 999696755, 120890039, 439465797, 446824513, 880104568, 496896609, 580761072, 639751704, 849610327, 449631084, 806570931, 966311847, 507624602, 529703130, 649140247, 416194290, 300495415, 871556617, 236428696, 815055005, 648506392, 540570887, 127069885, 746721027, 947565850, 5857158, 700537137, 290026180, 298369337, 593237481, 782717445, 379426963, 753325096, 749636335, 170158079, 497759116, 672881385, 757885868, 4466502, 909811241, 800724264, 972166688, 868000524, 924299787, 763446304, 753331299, 898075445, 886275269, 307587798, 987369436, 408756540, 415027875, 307850499, 420213033, 946323607, 434017010, 234183651, 216606095, 634916315, 333104869, 964965254, 296209157, 436029179, 713959059, 75801033, 1273535, 525224922, 510575760, 856984782, 470644850, 354246214, 221840668, 987661145, 313270532, 245639985, 985130079, 487958285, 5773910, 860856227, 345183228, 654318729, 153734895, 480236824, 166106189, 91344011, 276646910, 697049374, 61176357, 71603297, 372912075, 605731115, 797675438, 563759754, 855896145, 549988314, 665614910, 965060778, 589450433, 814190612, 640707965, 454327646, 274606910, 646779481, 684983035, 723225364, 33871995, 101236729, 672254554, 132924673, 180836468, 53727330, 41443142, 756644582, 607067045, 546467969, 204224107, 673082262, 874904141, 174387322, 116465880, 993769094, 399734166, 744804579, 615195961, 581835792, 713212786, 27892295, 815957164, 470098636, 820476336, 68463395, 617300847, 671367815, 857725841, 733964534, 50479590, 713197153, 446669862, 244629872, 343627878, 918402698, 99235955, 217530490, 110156434, 307244075, 423138757, 762486323, 434890220, 689512780, 571637705, 660990103, 261652863, 361659612, 146800528, 859675546, 22695076, 680390839, 760222504, 921922863, 265026897, 353817277, 16374254, 322811025, 977867601, 160333921, 97898034, 369462892, 877700045, 788675774, 703889020, 600778114, 540205598, 944831966, 196410141, 840010888, 250347239, 878530282, 105858086, 7057011, 140453939, 12166011, 481651558, 114120649, 147141964, 140423549, 89928578, 413966293, 716989784, 460042062, 189133357, 243642627, 689612880, 244699992, 952730642, 484090333, 4754349, 154863992, 54276687, 58835099, 414247588, 284152528, 568135, 193535357, 425959124, 225199801, 464199197, 918149696, 946820058, 323831604, 981093654, 120856745, 179027436, 273965055, 259972242, 362774270, 194888089, 30107668, 820534241, 645757170, 66079343, 351886039, 875818489, 570368390, 829391461, 792637908, 576664322, 268144563, 704125171, 493571481, 787839274, 847094012, 175994088, 50021030, 533017728, 824139982, 585195002, 102724674, 790926848, 594601134, 523717774, 468946898, 187984388, 425942692, 134105768, 206622443, 364787997, 790377434, 181343735, 333637526, 964599333, 537468369, 530080001, 565543778, 456661991, 487266339, 588754312, 862756215, 40973867, 421003934, 178692051, 836531531, 940927985, 870841822, 37704256, 974182202, 903516511, 438105145, 515931672, 102106384, 910983749, 674494620, 387474051, 917569633, 161774830, 357764687, 631045637, 54061580, 441268019, 248396504, 102420121, 582020154, 389431019, 319099195, 115333091, 940075359, 981681655, 659864992, 632602495, 89300642, 268767987, 563842155, 268578576, 549582539, 383052152, 136215215, 851944631, 391912023, 900437569, 122217950, 687815068, 462465620, 714137955, 516963590, 521130083, 868215493, 996358037, 294968179, 690426283, 830179762, 317963764, 227005282, 917019411, 134746899, 380937219, 340323074, 935110689, 936859168, 756949799, 941998958, 807176184, 487292905, 765784848, 558792140, 427797890, 777654092, 237524460, 583454621, 548795640, 402184550, 274023206, 348632591, 696234531, 713232157, 470303292, 401630611, 38514747, 578286086, 717560588, 625714009, 98701417, 739163052, 326548140, 532428798, 723669226, 204934587, 903956987, 527045216, 380335089, 979509882, 357846460, 177894821, 650686188, 207934070, 214691642, 737062157, 783236802, 682363581, 60948933, 583004747, 131553293, 201829450, 67082417, 12003021, 104519186, 730764119, 773926429, 736854294, 219160891, 589482064, 282102876, 438003158, 207536535, 887312058, 318702056, 845224334, 947698361, 552821194, 897346584, 55766766, 98548647, 905604443, 650048640, 583251551, 521173554, 178394290, 325333936, 228879557, 761298389, 686909071, 411669304, 417501771, 5246475, 648069974, 967794677, 591432370, 125017708, 878342093, 225505174, 487572579, 181140279, 838662818, 761549005, 171016371, 471279881, 278773949, 590965204, 688885218, 737933939, 839693034, 24837354, 6513958, 26237575, 997503380, 644840836, 552324947, 35918031, 940788197, 36938670, 43714438, 197224579, 218752371, 545699949, 274357040, 920083350, 119426184, 4431501, 123538871, 626984560, 881113926, 369301616, 935724691, 178719861, 796787332, 115143961, 193918994, 533740604, 576235461, 693407617, 668908638, 279869577, 779618354, 964269013, 324349421, 694331895, 688368454, 25495386, 312089729, 974781098, 297588150, 128397303, 176876657, 82763630, 401453245, 174432376, 766252638, 29506891, 588549830, 350185309, 350305463, 292332088, 611987136, 335759602, 652048725, 12470225, 55939363, 646782990, 133024798, 880148495, 746542453, 80825777, 662155993, 507991013, 849560094, 306082353, 828268772, 619192389, 736479099, 441479125, 856784533, 200264689, 837520224, 389328730, 799118468, 727376171, 178317256, 338322466, 412481252, 276624845, 318245566, 372957214, 207744739, 704471880, 906112400, 3298081, 777434148, 495904341, 859622426, 775260077, 217854192, 552089338, 676661217, 82554080, 333167971, 749984064, 645557647, 391593664, 673905395, 696363946, 186537503, 688670822, 344710811, 395999042, 224374682, 688408109, 136595521, 203861854, 748709681, 405153021, 698386513, 802742687, 748265860, 670561067, 855759261, 675185969, 515093739, 677457843, 532012464, 514751937, 380646884, 647774675, 836623091, 435817449, 989616991, 355013415, 561720875, 946192136, 126566232, 789596191, 431067809, 985044609, 535365034, 876421667, 930889724, 736711158, 730606695, 653117330, 338175558, 437860048, 532592884, 677197113, 699980663, 942770849, 562426001, 269746494, 952929389, 801998156, 587469237, 166545236, 370744751, 689507563, 696002151, 834969378, 448884092, 17192481, 149636134, 22474269, 5239684, 626904078, 339828706, 254514218, 602261228, 118178751, 410553994, 212919190, 546695835, 443622569, 304496157, 990308364, 781457043, 620751953, 876223785, 957258696, 407383959, 439547484, 123018851, 215399155, 219130147, 28948544, 598932834, 113919780, 902053490, 607639061, 178503159, 101319978, 832352252, 493653333, 533657302, 844357154, 574213289, 354589466, 887904180, 374575620, 387442971, 961552682, 368731143, 895218987, 603514485, 616578146, 177009098, 592542777, 378947859, 339594312, 827478175, 490622346, 153246543, 190441373, 760611529, 309642188, 802267405, 745686481, 210282326, 537639965, 927739186, 858823083, 460294384, 22830755, 816651389, 612497045, 117543171, 589451481, 712895896, 132801094, 657688272, 562662182, 279467897, 131944486, 56497955, 317252713, 529382339, 215813294, 688411278, 586948106, 731916192, 431927438, 821287886, 921092388, 90944553, 206368498, 817817164, 616559831, 79896268, 135738921, 185035816, 534550099, 647753285, 782317931, 622637257, 817116397, 340716714, 561018756, 385667685, 705119438, 738845371, 233488997, 276658189, 378163585, 40277502, 383471555, 319928512, 777268780, 33251613, 902130974, 208018027, 460113039, 490433410, 449457494, 507734460, 727397482, 635865122, 749931453, 292168338, 94620549, 615855306, 807597721, 781120306, 645173949, 697002333, 361535693, 468844494, 509902171, 654190392, 872507, 44848103, 406173025, 136920853, 390183127, 189313159, 770179002, 932932385, 969282877, 679259496, 846223558, 967198990, 282428103, 513329215, 822332194, 825426119, 51487530, 235296922, 950681621, 14421021, 66374474, 224740019, 521368099, 457784369, 241012360, 884400706, 752081826, 992214110, 886130535, 715238706, 634389812, 33778937, 407964896, 739963869, 854900191, 748543265, 345036387, 161919012, 500270843, 512877832, 357282394, 563654588, 759530866, 266448287, 993384980, 395069198, 386927783, 158909064, 165002881, 587054413, 304987232, 983070120, 663201978, 283161356, 333683117, 903480377, 469457513, 322718136, 597749169, 109875345, 63682632, 849725861, 978339492, 89120799, 22194359, 912675179, 367642969, 392910141, 597658540, 563873199, 231077935, 289612770, 403090720, 956207020, 901012480, 136842219, 486830515, 111200305, 940072948, 645520056, 408027316, 257372283, 815359272, 998611693, 543773962, 559646065, 265184439, 36387331, 388951291, 163905612, 772511253, 742341165, 793336947, 165958912, 157285369, 759035838, 682122174, 762962057, 455268705, 146757186, 644743935, 346037888, 195062937, 794001404, 257377436, 997956028, 240372467, 207411219, 82533241, 169889864, 196408175, 969931791, 786386914, 676251029, 782561118, 715619931, 138273509, 938089372, 574693641, 975462087, 924967578, 577298773, 395815537, 260223804, 930478538, 551090782, 826402671, 243874798, 950804906, 960104816, 198175761, 849260422, 171866003, 574968826, 420024854, 995016192, 161494983, 950566930, 894054072, 215747748, 241622006, 666200183, 109486746, 17300114, 680219456, 185477279, 839609580, 967311950, 616149904, 660004893, 372307654, 351272777, 420513710, 15459239, 594902259, 713314100, 135301830, 113724553, 605357291, 809696843, 61261743, 990313708, 431668880, 620746384, 798526934, 881642327, 235418831, 522742257, 464007402, 925815376, 977708531, 52398527, 731465095, 623083227, 372657671, 362538099, 124755512, 341889021, 330059247, 106496116, 590248943, 368360497, 858936781, 113444460, 163723050, 855420878, 792126077, 577705772, 113126863, 428571148, 531241459, 24466701, 199359650, 946843436, 602300729, 436460455, 718422396, 131733423, 909935008, 319162645, 438816914, 804689829, 605276004, 602701260, 801788835, 385150834, 667765914, 299521558, 549426249, 884347356, 716079510, 481452000, 788388129, 687079302, 720934569, 315059203, 966765228, 698915713, 194838713, 458411113, 120941828, 131665352, 258041690, 295853635, 964712419, 290913812, 839735017, 320542231, 654742030, 448074827, 621941968, 101901972, 458171969, 202300886, 504877078, 846277537, 540105781, 601995265, 607796043, 292148172, 254555522, 537477046, 59094506, 416095374, 379970310, 43560837, 584192101, 530622959, 932239197, 58577484, 563760127, 497185823, 701261782, 841723731, 398183427, 113101095, 349268237, 193477997, 146677148, 129921292, 831229447, 344335204, 455281043, 759993671, 796947804, 972889638, 414467863, 148230250, 830499287, 78502687, 552897087, 924672353, 137822108, 108582933, 178947629, 643344942, 607477738, 445327926, 687774364, 864012071, 1776041, 472339155, 295832635, 45993972, 697159033, 857039543, 551930713, 585148819, 111323971, 982859592, 22736062, 35227277, 453586489, 35211570, 371715687, 705845724, 336900639, 688108006, 399710800, 446842458, 432312076, 700740148, 570996012, 86519957, 683486054, 992698373, 960908158, 565643468, 675006556, 601777921, 481845940, 237965291, 269378642, 372485941, 938060743, 611976244, 605750162, 733423485, 371571583, 527633644, 49665602, 673606505, 61874247, 478808646, 557758139, 151688064, 28126311, 844870671, 711788335, 782906106, 828987419, 359382416, 500304556, 366747097, 927055079, 63316232, 560996300, 659948228, 545978179, 344050651, 541212292, 793132400, 959266730, 809243606, 783470842, 326261577, 10671608, 413281131, 277825905, 399369152, 746927055, 240550159, 773951001, 466403546, 118829076, 281558671, 455866711, 626706668, 469092698, 358052491, 602287439, 47480208, 318700600, 944087095, 937725162, 768905914, 691144669, 701381634, 396977778, 704195650, 436363249, 55413275, 900388652, 453900068, 963168091, 858797415, 58264924, 536353215, 678954077, 62740151, 692059052, 914252117, 325083153, 191371762, 87504511, 906511376, 197044818, 634270935, 818059986, 878731819, 885446183, 95378813, 818142044, 126284377, 35827529, 402185310, 953913587, 713451083, 520847361, 847596235, 801908074, 511300733, 773509037, 170436938, 824156629, 935110162, 902329707, 532858770, 210939282, 231015677, 389765741, 366951045, 9277130, 33982568, 972323439, 714525224, 802887084, 270690086, 195661736, 974501628, 602676894, 810773563, 796990143, 184160087, 53629317, 114212536, 957111533, 362486255, 607121299, 666751328, 84527595, 736148535, 513286025, 78626521, 236212721, 653072260, 640935560, 293521642, 220770316, 361585513, 165293177, 92899871, 767797447, 99919459, 999293002, 599883617, 704645882, 562904565, 538474681, 272243596, 219150458, 844069543, 715961930, 500472380, 190126630, 564120574, 908739685, 844467938, 380999315, 304812327, 733637415, 738267305, 639827703, 737229527, 941412245, 922720387, 934814218, 334615247, 15918369, 799102094, 439370523, 675467561, 728166587, 378668085, 293016275, 233025731, 187642020, 415769617, 425947449, 209796673, 471090123, 116408757, 283614600, 238908380, 332266462, 116776199, 9280663, 546338283, 394980863, 892902323, 391367358, 674859077, 867393733, 523360110, 500832834, 573268530, 866459826, 537252124, 221239879, 246532780, 154783621, 200669067, 980292038, 907280977, 712803507, 670396368, 273437556, 905951877, 815019106, 793755455, 746533735, 965673350, 464964024, 205226008, 787846929, 196129965, 634488485, 835164510, 750755817, 510566329, 658704696, 362970623, 523211319, 635063523, 66945831, 317481004, 985185207, 96246545, 921557540, 800785727, 647378658, 59502565, 769889105, 534449625, 631094998, 362413357, 780186987, 538442190, 452839278, 281732647, 516131363, 109941544, 218205692, 176727775, 391864958, 840839122, 250407495, 443662000, 216720306, 848100356, 344441256, 739312001, 604399811, 327862618, 637125599, 245572226, 98470376, 611524532, 565505807, 9743742, 185945560, 805753659, 921270645, 874081868, 355139046, 25175768, 242129661, 645500965, 81045057, 229147632, 348445409, 799255993, 707988196, 588687427, 792006149, 108727511, 234836903, 608991990, 191123004, 350448282, 978342115, 805061324, 66991781, 837842341, 426730457, 43060715, 343931276, 578966560, 924162253, 127687800, 284554615, 495120211, 983133376, 350251051, 961919695, 550249537, 384990600, 267008290, 536899560, 7185992, 774765205, 543360069, 1150171, 71970530, 211657778, 700432034, 593852659, 641606239, 308541257, 95662924, 733282087, 755405990, 743685960, 146595795, 616628632, 68919755, 92770139, 875409327, 884505821, 578751241, 335990956, 28946209, 440887116, 462669687, 392681095, 431678032, 586433861, 483689998, 9949585, 620129903, 148398668, 440344055, 504633754, 248208612, 541431832, 464650614, 124969015, 287675331, 867470140, 163192047, 256748302, 707454320, 400281541, 220558276, 785697945, 824125595, 163201873, 942193093, 555536404, 996912982, 346550020, 270456420, 431354163, 727865480, 876828996, 138502374, 823110363, 872322534, 55548611, 250954699, 103976696, 289885051, 973696761, 252149242, 300950526, 991690952, 644123445, 303615829, 411900173, 551538969, 754047146, 60650002, 313368464, 638750126, 141185007, 34414121, 474448216, 381081341, 845717576, 577342438, 973147443, 269573854, 438726068, 286319919, 625653806, 363614513, 278696948, 813233122, 480217629, 22131446, 965632194, 461485822, 511653024, 594795610, 819031503, 251337725, 324369335, 43743763, 526764447, 761269870, 334648260, 731663288, 444647527, 298967034, 237321485, 479590443, 27278412, 917203052, 16530896, 169340444, 724610847, 91796431, 511614806, 142207964, 116932048, 399837753, 186569323, 944893595, 647982620, 395251732, 330892003, 909952072, 407893734, 345206422, 161106238, 233178977, 963647512, 374032953, 627467123, 991109433, 27285757, 554354455, 646865025, 506165796, 730226374, 462485828, 806753673, 637798390, 887851165, 973022373, 430688681, 959055158, 485473762, 106339254, 271106036, 172139453, 197128874, 582803061, 736930420, 267332215, 688726991, 759701381, 993513706, 702130339, 518645738, 77813789, 827995299, 687183898, 290734407, 771607381, 194589395, 616172696, 331885758, 67379419, 965615656, 428050889, 277471386, 644618226, 850743962, 632334858, 305167353, 715987705, 7162525, 704127246, 606593896, 97070113, 522405953, 508560131, 98505081, 213438498, 779596113, 426039615, 133350010, 620185704, 149730437, 837208157, 25204385, 991247011, 148162015, 817197797, 296836818, 425124708, 577357279, 967077004, 362582222, 35767441, 385244847, 941425912, 440758775, 669259719, 990864490, 663554729, 659244758, 263106642, 164986407, 606615431, 868564459, 891510504, 550410154, 535353803, 443345743, 783537113, 180878487, 849285876, 4245008, 467469790, 890020904, 491570942, 225531120, 33773351, 780489641, 247239759, 396096115, 854846223, 538744472, 249967455, 482355430, 831765996, 399139136, 310641538, 21441266, 931829893, 932393931, 236815740, 87485278, 420148048, 185813437, 329220514, 329224107, 71603044, 667376274, 528495906, 168194693, 669601395, 459280215, 691333469, 723508024, 55100375, 148012237, 69144641, 495583883, 758211616, 283768133, 161561536, 673481509, 22713067, 921055576, 396201640, 139477743, 815322231, 119188916, 81118806, 151980713, 881865377, 417977793, 456096617, 79706395, 707319845, 297501035, 514383389, 17099547, 700006562, 483484651, 965538213, 133055659, 830642090, 30669745, 969939495, 206471945, 185118106, 493994268, 399967291, 521596, 727912512, 825701061, 783984305, 513959503, 144917685, 718500636, 812779722, 243688792, 732621628, 556357480, 305035733, 10096040, 217723094, 927799074, 336742885, 67833301, 886757442, 917243870, 739365341, 472596354, 555193420, 527939695, 599856117, 439746645, 833400348, 627071476, 965097057, 356775631, 40397345, 819285560, 894859940, 478801932, 377517882, 43627402, 357942315, 151733691, 337629268, 568634469, 843718445, 621899449, 637009510, 431212815, 971908948, 15940301, 405866091, 407355051, 447075427, 136781787, 752624974, 460581318, 815709527, 533436441, 222238721, 372874250, 842493527, 680947906, 828970076, 828266178, 519545720, 876918421, 672734850, 500277239, 101802624, 818738852, 759029173, 213756136, 361309288, 45608080, 756009305, 698244200, 330506105, 376757542, 502925920, 893597352, 756922076, 571801115, 170030317, 537413130, 70474343, 220743711, 631093554, 953084477, 280577159, 567345526, 692334538, 439061610, 247994955, 601922509, 25861277, 731415611, 285760749, 818366059, 611320344, 417036283, 424056235, 253151081, 106913854, 150348335, 667275645, 557749993, 149342135, 577924680, 244952850, 608997896, 487046208, 507385967, 849198400, 390287218, 409664451, 850993830, 593064803, 631378429, 387821453, 91755466, 61770111, 750339680, 156215602, 824070067, 683036075, 312212119, 75755890, 296968634, 514560442, 720646896, 881481518, 217988139, 570758302, 218668206, 422245624, 90805783, 655483168, 25760322, 226814974, 975959041, 900664233, 537587844, 117916113, 654581229, 694645424, 466152775, 579041369, 914921679, 249727975, 801529165, 719563996, 951938652, 237108551, 866146831, 407364981, 552282137, 970593107, 960394305, 2973596, 665324199, 747061105, 303327675, 844746006, 240338494, 283045072, 637123777, 671275419, 457597842, 455428521, 996543055, 854396869, 430909875, 628199816, 643851709, 246794749, 975380442, 958467504, 355744723, 650673529, 694009317, 781374818, 104802915, 649216777, 606369340, 767749866, 915688463, 387397951, 217678789, 208480332, 674756531, 62047850, 286415897, 46024280, 436507494, 737898597, 612211561, 324217820, 300342786, 946016756, 616543869, 675389661, 341532643, 780199232, 525967968, 766528559, 296851651, 419401149, 490307351, 834274856, 660399916, 309132533, 646043000, 680482853, 389727313, 724467326, 799115960, 530424329, 206356748, 562565410, 179950820, 13136201, 787947879, 570359437, 40867205, 160882565, 171065694, 717525907, 791573614, 691648758, 14715559, 919134706, 152838841, 611332401, 794939275, 95198238, 529893342, 892622396, 416942579, 844008912, 287763599, 222869397, 860322789, 933018034, 376318595, 307970374, 726169850, 851533865, 749814020, 262054458, 355754521, 97235303, 161514931, 717443755, 351643578, 715107421, 204387184, 902138512, 413535369, 402219922, 785949336, 322270323, 498120546, 778862131, 169864857, 571983046, 593844490, 140468001, 70687913, 542937267, 184954561, 197708397, 207123815, 214467284, 615532984, 3776126, 351440176, 785225808, 51854992, 353842423, 4761978, 478680802, 97961198, 483045478, 662439594, 956070628, 933877955, 846084856, 655012272, 657389489, 625826732, 116735222, 169663809, 535506656, 312687683, 269550154, 808097964, 110628572, 921017292, 173441313, 249977686, 904639752, 427793417, 754511282, 594004063, 325099800, 834520635, 575499305, 301184099, 352727713, 508564353, 4945609, 756486720, 630604672, 536361406, 782427976, 236575850, 184947734, 866971942, 841178184, 429252776, 3847308, 250822932, 191626512, 997360827, 230356594, 248058557, 212266859, 183366539, 102321390, 407446775, 736803903, 82605363, 102605007, 362555721, 282766991, 679818112, 514777841, 147337434, 686720980, 806630776, 716745432, 968215241, 96750695, 478730322, 425445962, 765224370, 124071153, 253867704, 167387138, 892679949, 731263129, 495087770, 598187662, 880922439, 752294489, 821694966, 380013369, 205388410, 979920539, 164255341, 358842106, 373081374, 314836773, 933246850, 104369951, 484211803, 62681534, 54884832, 986230998, 389716249, 845509808, 909513394, 352436531, 626224580, 50173880, 911384035, 204112612, 931770659, 339434595, 917725920, 904828047, 422278322, 637128439, 890149501, 288668728, 357192025, 711973773, 343429550, 995252631, 595061412, 517123311, 44249702, 124923984, 487445130, 891590298, 304725860, 628680201, 874782577, 674568504, 4671937, 531285747, 269698488, 592998892, 223471052, 712330040, 111172700, 616407324, 450648159, 173367218, 272138670, 434968397, 79940975, 966933202, 435738102, 471686218, 162394966, 654496723, 65496703, 612313229, 352155309, 557599298, 324159873, 66291592, 949975204, 186604286, 862356676, 686503768, 85072074, 617838009, 136720139, 74154761, 823924692, 427967808, 769168727, 12059754, 171506934, 283162750, 4414218, 556349507, 886200667, 651181833, 184770883, 789971884, 808760994, 338611196, 40067476, 240969197, 227958470, 392188707, 117128928, 191405528, 84251742, 587804629, 848861880, 414587638, 133506847, 432969428, 845595034, 141941362, 382874545, 115336105, 579736041, 227879853, 911470597, 48881743, 635644404, 593695512, 193397099, 918838310, 793892843, 59815077, 408582493, 946421972, 834768151, 123232037, 159829314, 394405864, 278597486, 343030014, 441591800, 701494358, 745026921, 35156027, 152700326, 384008708, 402582125, 584814544, 44183387, 535757906, 126921081, 1039739, 690125446, 218660223, 108887495, 863733510, 717990834, 577823341, 268090637, 311712543, 667216684, 355078971, 369269726, 523888981, 759725451, 392515303, 703912910, 798181773, 284868555, 793210213, 308113371, 903553257, 61725255, 300355050, 360544182, 965871929, 26730451, 617487362, 265746854, 468315041, 73885322, 244268657, 278989890, 831826346, 942021501, 751137585, 518088211, 1844795, 537988821, 480449901, 484353246, 241191423, 113762202, 75167852, 163764219, 539351015, 3594222, 291987445, 810810346, 237140415, 700924427, 922998252, 954070703, 444041740, 979952252, 657075954, 22095089, 364581038, 106187851, 237280391, 452210072, 93174127, 407810465, 342485350, 696240904, 667013093, 137529271, 299339608, 160714787, 280807511, 274091465, 656255036, 335671525, 52278621, 844424026, 827702028, 711198792, 70105451, 80806144, 524748145, 543160532, 816904971, 727749020, 75663680, 553756062, 89493828, 43500108, 292898637, 461920538, 266120288, 123810944, 409084683, 84297699, 966792860, 766951111, 245669461, 32296760, 904667882, 702976562, 389298264, 870910567, 329634701, 860927371, 595650131, 938511259, 796946569, 506106074, 820596295, 284977016, 210488412, 390822377, 265236136, 337187981, 461049625, 158413150, 233202042, 820142814, 601500345, 159694991, 282769262, 897411259, 675443362, 775138275, 627830369, 855093152, 682988548, 563410474, 669036636, 499062347, 875358527, 623070363, 384088260, 248719041, 592212282, 265029279, 794717506, 254204212, 721209901, 583843658, 286835974, 958385229, 280426965, 321527331, 600696303, 749830406, 713220154, 833348252, 978062460, 534648447, 262146771, 842380694, 519073785, 114806894, 37186361, 796870915, 352119886, 213116596, 274758219, 715075074, 733470569, 937881810, 171924737, 991135715, 704867531, 61841678, 21401596, 898829499, 224855085, 770238743, 347700845, 575188869, 311445689, 873661583, 441985505, 428759978, 726017880, 981265555, 243573976, 807713414, 403095565, 198972471, 766125087, 765385900, 366994660, 241855698, 809747204, 675757086, 588359219, 224052322, 123552502, 885093669, 216332263, 803952547, 782384272, 448853536, 611682152, 974244262, 207248892, 695819513, 992362241, 911852770, 774662274, 518425127, 131202132, 77472243, 945774311, 197741438, 410538048, 423821545, 618557666, 226362330, 637939827, 410441960, 210663571, 741400071, 991804863, 357980516, 258261314, 878249716, 252062936, 543792122, 189566546, 945443439, 132749441, 686957004, 452686068, 619533368, 649476613, 509068599, 805592745, 353435057, 61456867, 365195955, 94713071, 811816795, 854982160, 870564615, 352283627, 830305008, 267877781, 527785315, 691087235, 253127298, 792132227, 924614507, 490173961, 297709871, 989711160, 545456018, 82393980, 782499239, 335708949, 867533615, 903396160, 965602133, 156569940, 234519399, 965965938, 491891408, 863826040, 684159479, 649108270, 950891098, 880644964, 461360976, 181485354, 626672137, 78735614, 166559618, 929970026, 719532927, 73546155, 754946490, 864330439, 133698417, 792080513, 964073167, 795179547, 583587221, 845160667, 438101185, 435800531, 381406442, 904733788, 641570229, 992573408, 717809136, 739208433, 660806966, 234873380, 583996484, 666692389, 559350115, 92342838, 706594372, 496976882, 455369151, 974605761, 7524112, 570267326, 893743323, 643237493, 365088037, 28020081, 55695538, 55805012, 462305612, 2296517, 727229601, 642131392, 276457529, 141842603, 824495446, 476455199, 704616685, 254966505, 884299656, 118649705, 961221993, 569279229, 461818747, 446854737, 864113074, 279555390, 755360346, 372493292, 893766258, 688516578, 258059512, 720767715, 720490520, 843904149, 543063544, 176088404, 991033085, 16576067, 702887412, 461079055, 234088350, 172620874, 181211646, 50660843, 654656785, 859001734, 647379145, 466108187, 340191951, 931536316, 248503945, 208417780, 888209680, 173095166, 973792267, 970174113, 914663052, 288411507, 945627689, 127304889, 750474748, 856810124, 39138933, 76936454, 984226476, 752422125, 676810205, 898931315, 360508974, 347897292, 753551806, 829719012, 14830269, 699512289, 115796260, 823865876, 428702277, 5559333, 738879413, 200399753, 576042724, 939870020, 271715217, 51573567, 148039160, 736675762, 460037473, 86194636, 200175632, 836095533, 26892683, 373658231, 10835908, 76185570, 777569336, 549389603, 108278716, 637071382, 869476009, 236326160, 818703907, 62753603, 898035027, 973558145, 392779967, 526632410, 116557112, 261687138, 885503084, 992760739, 148150582, 153156894, 734065303, 602987893, 842351379, 810638672, 348179321, 575428689, 705058858, 425468241, 697174863, 652912320, 266524479, 19535169, 362750804, 407999673, 566829018, 22149690, 467569170, 812535181, 405253990, 76883940, 892275502, 575680579, 301563014, 758249348, 824684043, 709633341, 511810080, 384434411, 352186998, 891236404, 877328292, 297623844, 309582735, 547031588, 860154813, 230928767, 898939090, 873790210, 566729231, 577540685, 410900493, 922145212, 560813740, 928003989, 620429813, 193135106, 680848276, 415274977, 192158730, 421611254, 581104427, 280567130, 633111355, 636395165, 539318215, 337261891, 759088696, 452178161, 632504044, 145777863, 393311920, 212175368, 330833300, 389983325, 335179166, 204186250, 493604031, 684133095, 163041912, 312845132, 42347068, 52740717, 856226068, 91133443, 292748928, 569210719, 791303544, 822978571, 127616978, 746899626, 272084997, 576881550, 761083099, 190487972, 73910625, 76299329, 833568731, 275748331, 131866223, 206158883, 634358775, 54855144, 937648665, 222156499, 34097309, 612009955, 372955074, 127716678, 291445266, 852910420, 987725148, 439498929, 128723592, 210946494, 932864454, 943827789, 101713503, 833645698, 154862818, 881979208, 126522871, 425882922, 683353126, 150431759, 556568258, 617431259, 528397207, 613188744, 663563052, 416942747, 66167978, 967003815, 452180920, 700721596, 308820738, 540075595, 650759880, 137914189, 639205811, 846002958, 940824116, 375667805, 689462802, 359533188, 407667896, 489432287, 240467563, 907519370, 408189660, 362489494, 630052145, 549651337, 126552126, 291748227, 378953356, 123616249, 279185547, 959461286, 593769409, 543992818, 835900869, 640072309, 947576948, 698103094, 979822529, 225010199, 971192022, 134220066, 765597334, 215475650, 905919774, 267699345, 168489427, 87134744, 162338892, 101473351, 613066315, 819403070, 579442457, 22523320, 988690992, 694061808, 444962799, 175892378, 802981388, 627270660, 712572931, 610020242, 721239416, 212574161, 700086982, 196211143, 308391303, 619517195, 400385741, 255588360, 808651311, 143560023, 852239888, 629150159, 135703905, 443023354, 765586915, 139194501, 460657346, 211462272, 34973323, 698813260, 14692794, 318066940, 931305711, 277807792, 536041254, 137997768, 16873058, 216749462, 64270070, 806615881, 717249219, 534952477, 391797869, 862664999, 317315035, 377985536, 632887612, 544056609, 813927888, 293830894, 170768906, 79547257, 812790711, 301394442, 562578675, 295161304, 613042164, 487283740, 304027023, 885681292, 326326743, 309491316, 948288988, 8914700, 111175697, 378176012, 612173809, 326982181, 691022719, 241944522, 142737183, 8184896, 910920758, 454518315, 27566716, 442330016, 965424900, 906613103, 827220077, 185619511, 667090560, 479631043, 977763868, 252408603, 396338437, 532188090, 717963293, 807875786, 841621206, 383147241, 37255495, 14062579, 268848458, 252557169, 884827773, 837060445, 981683539, 701888975, 914166581, 251863759, 33398571, 317529210, 289325835, 258293571, 431103697, 922197265, 466233341, 774866513, 556625043, 474417091, 60729505, 159576283, 402586201, 666620632, 755497643, 938283602, 41346273, 116576352, 831886359, 764187690, 856008071, 365321463, 77970099, 465182013, 9624230, 996253055, 177349635, 395404015, 639108288, 903243859, 798640911, 218422114, 966112404, 108517197, 715766866, 982458286, 713005298, 175313264, 929612665, 651369927, 644184793, 135981868, 815566386, 502873932, 446521640, 882094975, 94162055, 414792239, 736743294, 438843018, 588323666, 771417552, 155580037, 74442984, 576930824, 11547951, 134080528, 870452327, 362798743, 769140418, 611020846, 962975962, 175797091, 541848710, 112311248, 646349974, 885470323, 928042900, 109372573, 669750926, 379064879, 687534129, 477748388, 830140326, 981704927, 974446822, 444555101, 532135759, 640836038, 15984568, 570135044, 220741738, 74326851, 887401541, 240317566, 233393459, 765189252, 635876401, 206621287, 310089674, 637874625, 97592768, 598007848, 772579288, 634721593, 889681467, 673789544, 535216443, 639895171, 906931817, 278112291, 859531286, 908146707, 852808916, 803070776, 496126252, 460376563, 241246986, 824086635, 591850589, 862454701, 711020227, 932290595, 439230456, 51516474, 23521693, 165795604, 534481471, 850548087, 666295936, 51175224, 636291745, 214654740, 668888234, 11316646, 820676074, 318019679, 756113774, 375793876, 440332063, 123506484, 381476069, 319590417, 77481163, 330915519, 702260276, 305049682, 886713564, 619988708, 403683772, 529551247, 704982947, 90768581, 12807839, 977532937, 988825173, 460031509, 508965639, 267276052, 164287370, 811924254, 213335786, 110902331, 702676431, 479189088, 104245117, 472551217, 46049772, 425782693, 362195622, 653941903, 717887987, 297175460, 30647044, 779311609, 204667291, 711212222, 576254206, 277199012, 349408928, 504774466, 68047201, 380945021, 701233955, 882656289, 158561163, 50150846, 690138217, 224963775, 995320261, 839837458, 977748036, 420599165, 90490209, 901937155, 644246261, 865559203, 95335241, 704485356, 901495456, 133561909, 979448313, 648836389, 520818460, 528018688, 979660215, 463476563, 213743406, 516868298, 182823563, 316383655, 918508134, 602752228, 108171547, 946810634, 354194609, 401415851, 478829899, 282752017, 772095578, 72165430, 429671539, 837199939, 632121035, 807263075, 401708558, 470996043, 784424894, 116509403, 434378783, 82601126, 648339587, 294160529, 960992367, 936386933, 776555446, 401857899, 11720253, 858535377, 443102806, 983150048, 347875860, 599738004, 610813279, 950051014, 205245251, 763281195, 636082570, 808403065, 168012472, 91539023, 848218517, 94118780, 723341988, 720621369, 788036898, 397564801, 259307431, 733170833, 573684704, 307496402, 474215478, 857741297, 182055250, 935503628, 922648910, 273050106, 772436496, 860363366, 170837263, 754712581, 804551805, 609470052, 563467915, 18755940, 283513412, 683948691, 566999577, 774847359, 552582856, 763813859, 612986582, 333747554, 260004250, 758384953, 494331682, 594450379, 837052799, 322013459, 837006756, 618718243, 153854667, 147750005, 45622353, 408502008, 754358907, 741452171, 947586557, 954750740, 46928052, 206489149, 389971754, 144852515, 795714884, 777451050, 829682181, 904000798, 380188750, 61700438, 247514823, 286075425, 151964663, 58506296, 783992214, 461148294, 609128508, 735981597, 853016096, 409457333, 963396497, 688619738, 906930577, 256070011, 275708717, 201153312, 661836255, 611050928, 358983541, 1752322, 56885562, 821960304, 483199028, 951242550, 209449167, 502115619, 318089910, 982158320, 452741488, 806382739, 866292362, 980558594, 897119087, 989360428, 182110900, 481014846, 324429592, 995852013, 261435381, 508693529, 618454919, 113496459, 12535884, 885144625, 47991920, 182044023, 610418297, 257169632, 787555024, 897579062, 889007179, 941586708, 486911183, 758788635, 271845560, 402396427, 741206420, 702012621, 300345051, 237208815, 551463847, 400029779, 753558019, 75763326, 815388429, 13445540, 568378901, 470480531, 424627723, 253739389, 272295113, 463288068, 548417248, 237434894, 577743131, 9667429, 519446006, 767158089, 152529574, 509444561, 537186389, 516348591, 657798496, 537485139, 675514259, 989762196, 349935401, 326419353, 598912692, 545676167, 916780862, 853061709, 821595923, 184224880, 341138846, 203151972, 178195156, 762468954, 865141993, 230270972, 532674382, 352139829, 47490043, 305242407, 686277883, 154712341, 446580093, 435183225, 113930691, 280380642, 732265494, 698318310, 219779380, 60276080, 342123279, 730662952, 975500986, 505704979, 2120425, 643540033, 765013350, 715930443, 675825932, 943013827, 425485512, 25526509, 3692114, 532397072, 773731517, 589661097, 838491815, 573023399, 192955373, 70515896, 150294872, 634203702, 134200559, 473916698, 475935611, 889107083, 533272557, 903760893, 523867088, 173779186, 904502638, 457841006, 539920391, 958391120, 823989393, 732543651, 15555793, 334762994, 910461296, 152871393, 681897434, 370042943, 535246064, 376642780, 185187654, 284660207, 641495570, 556882638, 695805725, 146913124, 598372846, 365936439, 312931548, 677054568, 622115733, 701479710, 928307553, 17552486, 348448771, 583605166, 490633088, 823804311, 563931617, 92777458, 122891981, 104051297, 238310863, 405318730, 636413238, 777195536, 689762201, 692640190, 533026410, 900696645, 257245209, 474405403, 830746206, 718381376, 661319845, 333814388, 59057746, 828332472, 815043751, 853046910, 704017323, 147071166, 181911867, 266603711, 10612834, 620978895, 429872829, 938240670, 603034041, 92075614, 132138944, 719020779, 141475353, 823200226, 510962913, 748338206, 99542156, 449220619, 77912323, 183161366, 701397317, 779470699, 656153953, 232926996, 668977679, 25565072, 247434719, 550817628, 14892645, 909380113, 378234074, 194522170, 702518046, 634003595, 709588302, 646211653, 800175794, 501468551, 219312711, 761174946, 777798206, 596057004, 988762639, 683060351, 568373152, 837117066, 745178307, 698577068, 345396236, 189859385, 930248139, 715290634, 181691623, 895007934, 989575405, 291952077, 915204091, 342698331, 693624256, 565911866, 926577834, 273180525, 784845843, 562319136, 464943295, 150839530, 579984899, 625279712, 513264459, 279684018, 147049359, 189433784, 529097415, 558410381, 773285811, 427340646, 21938064, 243650505, 457404677, 745793273, 689396602, 435289201, 308171889, 365728099, 54255110, 455975989, 28376409, 46795102, 766479011, 818971081, 630418224, 95751474, 533015264, 836159419, 317722670, 268656429, 869688925, 410577926, 480477274, 170814437, 762507474, 660433542, 760134917, 652326007, 377707959, 540744185, 391880602, 856574432, 292732359, 45507797, 933217358, 701009115, 2589820, 631787405, 994825926, 504953938, 398844505, 809510758, 269757501, 151316850, 182008407, 318001860, 907648053, 840148018, 674906568, 574934546, 251862314, 367393851, 235009560, 848327440, 203690617, 155331892, 399342383, 268932670, 188236547, 382533187, 94294462, 600351714, 455592343, 673295761, 834210572, 688781978, 280816014, 417092080, 569821123, 686115571, 227524500, 634926055, 685774429, 721741853, 521133022, 718955644, 302085048, 575938266, 138745390, 675462927, 54468897, 855438181, 958486514, 371682173, 688318434, 227225145, 636262377, 869716360, 173106126, 11750308, 624626883, 150375609, 504453731, 304538931, 934542598, 519242443, 30983153, 162629404, 359647054, 542453630, 312621360, 836335857, 720398207, 829271147, 458772111, 690705949, 206963319, 498081143, 566330462, 401038468, 287289732, 538237061, 539768833, 666922888, 868511951, 68137389, 917041880, 566574336, 580758522, 135609135, 693365575, 759201414, 929370538, 919520187, 668928730, 425595587, 450261837, 932011032, 28725513, 406300215, 632182945, 692733297, 538429891, 505692371, 774782405, 72616541, 66594590, 980882929, 672521613, 300233092, 812172558, 512972450, 726249584, 385532209, 949275286, 889049887, 886012223, 553139882, 851160690, 187556942, 128132086, 469569401, 571697328, 277833312, 731665939, 800476957, 989420382, 242105627, 536946065, 468910627, 360564872, 780377518, 244761196, 1190449, 491412313, 66900301, 853933935, 965200138, 460047450, 602461564, 34411581, 166170818, 152073781, 110618931, 429848998, 952484374, 53858109, 255853037, 571602662, 496849840, 533941896, 66780620, 497465701, 237495271, 379120579, 617790605, 85829433, 754572048, 823438638, 905649970, 232004551, 229311152, 535287716, 892492093, 777805215, 764861916, 920662253, 780812850, 47264149, 85579073, 5779214, 732195917, 522578141, 678912944, 243381836, 887561462, 90016939, 673121380, 633024304, 280304104, 824587711, 620307266, 93858150, 199334916, 662857431, 306537773, 768789403, 673954312, 40922635, 295580651, 471673882, 701635344, 713042015, 180569292, 566048846, 149752857, 866205591, 325660279, 916129039, 933403887, 318612754, 243592823, 666767248, 610778727, 534212719, 555116868, 626047098, 562623720, 596419261, 263880210, 485541849, 478655963, 378132145, 898038956, 94092467, 950063379, 232857687, 711298951, 20904592, 596759695, 835371916, 100610969, 11003297, 678768641, 10339221, 62869105, 15141951, 12236153, 864803826, 672635734, 374613492, 852692600, 616812109, 772841577, 119304191, 786272252, 601326326, 510751956, 159568746, 960725184, 292291050, 628742287, 681423943, 211609337, 679216162, 95774999, 500855925, 397829871, 69022560, 66394485, 469883510, 859398408, 701541782, 552649394, 624897146, 195890344, 55407085, 597462698, 104079298, 706297694, 934022146, 986142069, 362467428, 909249110, 666023021, 893200404, 880564869, 344075560, 407961513, 993318794, 898377631, 546116018, 901991847, 287910287, 519588941, 621952242, 770423883, 935545314, 755729709, 719830778, 445219932, 489456035, 931434118, 853472789, 204216016, 331259136, 191278026, 794074543, 463648004, 51665028, 769537229, 766460897, 793057831, 541947059, 208655022, 326897640, 852678972, 391031404, 838700918, 518776128, 299941109, 926270863, 93794074, 291636247, 787996582, 312643510, 568274571, 780994595, 940945163, 168263285, 324274887, 747271084, 696888882, 998342808, 221993795, 780924546, 164943510, 81364258, 974509213, 966997537, 766106903, 981437259, 899641067, 469636052, 913854986, 474972062, 853241340, 794549359, 333993003, 247085736, 285617942, 735563743, 785396802, 968515351, 28773278, 105996208, 979681178, 72701131, 286109606, 125999844, 42214849, 255080991, 834491259, 839625133, 540133599, 749173465, 72395495, 319052127, 93813644, 986921581, 539806827, 864257523, 465536786, 86658295, 843221981, 8042776, 109764124, 341624775, 997727930, 947828039, 21997224, 415246995, 738472431, 28655168, 20258610, 173521538, 15368985, 963181496, 187132297, 501049266, 812175468, 640216239, 392912994, 923731862, 100207717, 52680264, 795869656, 464966170, 536317800, 753953315, 846929484, 957127661, 338260839, 306488096, 610032848, 18157356, 653095078, 702049014, 219378244, 595829826, 655499348, 600880735, 45108431, 35218321, 850606691, 885546600, 302206556, 725382202, 521167386, 951415793, 787137375, 958019500, 777997986, 24953247, 533672248, 724379642, 583454424, 164928976, 392175584, 282914479, 807883418, 871672722, 579138162, 319510586, 887537491, 595695620, 105818651, 97127347, 133123846, 538291924, 5219511, 547759455, 320091144, 759604404, 209612762, 783800829, 24955559, 579031489, 822190478, 611406556, 355767096, 756067560, 636533093, 607468146, 875234688, 472679793, 442697283, 72834019, 449118702, 475550677, 351276524, 154660735, 352430159, 140594959, 122466572, 441601097, 451776235, 510826720, 829668939, 451357705, 285657620, 715224851, 296926366, 690671783, 995044992, 935172954, 262423352, 975191013, 848580591, 786259555, 946407549, 641919781, 671556279, 13277141, 563413529, 280861206, 254600255, 930444091, 398211365, 693050426, 384973474, 308902701, 220844322, 436321732, 161408912, 574520240, 428126970, 870715951, 772370641, 359447729, 669563022, 67292934, 615068068, 563547109, 979398254, 48677368, 224391711, 783806926, 891996002, 840994661, 306255519, 592158068, 837190393, 515308817, 143450501, 819244490, 293648096, 414362939, 247765934, 592621373, 181481347, 490681209, 240694428, 918067686, 760182896, 24104897, 462340137, 884437148, 599689635, 63794479, 754122738, 338872236, 339851939, 615865453, 904202172, 191457158, 265685305, 536249345, 938691257, 626843291, 398457498, 207009842, 695986159, 282735321, 35411333, 170069416, 617397319, 718263865, 323694635, 488158838, 420033539, 678910170, 625635285, 332868247, 641506201, 718903983, 887513654, 687950715, 80053748, 198668379, 617508138, 382887546, 941935740, 34728925, 800728955, 856486889, 774050807, 579806602, 892223937, 663085630, 622976980, 897177516, 358837586, 166533664, 863290964, 736484149, 571869039, 224406360, 561156232, 978271328, 443010690, 809074415, 872878773, 268419083, 230620575, 730341564, 767205614, 835076286, 855460260, 514557632, 942524072, 561132927, 763387988, 646220809, 749951355, 486861897, 68339381, 882253626, 890130965, 853850711, 554734341, 269202736, 835371363, 684407281, 287228328, 985629277, 373653722, 888397075, 685303746, 379702368, 527916889, 706183499, 574843580, 620598308, 283904964, 813757722, 809024748, 29915963, 674720330, 943091070, 249476957, 158923499, 65286107, 982537829, 799193459, 991710837, 605078441, 669350910, 61988517, 291950117, 719405552, 777150540, 100841631, 687180627, 548168451, 142352459, 366345926, 398261641, 813741542, 462795099, 393329621, 684164667, 467976741, 840643524, 258749430, 524707792, 274136095, 411362894, 249092657, 470231670, 816960839, 132165559, 136756497, 152157753, 340128275, 409820573, 475379341, 740366554, 818113043, 746262416, 140461432, 722806023, 501569567, 202574582, 763465149, 460901013, 29699707, 177327164, 184500224, 631677998, 433626411, 840574191, 623707027, 948666443, 191522871, 775281050, 693551373, 407353256, 312699429, 830281153, 780662240, 362602097, 42882566, 10552407, 578498347, 61053137, 296777173, 38316707, 687126052, 96175943, 940481375, 313204701, 782933899, 792653681, 53786060, 619328269, 756627219, 55695050, 211576827, 799865046, 927423460, 534600050, 601133694, 405143378, 403348063, 692005571, 755006416, 333140197, 620082419, 629761599, 376791681, 750700748, 360610990, 362661519, 965673631, 759300205, 918824078, 803730958, 582477843, 763868339, 3021891, 551939585, 738678730, 992921476, 166345031, 396866033, 902204929, 471376618, 723881258, 759318260, 50962143, 257508480, 812994381, 940014501, 295101623, 314687550, 946040917, 195001786, 669587990, 313723074, 363738312, 363364906, 605766724, 568993323, 673443391, 698344864, 194348457, 410865624, 2494318, 412305715, 458908162, 990522437, 383256439, 349413378, 928919227, 790123145, 763162675, 677136807, 976388811, 81773103, 996041982, 109881188, 497876649, 195235472, 476180050, 556533934, 424965051, 407009889, 14653547, 394413511, 983648904, 548850041, 578354863, 972427792, 76960172, 455129658, 273735255, 829279418, 404872746, 424773569, 793114615, 696164944, 364645766, 702904261, 643119729, 601696139, 663423029, 549956152, 536506603, 694003547, 17676571, 710629513, 84915184, 688706953, 866054240, 217838114, 961207749, 443110060, 511510634, 104673863, 977980387, 958784126, 674539557, 176717773, 514905675, 38799220, 649809007, 985972980, 633504275, 559460397, 902003165, 101687828, 262442539, 973484791, 845337535, 140905181, 89329633, 885068303, 614507807, 79017420, 303104624, 607887671, 224710435, 212975267, 878207325, 193394233, 796863920, 146529283, 144560216, 272250683, 100425559, 913066970, 31739787, 748809244, 501286930, 836199464, 899403813, 502148459, 705908049, 410099630, 446268527, 243939592, 532065439, 806174625, 813663122, 208511984, 917793394, 812799150, 931510516, 901619203, 178347579, 322526262, 45876758, 61578873, 938181220, 496334495, 318293793, 631306241, 770994394, 731611635, 597764921, 17584888, 285994334, 475825131, 837279535, 198474067, 113403883, 806842901, 941050736, 474421196, 532709292, 356957311, 442019347, 440252210, 697358611, 765346075, 51243917, 177700775, 794558430, 845298191, 983350179, 528446450, 207832322, 496988063, 224135375, 703815716, 467201351, 336902098, 197397480, 943754881, 897819728, 628029171, 2222154, 274253113, 951899941, 296561575, 371282645, 679912729, 895077630, 884892102, 451226614, 159297393, 94556892, 916398554, 827371325, 500637101, 776178696, 503574214, 230166281, 604836903, 70718648, 561911147, 49344218, 612434626, 809242599, 554161456, 388966335, 879553924, 529621328, 26001072, 568616515, 596936970, 596382379, 65051467, 287576382, 163245484, 507081441, 938624407, 398094520, 744152226, 178817507, 958561407, 890833167, 864497687, 261846026, 315897182, 648492411, 46851557, 761207616, 265642676, 43294595, 870229975, 200029046, 497831526, 577928323, 25040856, 543231851, 104025235, 245027041, 886169223, 495053409, 351165135, 909849446, 521768117, 35951500, 249956023, 791579019, 891162436, 119778181, 306183479, 406305334, 268548313, 391352262, 311619117, 41051091, 833288745, 913612752, 665978283, 140895839, 396153418, 542836695, 715018542, 308935940, 443984851, 55960943, 803717962, 124858947, 892847096, 300567676, 870775003, 878880132, 677855561, 338654356, 95469617, 411421638, 98263367, 754678712, 503674916, 136581539, 799492795, 378939554, 904101555, 396689955, 426618230, 382352767, 244193206, 235468352, 895187206, 969831416, 184630151, 755652213, 5052621, 630283867, 485682922, 695997968, 917463358, 419895565, 1433736, 884646032, 203698780, 25521506, 101709097, 959326051, 374858200, 552409878, 227634188, 9271153, 478616435, 915293900, 957220118, 450223586, 373945555, 263250615, 988397408, 137649365, 4817765, 230564308, 45528992, 448514216, 106052841, 91238612, 368320297, 584553213, 612000029, 397279231, 762557074, 286699094, 139554391, 445929235, 272164375, 534924913, 105161486, 373028766, 365498727, 469183978, 345685074, 934282324, 904962947, 709936117, 221815494, 561390030, 998801493, 835273792, 681640152, 587057163, 811788022, 362539706, 577544879, 545309782, 71175465, 360528385, 540904217, 675484819, 952723713, 893648619, 343621179, 414408235, 789982070, 681000784, 705231534, 463873706, 192191715, 823514827, 839394800, 384893518, 552836631, 173027000, 602289511, 103389368, 556388168, 1683933, 539318218, 412198542, 50226450, 205012015, 69895928, 435352863, 473664347, 777800690, 755595285, 429480358, 649037145, 713370123, 579914852, 710479971, 111483029, 381677859, 790162431, 663015729, 214791300, 993514481, 647316361, 420131319, 403354129, 541679384, 493200468, 253586256, 31931072, 99487307, 412348457, 171615837, 882929018, 866683265, 314454702, 955454962, 644651219, 751503986, 508815060, 560931615, 918142013, 203733732, 505392097, 596190495, 490855575, 445810449, 923923165, 65980494, 401976115, 487692905, 216814023, 915864152, 981867614, 328798757, 722576535, 755944432, 601244750, 476911831, 785703109, 267677004, 416604830, 143281640, 707644712, 412002291, 333642380, 617259773, 434690069, 697568098, 849590931, 830629681, 556644421, 610871081, 480970895, 55371584, 178361047, 161200397, 417632945, 166548564, 754562347, 573361014, 315655282, 339959864, 742712007, 189180935, 89651305, 606832922, 476409297, 345820577, 317917693, 421602452, 968675398, 294524717, 811625618, 683703044, 740872112, 658348486, 589386388, 316311552, 894334021, 406092775, 478478734, 206380379, 791377086, 147794332, 77832909, 942832665, 693935633, 350697539, 237014872, 278033551, 533158861, 501640984, 670953246, 498286487, 363675800, 484706027, 963751472, 31316687, 16739188, 133676451, 75535533, 568082351, 310497931, 428978460, 487356264, 787193191, 791686632, 390375233, 461939745, 67707094, 681629714, 495938077, 151214650, 18935001, 546523758, 667184407, 889375775, 641395406, 198518945, 860662687, 587151140, 767151403, 855686521, 188127336, 371056669, 348956268, 594124433, 390418175, 860824402, 745219266, 350001374, 167600778, 156311380, 412337215, 722052300, 963604829, 40245698, 458296852, 768216085, 828381815, 945929253, 726505369, 174780025, 610429120, 202517637, 227008153, 298536682, 705100718, 792708006, 747648115, 405153852, 331806762, 133410835, 237911161, 883849430, 810061940, 152670315, 241685954, 294553501, 200795292, 409574027, 392084932, 799099563, 604698303, 679113358, 441746297, 391919400, 820944233, 510960170, 802704138, 778029752, 857644994, 849040239, 226139275, 214710483, 855339806, 304751268, 718589214, 846519010, 125169028, 857948348, 102631660, 417937447, 152420133, 485426247, 410279545, 926789216, 177716836, 87818627, 209903883, 645130011, 877379426, 58282192, 64538488, 600597145, 558139604, 683579700, 132956832, 682282836, 967284680, 166491072, 374414163, 506778017, 679018573, 822456110, 11011998, 84268774, 285663173, 646956970, 564054883, 254019505, 911464094, 346549752, 745229707, 976146147, 630073380, 347584387, 455212558, 395274678, 676678906, 918419833, 725878773, 541768093, 460182412, 243967550, 234107891, 696345790, 283697905, 123856573, 333078346, 209066182, 187045473, 623935737, 854668429, 451175779, 865915397, 855895409, 241310957, 173170391, 323095239, 919996326, 50228317, 911045527, 324460739, 498958052, 970536351, 669884319, 286310899, 818383061, 758958882, 722446141, 748737662, 648929425, 794130299, 352272259, 856667213, 136525958, 573417435, 57639453, 505118400, 477980179, 428171134, 841298256, 394676854, 277797524, 937623644, 52315773, 571908689, 819963924, 702547921, 613291847, 565611817, 517860342, 657162948, 537789945, 936509657, 615401877, 210834833, 285749912, 258482108, 316588633, 118071239, 396495509, 632052721, 146785252, 773227944, 23402830, 227224079, 580521734, 518558291, 25702943, 866606920, 569619372, 314082546, 700942125, 411479128, 186029050, 317370140, 189415958, 975472452, 909620405, 210815467, 800967008, 114239594, 959942613, 389626136, 360657539, 55431343, 714689889, 337948541, 670463951, 594115834, 111832974, 405257606, 671801637, 276663315, 769884346, 591451802, 223179542, 156199376, 878355716, 842075482, 763594697, 643977528, 951139777, 343696178, 550607963, 941465815, 48635955, 157735270, 900257345, 138566244, 548494287, 243780852, 796521247, 667827024, 917728454, 822133164, 985609152, 563392824, 260838752, 133766647, 291141444, 570761122, 704163113, 367802857, 51793523, 608790072, 546556434, 36804571, 678388499, 772195728, 212621923, 564807794, 461939669, 723115949, 189460333, 608660165, 980242078, 292031106, 775263909, 450389567, 907795427, 35078459, 835271226, 791590032, 288945002, 243230353, 514760031, 954351697, 501828440, 199302890, 561012744, 201210138, 788496991, 963758886, 428333719, 231000237, 778051598, 472013657, 950182484, 872688047, 408933320, 806327084, 266717879, 120332920, 671301581, 305810969, 222389837, 692944752, 660773472, 391379759, 770056039, 514052725, 614609138, 650637221, 807879708, 726495189, 469789579, 810931231, 971686548, 763025194, 134852396, 648785427, 406482397, 370623392, 107922533, 277578481, 819063921, 459037230, 835395901, 344299648, 542224615, 902857249, 569002164, 713251910, 808382168, 718599708, 695610079, 597899999, 727918699, 758349522, 91010614, 429288972, 85354226, 626540643, 752177062, 897088834, 889198867, 717077454, 273949097, 174817634, 996093909, 129157753, 857547760, 499342760, 421874982, 656331495, 810471732, 670725399, 20218032, 868481222, 811402404, 866779664, 3754455, 106143667, 252419989, 349423501, 1255751, 581038705, 427680765, 581719812, 378896665, 50821580, 339328315, 47251692, 275217084, 461622057, 383965146, 539680256, 127292647, 115732721, 46712860, 534612106, 230292087, 4302154, 729241262, 54320418, 673040640, 48147376, 329725477, 590838520, 530235982, 764098820, 672252189, 340558958, 486307893, 770124383, 771650274, 938072681, 304836278, 604198410, 883675862, 999884335, 554905416, 217075499, 530294739, 314149471, 677860570, 939024568, 822900855, 126815273, 414658674, 20798620, 33013246, 316714386, 75409312, 419524045, 546918013, 703891511, 638683567, 683562735, 120394546, 518761753, 151382291, 873200029, 679468949, 677149591, 885393843, 406409081, 118900835, 554338807, 720916077, 886361817, 256959825, 438800807, 226198678, 303669383, 250852673, 766192700, 148479575, 467308480, 912435103, 458749933, 86546562, 294022078, 867368192, 98752340, 273767103, 854981613, 20104337, 114922603, 789927777, 830032837, 255133757, 440347995, 330163783, 708837960, 787419182, 522997599, 148261815, 41798519, 8328983, 590636822, 454399255, 769927675, 439441807, 705783552, 122075487, 753013305, 160732619, 803605666, 93672442, 392869319, 767261304, 717691918, 962553715, 622242070, 890264995, 151712445, 6911405, 904535485, 48777538, 855683905, 477779337, 774180630, 211182524, 801319178, 139708127, 887475377, 966801613, 335913638, 746820320, 433162861, 273287955, 616122082, 612833557, 463757085, 67768177, 464745110, 563828034, 442018716, 286321651, 212478274, 344444907, 168506609, 829990953, 565303865, 378569676, 926930252, 350025841, 856973175, 927145946, 373895396, 246263865, 676345561, 141378310, 370131386, 132441301, 808251215, 116074613, 797464422, 69542154, 318469432, 568434058, 249602712, 728468196, 12041499, 575246317, 338053405, 480074453, 272473788, 983286791, 527457644, 852571873, 812245531, 707015478, 676284862, 379590405, 157705807, 929184098, 53241274, 625262656, 159897286, 200655257, 161182820, 877040536, 420761594, 986468805, 311317832, 248928101, 964265830, 656056504, 458916092, 931966778, 693649526, 18666773, 581809370, 646615397, 72547025, 98595547, 282921336, 891244519, 3078528, 125241406, 866542423, 967097591, 672315259, 560627615, 796594064, 447524266, 770310095, 435595610, 767186413, 937674202, 57789022, 827034793, 339009330, 906499854, 491913144, 789365006, 943026748, 54814097, 186579121, 862578403, 930138122, 813275910, 937196815, 848421047, 70067598, 918616279, 92752536, 878565962, 48776254, 408512341, 138608920, 106573505, 823554809, 713606781, 495981267, 680401474, 807776197, 241204779, 114069607, 185852385, 567238228, 772128461, 341950361, 637432391, 506109916, 898096606, 587403416, 310104234, 105074762, 876242662, 532851263, 286176831, 93392153, 745168999, 490460911, 768358615, 68963636, 959313804, 753600220, 218812470, 688503995, 445114781, 249751706, 33339558, 279427295, 206792510, 209538644, 218577215, 310343008, 969765029, 746527546, 808489901, 257637124, 992395651, 618132812, 314986788, 451189660, 153589298, 747502370, 492843717, 106221050, 564755810, 202185354, 662193460, 938698648, 695211839, 207977055, 306316261, 479988441, 190855300, 260173292, 562237392, 885504501, 861700286, 357444093, 938104458, 52974818, 692036584, 360451907, 603637899, 43506614, 23499271, 4190406, 408735096, 467406201, 81892047, 604140525, 936255612, 597903485, 432288364, 960195805, 399454689, 474314012, 663942099, 160986410, 273111409, 24082230, 504850299, 681076347, 401097203, 262999536, 108535350, 549142010, 770779255, 22885166, 933662109, 585074099, 731942111, 449151492, 367686862, 711221975, 531128804, 313265050, 364424315, 477965254, 969037117, 856134057, 417204272, 513241353, 334220060, 821493646, 465343988, 603388121, 396883630, 497146009, 120491203, 517040674, 319760815, 206623371, 523071771, 412193630, 575451734, 700740331, 993644817, 291903230, 353567634, 729120748, 876993592, 537395891, 972009310, 926494123, 24170082, 172758179, 450886950, 525996816, 366594665, 704053621, 496617224, 739095335, 162789808, 559195905, 652170110, 75969646, 105621701, 539713632, 536404837, 776484050, 209953623, 540222357, 106545177, 593873608, 576392151, 115252944, 254021368, 845005867, 787126479, 772368345, 216533634, 456140170, 712182230, 541483603, 468937005, 808922602, 948565320, 84128486, 283315516, 361796103, 737577418, 92411062, 182617005, 218128014, 177265145, 148436725, 759732480, 317810026, 242972444, 983109851, 271500265, 243190468, 122052733, 268062690, 357632535, 467704481, 190724278, 148755744, 91490518, 902217013, 287065885, 501053646, 858680633, 76991692, 162862903, 520261152, 879720198, 32911667, 294377151, 737304264, 246325738, 442485939, 330401805, 26754451, 64975509, 923309851, 216841899, 253250739, 144032880, 866575160, 714459551, 962302157, 987746149, 221642771, 903245276, 277215735, 919229719, 15825550, 736835562, 137355944, 710777524, 736861131, 37336669, 527891079, 524817522, 299124115, 20611430, 861405649, 841535642, 220927991, 934228758, 465869503, 496136361, 178323699, 156426016, 298308346, 179577729, 597915152, 679795515, 734352917, 390253808, 176701410, 836647793, 647943268, 235460144, 688444871, 486092125, 992695351, 901395944, 109948934, 683326822, 587867715, 661416006, 384800302, 37796699, 86271800, 48809048, 896399161, 165464108, 974398964, 140769624, 847433556, 461962008, 481575775, 550065543, 331296166, 34487639, 386452988, 548578642, 828479099, 827484143, 134105055, 995309820, 920358191, 950890555, 37534229, 484031607, 394903123, 807025120, 250287855, 263409561, 343541429, 767712870, 831323333, 664769409, 105912500, 274811428, 663867576, 29615203, 261138347, 18619867, 137639557, 799375998, 822743810, 253993973, 485570682, 941094080, 348859006, 279572102, 547438877, 394577176, 178418406, 714497943, 606413447, 73333466, 529903660, 455054596, 697489083, 945766605, 762007261, 239103505, 31067705, 713052819, 853873238, 200943874, 385978832, 600777774, 191134070, 788965452, 170440601, 547151930, 369798858, 61120286, 10408608, 194378154, 280713126, 367581769, 922699794, 287379297, 493036657, 160949710, 373896919, 875306021, 934297297, 467112668, 788642571, 100031346, 324561386, 121131882, 366936109, 915289537, 1475764, 20216972, 424804364, 600234840, 285867318, 221224006, 640725930, 586628605, 162971234, 86877940, 4778310, 565470249, 856571956, 821548901, 185253587, 592970360, 510185583, 651915202, 98113635, 646283979, 82420573, 107670663, 863141806, 143155357, 45763048, 661037042, 721949595, 357324445, 838361531, 450851336, 26233033, 414898721, 543953303, 767676023, 390865575, 527066794, 705157444, 546261612, 326456694, 40273077, 139500849, 382025550, 697760511, 103217379, 286487654, 165458909, 836794760, 67498782, 550915522, 569002456, 556716773, 521786281, 617390597, 904903502, 683428415, 227327836, 130201115, 361507270, 20707653, 340315951, 897283413, 945217036, 762518688, 846932848, 271993896, 643470782, 657631050, 310195678, 464882151, 24631733, 707663755, 803108938, 768874309, 680890202, 695551592, 604709245, 9220787, 483636726, 477703572, 122295984, 683994745, 515254332, 950369601, 939599374, 906982394, 371906861, 582097847, 746680117, 348417439, 212806333, 649446847, 170804157, 258703038, 667275181, 246831131, 58302739, 858558547, 836248285, 636328941, 641951847, 847714920, 76380807, 720223042, 710011833, 437087851, 566241818, 527092585, 372186712, 647421116, 673422870, 824784846, 652958938, 499609697, 84967887, 470872862, 555702566, 213312417, 715847477, 343929058, 947596153, 19632418, 778931717, 313223369, 805094041, 889012724, 828479901, 548173607, 808004542, 875816040, 9876599, 884919244, 1728376, 808835597, 291503700, 602949468, 874579332, 64535102, 866003040, 248424858, 985457118, 199385257, 184111851, 616721877, 900950300, 37643113, 891730044, 454714707, 662521909, 534355838, 979847019, 166614560, 315204842, 877469267, 561919537, 408272773, 107744550, 264390846, 28606098, 47054319, 643981651, 240536473, 25631669, 860914584, 145206756, 676222653, 706143193, 951409261, 736136943, 795483730, 61300280, 250703515, 144754510, 895565068, 548615915, 631896751, 621789598, 12285255, 410578968, 337457018, 506805822, 737013268, 806635309, 340235325, 927539784, 410521299, 940238942, 820911093, 921787887, 635086182, 459442729, 38167510, 991440721, 373059554, 108064996, 685804625, 12688615, 234734703, 841122494, 912404988, 290683456, 909789492, 634692207, 15838697, 546866540, 271688697, 850527315, 332745889, 773703605, 630446247, 83168267, 158836468, 818288457, 14656627, 94733030, 434711526, 746425115, 902978371, 528859598, 564827984, 342418967, 157460761, 394893584, 867591070, 347473797, 393101569, 44176596, 240677388, 340004926, 842177109, 279280418, 349341989, 421601912, 735349225, 785706534, 370434017, 326185275, 911472832, 456701704, 287842135, 526182585, 161510325, 580308005, 781724978, 484902550, 502057196, 505014137, 474095604, 318741368, 866407318, 784570283, 371925159, 788230007, 360064970, 253354322, 335665219, 824583794, 705214696, 789000190, 735692685, 701530997, 197254683, 21908880, 897417229, 719176556, 335118204, 383511020, 756192631, 351753391, 632513525, 97386273, 361337339, 922628394, 39553911, 459095664, 809541236, 795341304, 211132398, 708257899, 954071948, 134798455, 114626529, 63681783, 169537463, 770879205, 444279070, 272152203, 893538775, 323186984, 161239585, 94370483, 28508479, 851337827, 564275079, 13957061, 290692364, 998169005, 154533826, 797156282, 135784025, 991817759, 461241426, 575093122, 455348546, 268388357, 2326825, 197275168, 972421145, 716467624, 861012581, 480989718, 202389488, 175553939, 814095752, 398331314, 766153371, 749293425, 911876757, 524375293, 652771915, 380137327, 468019884, 900707294, 495670176, 42961076, 996933686, 973243819, 103630224, 378206985, 384995476, 258935043, 166425520, 912055936, 611827887, 804203268, 834598820, 72264354, 437705385, 577227688, 848058205, 959862286, 88088045, 572547371, 707147066, 846406935, 552958661, 199752823, 732287082, 144736189, 301467652, 32749601, 146986069, 256076231, 864595041, 610706566, 443133137, 276386076, 618007105, 689156969, 846754126, 602623978, 403659599, 26071822, 536299758, 685783365, 15414430, 611394381, 307194080, 604458882, 279920105, 578048554, 170497494, 824574457, 211492823, 662868079, 328416953, 30850031, 348015925, 892787567, 224463820, 985168447, 190583155, 854707641, 70939814, 857965270, 494998991, 815396359, 108876375, 18762342, 285657965, 603118603, 914946518, 281294314, 209579083, 361091680, 47392163, 972721876, 433647728, 976291824, 536524766, 284083119, 786169441, 701831562, 171134623, 634307762, 280479947, 114116662, 144541641, 251546864, 15477467, 912439823, 782569770, 425738748, 886958947, 418698832, 839157249, 212190861, 735870430, 895658168, 642305010, 71485661, 567066358, 759965954, 938894627, 751188842, 242117365, 137197465, 435680796, 344996503, 337260733, 124032927, 57021497, 745104598, 299695156, 954482345, 208451735, 583276952, 657687115, 86223783, 664793927, 393704621, 515071175, 400840602, 351019775, 654304196, 654557775, 98451899, 303398540, 31095099, 734286792, 127548696, 839363204, 634009942, 355461736, 990244452, 144353282, 455547226, 175610700, 52051887, 213422787, 40083191, 923246444, 337761884, 544869840, 259255923, 812641283, 188143599, 524490679, 911345630, 905751050, 429831294, 201341532, 761229004, 955606371, 188422068, 471673776, 271635114, 550348765, 140775751, 30335588, 88268056, 34527570, 874406183, 888319835, 163240965, 719151288, 728351403, 720583939, 52467042, 899538011, 744428277, 456425822, 286404401, 989189219, 31908155, 81914223, 579791707, 640588106, 328684644, 1155694, 806778748, 729492828, 467675375, 452132763, 339905689, 79542026, 816809535, 784866132, 109219495, 739621716, 164109245, 621452632, 965618422, 533979757, 435024932, 460501311, 686317965, 542498814, 654683084, 244806643, 746051291, 528526685, 979357312, 861019878, 344696274, 286874720, 487231730, 591213247, 329368228, 985820992, 632354405, 120125506, 616317174, 753521190, 460348153, 216659135, 274103441, 935908363, 268290676, 583083406, 577089083, 446549932, 142783709, 738639190, 214713959, 443078728, 113821662, 940400180, 181575615, 504429608, 837297671, 501152467, 625086256, 165489074, 236841091, 571045731, 222588712, 565072745, 33575541, 997404894, 106603878, 424362973, 632899201, 875574101, 499334110, 93735580, 800498032, 316747941, 61121106, 556433127, 673431966, 800216628, 611675383, 768157615, 824245796, 735441944, 73368930, 188094335, 50769507, 459742886, 474279079, 529380431, 794379961, 312401242, 65143226, 939574056, 730386554, 765297069, 494369035, 644915602, 725257084, 147655742, 91705147, 42521784, 282341114, 442889986, 544260349, 230347671, 62939512, 630492317, 689580853, 9284684, 734962458, 514705825, 986788111, 815409328, 265331063, 124912891, 404361300, 327623814, 636869861, 360959921, 349435273, 547343667, 242171939, 58130580, 625326598, 738726436, 336834765, 402926237, 245667726, 428216389, 60488899, 515607827, 288482147, 681359805, 825902239, 18662959, 450207620, 416596909, 415028497, 468291538, 322521560, 428750593, 847034586, 448994552, 371575983, 710137137, 829608269, 767457458, 953353535, 831673060, 373002263, 145812030, 575739185, 621224767, 60031716, 370491171, 784865980, 828904606, 725084056, 367526468, 843665140, 119845931, 870373646, 633502335, 375314368, 228291533, 73654512, 700923545, 348635162, 700500976, 265501683, 157979240, 282974122, 563789132, 719604447, 170839007, 608829012, 92599839, 317264843, 657774622, 748355319, 430346250, 758197663, 737151130, 520107476, 765050184, 528705043, 929859415, 914616080, 887871147, 938551169, 475515607, 355716912, 219400178, 885957169, 507870557, 371610785, 475105878, 682487491, 234297477, 821396475, 785817483, 156148078, 969772017, 765158449, 818324143, 94874012, 961671785, 4059471, 119164214, 527456429, 649154255, 911287668, 104161027, 585843643, 621325587, 568396233, 271307138, 155639302, 957411785, 861754206, 89895556, 569199197, 42896835, 877589858, 993197844, 962765578, 660252492, 407261062, 448210819, 954201250, 245172581, 793961582, 322755476, 76792199, 59024701, 36686140, 506234742, 337370633, 854105349, 428949730, 717082853, 344102103, 334115098, 469209090, 565719468, 642499060, 430638411, 337548634, 807609592, 426647324, 876789421, 886906055, 86140554, 972053768, 502387127, 668826131, 832727537, 519410018, 809732046, 300515653, 144879127, 394444280, 850471180, 558638562, 636916453, 877651016, 909012941, 394805899, 690482381, 92877209, 431066446, 5939602, 893895844, 647279518, 706004639, 377334473, 698267232, 490273425, 749625595, 314196165, 139780541, 149056042, 59710158, 26535812, 996908975, 592062475, 472350743, 617334512, 932834071, 795038593, 70222965, 22255393, 773267412, 6027981, 827320626, 516071339, 5913728, 762131217, 482263699, 571339386, 22213960, 798654136, 986157280, 918283794, 681858625, 427133795, 37401418, 954779252, 733030610, 63884762, 889206539, 916879540, 367220747, 819524617, 312283404, 853151737, 759590100, 700694169, 163380251, 434002398, 469478295, 835115787, 556168856, 249904824, 60485699, 992375750, 466720258, 156415794, 513110829, 500859319, 639300652, 649905813, 285904347, 418081901, 711571419, 945127379, 840661585, 59796559, 340820415, 128692384, 417408955, 157358799, 631479984, 720403144, 568232292, 241769481, 55632390, 189857248, 102435652, 309262871, 567227957, 852337423, 771435276, 239040734, 124107073, 284097399, 494047332, 684859742, 52570071, 834962966, 671892848, 302455629, 858950836, 52131704, 674283637, 34971010, 635245405, 311014927, 537917823, 689868700, 928017296, 454868238, 144425636, 928108494, 114092322, 776353924, 499423801, 34387118, 208103764, 641313332, 765864202, 181964253, 173312406, 124364768, 366853970, 582378605, 988373894, 845891786, 107292701, 630829983, 504614152, 523679158, 841363900, 432380775, 466259209, 173900923, 107571038, 861368086, 967690490, 272008843, 681144556, 441123332, 642469560, 656186169, 449231725, 491722085, 317962720, 615018300, 130718253, 5832717, 467501365, 127111398, 241701549, 864036765, 537087418, 940733591, 819370494, 939521534, 769039903, 100296847, 752939101, 330553137, 617801357, 798993366, 10065165, 487514189, 18689427, 33108047, 756502425, 855743617, 493875944, 644606193, 756041235, 330741284, 696555131, 409107609, 589246385, 762331318, 178020074, 840973930, 619206234, 504851522, 283647472, 923566177, 504738311, 400747754, 393232016, 550702026, 21235900, 342337283, 557302346, 292499470, 662961066, 809699797, 668100881, 171713679, 306576166, 943081930, 606204011, 833867705, 688729536, 341930644, 471690046, 530130238, 24584877, 654997070, 726389524, 366690981, 578989897, 696619521, 209853769, 188913832, 662510803, 106143543, 813398263, 540151121, 76880916, 492670503, 300786641, 980698926, 201333243, 204161928, 286448338, 56110733, 309177339, 457210790, 292152820, 233892670, 211528048, 522688523, 548039837, 33046475, 232283363, 597074497, 69934139, 828176175, 655536877, 352449767, 196826753, 199795677, 6359930, 46972938, 569965940, 325595181, 5132451, 138019858, 843343534, 970955988, 437079243, 860963015, 978017735, 460468240, 64490317, 283208985, 464059920, 886509334, 144060798, 527117704, 812658191, 84693371, 427699053, 183285265, 240746590, 181549530, 507091615, 167961349, 147298140, 225231603, 267310442, 183139521, 41065704, 163066644, 76666747, 714204153, 725767097, 449450552, 491238894, 307831468, 668089601, 99666096, 412516272, 68546245, 825757530, 300088583, 204457930, 330053210, 702198844, 587909011, 576189167, 956435764, 560755885, 299386102, 439332956, 27042621, 705077949, 598759396, 96494039, 177315470, 458461254, 520704878, 284019594, 367591841, 141232595, 771514961, 92161279, 498780001, 25292695, 364296404, 975787973, 597443233, 499927129, 544285426, 610239523, 657274486, 246430071, 315176779, 435385113, 12939751, 486783156, 284868583, 12933841, 957979710, 145922165, 773079653, 669923726, 401198943, 547027064, 847390669, 883255694, 929320315, 461518868, 787679993, 766359832, 58575229, 633100194, 812347441, 884850482, 496779588, 207597193, 246118964, 869763357, 979375914, 387393609, 308667639, 898134941, 266327973, 212591269, 627536267, 918060287, 876397815, 755971342, 820085242, 929642399, 567628587, 592809188, 134223767, 905234083, 570422722, 17056838, 649617201, 220969364, 959513123, 307114969, 60747716, 701882564, 142034617, 797803585, 946530219, 478351523, 708015374, 700879132, 499732580, 785817112, 496655262, 660766046, 724915339, 614259077, 953971126, 789407625, 925910692, 647126048, 693646670, 870601098, 392035530, 629561884, 479554181, 582075056, 436153166, 469499700, 62089322, 497048727, 386132947, 567241667, 375443983, 989913584, 983568757, 34531102, 258770802, 866973170, 294042989, 19932636, 811429468, 456555907, 139184699, 678088056, 258276080, 467650384, 440663787, 809979911, 954019784, 325438014, 582821175, 931640704, 972648738, 345238421, 769760537, 253583498, 511920939, 972620211, 89982886, 129980264, 191590372, 974851306, 836164222, 865229289, 593174198, 750678757, 355754112, 172209213, 397889446, 213433012, 906457071, 18501000, 216485308, 332295159, 142679709, 115941999, 229502993, 391012764, 40366557, 834148509, 87727989, 853332724, 397415737, 558962897, 59820882, 793716209, 87790435, 560461812, 107775499, 836915561, 119568641, 344632922, 719757075, 891706285, 472007763, 292479230, 380514879, 136463587, 649009481, 519754307, 849298447, 46218724, 414361161, 928080183, 17781124, 368631212, 525515215, 597055515, 34697460, 856027153, 959056500, 188059294, 997331920, 668972113, 344205262, 975016462, 695781684, 910212631, 149625428, 476955014, 973019882, 85046025, 129260128, 536145321, 835526409, 212872417, 997795722, 504715649, 525631558, 640681462, 296580197, 717037414, 76985477, 547951289, 256321116, 935853335, 562260354, 50998756, 127895356, 501979036, 470194635, 205866601, 367326448, 711187330, 349545191, 609678533, 682270358, 296162102, 580963958, 707511892, 218998674, 436473118, 182901837, 128297764, 535595968, 171221772, 752632164, 594803887, 380303229, 881899924, 259236958, 778177642, 731039779, 522596128, 347599778, 192580232, 517696775, 929500904, 189904189, 681310382, 535121446, 994733268, 660403015, 144607581, 838645885, 542488959, 805873601, 562962408, 551366401, 195957174, 798272162, 934273488, 411932120, 260657204, 92410438, 95805501, 504744731, 470779655, 372640016, 226241405, 394790246, 994368035, 697585140, 420697416, 420628562, 800583855, 596678180, 804467167, 438214128, 607382148, 777615811, 981357068, 749717861, 882280975, 724090295, 709401560, 582364474, 909126710, 542439513, 336761702, 671970678, 54423687, 83046324, 166523254, 584899259, 364041857, 685471094, 363019324, 700272536, 48948183, 561334351, 359307661, 303832631, 548594366, 26014125, 549837610, 189626124, 530202915, 245198931, 959715596, 363027156, 321372849, 620431993, 371362884, 212826737, 848402570, 953846516, 582330550, 687207912, 100365915, 902395461, 230615858, 497772581, 847453899, 365785207, 558214530, 30825534, 23648859, 828583703, 361587116, 23937960, 336813705, 881237978, 535962053, 857520590, 998905399, 277782580, 414800941, 872046034, 88642217, 931221621, 779111592, 607932760, 804288581, 181855671, 626984657, 437773055, 750749291, 347557163, 407008222, 898312031, 557058738, 212122296, 171572681, 395002663, 463975319, 125686033, 870494121, 621797131, 306921385, 411533177, 352776725, 672154680, 750723622, 93291355, 594822319, 145702383, 891025416, 117092848, 786502860, 38249843, 972264243, 811182593, 281632313, 186352250, 503656649, 641935667, 856562302, 36602395, 365501156, 35521935, 839781882, 900139749, 407016498, 240153658, 166097780, 436847333, 344835227, 811515080, 734324616, 982131653, 690958500, 416008065, 242524271, 785989906, 429148308, 541941373, 819408780, 836390044, 40720498, 313846149, 898942400, 879946046, 877579997, 692094881, 482073973, 917355865, 815036668, 624733614, 318778113, 520209747, 847632987, 832226459, 643988717, 22032450, 403868986, 352714578, 931167556, 710331134, 700156070, 595565327, 902379826, 22337004, 162775086, 788689133, 291028587, 556713999, 56037721, 393824702, 37024032, 463837530, 768490257, 390372174, 686200617, 457751453, 352504740, 860584704, 230459087, 625686853, 992860564, 79068577, 396783504, 951457026, 671149998, 471145894, 93846629, 497673546, 273179936, 490977570, 582847731, 933806979, 889062547, 258001060, 282966204, 381240910, 271166515, 282694417, 597508658, 226437621, 36156604, 625969624, 572667073, 927576461, 601893470, 246034155, 68024443, 710207389, 38739410, 240128405, 989781202, 970565026, 957234120, 513293189, 266018844, 101919005, 173303271, 751198228, 510334022, 735332085, 723386403, 142005866, 108615966, 122696280, 970363649, 404058847, 307767444, 668327767, 813768244, 447207147, 849704700, 269871530, 537802563, 286636749, 286992772, 145288502, 891557991, 518548408, 389741530, 613803529, 786450278, 235249454, 850567829, 214092932, 407251924, 780859227, 846310680, 178037673, 805165202, 851342208, 617694414, 314020436, 162332983, 450052901, 638177023, 912156420, 407605218, 645329929, 210146996, 960475071, 216225751, 455730754, 290785989, 964349150, 758599693, 965892032, 147555090, 59521971, 981457257, 59815275, 518353569, 772042176, 55776189, 89225781, 142488491, 327930282, 63459253, 931376456, 219740805, 845341237, 35056938, 64916695, 272139711, 204461271, 849597445, 41071069, 109834017, 993562530, 800823605, 949410878, 140119924, 363672953, 559671521, 965627644, 659204362, 6897945, 819723241, 101794344, 636124840, 583791104, 155644105, 748279357, 868265814, 3456893, 133754598, 742787596, 320392631, 492673668, 56516863, 283677725, 478795640, 115150075, 646872874, 860322257, 38954548, 582149454, 646913227, 874436384, 853692393, 794594859, 533686252, 946483726, 161553378, 466562672, 454905255, 592868155, 378259938, 957356969, 658582078, 784483927, 356459155, 823003783, 234623597, 717421607, 797205810, 744186692, 624290935, 307893283, 484645382, 762309669, 665626487, 646870942, 772886328, 36438057, 877543780, 727054860, 740407333, 18727342, 175262615, 813038017, 832126770, 696955989, 863936474, 432971339, 937876079, 384616437, 132727752, 14844100, 934192128, 174150175, 581444319, 257580040, 641997908, 985030596, 339004166, 868388981, 828062509, 515260857, 269539307, 868641296, 415988118, 486160110, 130788399, 233623820, 431250585, 859717484, 573411908, 176987364, 246632221, 68486750, 885657448, 283235370, 608325499, 151507599, 195283967, 97913162, 57304220, 83110134, 969767975, 659015930, 897632707, 963803651, 634919491, 469007851, 521762904, 313139986, 792324077, 791509988, 944572163, 292580065, 997670183, 119372554, 236736302, 629418524, 844618701, 119023569, 453638803, 36493455, 138679160, 205535142, 726204489, 846526989, 301070741, 531423175, 142325222, 969061643, 900400294, 986722344, 526443565, 891771637, 258082404, 123743495, 965350153, 831906275, 814177511, 977317886, 649016794, 151163731, 38645361, 43312909, 550864333, 468538546, 726128175, 907508414, 378867422, 84502578, 215624126, 273155170, 995955790, 107702952, 344815294, 205589240, 987893758, 697371931, 502443701, 489984996, 620760802, 230217541, 373110783, 931421783, 303812168, 726189235, 91814143, 870481094, 987607691, 999726590, 600059929, 818919150, 363257268, 706547202, 5173574, 939917456, 328420592, 413602154, 52332745, 554232934, 495809540, 202858253, 35434223, 29069241, 249506328, 278398150, 381743860, 666788496, 855759134, 336092471, 950809664, 309865004, 69495401, 882031999, 531863323, 180387250, 601302751, 363310767, 60888525, 27776868, 646306044, 157374, 169872179, 361438816, 846946654, 726247719, 106251863, 406177255, 15988399, 970236455, 283338646, 301048742, 907331619, 115740262, 334866864, 668117987, 349494333, 31929703, 270976449, 80047082, 461843293, 139722368, 569363619, 406703307, 416498613, 732306562, 180662564, 299786383, 129026475, 932668188, 756346697, 503650019, 515860494, 929219046, 295004449, 63288217, 616738983, 652795497, 93898919, 602486935, 525241977, 935178911, 552201788, 901468484, 638009695, 82121334, 132232792, 171617837, 463265095, 755725276, 226377234, 797606575, 672762778, 415060141, 443733746, 886466683, 548960385, 670220037, 666415301, 270059817, 928739168, 185542335, 717493934, 312548323, 729949549, 522003165, 403252593, 829137790, 200300469, 499647408, 138846613, 28439745, 22405208, 103959656, 294220890, 539009060, 701436117, 805392847, 936505029, 742084390, 152963988, 90093349, 637574842, 736461700, 159405652, 177920943, 549682906, 583561611, 971161616, 765150239, 611196424, 118801039, 595899955, 67604435, 583062965, 450700263, 269691643, 924423430, 679870523, 631081710, 43037076, 670928620, 869492725, 823068253, 778238650, 885846390, 972195954, 678636778, 400016237, 436040935, 679302863, 103061344, 742848347, 850089417, 731056777, 541876007, 620305444, 1686468, 587469711, 199074283, 340269571, 897781464, 832470779, 278424470, 992103460, 914910194, 125299063, 613780801, 144134398, 134188032, 325604938, 13265784, 720489830, 622409033, 655808846, 690535431, 889502873, 716957821, 925592163, 932780801, 630209849, 788808173, 805499326, 559500935, 427975031, 609517045, 366280111, 779790835, 425711840, 706301337, 296938033, 312098776, 338270519, 412251582, 972504000, 567611014, 304588033, 141543400, 700267540, 281844448, 893822170, 806295061, 853521146, 435887373, 478049855, 51764636, 477583977, 977655736, 290897101, 721769314, 813207798, 587618578, 482285361, 492677988, 484153978, 210716623, 931632374, 95814331, 430612466, 218581082, 909510675, 996441942, 338382668, 710926181, 327861990, 998025669, 36743748, 76197983, 73211792, 623809298, 613064962, 223652411, 946178713, 811515499, 408916638, 966865758, 12283134, 204053560, 684627545, 292633171, 440491500, 844241087, 657616835, 479331768, 861030301, 551640913, 698796904, 722230800, 788014702, 108467000, 930388340, 897196455, 534162304, 863990448, 39173849, 788790240, 503751815, 712966396, 405425733, 264110920, 886632629, 259315989, 991246717, 421880431, 760213493, 649886864, 361109357, 359447759, 984089779, 39491426, 384783535, 363041081, 602433068, 850495806, 49673389, 419638367, 695536673, 612619379, 177647788, 208020155, 242591679, 210386310, 618104386, 114340549, 194821023, 724210843, 985389280, 13198246, 113121256, 488031560, 702704596, 590571566, 157792524, 834448441, 479180215, 524219707, 816472500, 746276136, 407492818, 415186889, 526478486, 72823277, 596096871, 237254851, 996391969, 882813173, 693129019, 855164662, 896958929, 901688247, 26906266, 613468966, 475442212, 48448345, 808425853, 895412565, 69397183, 929402627, 701065306, 873687661, 549280556, 946708194, 459327927, 408168130, 589923428, 763495671, 439712904, 524626744, 505825027, 781791280, 892428661, 552755582, 647124787, 920358555, 387989910, 241023160, 15855825, 747063631, 149027524, 197622189, 137915592, 484196758, 680843611, 895803462, 570325768, 737350085, 823068168, 135436680, 922318992, 405959109, 953751476, 790805432, 534047605, 693566058, 612928036, 998810680, 735414973, 769214490, 657516705, 579563193, 911764595, 680956226, 797270156, 364490152, 306704822, 640266002, 639138626, 290577661, 603537991, 573706656, 510463997, 743360622, 61318078, 576515486, 454843637, 774427751, 728860056, 264743827, 238395649, 566796692, 742368794, 718000239, 862765523, 328426130, 523967910, 521014653, 766699087, 878409224, 507754302, 340140519, 948734759, 639268314, 152829051, 234966396, 456393709, 164423055, 800945478, 755908560, 391966923, 463621722, 563367741, 219504338, 837557693, 8761172, 734398923, 480009055, 579324159, 602111728, 62585993, 942193450, 603468469, 821531424, 401566867, 790641723, 291055238, 417444885, 571654738, 239211783, 765496796, 666778986, 911577915, 204878394, 402671254, 11647362, 691613209, 127263152, 629747140, 133382831, 358275210, 480656534, 648980564, 691306937, 755426026, 73344420, 434932397, 72192093, 220409333, 540454737, 506024993, 942459058, 797722003, 899804849, 943151820, 104778845, 816459438, 783498977, 355316124, 912006376, 74975394, 375831185, 321068260, 826661146, 549620597, 408649210, 94348313, 343827604, 758840287, 692023192, 459835735, 746380416, 683271003, 759875166, 343629051, 512542791, 953094414, 870986527, 457895969, 494622645, 836089706, 773175637, 460045163, 912816499, 496446229, 183672060, 636754357, 748235737, 743393379, 39014252, 846032292, 463033717, 440973918, 707212350, 983217551, 633651291, 271860763, 949262576, 403328849, 152770092, 33278314, 899795464, 481683350, 341237348, 756580817, 963063973, 44458467, 169273312, 167005195, 417055680, 927571095, 701804831, 217046965, 948824954, 115618868, 513863540, 175997695, 16033409, 845915375, 555693160, 846428484, 591202741, 9514537, 887579090, 470968001, 488754781, 731084055, 33387338, 940596944, 693483314, 238047526, 449895790, 651281130, 329975916, 322003678, 631379764, 860883851, 600784689, 896927993, 97351088, 681121914, 305033280, 730040048, 67631635, 584617307, 781172295, 836940511, 462562202, 327814786, 683358612, 189093893, 984020746, 78463700, 376994162, 944218818, 696898414, 897522757, 296440900, 57698549, 577684924, 940628545, 104525376, 494162243, 885488252, 391700797, 700801216, 700040051, 198444317, 750998319, 129999706, 80129489, 372051383, 151595970, 514830248, 843054589, 489710987, 896342046, 780235499, 231228380, 851614392, 751307135, 65574036, 432221043, 546311165, 823175514, 154473388, 292106673, 458772100, 476695577, 432824020, 641697103, 780356214, 456235108, 309344773, 441904427, 136779744, 712213857, 717954678, 736651556, 329170303, 225561387, 708699467, 908115377, 70345849, 975421785, 689485826, 990837193, 831838595, 360333798, 674145655, 585894344, 837536455, 186534844, 423359103, 952474652, 921247093, 142164883, 736286815, 216016778, 756484301, 443547665, 19949100, 317025621, 463607401, 167582614, 7195469, 106055858, 138669455, 558703203, 463484874, 963533163, 275830002, 494127637, 177225848, 242258386, 541825924, 123790100, 631415406, 749590390, 308082, 315149483, 179153826, 355635213, 699393862, 108396143, 168115582, 520374648, 729590142, 75077162, 38876688, 17711487, 582451559, 295177651, 343677016, 455713957, 675046418, 745232114, 723898286, 534021941, 586887238, 692146784, 732787654, 473772359, 762547472, 99899034, 218287457, 966406324, 471119093, 825956461, 219915527, 215330308, 352432339, 6855044, 928493306, 874197701, 505776002, 66432587, 186099068, 548150766, 352950361, 812861020, 155951008, 665889285, 232469607, 973781849, 281261132, 963866350, 486106243, 115594100, 436897541, 970294252, 632168564, 765137466, 573593594, 545464550, 584047650, 709713016, 81646111, 72106421, 685462558, 976020850, 645038625, 504522468, 450438002, 724883480, 470968800, 282931665, 118218385, 572492764, 707811284, 54350708, 463168518, 131171096, 637319372, 852420645, 845036353, 251274113, 286611995, 269158705, 379025665, 556612297, 44756362, 575312949, 969705501, 493588987, 648134840, 778604629, 518440597, 584051070, 645448633, 420255465, 674184512, 272248429, 751870515, 450001054, 582333182, 83238185, 294180080, 944506912, 165124951, 406324634, 413080603, 214528160, 292449585, 640826607, 731849181, 555123496, 410032272, 111186863, 931604259, 681406994, 872437753, 130214958, 473825660, 456044643, 138301185, 975032560, 395801904, 829607388, 350995447, 32507525, 377315596, 57622778, 492967578, 896174455, 839007998, 364662804, 411484531, 970696256, 951197407, 816445913, 176598243, 337288251, 30351478, 868803481, 994069038, 915134968, 950163559, 393600332, 303744450, 75719396, 347707052, 127375871, 74838388, 185420482, 381041975, 426397905, 59690303, 792162410, 646592153, 922841582, 347313637, 907383105, 204201797, 213658052, 697039260, 628185314, 768249854, 885694861, 695684302, 284667139, 174883043, 538748018, 312510524, 453995002, 219217135, 656417015, 135051235, 43395611, 288782368, 525822025, 311003604, 564860088, 580709840, 297115626, 409939697, 329183474, 248959210, 767488724, 557157658, 919047528, 290400360, 656351390, 616413856, 599901953, 454713830, 53419481, 85499068, 708548673, 513919083, 953082243, 248775053, 811001222, 326959088, 783905197, 657555813, 525886604, 732950135, 385711856, 824868101, 763259, 394584839, 19115917, 830300713, 718311617, 614806119, 329814467, 923318832, 700725516, 636662214, 575937371, 614210894, 58934382, 253797563, 63921872, 34938455, 836881185, 209735361, 803473226, 465966299, 218300150, 903390550, 50057934, 748601607, 595911396, 302587359, 13222739, 302206455, 153296781, 541597380, 432677964, 239348349, 859648992, 33980364, 961423325, 873618559, 951541358, 294124622, 246283618, 557553847, 986399454, 697473742, 217240581, 6009515, 405914635, 981860423, 63382017, 49258620, 932194439, 801593573, 868538956, 516762546, 976933014, 50412401, 863514122, 239250839, 11858882, 33816907, 643388739, 12671529, 271835321, 167263192, 108891603, 907872922, 619668637, 763936169, 225946105, 855514423, 559864268, 732361595, 816921211, 859598553, 777001249, 458807262, 96122358, 996039658, 936733911, 129075752, 570933365, 684272545, 174487870, 418177881, 480225340, 188944974, 211937969, 271429292, 136989389, 231171104, 485025943, 659358630, 105442763, 87681954, 113893106, 121941586, 675452145, 539584691, 647121765, 98715458, 21779299, 484623699, 93699883, 598914850, 202271052, 978228431, 343270239, 765748970, 752195213, 327207555, 876228531, 630189403, 471250988, 127225010, 751054259, 24974817, 652660188, 165600830, 573698516, 768158879, 299086563, 290055630, 498297309, 830486878, 497277450, 349030525, 785473273, 431740933, 413973549, 773709788, 172501213, 810542900, 437195997, 518426258, 240475548, 534524892, 674154086, 496428800, 69577305, 912218004, 473805726, 349559404, 339150836, 581834701, 645452385, 13105837, 101889876, 617167403, 437080171, 760579995, 269584857, 836426537, 139317248, 595107659, 124436301, 610897345, 604226580, 254589782, 35768642, 485046882, 814401029, 707909935, 915026482, 921356423, 979347731, 849014116, 722947074, 805900438, 192423718, 868221595, 68494127, 312508042, 261661972, 727344404, 902343870, 112729468, 47841025, 721933317, 902866390, 578900219, 996448539, 529518272, 975890670, 26140739, 190586066, 960941403, 817600174, 822930968, 602555704, 14155095, 88411875, 500981063, 543064248, 657736479, 923527936, 550977679, 26811623, 507971116, 648566732, 711314385, 79945085, 910782770, 98528487, 318103126, 870560853, 194702589, 734595961, 575213274, 213207724, 859737578, 373476776, 712869946, 830906650, 571603005, 502567806, 677202610, 337444882, 99349917, 165095493, 182671101, 215254233, 817319645, 327364475, 976533984, 339824123, 256007977, 492390835, 531058253, 66157895, 392685762, 301953576, 975906628, 832481311, 384309839, 717322985, 82016689, 381624503, 162478062, 968019096, 789882367, 62434861, 855520637, 992925170, 537852749, 194806482, 603983592, 515540665, 16460921, 103649435, 128932424, 876066080, 152527657, 412697953, 537604128, 464717943, 632605047, 613066789, 399677336, 502852885, 352009995, 199523703, 491700329, 673308923, 934365853, 941241731, 403825482, 722125170, 219377478, 463907876, 806364190, 127615451, 407664611, 387636698, 59881019, 840415801, 348776745, 543284756, 600018133, 675519480, 234775967, 297597421, 228552316, 581926959, 887693326, 816070195, 810238186, 14347864, 503040993, 570855685, 833079775, 539116050, 766855195, 490343886, 766000433, 263666656, 794294888, 483498738, 216361732, 844522636, 372202960, 816492804, 273757694, 828569383, 387436831, 342157782, 493480585, 622746283, 490193260, 73903955, 949752915, 471832254, 51805266, 117197415, 931348621, 44680196, 272196703, 965016540, 493675481, 933120446, 84203663, 552212138, 749575400, 164060198, 538233868, 861125877, 508203915, 765074605, 40084823, 216665946, 924296185, 744511133, 315545311, 741773469, 260000569, 761245850, 124573764, 335531428, 567045832, 687979441, 835436902, 607172283, 845819239, 900392399, 928360363, 44781284, 146723738, 833242828, 386173633, 427796231, 94544717, 291946400, 239296004, 510407972, 644882184, 279148705, 842325105, 204029909, 351401999, 36960595, 591125245, 154499898, 415910799, 408377642, 463076869, 521100662, 778936519, 322462246, 882863514, 899829046, 422062588, 367608393, 779638565, 2150651, 765304684, 221370814, 656221586, 522599919, 520776811, 269196600, 836734957, 193255057, 102723761, 687535316, 276277697, 723078127, 482292720, 251966144, 68169957, 773790571, 187866347, 151388783, 13664664, 649289148, 837543342, 899958990, 492563785, 56002995, 912191000, 368596894, 996420602, 325100293, 687428700, 133608546, 175211638, 486029837, 103280771, 915923726, 711705897, 437899484, 682531683, 292308722, 61961096, 357132846, 208747750, 561371262, 233910753, 315523067, 783753157, 666888825, 463864454, 125297506, 717187137, 985595138, 459659695, 341357870, 952354657, 392954631, 654626631, 314137109, 861434152, 62982295, 354241633, 363395807, 269638882, 645847741, 396612493, 574697221, 99511550, 820096220, 44213879, 169392506, 391123002, 276836490, 209453525, 635306878, 788439224, 818320604, 747920043, 821094872, 206151311, 342619830, 354396525, 662309751, 304280761, 43824969, 802757469, 220768335, 947797234, 5521480, 934052313, 111135725, 272954407, 284532928, 276913260, 899723020, 612054466, 770080261, 254633760, 540423177, 763064265, 30857239, 120978914, 661833803, 69502673, 932896592, 774144866, 221560374, 368221722, 4572121, 395996430, 72347378, 722584719, 238346461, 453576391, 290719238, 129090176, 390047114, 947365924, 911736734, 558238108, 555046720, 813862561, 684503577, 610491046, 685573985, 834854420, 550605315, 513428729, 496260259, 537771094, 537191728, 434567948, 521496589, 302185702, 204217313, 801995549, 45104525, 55763346, 302208950, 869944195, 5833984, 252035931, 174317093, 217917198, 309899002, 599214900, 195521939, 119329366, 234304189, 38033234, 395662752, 443389313, 599976670, 974518098, 27372690, 969819536, 799665894, 217246590, 276047437, 315501804, 995858751, 468486908, 516729326, 99128196, 526135730, 806453489, 32177077, 377449955, 205502665, 796488731, 999646236, 310167741, 354096090, 980344544, 697897137, 763915543, 967595268, 776751008, 688389269, 365948428, 320789182, 348158507, 526382212, 553400212, 944658677, 136713220, 356244688, 870670441, 912126985, 58532887, 696586206, 756414453, 391979370, 575192536, 896624453, 558574421, 445139551, 178584755, 993486249, 144439701, 158762936, 268108681, 121368286, 676445461, 405777754, 434886449, 367429899, 523998558, 902676876, 16831311, 90121058, 773587327, 703728570, 941877109, 217493020, 587143951, 736674328, 825370239, 540770243, 155145412, 638506087, 80283680, 275960641, 613381937, 923560861, 919778231, 21428197, 959612057, 386436602, 110431514, 184704206, 34756746, 764381876, 334678854, 855663078, 279900197, 413961878, 51487706, 594206974, 154597102, 218529027, 878250317, 787779345, 97933587, 25640218, 89851163, 393668962, 626906668, 763462484, 665385325, 697641165, 170795213, 647861769, 528298648, 455033124, 264002097, 549857112, 237438489, 294134751, 83620871, 214879772, 510704139, 780662731, 800474285, 873230246, 872704969, 611989109, 167532069, 432254228, 425956074, 732839994, 117518106, 344310333, 570908240, 372333040, 950283303, 202724794, 387037174, 281456880, 401963999, 551832376, 635041373, 502825694, 437293191, 45006452, 282816702, 447794921, 557935540, 409260410, 264420172, 304065657, 266197200, 321759605, 866851195, 600282904, 449826949, 520783869, 270939666, 230720071, 782798601, 314239416, 986210047, 894592160, 97660971, 678688365, 441659025, 863700676, 467127179, 850989873, 951864723, 597430734, 722964835, 935050914, 266517644, 867936979, 940009267, 107589410, 184646184, 831699967, 877403938, 390151160, 899103545, 227423716, 33954993, 294550919, 508308169, 268280664, 994594593, 953648388, 925229404, 978769327, 481976662, 587858293, 10431529, 11534943, 183955922, 128386092, 294014899, 446563746, 874347366, 904278785, 347132384, 648696726, 942118494, 497040448, 349732234, 828803262, 685515938, 748426338, 899986139, 454342095, 672989597, 847907228, 399782838, 652569862, 608824630, 967519866, 389075993, 296837346, 95129840, 201344373, 178163391, 275780599, 833552581, 111820532, 190736163, 983862500, 597984038, 736746966, 323891399, 290086189, 360199298, 978921976, 332796142, 864523623, 212273621, 959762729, 349986362, 692526723, 731588449, 473789727, 605445300, 593762896, 699169533, 672568468, 702556106, 232628616, 228334357, 735998145, 592305960, 92279894, 338425272, 368395377, 443423861, 684365010, 444877609, 735142486, 140116518, 659765951, 832012033, 241618205, 996120973, 408025636, 411346067, 896342598, 291567606, 270430025, 530774814, 21899151, 100355716, 471133980, 726529716, 183484235, 812879265, 56046278, 921020059, 789632956, 492655974, 847316591, 292987954, 251811457, 854165986, 972885432, 987400741, 236282712, 118854828, 897401486, 124589044, 521996293, 441607228, 167140076, 816586136, 555599579, 170189756, 161714215, 231073057, 333894899, 421125894, 681502398, 676693273, 445648708, 808104813, 675444926, 329130016, 349765492, 598391315, 840388276, 19954176, 196249371, 632878375, 830194291, 991544010, 554677634, 786589938, 625716335, 476701474, 80826055, 935622243, 963050739, 464836868, 412661176, 928260080, 97924507, 470797716, 205839649, 907826860, 976573163, 811813555, 69290870, 200656371, 978819280, 929129018, 697045861, 482923758, 518810061, 243576838, 23155070, 816022030, 542953819, 35011305, 519663017, 796006741, 698849963, 885678349, 791356676, 976909418, 26686017, 856523920, 863672798, 629081198, 464671325, 490020614, 102203175, 270653413, 116749176, 432868932, 951625920, 884846061, 259034432, 2955757, 992995328, 239734681, 481077611, 365020152, 488709785, 890817690, 877197636, 338009351, 304383790, 631335696, 608080504, 930038211, 435301435, 477529863, 894800446, 781446909, 145147763, 612341635, 924940066, 843703888, 79592023, 881982351, 220020557, 970992195, 325380641, 577450494, 449496356, 639869841, 857805364, 753631856, 349159140, 500455969, 648952652, 790592504, 643711089, 837773443, 434949092, 568598601, 418415517, 10582798, 714369296, 432857119, 691233525, 673005519, 286634204, 116875475, 578101007, 214721834, 370198229, 897161554, 725907342, 42872030, 843169128, 592931864, 218890334, 909637669, 360237745, 66725910, 336152271, 742193238, 282922542, 540044021, 803584143, 699436543, 335806964, 469257620, 473172026, 594658782, 969225095, 604162283, 368171446, 704903489, 104111579, 124651, 898309571, 727804389, 990074410, 308156646, 127421141, 124834272, 288222943, 431130601, 880455472, 839676116, 444018840, 86341442, 269101619, 864623592, 643891553, 28324874, 928519547, 623591396, 472062984, 441439879, 728119100, 39490245, 200672357, 356166200, 867949939, 303135915, 319567476, 212117255, 104658090, 713658530, 926496855, 492163186, 413976056, 453966316, 192417921, 128025907, 458812149, 195671244, 481134710, 479668669, 908445520, 768373739, 453916171, 742664867, 346900428, 103459266, 851282855, 148599811, 401999259, 913543301, 202389950, 207454449, 771017556, 742216025, 49862454, 776557160, 545573886, 17053840, 624729277, 949861414, 503777665, 630306663, 942521536, 383364572, 318295712, 883123679, 29289362, 463204752, 228046417, 151408460, 872608824, 86836035, 76694232, 903873184, 571329809, 19601486, 564754083, 919079648, 996669466, 675490018, 252528281, 708835217, 118418333, 805733509, 471004553, 150006428, 37784857, 171580579, 367059497, 730636406, 916155891, 715479260, 934784961, 970022542, 189014651, 513830846, 740532624, 826173095, 316404356, 194119538, 745568510, 375214815, 159394244, 861052598, 424633165, 421805977, 750911708, 578475239, 629184588, 240230395, 49656966, 330479601, 891744805, 876852062, 829235222, 814058485, 890808694, 611183302, 422199996, 319187147, 435210093, 886726435, 566901821, 536676962, 942110733, 44974553, 17587316, 926093481, 202222554, 132502636, 628914558, 44915586, 153150966, 101636613, 853049251, 803750637, 282732747, 45847680, 971153151, 791054803, 773043936, 138142821, 683574118, 558845845, 886098733, 917628066, 623972016, 413748563, 873783932, 100909250, 180261893, 146912395, 898337985, 622954492, 488587759, 840028225, 102171159, 558296370, 656309039, 51841538, 284641787, 474545894, 143232770, 780224325, 393456955, 372083492, 259718971, 646334573, 168734832, 277099406, 807662633, 916043886, 631479145, 120730395, 820477421, 396674634, 108573349, 460679860, 233384197, 125800369, 468179023, 315900395, 368555923, 676315790, 102648269, 7959044, 75230228, 766332976, 332781492, 708013061, 407334819, 383564302, 758167396, 810236658, 730459750, 443675886, 118317906, 125081378, 77500909, 12963634, 298788722, 204404178, 821032170, 836029270, 248100384, 716145989, 662718263, 151767115, 879763388, 608706308, 186378177, 149934708, 942174561, 714186416, 908473953, 960640737, 169398368, 319558738, 740847603, 455972200, 694251898, 795179681, 575288215, 776457449, 223201147, 539927588, 290509760, 47597483, 424531737, 890537771, 214717115, 727363651, 258878725, 763403164, 126228380, 5211284, 715175428, 750732128, 551214932, 148582032, 131327015, 36296132, 483477578, 996944210, 371548342, 642633478, 805557301, 349937367, 647202499, 992165820, 92783701, 418516440, 240255316, 896267125, 141713842, 861839991, 51524755, 718895564, 74121854, 267488056, 948505133, 406829195, 323813307, 235684805, 364370716, 111183112, 41056069, 573570631, 722912239, 47715794, 369988942, 974336584, 438225691, 410699644, 327838216, 593142636, 205204694, 892408335, 978754937, 762646738, 458234586, 211357170, 873417244, 427774427, 669677275, 51399785, 322703642, 29822420, 891964989, 816185863, 217604731, 730708458, 660614801, 691548478, 34301966, 437172545, 98342578, 53946323, 783443974, 609294744, 119693408, 724872134, 217144378, 468264104, 606548066, 261017817, 691370102, 763964123, 752875281, 947382269, 206076912, 546986817, 743416780, 8580357, 677923784, 323736345, 609276681, 366412921, 856867180, 405555621, 51473203, 414811419, 140705428, 701890005, 149446065, 897640930, 860206090, 759662044, 758699746, 867664352, 717958521, 26432677, 332796939, 177577544, 822159632, 897470251, 621682051, 114395444, 298066984, 579979237, 257142274, 709003061, 616700998, 16584698, 941864866, 801050735, 587865367, 906468345, 899135707, 690554500, 105446697, 190115694, 587449271, 911159404, 557856890, 356298780, 83718338, 295296870, 974646486, 507434943, 121464480, 20665584, 969856833, 402426209, 493966725, 647496905, 136312593, 173328348, 118817911, 119476035, 621176551, 652813091, 249327216, 364540916, 364348940, 414905812, 842467266, 114138308, 106383794, 269388092, 425443595, 761963430, 461167024, 580610493, 194449954, 569246841, 258294053, 590741223, 543777605, 645221259, 993731878, 625046579, 548464852, 692003025, 664143643, 240822755, 851420444, 215243226, 778882702, 811168947, 646868696, 878968154, 452797660, 993060553, 142725853, 587764847, 584175891, 652905472, 543187350, 752803180, 782561561, 937805579, 476753861, 187500158, 225506383, 44054599, 868712952, 661620931, 84558364, 810286712, 138168396, 150199994, 905073157, 863655258, 316242877, 602911358, 252013146, 453574388, 101346861, 54206297, 973958370, 154564342, 92606776, 589365512, 317389643, 247132202, 221654148, 565879107, 93721580, 44016412, 182436086, 82668293, 245843586, 914883665, 229724435, 147039497, 513429638, 822989858, 482939604, 495188870, 782650486, 261839888, 154778116, 187176746, 501083076, 898163949, 471434064, 392596953, 244186465, 65869183, 122977145, 238388291, 865996370, 201844834, 514418381, 171706748, 142352227, 892675911, 332551345, 481712150, 833034958, 813024397, 450771986, 189373502, 761590270, 160479808, 916380283, 725069727, 233574649, 404083299, 905862600, 48033908, 226830346, 215717681, 134118153, 448734913, 367358568, 652137268, 292219024, 48596927, 571822089, 411558767, 200135680, 793924945, 714775119, 572886182, 850211668, 135530538, 997700956, 573976528, 256271674, 89189170, 483884365, 828019771, 94578817, 994607807, 845210217, 20682786, 534552728, 311339225, 110180324, 930082943, 163510516, 167079229, 816191632, 847831654, 279154452, 26622699, 548347692, 329865399, 461062487, 221231075, 219011467, 34736394, 799602453, 969233227, 969669391, 395770144, 667647203, 4448245, 88128633, 97266273, 867882960, 951174565, 664254023, 497708306, 570794069, 637088492, 434479395, 74774730, 737755649, 333500585, 176737745, 879779340, 153226763, 70610878, 642833830, 351400400, 145407136, 499598035, 814489119, 645638862, 620819734, 482893596, 650922500, 892200833, 924074230, 557987129, 77600860, 719322264, 450207786, 913501633, 195366551, 210789466, 498768768, 338626798, 460229257, 215733096, 785868947, 593202807, 166409736, 358123017, 925860426, 407738433, 328475050, 243186626, 609724845, 368134069, 528033804, 683607067, 345769038, 751710357, 743973112, 999179307, 137121487, 262433981, 902042339, 764424840, 850004008, 782366038, 431048439, 14086319, 910169286, 985321270, 76376407, 931546530, 235302990, 631715071, 250935014, 796816353, 868012126, 580913288, 751660917, 51500459, 986860534, 932153951, 53659196, 720389898, 131605929, 488494226, 225668101, 13772877, 922267821, 248810711, 730851136, 339702589, 481130908, 125361066, 749030422, 321570406, 99755525, 372018969, 275386075, 178126325, 793604658, 91753598, 300831170, 61308874, 575097901, 505155056, 692534319, 91756207, 100780726, 4410418, 977153709, 698979963, 818678984, 648104829, 288581095, 510886854, 210735142, 968956310, 56866508, 173499456, 588481155, 189406692, 568650350, 517513576, 488392403, 598967650, 235929334, 898470076, 680201439, 305164575, 830447090, 665884645, 141656361, 426021007, 481243512, 380585275, 42959947, 236029643, 671649891, 517208739, 710985616, 353439617, 920071543, 853146085, 800278803, 116385838, 47129723, 749085399, 834285986, 998766469, 2288658, 690305750, 591847271, 825212606, 660071496, 255270578, 292211324, 82148232, 867430625, 116968626, 727088211, 44667847, 6024695, 718927283, 234770249, 688581974, 833484455, 209318168, 403633905, 535891861, 671162926, 812902457, 563349814, 690894733, 80094698, 420613857, 873139560, 906941315, 537186683, 567249722, 189833238, 319682221, 876505396, 352308784, 96169804, 520576963, 345782044, 513772173, 125127353, 237864632, 709572800, 211678000, 638770115, 514950938, 499663365, 67925927, 770633697, 969188777, 800498882, 874459644, 91167378, 364480671, 921252516, 702699249, 289951191, 202077892, 94585536, 520590235, 566655730, 998955853, 417744422, 839220317, 285788748, 375324138, 970724414, 214426213, 29092173, 915875034, 786148280, 704329286, 252084395, 31933404, 658064309, 277364930, 108667187, 689807751, 98920916, 348245757, 765060123, 169419581, 442991381, 786076339, 203904620, 246555422, 443889100, 855969734, 213330749, 943097610, 829034142, 356633785, 689113234, 912570969, 815411199, 493809745, 893650222, 208489141, 307758969, 632134403, 945599459, 851189756, 509154042, 932107563, 803584625, 349525723, 303439222, 348010894, 315455594, 596705657, 1936150, 591063686, 373264290, 564606997, 176184617, 908481474, 23069753, 183522710, 524960203, 64832670, 67066409, 464568689, 766275302, 653668014, 690775732, 579784765, 423133131, 368267284, 172432340, 898748036, 348038168, 198933631, 166757747, 592452934, 967485460, 197866051, 842579414, 361427607, 414449714, 610525521, 59775857, 933305384, 450217164, 981686534, 545040469, 191378106, 137794437, 588862475, 526937701, 840986811, 709087587, 445232411, 125761282, 494427484, 56478657, 515059588, 270578762, 482080504, 717145221, 761459794, 293628676, 778438948, 191385050, 961065216, 89047853, 244882016, 586358502, 463348422, 75658051, 997654992, 885302677, 426742470, 920155114, 805728660, 69020137, 184764891, 5721817, 410009534, 657680976, 902247393, 808619719, 42262127, 216603678, 272929982, 617135623, 521351649, 792568224, 750598892, 215069428, 954954669, 991791460, 891835452, 975161860, 596474634, 660889834, 659172215, 214799427, 303928426, 149502267, 325828647, 446554118, 176498835, 764134778, 850745848, 180719371, 153647550, 519599635, 606091491, 441303041, 740688505, 317170271, 400655871, 412643412, 180543844, 837988133, 376305288, 415863409, 590217033, 571090059, 973032297, 230912818, 71490821, 817672164, 660642305, 707042872, 115950633, 219583688, 925267894, 859319196, 37422511, 599433456, 975556228, 991704435, 925736275, 887784963, 143770724, 605367547, 472465107, 663433296, 834843881, 357628373, 921551870, 644852748, 477555517, 358225506, 76205886, 75791158, 340508807, 966091693, 43727293, 99979056, 362149567, 844416062, 246360515, 202979379, 756321139, 186030008, 483818976, 603434052, 490455098, 193455424, 456353419, 42564254, 573445041, 297055404, 430337491, 80088968, 156310076, 406711603, 179447370, 936976356, 159715197, 425671964, 306701669, 794025587, 725457116, 708317232, 951014200, 503615654, 656285397, 994627845, 581438899, 16850240, 275216204, 772030315, 142415302, 512081744, 521292311, 619383963, 859682855, 602897694, 452487810, 811281879, 465567150, 955135326, 861655485, 682803899, 618428638, 258207873, 435943294, 170747363, 224898484, 910192351, 922595228, 503431080, 447458760, 326715902, 151202329, 236540776, 786321128, 569633919, 463931919, 328948897, 271917373, 841057550, 979555501, 210251566, 61351895, 334651321, 63683336, 534809140, 235888850, 997408518, 608786674, 529313336, 214705953, 393092114, 236552447, 202732602, 353916470, 251678102, 125530829, 648948747, 841133418, 80148309, 234974793, 782224244, 437042486, 759729302, 292386790, 412398049, 356131887, 756566502, 571234815, 620922285, 282145343, 920821246, 794275425, 366595195, 352226615, 660717135, 632755017, 684836899, 639545669, 587890068, 447361815, 669163963, 88698988, 395295590, 615292669, 253859131, 671061608, 748637260, 849659433, 206499902, 974446315, 289012077, 767508334, 296038601, 691226102, 242733730, 945617713, 569934582, 155298490, 842042929, 754811123, 669425012, 537381452, 898883179, 959256304, 755929486, 58411934, 776433488, 509539113, 349609865, 917239319, 558540828, 597092950, 789288650, 112369269, 332529902, 194919551, 36176805, 223868575, 355478545, 49600355, 687740032, 345909996, 697227928, 308319050, 167198386, 514573485, 959667835, 29238172, 275195847, 137204548, 114579172, 433610449, 364907206, 321477927, 926203607, 623033468, 973203759, 847934908, 858951600, 768505249, 980702870, 617297611, 45156329, 748565350, 578655610, 988841231, 26889693, 124977329, 59517243, 620160197, 375381584, 101862345, 676501890, 166781046, 862109739, 256818488, 60591038, 14002598, 216755479, 156078609, 607638277, 193391078, 778014026, 118883319, 359839858, 572889314, 237448762, 291872110, 634715026, 169318149, 471362410, 568833496, 229977834, 328639088, 220581915, 16890274, 712578305, 77034617, 409118055, 495442960, 498117068, 587761675, 495380603, 265305358, 307051932, 522497494, 51146205, 331598869, 472486390, 623454110, 722293827, 702960994, 435315774, 250798743, 961216645, 594159483, 312874200, 945612089, 402587338, 660546472, 864913257, 925753349, 547414867, 809448577, 46137744, 375306113, 874697457, 285064940, 402395846, 403693943, 33718557, 526856534, 440836317, 17727712, 953841211, 576117069, 360708885, 477046685, 989595496, 770334673, 259074694, 359068157, 77905314, 980534691, 751336807, 349657601, 742694837, 174121697, 67359579, 934655830, 530890844, 175435208, 586973838, 175584235, 45886903, 515376753, 837900612, 183439297, 459112214, 489298948, 726375027, 589388574, 314721585, 556122688, 714074065, 342374438, 687948489, 262204387, 218541346, 354606248, 573849924, 985881754, 801270958, 270249022, 340679914, 402697738, 767436294, 146768380, 510179144, 3226099, 512050257, 784149973, 156305411, 170361495, 994464269, 206476257, 502798679, 280451321, 967504345, 672075335, 699058924, 53933284, 240281768, 582753253, 466091038, 417324844, 469084609, 146238130, 468456494, 352906795, 183850357, 198799346, 228406623, 287223314, 81056196, 622658307, 748890176, 799297480, 640161662, 542691820, 91210262, 127548942, 94561506, 219593584, 133414776, 602644784, 309615368, 511304622, 440556506, 719935222, 740393313, 194277805, 830247945, 457888388, 162274114, 783373001, 185135061, 14489687, 400800251, 724891675, 120682098, 458253696, 530868018, 32793721, 451191933, 557394550, 981210493, 209938642, 410896252, 721307707, 651121444, 407139616, 835730992, 186667534, 426833780, 834069058, 906818735, 176904350, 566768317, 169236123, 8226919, 866426335, 550503349, 350398862, 521410337, 71213440, 886273799, 963827355, 537578024, 768878813, 27045408, 375148644, 579786357, 240975116, 997097398, 538189290, 737464069, 87275530, 72422393, 846133691, 728392971, 393200638, 85664541, 837909168, 185381666, 848450797, 239393366, 121552482, 26761704, 451420555, 448516647, 571438787, 334356913, 193966638, 582721984, 565074378, 800715651, 478737062, 985373361, 111314213, 511186469, 889342725, 760617231, 122018223, 591223501, 944630862, 97878450, 933885922, 740268933, 587915361, 946628364, 214616161, 8865944, 743080072, 154777483, 367930371, 173377626, 199017126, 880363637, 925094663, 701633207, 603686764, 115956989, 489559097, 215471598, 417453048, 150391003, 302666386, 997427613, 777138862, 345448410, 761310439, 346073369, 78747295, 274197518, 163787462, 739897097, 586156870, 790371942, 470113895, 784737852, 599622877, 204442666, 49488077, 835281360, 53283333, 991924231, 266022470, 74498090, 182199485, 873555897, 819642482, 836531271, 294405582, 527547413, 794151785, 666152247, 476596558, 676488653, 630260587, 350903611, 507605057, 478541112, 748972029, 251661507, 53994243, 653845104, 138806246, 125485063, 27956691, 912702265, 115279980, 346586986, 923559677, 503719428, 639181600, 730443111, 556288759, 602653517, 310071215, 97201001, 552005145, 822859546, 176840872, 930253504, 229021228, 212527309, 804123709, 325930029, 628706582, 166793182, 90398172, 888621251, 349758531, 918851851, 736863442, 811033305, 297016457, 884735791, 76999960, 605143536, 699267998, 172622636, 87286992, 746410762, 273864946, 471893084, 646916838, 405148811, 192663356, 880996054, 476027488, 46382804, 175610128, 562121467, 213263686, 982633978, 699854610, 552312352, 219169352, 588709931, 169583049, 227302557, 786387865, 197017651, 549548371, 917919621, 261931782, 280669366, 989824192, 174428362, 161054216, 960346525, 215858798, 648392181, 928618094, 689150496, 132556522, 655996120, 925991096, 653503830, 8755438, 182869537, 559532408, 38174860, 92294643, 71250240, 610428719, 153927773, 149769877, 478583098, 874390756, 245509694, 256509611, 833739133, 744573871, 407535451, 208153270, 334011565, 985093918, 373127868, 181728442, 248330622, 474461762, 835269526, 342567128, 940103167, 419777818, 421811867, 785650831, 248103855, 674032606, 428792200, 570464302, 119140665, 918681491, 57042419, 711434755, 845758505, 704568539, 600899820, 306299997, 937341043, 768953221, 460948216, 572664476, 917985373, 173982138, 591097683, 628241830, 971512500, 370262338, 949331822, 937908427, 705067199, 435350518, 288415039, 888037970, 877020895, 456096625, 482080339, 334504555, 217691440, 719639698, 169706611, 327601732, 851498181, 866339243, 385476577, 307291995, 52184099, 460281995, 448065169, 725610851, 160817100, 358369883, 411956114, 867459377, 561232004, 664531677, 472873279, 674189050, 89617195, 314683178, 538509213, 757046677, 497187148, 8965529, 783369602, 268920115, 720108916, 208935090, 425163207, 990152557, 361445971, 360355917, 664962773, 247449824, 965838835, 659371444, 848017304, 291509239, 465199755, 291983961, 944288706, 238948645, 892913389, 858962428, 290652257, 433892748, 941590300, 263972396, 654320881, 658477434, 821472903, 353428393, 720609153, 182695136, 984731433, 535726048, 41777793, 441321035, 822028960, 198611508, 29094273, 674815454, 624904258, 636686535, 749638161, 20948141, 240265873, 872142907, 235372112, 669079913, 684039393, 127700032, 784322431, 160819457, 180356448, 45380839, 444339616, 960466653, 738222402, 987703824, 459155744, 814480558, 171120136, 384667177, 950834923, 662297996, 135663281, 318647803, 825388482, 261356667, 445455392, 133542897, 416411617, 266016441, 346329502, 280433024, 347228783, 539077733, 988713169, 45985735, 220624114, 546451426, 529826933, 226882740, 509619717, 741286744, 461046421, 250582557, 479011701, 199858986, 379098465, 649850720, 680168601, 252546503, 856626759, 247639795, 307088285, 580842190, 897212431, 34072811, 941871790, 39443608, 241245389, 778646635, 349653384, 355550024, 690453221, 467419376, 728176695, 519964708, 989191383, 40246621, 152601993, 801203240, 677902115, 577534714, 540225675, 424531520, 941032332, 250952048, 700114895, 207727249, 41262068, 48453724, 347304280, 75797868, 435254944, 905612485, 640855083, 841272981, 107620025, 289108076, 216089752, 540001142, 870108368, 462190806, 789244672, 879233408, 881955335, 679628001, 267742171, 364677558, 791294597, 126923224, 334468716, 803638820, 346916131, 745138173, 778208825, 55280455, 199168618, 741001679, 778118263, 970163121, 362854432, 816991415, 612233831, 657661957, 72712356, 388247308, 825447912, 763075403, 315895517, 167802836, 77414215, 288229890, 306445936, 860885854, 490312150, 750522878, 153105249, 979352325, 528914424, 659070105, 347158478, 443376682, 481000597, 58672788, 201589078, 568480622, 883443216, 166257039, 97422312, 64875607, 453038088, 97635258, 638670005, 520769549, 729857140, 468761634, 20020015, 849022912, 907435553, 387862667, 2395494, 895311575, 931945954, 673046352, 116926863, 307064084, 200437997, 905773789, 850731560, 837387576, 859985989, 572063239, 891960272, 261609969, 831847518, 151971641, 311174886, 658576975, 328754211, 628145707, 250464363, 143043660, 122804842, 791684300, 12757955, 954908613, 474829868, 497273649, 756858005, 357467185, 808641534, 402692828, 106413021, 581749299, 333459306, 660511138, 50856468, 822805073, 759591586, 70466217, 172401729, 598589693, 83120177, 118851892, 954335766, 305879744, 492310520, 580974527, 939952180, 412271079, 883449480, 107078839, 306912775, 476705278, 49475502, 391482515, 437632560, 37199009, 359403267, 628557821, 581640338, 654330437, 191704696, 846288699, 204951177, 597309404, 90112889, 818202199, 477049060, 268647753, 478287900, 315691076, 848540577, 723130610, 896368497, 12870863, 121729861, 285792522, 882201044, 968641368, 382341781, 845401329, 652988664, 906416136, 906523941, 272936109, 540716375, 567632396, 490137447, 210942959, 657263655, 602660543, 740125813, 153395882, 297044244, 924929411, 591001327, 916126675, 864384449, 348652700, 175241856, 904392131, 72244704, 600861388, 249262364, 582805791, 292719109, 147408481, 733461587, 494831639, 334005905, 237202864, 368590468, 108863063, 856003501, 383037375, 982971006, 126218960, 716001308, 569640819, 754607363, 550128779, 893040210, 358488009, 945009669, 721900922, 160688160, 181567720, 839685758, 461676816, 501155481, 181984896, 328092086, 36035942, 263456441, 387734531, 480390777, 166100858, 691543005, 793018096, 29368549, 296473355, 546835031, 562408174, 126163636, 667232281, 733629498, 333317614, 489390954, 956735226, 454408214, 176941344, 254980067, 838888542, 252008627, 416403725, 259547682, 188434512, 539863518, 997171230, 465588022, 760902495, 796179732, 588662904, 129082347, 407350491, 515564368, 446895682, 80922841, 684631501, 246741545, 390034803, 963443220, 465306672, 588579306, 180612001, 694676573, 107005899, 654287534, 7243640, 404520370, 430441451, 41839823, 962132404, 8412489, 663074754, 543256455, 434605783, 48209925, 526769807, 305007677, 733273942, 625460514, 715041092, 74572869, 737837173, 771883710, 18744492, 533253289, 966360783, 717801084, 951132637, 988195899, 194488553, 774613469, 714095105, 788120112, 153521513, 612390506, 325907172, 638491722, 854867997, 291868355, 531748217, 399178910, 592506857, 192325965, 968749414, 677520989, 135306761, 104249826, 587100302, 444077861, 713620252, 578445974, 347022428, 600058252, 968150223, 613720603, 112820313, 915333847, 649290016, 777690286, 488456614, 581654866, 471473531, 851127873, 66570268, 912054781, 221164326, 714447656, 112508241, 306724826, 121023376, 994378985, 99060275, 123713195, 353153058, 161695846, 289130425, 376884720, 934896155, 748074748, 260746664, 846073088, 764652801, 980207787, 117772535, 935562016, 944481355, 245651466, 180422570, 611940237, 882594738, 420581494, 343602753, 539094723, 95165372, 434746166, 985489736, 252582975, 233773286, 397551859, 371445605, 244610673, 670724063, 81587436, 154330981, 119299290, 775317143, 707945726, 654593285, 25818178, 326143377, 915373382, 64271696, 717711136, 744559978, 384938044, 681379637, 436381170, 939877065, 721304759, 102062353, 881496828, 194637660, 440071887, 74084471, 83170270, 723961998, 623588591, 974168483, 119893788, 325455142, 835191996, 69452920, 73484456, 261313021, 410374938, 317411947, 981091238, 26696494, 268931473, 577025828, 209040064, 957369038, 694397276, 987185645, 133981770, 586263159, 364768250, 776317533, 982614720, 239483410, 33120905, 520009871, 599609419, 306403006, 62519874, 954977535, 935062672, 562610892, 389440590, 348944952, 401392334, 657117881, 619328330, 17621417, 771801458, 148675162, 973922669, 249943219, 912745274, 969248180, 596438936, 130553666, 788004239, 552319760, 799351748, 355921946, 604387465, 440894776, 341100327, 926936674, 553695055, 40653985, 424413641, 794384085, 73526854, 770989570, 610205267, 377273641, 56040855, 266735773, 881780076, 206396518, 271430362, 501346767, 140674804, 85876205, 792741720, 517592524, 616350883, 97660152, 79219532, 607571920, 638900444, 193687062, 969079631, 906943948, 274067984, 868754011, 987864708, 580649544, 534218769, 876248501, 914780640, 940093768, 404519963, 816574900, 356531920, 706002623, 589071801, 327279354, 583701527, 237441082, 446909262, 664571303, 476389881, 221035246, 26308624, 474282323, 934888328, 363503237, 186728324, 737170319, 864809996, 854335840, 932443373, 530622033, 834929173, 751373134, 556768547, 78830143, 583379068, 878653435, 498963217, 280430003, 932855899, 579142685, 705931643, 710895089, 691105242, 291310943, 822119739, 109834564, 538376402, 696684282, 269751145, 23808888, 431731563, 682932205, 242910286, 826339268, 286242531, 98831929, 726533852, 730073099, 876700762, 33583446, 376473775, 309645575, 461305117, 955762059, 509523860, 660274873, 829801248, 613688868, 541477337, 486571011, 31238014, 12357261, 64427180, 103725149, 150310848, 568000148, 667842979, 653152383, 438490973, 860914497, 102462962, 170480372, 188261173, 106813966, 937917448, 338516929, 491856484, 801409612, 692531522, 128186635, 415241609, 839288515, 998628725, 779684058, 801127188, 238859940, 68126485, 200350010, 574872965, 602776772, 213543162, 18634668, 407816146, 702816439, 855329474, 730520699, 501111046, 838226275, 566117007, 64027776, 155723676, 110404523, 376060094, 897823485, 877638410, 758990028, 293628548, 5751870, 914347358, 191819933, 701376020, 625268451, 166213391, 619881142, 207929257, 249456344, 372269605, 824426897, 972991750, 466449188, 290545804, 830958636, 891221071, 848364313, 878809564, 802766990, 916506142, 757932005, 407453735, 963407254, 253027365, 370225520, 177920403, 558249527, 645938725, 896976204, 325180945, 54692005, 350952121, 78907942, 343153999, 985435268, 746396700, 285577491, 374059810, 608788383, 323285458, 780597437, 928240440, 299901007, 600639099, 728770661, 740532600, 709688524, 877063526, 890038218, 528999222, 118470382, 381159709, 701038046, 917920687, 224806289, 756535465, 174939074, 985081058, 88374872, 485903620, 403093469, 531932665, 381932035, 882109401, 296577842, 979262053, 27311836, 209763168, 987129786, 850934635, 831852142, 102378902, 822753538, 890931686, 609896877, 972557810, 115849280, 668743401, 181795153, 859777453, 770686186, 24646334, 217374613, 964063942, 23091813, 38571824, 679844619, 673307192, 509273078, 735202380, 171763460, 303357898, 145547069, 935518094, 820740955, 2321503, 598680510, 758331693, 951646075, 899238601, 818948135, 364857159, 91235319, 790368125, 552378639, 106952187, 549997291, 65974007, 43372246, 437257380, 239110141, 975852570, 252663455, 951407219, 413962513, 816805959, 810001754, 711042016, 570088350, 847452045, 800869091, 924334389, 849340533, 696777547, 155789188, 77388473, 654648644, 424050493, 32321276, 869582836, 62745949, 693054998, 727177979, 682867287, 819207566, 780478102, 646992579, 567081518, 496347248, 178717426, 909618730, 311504284, 182676257, 178935174, 57027442, 154649046, 339984433, 858582837, 896389212, 391353591, 538287399, 81279564, 845806717, 842776477, 541785221, 214667134, 624516281, 358720439, 322251328, 239462180, 538478769, 557011598, 664222104, 618033194, 149080454, 287806591, 401538091, 80592934, 441878385, 508013610, 897132073, 798312039, 679425779, 568626898, 365817555, 32787239, 881443395, 965517471, 359101702, 168536875, 707468446, 765269453, 947584223, 266591198, 367292719, 238713135, 494467821, 639861322, 448945285, 51480107, 766475844, 132411810, 648582412, 260708109, 397703418, 234824644, 598885168, 129017993, 52366464, 220405599, 100008588, 585050194, 964849654, 939140787, 837642932, 826573145, 326934320, 511648587, 733378085, 312921601, 609152200, 610602965, 717505902, 766922503, 718862873, 121372975, 42102975, 496726658, 265966910, 484285786, 971618175, 262096624, 775399552, 914471827, 137142096, 994291288, 969154385, 41712820, 344631661, 799395255, 26765048, 251307071, 656670108, 163585431, 401624438, 492968886, 503862094, 496403877, 633935291, 975461315, 768580739, 701257770, 213493824, 956623802, 648119544, 151556361, 249290287, 861355497, 615487216, 94413360, 384796174, 861937845, 101081086, 514665248, 422114607, 666951038, 313940452, 291343188, 857502209, 252980066, 139468673, 12480926, 663957419, 259627151, 616336501, 322806341, 920226928, 386005203, 624131659, 372606050, 135430083, 599329182, 607507113, 31389059, 858659488, 618772725, 575691538, 286709650, 578497045, 675012460, 5919535, 256701396, 362222807, 519790672, 67052611, 650594904, 650119909, 829953704, 520403129, 248549120, 438318124, 948920314, 927399491, 271592080, 230423178, 507341440, 655268204, 310048315, 548472897, 724865905, 11123853, 530043433, 769333382, 835339831, 162328732, 629878674, 773580845, 18935034, 194672017, 798327089, 188096547, 366669363, 220941157, 513800436, 487329624, 354837452, 663382948, 738194283, 291123744, 86012865, 404140329, 137802516, 401225424, 214813761, 406411287, 58223255, 408600429, 813962029, 548052223, 547497912, 445523769, 660673662, 613025204, 179547428, 262344789, 903029868, 385782914, 519092267, 179310379, 573070868, 262805317, 54317506, 360165194, 779733684, 427428165, 363677386, 269240179, 349682808, 428805306, 747098038, 617976313, 406051890, 654627541, 442597776, 760872680, 388293706, 753971693, 668974827, 766383822, 323209940, 166207688, 682289867, 287471031, 248888285, 621865568, 836445597, 66537324, 571010356, 262525898, 640585467, 776052990, 481295764, 177860915, 272753841, 805987271, 377935359, 159604821, 194018495, 315373301, 192151930, 144165968, 412727211, 755920547, 468087846, 379637733, 109125886, 374580388, 577480966, 635787542, 68816518, 980984703, 151422846, 831171110, 294798177, 385661167, 297250570, 31648886, 977074567, 639525633, 694110128, 278499690, 55396853, 974000411, 198215966, 1660442, 981528287, 471372750, 792333043, 12753009, 122276366, 801936745, 62178312, 972760253, 80771220, 204724867, 162383733, 520069026, 979984164, 460670062, 562735763, 783885443, 174095463, 131450890, 551567492, 255930003, 582402756, 546932087, 40574719, 17357198, 934335719, 816380623, 933306005, 650815690, 999150230, 538360330, 957162102, 248137378, 839953586, 660042459, 482957025, 258291247, 934403173, 831534791, 498864730, 259345112, 666106470, 739282624, 484289830, 597252777, 342227307, 840904041, 772856991, 43196302, 62721306, 363956083, 227388435, 900102022, 357261987, 880812235, 894249331, 809130930, 175970160, 50203267, 724086898, 766900605, 809811556, 751800177, 576247186, 467115772, 294245177, 550427827, 675952848, 65125038, 408203064, 629616172, 974912656, 230613245, 259741782, 484799152, 979342534, 75361391, 332286959, 130089594, 711996394, 145370536, 150510632, 300245257, 684893680, 627820221, 120587592, 129969609, 18158211, 25713959, 238228162, 11095225, 27161795, 868178722, 810034740, 599200078, 167272928, 308193234, 48371434, 911777012, 210982431, 538239086, 216236220, 409223153, 108620201, 134933232, 108799992, 810917771, 726222374, 249971976, 500485232, 99435894, 204910538, 209893196, 778005785, 101979089, 227535029, 946870646, 461866607, 676889054, 935003079, 600498087, 487633444, 305083572, 517139894, 353025696, 246887425, 221621280, 688038440, 849532706, 589809115, 231976351, 526961779, 72070368, 643048733, 260321697, 910420775, 139339344, 33397351, 464035014, 241091388, 851760719, 516507172, 742875604, 323778093, 547284303, 487708228, 811460596, 308698813, 230196980, 133516335, 614634574, 403671579, 377120988, 843053161, 883566364, 656878409, 865674752, 627529331, 701486270, 302370805, 590782223, 184501362, 906764496, 131107123, 682305980, 888785276, 877716421, 901775730, 630435691, 179881698, 558153861, 489943320, 261527836, 65245594, 481070735, 904646153, 2753971, 503549929, 809520979, 850336076, 582110568, 751308446, 449738338, 112900612, 169155313, 860964058, 813206788, 112435232, 671567454, 722734337, 417154789, 625909238, 456099920, 968990349, 511962751, 989584308, 733929146, 225345976, 316522486, 63727773, 707498861, 548848752, 664275701, 466522553, 311929190, 1638951, 697706286, 251951826, 925956926, 277280671, 423130416, 499618843, 605817013, 20558466, 472133654, 680359245, 41782037, 958657720, 36756979, 868063553, 434840028, 204362438, 588106746, 653892477, 560946542, 647593989, 731910967, 441887638, 90754564, 642060893, 430909726, 219010666, 897038324, 622509571, 861441374, 743233768, 229107208, 885205516, 423657932, 986998917, 330243802, 809200615, 808916708, 648788098, 735240941, 44743977, 20756532, 935538491, 482950668, 141340140, 1039019, 10902438, 909453865, 365428008, 229612736, 590168806, 792813411, 798406329, 404023031, 382312592, 84202352, 468903349, 904919777, 257112433, 140518253, 500408436, 486826722, 356067452, 123224646, 365956235, 115337353, 567410166, 806825066, 338030549, 79799363, 63991133, 977737904, 820496318, 799043854, 863762995, 75420206, 668107039, 676625856, 834811447, 643647393, 287571592, 96333184, 620264681, 722325327, 545002383, 540943107, 296417490, 842080134, 63979876, 591738113, 578962142, 607774433, 863224804, 678596213, 744077668, 744096641, 433303471, 782503243, 314679121, 817535137, 593035432, 172388483, 291780674, 465033176, 712458311, 850143406, 489710243, 150075483, 448085106, 752812398, 867855311, 396311510, 457567717, 421154269, 471328625, 944296304, 35912342, 34286984, 317646963, 859256326, 111863076, 164519783, 284700919, 162814839, 490664146, 486774502, 532616145, 620912805, 305318971, 67299227, 528341352, 299052773, 816461095, 814674241, 205523869, 987322135, 567324003, 558240065, 395082591, 353612769, 113564498, 744977412, 491691238, 604481893, 35498241, 758700134, 811703145, 25972786, 735460206, 96321096, 864787351, 724239220, 369528699, 52489096, 479940337, 634509599, 748258276, 556555355, 97366267, 78865127, 382045895, 993546660, 233337784, 838792099, 956492371, 385641239, 918826885, 940296642, 524430966, 158625556, 573509591, 17579587, 566734462, 157961393, 570468773, 847254059, 350433846, 248435202, 692269780, 338633915, 860680297, 703940043, 747600115, 383850780, 983391729, 197500515, 852083090, 267056559, 150039944, 562369777, 932420642, 25841222, 166774748, 698031213, 457543382, 295787420, 994828834, 612567474, 54642749, 381431325, 413610168, 460642029, 208658385, 970221718, 29868171, 526453251, 220737784, 731224358, 95514176, 656463428, 714698515, 991093394, 666073751, 70591517, 473520857, 399761511, 27917622, 10509502, 602456883, 297688882, 355460673, 637330457, 384275097, 527990492, 905491282, 946746201, 640466405, 642568384, 331672920, 633090110, 95494636, 177326078, 52486483, 703268454, 563317346, 586251642, 483969267, 994636543, 772405441, 549321473, 962045851, 514085086, 108102606, 985917886, 495198059, 368740016, 359177757, 640843417, 120030536, 40050934, 460165477, 462850144, 270293990, 146566766, 818114197, 546684118, 493291749, 411255123, 49358560, 349392382, 294212480, 758333673, 986595052, 773113034, 766600742, 452713580, 604883373, 659843450, 212946329, 20038987, 319779493, 106899399, 198381524, 261233167, 246165201, 68814417, 538383176, 570993541, 450320525, 841677836, 665931733, 629596163, 365073523, 789595214, 753773748, 415666205, 469811672, 660498591, 548270885, 63420434, 907588811, 313792884, 880667672, 977986680, 369546997, 785213350, 704866347, 27110983, 115097617, 532675199, 386879706, 644504608, 410154774, 65242082, 862015587, 633119701, 288565978, 726569279, 656474170, 267640581, 381094772, 804999041, 48341709, 16332473, 303551564, 183163751, 791282995, 417502507, 945115242, 653536102, 575059585, 649341217, 162150246, 194637185, 338717516, 700689048, 175391969, 301472081, 446274109, 245121624, 920322199, 91948700, 494605193, 913177136, 915918888, 286296730, 7894854, 915118481, 669212217, 64076977, 941232674, 12311898, 634420351, 698036338, 544488629, 500041686, 664125048, 66983453, 649433049, 639960376, 245990868, 38961822, 107254312, 670759152, 71572791, 738636660, 655514939, 194380054, 806119414, 678361551, 649830215, 810360385, 480721269, 717252564, 823410814, 437046447, 555725192, 235771353, 624829899, 898663261, 483216035, 565504582, 891428638, 794919059, 492837381, 102884874, 360128246, 604250891, 733864159, 367469982, 196356638, 477326549, 680668293, 956459473, 702230107, 778582964, 504529732, 375779696, 551760012, 287017461, 757330999, 157976296, 155467697, 431611901, 385191094, 340340335, 916336474, 450250253, 323615180, 731983743, 483880499, 176980318, 178853359, 886786165, 199876744, 589760754, 168118369, 680080229, 989784451, 86050408, 966002746, 397030958, 642316296, 288399866, 32525255, 399688774, 118744226, 789875382, 638769390, 989527422, 847747372, 386692350, 115319526, 877872783, 823570714, 523914900, 688945247, 570450820, 744422987, 147804139, 650130365, 32534778, 182211090, 624774195, 646632757, 239933300, 965954342, 785081211, 566222299, 932871112, 499888162, 656596231, 958205807, 988068992, 954002622, 600560446, 508526130, 364948822, 151892377, 814859195, 463952663, 463798621, 764330793, 377611429, 905889997, 548260084, 816533325, 167726543, 743989274, 414002108, 50989301, 512541432, 935244155, 432689714, 838419095, 668081700, 928465831, 160315621, 961014603, 398282911, 737707955, 274363194, 76624691, 835924207, 347338626, 579908278, 47134455, 192912272, 216534403, 455492077, 942045418, 772225440, 575206536, 192735481, 655611829, 610574865, 889063603, 231927646, 495976328, 729072033, 474559004, 634998190, 282554171, 792646179, 591923547, 469121133, 333177337, 94856180, 720269209, 978584342, 276054000, 569920775, 548988809, 664043591, 836714475, 430693608, 148194273, 697614949, 70933962, 573989254, 197011730, 955090815, 219838034, 859646817, 748631945, 560633041, 702253170, 75356414, 48613149, 855626712, 281076158, 8177322, 730978321, 455465167, 427289094, 68489852, 324323386, 486243256, 547444540, 463797401, 416503535, 287285079, 238856305, 293486362, 860388041, 516219484, 126271529, 132440276, 795033801, 471342826, 85545937, 550481793, 477239756, 682343809, 920303238, 585937349, 53768193, 794962647, 554142855, 407297765, 13305986, 252984639, 269477551, 931930258, 13800193, 85509813, 724424543, 631434486, 999513496, 697923247, 927075934, 990540575, 575014350, 703190211, 770451276, 863279923, 170179104, 161209085, 936427754, 727701318, 650954023, 558241835, 319680643, 772474877, 365405981, 579747196, 152160893, 838041506, 795181460, 388437026, 599913952, 56445055, 147960696, 312429947, 744488457, 877030276, 234692108, 348240994, 64738018, 135482324, 450014410, 896920411, 3702675, 991557707, 338549060, 815071, 647585449, 185718328, 564831742, 941114955, 795922577, 756904200, 757545918, 830272170, 736679520, 556057107, 809863137, 567404385, 773019451, 800680786, 543976035, 431993237, 904673479, 339939366, 170525580, 982148488, 33479197, 103579954, 995462789, 557904250, 927941788, 36576067, 861752345, 381936560, 247541038, 758885675, 357982675, 330988136, 166839565, 29712249, 334694888, 912956640, 755772083, 195662536, 328436804, 534919803, 158421992, 852676177, 609326609, 567044662, 786732319, 572797335, 233442406, 726398061, 560158460, 965755285, 457881211, 830896805, 132852842, 921000814, 855079732, 659046325, 946590864, 459270742, 274124448, 76592776, 215950006, 68144691, 246728019, 9135160, 836175142, 930060380, 819755948, 460708725, 270645570, 836187018, 537558191, 612366113, 464737057, 901256163, 959543169, 769726381, 203349414, 624060723, 873901358, 166029948, 68840919, 148647311, 224208240, 520591903, 937536253, 9137759, 920064001, 398420007, 387059489, 610708356, 365110282, 478576632, 528442315, 657513348, 486661160, 569644627, 796050237, 437691955, 741293655, 795922617, 868640372, 298996764, 71252123, 148235269, 85749873, 604673734, 23858197, 371661154, 555602258, 494571910, 647119966, 187176777, 373844405, 227447079, 46182748, 689661256, 580082770, 796700201, 714284228, 647954849, 985392683, 784235176, 789930227, 266904410, 10054080, 830834696, 255487924, 858919177, 117276464, 718496470, 393778068, 473835595, 864964567, 298220324, 303926654, 205909017, 442786508, 3499713, 710557348, 897950429, 656944954, 405891130, 43611908, 890178965, 358341549, 184694784, 841313501, 549076597, 388211027, 297404283, 825021424, 875716476, 694161479, 55695151, 895124026, 936448228, 768629564, 182031821, 650728146, 658692127, 634401259, 946557988, 566214873, 109586331, 210945482, 19162193, 75632953, 555279801, 782065129, 687796997, 397024849, 592816671, 950056259, 890301082, 134749873, 666423000, 863316310, 883561042, 969253392, 909466253, 795036874, 578239006, 659286709, 390179898, 429936892, 72603517, 440402105, 387137399, 958948730, 802949488, 283856477, 808866014, 805372345, 407771602, 99920431, 133394252, 63970894, 131286268, 248436413, 18284607, 429401260, 922581308, 589757530, 313087082, 123357116, 644793456, 669837822, 894753393, 522694805, 362418757, 71395049, 597875044, 618287289, 856376597, 475308607, 964174403, 212869472, 838593905, 629646079, 681101921, 452850523, 61727917, 678661690, 144031356, 388816846, 31454975, 988909562, 284809928, 55868193, 225422843, 215749172, 897706086, 323937255, 907529934, 87635281, 406760833, 980807507, 519796177, 826621460, 783356204, 949981298, 783570045, 469233005, 705034965, 309424176, 611964664, 326765811, 167454433, 585114231, 851221374, 863170181, 437293272, 183371729, 518875577, 547454032, 301077684, 208869010, 69439295, 390636547, 284628286, 290989237, 23301445, 171986856, 539785434, 197559417, 376999209, 81591557, 282606673, 644118686, 394384140, 55029948, 778356238, 922713473, 752382048, 187787846, 17306609, 562732164, 16884108, 761816193, 983730648, 824033908, 500620436, 292180050, 761098851, 880715243, 649544080, 335956093, 816115740, 246597974, 410680585, 916987757, 30151164, 972157143, 81812312, 145744656, 200270534, 804306986, 229620510, 85241081, 160430782, 722162221, 288770360, 199558384, 253761055, 133452080, 991173114, 432770077, 191222878, 791535574, 734136317, 907234950, 465075006, 823771345, 484569765, 972660810, 106146670, 863655682, 202244330, 133048052, 812596261, 833834931, 846355780, 895007895, 661246154, 66901717, 626577205, 421349315, 720248972, 357543423, 368570503, 475978744, 995666329, 594256634, 580568428, 598128889, 605332014, 525980090, 833017980, 205038386, 168571292, 36560618, 178072465, 967687980, 930433809, 872586550, 870929251, 409847359, 320226165, 363962487, 24292515, 597243211, 163161693, 492912270, 338147350, 696764503, 200417248, 562229444, 409301307, 954686895, 44684197, 723210637, 776709902, 379474471, 67545826, 587347702, 869695949, 151798603, 123573591, 99370720, 231145980, 912481016, 89028963, 792163547, 51878702, 966664464, 917373488, 576563134, 77755639, 784855418, 898252020, 661376651, 902345189, 253853293, 492436390, 868685657, 373135797, 142136237, 876974920, 320933966, 120117855, 446357026, 379813509, 759603758, 775741330, 590371315, 731606059, 138374368, 224227891, 164134987, 817958199, 806772601, 360657103, 351583295, 21442079, 295306213, 914249238, 231022064, 144133041, 71564168, 571249590, 630992052, 479387840, 436056470, 358135527, 284598504, 106278251, 665506978, 65571504, 387729216, 938306850, 227364088, 496489426, 250238061, 575554078, 831122078, 303995522, 308713510, 902357553, 682828303, 917570243, 305466984, 31105595, 684395286, 224680947, 774169879, 723570126, 566749890, 125886084, 317283740, 919641118, 441548308, 842687032, 454402835, 309314816, 30389472, 558704107, 689869523, 736048998, 449618515, 471166368, 647062669, 151222830, 692083893, 425849857, 332476632, 6966958, 370474228, 251455002, 926200671, 567679615, 779565179, 687046078, 935695197, 566258610, 71815746, 878512611, 658273308, 801153686, 770863152, 175278245, 129441542, 160509766, 688145685, 449794712, 349184189, 93406794, 253435, 305804857, 445198735, 732783106, 668763425, 719638268, 971512414, 644572310, 836532389, 511050219, 575909868, 948178647, 586879453, 759120332, 553251136, 375956538, 365178008, 505926736, 353654800, 701200087, 519079969, 640050307, 863801845, 927811141, 670053207, 307025684, 918829883, 325660703, 502698849, 34976418, 9494420, 515772053, 268425037, 65277217, 152078823, 814632823, 858163447, 863257340, 530190668, 722659990, 590544972, 559682689, 262455076, 200854628, 284713731, 582497791, 625813488, 700777693, 671914859, 25021340, 730663478, 51978994, 722939103, 43845652, 503622015, 691468961, 107033931, 119530672, 277256294, 226398, 271910625, 266954511, 723049553, 612475555, 618982445, 677236869, 779167842, 377743164, 589136318, 839687555, 871458058, 794445310, 955203729, 648359030, 271213953, 813695546, 56830190, 605673342, 637001262, 88477822, 168475817, 557526843, 806383580, 170468253, 672255990, 216815258, 706535448, 796089733, 566027080, 191777487, 606643228, 497982174, 243228156, 512800422, 143819194, 807083417, 514410673, 379172046, 202651090, 171130040, 438101746, 43412252, 975087200, 268307673, 236063078, 840123934, 732968220, 671444252, 382572475, 770818040, 505596345, 151499802, 831765867, 418814856, 127790146, 7423902, 641681493, 622153963, 860399676, 676064539, 325658733, 761686328, 884349330, 886144070, 99938167, 768206808, 833842851, 616752357, 462903710, 680887614, 624982058, 805354404, 998873197, 404760187, 623300672, 52492674, 370908786, 389270550, 979620057, 371868424, 414983520, 119234295, 40339921, 724767295, 724729518, 263056924, 753300695, 601110504, 369680838, 474882280, 564932237, 472578743, 467771772, 51854543, 248478199, 173763571, 292845923, 320986793, 942580786, 373225206, 643135894, 900206379, 901099320, 504873838, 673309069, 35432392, 571132685, 986459897, 266575919, 27829263, 6334593, 389245231, 570115444, 546645566, 695177203, 984237924, 578389721, 6632852, 27018380, 920094009, 594447455, 687205142, 969565437, 291163795, 210284066, 517341138, 165663718, 269296846, 786498623, 213867863, 433263246, 586286058, 610639066, 311373487, 64729355, 880182070, 856610970, 662927324, 256050693, 169912094, 480720816, 848350998, 655159311, 51249148, 460525283, 179647500, 92819063, 879814771, 211164863, 716580375, 228619003, 545122597, 784277450, 813884688, 632663759, 663138703, 302758380, 294186138, 553799550, 702879862, 398385025, 524129690, 227844564, 735009454, 452068714, 344544070, 12609010, 580676565, 220635031, 387901899, 654357308, 306080181, 368427433, 693453718, 764121087, 191055661, 97104592, 207094691, 768401849, 286013114, 539389773, 830945964, 850676298, 149569118, 109988237, 326767722, 659136615, 171433012, 834566698, 289123601, 754730489, 104194955, 633763006, 36440706, 493470130, 171685069, 765289350, 317655828, 473441755, 974809377, 932977346, 801692873, 289380759, 383213382, 857862444, 828896464, 572480197, 827494240, 525018849, 501737176, 922657190, 181315078, 389131664, 691660067, 720074503, 501921698, 605723978, 889191250, 732808510, 367147788, 213828552, 721348731, 80804889, 759399193, 477073312, 410602639, 929053054, 20009919, 863600490, 518473024, 489354299, 504041617, 462853665, 519499045, 402019231, 589961503, 962445148, 751158257, 346035325, 644448838, 982197813, 876128279, 265005985, 928669735, 479053602, 928457867, 275300482, 354313363, 923856120, 178199372, 714627900, 41520824, 574601578, 574683623, 825187438, 229292237, 381369413, 943141365, 315689884, 444705162, 29526107, 936965341, 208415444, 867131043, 648959841, 586698884, 954407188, 600110356, 100593112, 614566028, 511172684, 619793569, 549467089, 183016488, 543140289, 402139032, 329002135, 627932905, 400719538, 247842072, 405351684, 664080502, 134280320, 458816797, 66042392, 161022928, 240672630, 516537557, 718852891, 932801126, 483812694, 513128803, 999207099, 713786090, 127181163, 83207770, 810951332, 501758825, 152868673, 48188238, 855433664, 74125066, 545925150, 295359803, 327498537, 536964386, 831781422, 370292434, 489844532, 934631342, 444393223, 604100649, 159964190, 549492454, 210100191, 103435889, 820123019, 474630328, 617431388, 329185006, 313893921, 903711969, 62466171, 543955133, 816454019, 957376116, 212719710, 891334050, 663416884, 764126362, 478469247, 520423130, 298703996, 584849108, 256333522, 928873500, 980172789, 308013170, 797279908, 915806107, 472607621, 652260785, 523855627, 378510877, 228453395, 965914113, 492123254, 454240305, 740174339, 696284483, 950940842, 875397496, 776021113, 711387311, 3543975, 875070099, 137347455, 855765817, 951806985, 89209341, 326146969, 847514477, 527809817, 565306229, 766124549, 107248254, 423246965, 247178471, 898510197, 192709024, 308192735, 533727956, 938107014, 827099096, 506981935, 820306556, 255773769, 554852867, 37828039, 625241823, 610775346, 486020121, 954845214, 351742238, 255891882, 243633116, 775039768, 335596463, 891710840, 358285895, 766749748, 220795272, 534345009, 896950762, 266607247, 973687329, 134174914, 888177884, 714208074, 685731734, 816395057, 46861663, 234787144, 694712165, 342707624, 768666112, 975504766, 482243085, 781049035, 949317814, 289678813, 653611082, 90533382, 899740888, 114329838, 242928810, 717308983, 499775509, 326233965, 170325340, 146262298, 253014592, 629753546, 128342884, 469932053, 89026275, 42101818, 53149592, 721212033, 882095099, 124766962, 53989921, 223831927, 259206112, 938506674, 179261787, 400581687, 971432378, 867182977, 484841282, 370634400, 75250450, 518807333, 811319819, 733348564, 738292018, 511488623, 981974850, 983238881, 526675729, 322363914, 473048409, 987596379, 399467850, 584727933, 133138750, 824187329, 724817723, 490699708, 735898631, 839328966, 889099780, 607508860, 375922214, 834266366, 522841982, 992677058, 289010482, 639573437, 659285088, 554552205, 800693154, 131112669, 110507966, 283989614, 120805117, 366810914, 209999961, 261844614, 173060636, 310265537, 301433072, 656516178, 895328390, 157492810, 889168875, 50637573, 903362473, 483311332, 391192165, 331399619, 888649506, 358659748, 196924880, 675483196, 567902391, 569572999, 536671285, 7100897, 742999527, 56927926, 748283951, 865843772, 445532316, 211486704, 539542838, 419283773, 707659567, 23322520, 371179095, 48755049, 713847563, 732467870, 306607131, 83114940, 571511757, 969330640, 226461192, 524911165, 875623672, 26535560, 600209275, 687510513, 337844999, 659821751, 225142242, 53183494, 15008224, 193696757, 126364854, 765324147, 27534460, 652882515, 613556481, 107536427, 862704474, 794018695, 333734478, 568280701, 317591282, 452758726, 280560136, 235149500, 988283833, 842586058, 718179428, 865879610, 684993178, 556193688, 278554929, 128665040, 345555906, 850174545, 380159624, 549427259, 453745596, 331310687, 487818864, 909681219, 588482249, 963656139, 941203464, 322957507, 922872601, 120632924, 474377603, 452210897, 162632396, 871570147, 528512337, 704540399, 46045373, 140525185, 326750783, 942237207, 907808134, 322292402, 552333454, 881214698, 386174370, 742964698, 265769400, 140479991, 493650976, 666519383, 367950671, 689356111, 407854737, 189267676, 78937355, 607610276, 627325371, 502334220, 894210465, 925343327, 749955798, 580866947, 181459987, 742448004, 232084835, 268839873, 796130113, 982711440, 569283110, 999331796, 673936714, 306308814, 269021160, 354781777, 12262525, 639029429, 847522087, 536625348, 836910126, 829271161, 310816965, 273199146, 923275731, 915450439, 218366315, 545056763, 753518464, 907546919, 37883628, 58850584, 694845225, 697106031, 489040843, 892551633, 553795200, 900741616, 966247941, 112170535, 151746402, 155956521, 444295588, 9542846, 303321384, 57863070, 702984693, 525393929, 60298081, 77751536, 498691144, 573570626, 731120151, 240856915, 841077558, 910241222, 964368009, 85838465, 201745925, 725348302, 893934156, 401035407, 720213845, 850049603, 584474764, 300149792, 905968765, 197229052, 308840330, 620516749, 944537578, 89878803, 157585817, 613877567, 526683659, 910519768, 211599073, 38296609, 971891711, 656761039, 141442803, 26844199, 344305692, 106237431, 88845066, 695224544, 562062847, 666011928, 472085583, 141052357, 134863763, 695077705, 568427244, 174497237, 497293439, 771756163, 293450535, 313853416, 657029403, 473841974, 443003676, 775867240, 188994049, 372482203, 11189979, 558668030, 711705025, 201596148, 9181452, 219329967, 345111552, 617618447, 162505783, 22228906, 649658997, 766274402, 357094777, 854206597, 508200422, 223924659, 492196835, 32967852, 777421067, 336786245, 548463436, 219495270, 914061458, 712339812, 776562791, 811735379, 338013530, 341837549, 650903997, 817048730, 163818901, 305844951, 840964075, 367983519, 212106449, 129312253, 897687944, 996482825, 117976212, 43750456, 614459759, 312899759, 264701169, 341170275, 703206079, 609421381, 180961549, 809060143, 744921791, 378199452, 359492546, 160223832, 528670717, 76657348, 197782163, 65319605, 614168611, 712489122, 492716606, 88917067, 70606948, 552752670, 319563082, 56538112, 875551899, 136150533, 520629264, 651552297, 601208136, 87804543, 972229837, 813438088, 979395013, 994140960, 768151788, 815742928, 704327474, 114125315, 589818868, 557120498, 457115216, 517642288, 331640636, 550363494, 224550111, 601975705, 64074646, 201729787, 589433152, 223380995, 537600714, 375686692, 592802207, 262510223, 288705961, 498713059, 215657654, 158724170, 336506454, 409078075, 548363596, 798254134, 283696240, 918520723, 137927207, 356287951, 270624733, 30644684, 851679974, 138496042, 219847063, 906264223, 544651891, 260959431, 235257998, 950024551, 237517237, 616301132, 836097452, 729857571, 587711352, 914892820, 309128628, 190154402, 279727574, 458017052, 296216267, 675621563, 764429732, 711636418, 29206542, 47351388, 894228675, 168566726, 186621806, 843421269, 479808674, 612130688, 423504573, 237151312, 774762681, 469432965, 155274670, 429394704, 901228754, 393170093, 13047582, 415831515, 592965428, 788143154, 246800969, 274476051, 39227393, 697353841, 73071709, 26573233, 171587742, 254011418, 321199806, 985438592, 102962338, 113812892, 744985278, 143638363, 910729636, 571481633, 494945124, 786345968, 667606522, 725351463, 640605782, 407469119, 265677024, 27100638, 189772334, 171843725, 630116003, 227116214, 269299509, 249823745, 716789243, 215642652, 604258029, 931143720, 481644727, 394064584, 326595098, 105642390, 977703145, 732174750, 402390689, 264420704, 773817238, 365664423, 309782322, 186028052, 523108512, 214176405, 215000420, 32477944, 615675447, 948280698, 843990235, 324981492, 710326538, 658163000, 26325016, 207868365, 139104141, 445362672, 858730139, 680180407, 302445944, 826422437, 5564492, 776029167, 418070866, 903708076, 807802074, 67519199, 390186173, 386628795, 961816789, 280470673, 654798710, 922370186, 727513386, 174947502, 720954257, 552504739, 381828952, 979150567, 974311955, 711038419, 627166263, 175655230, 168588262, 203354284, 641146574, 564036879, 704876477, 776244083, 913720064, 854492744, 323917125, 454543136, 118501870, 903568788, 717621061, 685807805, 526155517, 283157270, 294292239, 226817233, 709200476, 467678084, 387871217, 834493433, 941602870, 86886990, 419773616, 859024122, 307898523, 51697364, 530845918, 878719596, 224244002, 525078903, 786546489, 765451802, 847913624, 379255659, 771481498, 861476334, 571776183, 239664124, 811320541, 133694139, 149717772, 854950627, 247267882, 496638855, 162581140, 538537243, 984749815, 973966455, 11841089, 295938473, 963032202, 63041197, 662552388, 427069076, 315112374, 467553501, 733272108, 125050747, 388146090, 872191487, 965143267, 132108878, 455008246, 382310698, 948674138, 244714026, 980822182, 188567634, 479452717, 864621038, 127249164, 487698385, 658844630, 960209217, 441057229, 736231362, 310920370, 659455901, 579770209, 888353474, 430015135, 708862424, 909631638, 727045014, 848528304, 752638873, 570935731, 396080099, 338692337, 359666787, 632115913, 104705054, 333963994, 65667596, 587437690, 310383526, 248917416, 717614977, 66530750, 49525184, 436152022, 893940388, 797059420, 669854793, 131192697, 681372726, 523490546, 302480911, 906792717, 716531992, 243453641, 696071866, 778975814, 375859755, 277790772, 209816813, 972403927, 44893237, 348263113, 161811451, 652678428, 802937129, 251415307, 375187308, 615469047, 837238534, 9866400, 845610756, 122850926, 830991993, 148980323, 837303168, 160460211, 985896293, 385383955, 387886717, 963459842, 278403946, 327712231, 251102936, 965031720, 315139262, 216519756, 62132268, 197086648, 43148617, 231634822, 852759928, 789843121, 274850359, 631536114, 817246523, 8315614, 48559595, 814481437, 852152321, 551772287, 920173885, 685000436, 533584418, 572775767, 696195925, 565432726, 961102285, 413028048, 262154058, 941207211, 141983643, 350630521, 523558999, 953497425, 16549685, 985887569, 287912959, 482125131, 547146133, 637917890, 804628736, 634037729, 631855751, 590131451, 147707293, 156159222, 587540364, 273463640, 636568717, 915731537, 21349191, 872372323, 519269849, 757399118, 429293058, 291448442, 450834575, 579164768, 260835721, 356116129, 58971420, 822184631, 65100097, 939816565, 40159212, 353781612, 256448673, 208940699, 219932420, 605898160, 514329996, 97412897, 444593878, 723238999, 832729378, 238008350, 175609512, 780172243, 344745266, 143888968, 58078464, 269533365, 582446154, 975486846, 928154839, 629698372, 551529601, 871112523, 828460147, 399069709, 506807043, 424683475, 835925061, 292967810, 45263679, 818009778, 288667673, 151750108, 930487980, 689833043, 6212649, 484829685, 920396091, 79569626, 581438735, 18113967, 942847290, 509877087, 828254219, 906679162, 762960123, 444148201, 852721573, 685379303, 973382075, 995548846, 423723476, 424896650, 708523703, 504914361, 107899015, 59718708, 406383097, 518217686, 468825938, 644135234, 808001976, 342063346, 228249705, 803046291, 956022536, 950728948, 556941315, 684819197, 327525511, 720258396, 419658917, 373159329, 500943357, 538827119, 910424521, 5513647, 73930266, 44277180, 350515301, 575800769, 693957061, 360890811, 616294909, 336299451, 128048955, 884208102, 510785835, 131373940, 22088689, 334057220, 561119035, 447486626, 641538016, 28533857, 882753527, 428603382, 912595164, 448599321, 81082996, 691641291, 575992922, 459224021, 922986068, 567311729, 664987627, 878720241, 338856493, 138954220, 750027503, 445799021, 888631799, 696087102, 299495911, 399731336, 399124158, 389918682, 985462497, 349199957, 823897563, 543973629, 295425358, 398980539, 72644380, 488904197, 82143512, 284960968, 687225219, 61242207, 62205585, 946653312, 634428222, 26147199, 211449972, 212893945, 820169032, 876596453, 889405207, 864133764, 351455389, 422068183, 767857398, 755805319, 629848831, 885552639, 581807673, 166047873, 331906020, 955558361, 242518796, 251924324, 613827109, 185340111, 112405990, 314718405, 404083832, 73894823, 409087866, 18409382, 285763287, 674215723, 276654649, 173348205, 577286032, 152507305, 440009100, 506449811, 986866484, 206333349, 89016686, 211746144, 882786736, 41203133, 109048073, 184875043, 856242494, 459838107, 975017389, 882235092, 642244163, 886814839, 124932310, 247761168, 723292303, 948769338, 135886978, 130075073, 869206206, 604869469, 487734207, 8308128, 747879319, 174165017, 200780391, 904498957, 910002271, 862697166, 536666521, 833690362, 672783349, 640059057, 588434953, 889451352, 74032135, 367272123, 57164669, 168676529, 77114567, 349330084, 887525869, 723240953, 958112121, 793200434, 604420076, 48446732, 161802230, 70100189, 408516049, 69548368, 232171138, 330333815, 351186657, 654305984, 333417789, 385809061, 80940077, 827861392, 223558878, 583718853, 536411170, 612619784, 760804466, 382907569, 885914772, 400219500, 567595872, 889143239, 495656837, 264433295, 278106840, 307267323, 336725119, 94481849, 816459595, 599348751, 323941001, 735561854, 293234912, 767605280, 145778534, 708881531, 736946878, 439129340, 30401840, 791093988, 676495156, 277336996, 278359518, 372655025, 918516818, 370138698, 279471517, 105379998, 685759074, 449267010, 955364069, 854640296, 154540269, 842355940, 986554949, 434796571, 169064489, 432304938, 552053972, 134066259, 770576914, 57174261, 437699834, 373636636, 703041197, 56197678, 742077975, 583221231, 270718140, 889234988, 152231845, 412618635, 723240396, 472937165, 919956725, 581812585, 197940723, 217273147, 709293113, 763137849, 227801534, 445567955, 963410342, 408432441, 680792134, 266523153, 731683932, 238384586, 836252902, 942301343, 369726, 308259800, 138609113, 30668070, 35249329, 747720640, 924045772, 900441274, 301675547, 350837881, 264515468, 188077359, 36751696, 369999521, 607322107, 901498123, 435803117, 985940052, 535777378, 998956240, 796463296, 902970773, 299107691, 864663399, 570911966, 670939113, 92616325, 222140840, 228896365, 608910120, 758812541, 655696418, 578594335, 820012495, 722388216, 734263188, 198526824, 849524711, 141824212, 93113366, 93489347, 784256834, 778748341, 440398999, 896302334, 811154649, 64880898, 846269049, 669053954, 182555207, 394328062, 503202459, 702526199, 131031036, 486796105, 291903584, 65783669, 642143413, 794751819, 335115911, 644225066, 924967936, 212573519, 487399159, 666922383, 170653573, 522306233, 39294854, 768170928, 811588557, 148195642, 114971222, 425093454, 715440851, 305694417, 827572009, 711876954, 411688524, 805204763, 847202542, 2752460, 240470394, 846389249, 622366091, 900253880, 221892178, 351527436, 559051568, 44684857, 535671097, 989177239, 962141360, 632362558, 848649996, 291532039, 555391319, 345009919, 21086656, 474751630, 149444773, 960880852, 883447924, 469120399, 697511434, 358173709, 837444667, 344604894, 275403263, 151552487, 583772529, 735774338, 408391556, 670883067, 74701460, 540127231, 145983482, 513101070, 183528769, 798799816, 796748012, 870954777, 228835470, 677333052, 822139645, 680731629, 612703775, 42213466, 374671742, 193768328, 339016227, 647698915, 929587283, 262656597, 768382841, 755472847, 951526437, 573838364, 520160497, 506518104, 405460671, 126265272, 681373198, 239598567, 503460366, 445389262, 425235557, 360261538, 504364180, 891226565, 172601521, 545845671, 505145097, 456894967, 609610935, 421263106, 661014605, 626358878, 611621031, 315042255, 823722000, 295082146, 666426443, 88680885, 182100589, 807423461, 393149900, 510000764, 668371192, 193998134, 968097258, 464956037, 763420095, 723269346, 893349366, 628593071, 303127064, 851099683, 732475693, 980141149, 766514550, 19351555, 338733111, 501873087, 931758611, 96678792, 35098881, 185057180, 86243137, 658899727, 588040743, 189648497, 353608440, 121719260, 689641509, 286543500, 221199729, 856985171, 118335646, 751421225, 481455282, 24348236, 560063094, 281341235, 396280885, 905442978, 149234640, 163989708, 316369817, 781251544, 749736475, 930176747, 7438808, 5393160, 368264250, 608730436, 125376671, 864338715, 189265714, 295792569, 606847445, 383485934, 33880815, 883229442, 315290442, 861127120, 346815521, 806124014, 236245712, 838443722, 774738331, 477434047, 909460709, 31173124, 9891232, 583704944, 638774522, 647313103, 818537879, 242007186, 538952100, 599719163, 898572807, 591970514, 417999579, 578720875, 274971349, 445055730, 194312411, 318711501, 848080210, 595407681, 835842231, 96606522, 499945777, 429809885, 349111501, 300104186, 758657033, 224644441, 625899942, 215273623, 371808504, 736485162, 666250266, 567047446, 779899489, 426466466, 608886334, 992060489, 842459457, 996883087, 539391031, 559905787, 631788676, 464872059, 645463672, 880435628, 476547801, 314919493, 147848638, 594490447, 684475831, 647020975, 746638877, 679206262, 435260988, 843432007, 100842176, 621473752, 468216903, 467908780, 330889405, 951022745, 381785600, 469228506, 814703811, 219204211, 199114904, 854813767, 190345409, 776488204, 548594325, 899021928, 404217712, 763688358, 225044506, 814869833, 69107408, 521567496, 118175244, 447866854, 722971062, 443878955, 96486358, 899604671, 29325512, 313201801, 744765174, 473518550, 659001310, 585829567, 62708321, 206241523, 507821480, 462384784, 862032133, 625921039, 938183380, 895359505, 195615839, 901887730, 508415296, 70136050, 65852050, 219060738, 249532033, 724715947, 155652018, 550895866, 24515127, 386618889, 970575664, 975390545, 271153292, 808159727, 403256798, 1210165, 251035828, 33772151, 570048933, 792433767, 443548337, 284238952, 868956086, 898814468, 976280477, 904177450, 325469410, 992654119, 470571649, 566589738, 334617865, 937546971, 952701500, 192641400, 876776556, 182531867, 113854993, 350390049, 243949022, 293472183, 53392857, 370559257, 1848263, 961834914, 119536752, 100359241, 221885341, 434961485, 503595937, 509773989, 690024492, 761212014, 376474203, 742530564, 208203842, 742082229, 377470421, 499584772, 317062180, 242314680, 547894641, 98560699, 491580099, 965127673, 256218181, 278499361, 432343487, 93694119, 608059097, 955751023, 644099868, 711966622, 426562495, 394592134, 82083537, 363187867, 748324226, 967444865, 102523586, 689187380, 67469253, 271006764, 744774463, 610154271, 172423839, 703240100, 270967783, 867179490, 294572282, 351192759, 422950538, 290874850, 983266392, 820069097, 334017069, 817254321, 482705495, 604324687, 949877310, 10818423, 824674163, 214607922, 878258175, 56121033, 663966534, 962552808, 462955148, 999096635, 450780658, 465177780, 792011933, 647332894, 898924153, 522174835, 62872439, 472607001, 26237158, 333051257, 620831155, 379019471, 455860396, 702270904, 587008993, 925253721, 823463482, 959660203, 456004116, 98957956, 317161897, 206477573, 480921885, 807811020, 191457675, 998784945, 709546914, 401081375, 298080662, 689600725, 929256805, 310498838, 951742182, 487567048, 203054859, 173856518, 268465460, 977475307, 465718210, 503842290, 870236772, 42170885, 449351687, 110717186, 555400209, 418546158, 731295108, 304227136, 886326690, 471035451, 269841160, 457227727, 864851656, 990858219, 31230610, 20933706, 448267637, 93502516, 6988321, 585373660, 853541654, 673994432, 276007989, 441449797, 845771466, 181222337, 409873040, 567063284, 414008816, 313484379, 345176532, 987464752, 520591181, 775081424, 479669223, 328010848, 985345419, 26080796, 266713882, 886665850, 991375048, 708965539, 129222433, 13540702, 535165435, 370821402, 588925683, 191249058, 132831673, 320420347, 648936565, 544969386, 872944781, 161094576, 415767751, 145036611, 718928417, 573927427, 95624787, 652482488, 510689572, 472159115, 930738469, 345765299, 470461186, 590754225, 947397690, 160178020, 447293415, 756401101, 133791780, 621001038, 792657330, 861949549, 827823885, 638299480, 619025479, 673388955, 490295592, 202595799, 174541947, 441602112, 322555198, 550289677, 850906128, 270788508, 843100025, 473963472, 896276623, 413589041, 579024742, 916265319, 949994593, 582201520, 864609647, 751082061, 681598494, 376434669, 125037492, 519364197, 308267825, 204053532, 805563879, 578124901, 874631965, 706667195, 394247776, 397939653, 315105725, 93346621, 254697707, 238789081, 790670428, 747777677, 659513489, 918142743, 943242972, 582564974, 69210370, 53422604, 533828814, 811018965, 841790882, 592132993, 265531730, 244777119, 110979873, 294986495, 135898234, 830275057, 129969236, 305451629, 257194548, 926581986, 495306087, 916628375, 502606240, 535265138, 387333617, 710677265, 129877198, 756987017, 651116222, 198365937, 754475176, 608002782, 382753977, 190477329, 922558680, 833957816, 823426210, 320917964, 89002345, 729331527, 60141019, 785679618, 828333611, 2059515, 289516890, 187249357, 672145612, 412525719, 23228164, 977794030, 264445837, 279308262, 494322621, 503112652, 176260817, 471597015, 382179338, 185779237, 80997588, 112077662, 608523923, 896732364, 742026200, 25661334, 686602730, 869732741, 66019234, 625661645, 959997059, 646710976, 747440285, 25897864, 897599185, 526614110, 722562186, 412773384, 327667098, 354759410, 463910406, 75550549, 835461278, 96775566, 18195903, 367799502, 98663886, 654940927, 295675, 183314841, 826110469, 725040328, 547484538, 298663500, 931017258, 217196684, 384555033, 125887706, 842697446, 411775215, 97860390, 101488113, 77958072, 752288546, 744047619, 212117567, 183087431, 956724205, 457024237, 904493530, 929796327, 298397215, 291881617, 136827163, 915575263, 774189412, 728832454, 905032497, 867902778, 781674935, 352401879, 191704598, 58678083, 488640138, 116079673, 95760806, 750619945, 518164512, 466963555, 559047660, 106945573, 487539351, 334237788, 199642172, 365689567, 754348415, 696101488, 782851554, 99214243, 380073217, 883787589, 874536885, 916053140, 355968915, 339098702, 834166261, 97006930, 206858635, 159653776, 609684578, 170205083, 23159954, 105430139, 261027898, 327153566, 715697297, 610903358, 164737515, 31360783, 351247021, 265339045, 220988365, 644893836, 233441202, 517323910, 604543946, 836999171, 396200159, 215397395, 500981707, 305511618, 966930779, 926958692, 38818307, 708430187, 409418205, 253929764, 334638662, 731865563, 335398475, 342906107, 103542580, 271936512, 664021554, 590353215, 358031765, 689545937, 336066453, 241751618, 100036034, 319364981, 617076474, 203285865, 784844734, 624201529, 119742920, 106844466, 625461993, 228486396, 932990166, 712579715, 694543784, 125455498, 489757300, 252730263, 146753167, 649480824, 91499000, 371497275, 920928356, 542228368, 171749077, 171946578, 649300596, 631410782, 198043797, 731312048, 767789950, 308812191, 879334117, 715272772, 217420157, 715220969, 222935535, 606390132, 780059112, 373884200, 799231154, 37263027, 932994651, 543304739, 712914868, 519248742, 346410848, 637445138, 787533788, 93667620, 357470854, 373757556, 424180043, 955339507, 507017992, 56367350, 899669049, 680950024, 262994724, 348350094, 590251593, 173299634, 184460117, 355617191, 122003773, 7634112, 959847131, 292308780, 610817694, 180772549, 77323655, 458482807, 486470532, 881287256, 865596159, 895344045, 243656920, 14449328, 656107807, 174071408, 842818027, 435512498, 157712532, 634118174, 298575067, 205651208, 96222019, 587451889, 566495386, 26492059, 904909109, 488397167, 351083870, 728771450, 113112121, 94929422, 880502949, 355087456, 949957149, 418683833, 46658054, 17614014, 720883394, 78017627, 575002166, 607041482, 206447627, 584892252, 41842168, 633588593, 358116612, 284480970, 689232110, 773054154, 729127221, 573260441, 240357857, 406841391, 367312220, 927105437, 983918005, 446322803, 978116344, 583569543, 11325047, 395070800, 144534291, 438303797, 723800141, 543185481, 113076792, 875598806, 362987361, 94329676, 511853018, 378706422, 567346813, 966273768, 786093779, 289552874, 972406637, 132358723, 549051841, 491074001, 54533568, 407001047, 951742759, 277833572, 765832949, 913124059, 346324501, 855278591, 549761524, 973819933, 107901426, 544419400, 626729106, 199854451, 183611278, 386698525, 843845705, 72390015, 513903246, 38383501, 567733056, 999500296, 797988321, 257375810, 521627999, 395264808, 726708450, 3976942, 410796370, 773989401, 202413046, 342616183, 137987405, 960944808, 382613450, 585539272, 478645474, 246916669, 823451939, 762988671, 386652013, 943469946, 94243466, 329163026, 460004811, 82870593, 162854130, 385741602, 914838995, 503285186, 749477907, 375885950, 243283936, 205915696, 298630138, 927100578, 526489875, 743306694, 655337838, 382945982, 187667311, 488413205, 992100607, 633273346, 130727939, 787433234, 973454912, 148309569, 339980517, 958965060, 381982817, 337557524, 674103133, 905514931, 499141084, 509736742, 636910473, 70517666, 811739219, 647421190, 269617895, 262559311, 777229269, 997630218, 102548654, 50168032, 778361662, 699174078, 138250563, 661416625, 429283625, 266550902, 169008692, 4707413, 342388503, 573560961, 241061419, 917958844, 761737946, 491197677, 424355264, 243703985, 552028590, 336119023, 326421432, 778819501, 909443289, 627205624, 421834818, 713031677, 748987746, 3083820, 555863929, 257327199, 413041545, 699211250, 89352888, 73489425, 506900340, 662680224, 682817545, 394680780, 474386972, 190643637, 765067474, 99641172, 192307821, 932448353, 706508045, 366356503, 45904625, 259018720, 870586871, 25299654, 494181500, 51214711, 291836623, 903531556, 986813873, 581186040, 251478599, 812405009, 551390715, 605527922, 94351689, 682365921, 9055503, 601674327, 141134182, 524724280, 701516610, 20921286, 139183622, 219009454, 938721962, 954059089, 458072821, 541596479, 622031720, 212429134, 621136680, 723487700, 520456247, 981343951, 738666655, 879425060, 449178206, 599960305, 897865774, 835326191, 942793409, 764569470, 100531393, 852642841, 621198499, 969172844, 579432800, 803339775, 950000806, 532417159, 477239977, 363137129, 823347373, 483520911, 962251328, 772281555, 496257442, 323843779, 135980918, 131216258, 681354174, 149836573, 529862256, 586454542, 63848565, 917139048, 643759332, 994770850, 998125976, 716517601, 205821426, 916537496, 980667635, 437460731, 361036843, 548876724, 869388038, 866633709, 491419958, 374890725, 346138643, 614752098, 848980306, 560625642, 563953542, 269522692, 518047875, 99184928, 116538674, 492370786, 959912131, 34978975, 909825847, 662749090, 453926826, 959465830, 576612923, 995302269, 51620853, 706243506, 984218113, 17585395, 442843209, 549256767, 879211002, 66326131, 803991087, 482994359, 181349701, 12439005, 852639995, 813881703, 678432248, 341488545, 61988669, 336000450, 70023380, 762723945, 699849772, 863241724, 646726784, 481989435, 957857475, 313052816, 514114689, 321029299, 131068878, 794136413, 53319748, 792257778, 615931294, 512862128, 556084321, 897115223, 569628637, 362364010, 335679475, 457967420, 807180117, 260171061, 753388882, 363839940, 317824897, 962367157, 429234104, 377777401, 653272475, 188182311, 612562959, 20663482, 661413471, 977046046, 868687499, 152710624, 41352943, 195187189, 854381796, 334591928, 934041088, 682753602, 448754267, 875434481, 43685233, 695539860, 557780374, 264674529, 93999191, 929560466, 865572240, 38897307, 114087396, 257177293, 274379808, 178716466, 615047986, 62772884, 874588595, 667603588, 185282318, 106433813, 531090983, 793333998, 829158378, 684410203, 637051796, 815618100, 36084028, 236199531, 796066803, 313426454, 797671184, 815186717, 117583256, 518000835, 66188860, 627962253, 772451167, 332811546, 49420273, 516093124, 979476214, 733759905, 372540040, 628523996, 695482679, 874640264, 352371000, 618350123, 254791944, 402847593, 217720932, 349915789, 979985460, 643667436, 310931816, 150467278, 509138731, 19946770, 630749378, 111868891, 588669133, 607178544, 393588779, 301021292, 760917106, 988996305, 999663169, 857375838, 919353392, 913051099, 274665059, 534996467, 874368310, 600972894, 246325700, 794838275, 949024773, 171264193, 626312552, 875563360, 815535133, 22919621, 383600044, 367905405, 105248972, 988531890, 437083139, 695093533, 64415442, 971834840, 325441458, 757694980, 775399009, 48130381, 207742486, 358805180, 887357724, 230084537, 693394433, 795102934, 779419122, 963519359, 712545463, 489286166, 328947654, 353899920, 926801688, 795156318, 180950440, 471207287, 790457120, 219941516, 14265230, 535600679, 620246222, 837684351, 192912630, 768252384, 213664752, 510423103, 461529035, 167350484, 760159044, 337099899, 252913155, 416888800, 946669779, 964046338, 576779589, 782981468, 106225052, 173362907, 559108020, 383462122, 447886755, 781255217, 811168119, 544244645, 636441291, 875218442, 833740533, 126810430, 492583406, 244216588, 392001341, 643776074, 395018365, 984285407, 747059585, 959164821, 54442323, 219472020, 899965013, 336592858, 845769688, 980265752, 205626128, 887616121, 913701208, 645722081, 930606796, 806277142, 31662978, 382228003, 736837305, 268481720, 438834300, 490410925, 261459395, 751103429, 246774639, 665108856, 680939561, 457826393, 210727231, 624788232, 709630242, 711282868, 612801514, 522216871, 550903246, 290511712, 592314454, 77048810, 288036105, 721287234, 910485383, 627629475, 813968373, 232782474, 123994577, 140612176, 444081424, 309950816, 203054049, 645161672, 454858481, 659825784, 828201759, 494119624, 68595431, 972473926, 734855235, 728527722, 175397246, 450089913, 396753606, 612982951, 622389965, 596502196, 482616160, 565662127, 195207920, 686212969, 46678300, 4682535, 591064058, 937012038, 403734192, 576985145, 914376341, 161938823, 713848374, 127721037, 733137272, 318853552, 735219598, 915543232, 362895461, 971236747, 357928130, 274627002, 685000252, 27607711, 593947639, 696467251, 534641630, 790161005, 789738524, 454069085, 514828076, 734080502, 842632453, 708261853, 2863354, 949385423, 714845497, 142744789, 508910981, 334532490, 466080897, 620890825, 641450215, 823566632, 332732617, 223154409, 608750560, 900798125, 411652309, 413333390, 138329078, 140023735, 753889537, 782270136, 448219900, 905646877, 63250563, 475467673, 337324542, 491318354, 134908676, 81587558, 659508845, 725711406, 4166370, 802181809, 372802828, 399916884, 730684938, 971291216, 575232814, 71834841, 602776349, 994278751, 734362440, 440981012, 454325779, 66450111, 58675072, 205645526, 117066088, 492521847, 238753507, 190832762, 885949384, 456610400, 745773673, 897880447, 457569074, 765342378, 988516632, 364492339, 914759525, 919139893, 231340806, 934618714, 713453731, 584086207, 942783300, 12867961, 748050142, 885310923, 597422422, 845888485, 213165305, 657190584, 665873253, 984522372, 972893522, 452606871, 847799989, 590777478, 681259644, 825601708, 24611060, 764083918, 869027605, 99586671, 726329455, 139037146, 196900667, 921457083, 524365610, 997934992, 271725245, 143849013, 413409144, 477632397, 748336196, 341191599, 868112708, 48114260, 132911430, 677856498, 157071604, 568154309, 753471739, 273439596, 503824050, 440554088, 162731331, 291038721, 692820497, 632804911, 236166764, 783536488, 896387754, 162798962, 784917687, 777573945, 363556990, 141540119, 371664732, 996913544, 860962137, 756265059, 248048182, 692848602, 16457679, 508697426, 535692519, 696879020, 578336421, 221344859, 70458367, 201881710, 664366784, 832492370, 313510963, 38097297, 631836948, 171414172, 17355980, 644409304, 363225374, 500280229, 515662107, 742292852, 868616164, 910150929, 56173945, 390714826, 674046790, 281513779, 216105600, 740923930, 601024818, 836831793, 936859593, 491734352, 165276962, 225835905, 978194692, 682313268, 800414482, 649078553, 199622243, 493283664, 561421955, 18954577, 518332072, 742102462, 239270506, 999226841, 708757605, 247227830, 447570504, 195622474, 154768759, 980976114, 279285390, 517046419, 114936611, 857506779, 344740109, 340957448, 347753242, 529578889, 152351774, 984780470, 339956162, 238050057, 734067028, 269748288, 891762216, 605877163, 63923338, 596755674, 110006883, 411658224, 380584326, 218143032, 550169863, 342563187, 83890343, 331776608, 533865167, 384576726, 972385972, 434317022, 104178615, 896810345, 681053232, 12597217, 470910299, 294099205, 957537258, 339309212, 69663407, 400650262, 225766063, 468074568, 294931715, 381798618, 895602401, 844015341, 871459392, 171044505, 380514148, 126546060, 54093291, 802406810, 483285468, 597256718, 121186851, 884383995, 302137964, 203617447, 646969953, 806130295, 409743322, 794621829, 847076779, 586339434, 192379055, 395600223, 870847252, 141659408, 234464835, 434799448, 514180056, 781479795, 740708639, 145915608, 547202534, 399039831, 590916995, 538025497, 763811659, 112169978, 732161579, 280729026, 234627034, 371656717, 512118856, 602805517, 655033815, 381933878, 833827822, 550836137, 452744154, 129218002, 459290186, 242413833, 140090123, 931387098, 686166856, 832624371, 614775006, 364525466, 907033944, 423218815, 918579100, 60436092, 19729582, 779363986, 696476462, 69924219, 137306571, 764184788, 873947485, 102963850, 473443319, 21802653, 219858227, 86115480, 432590070, 408330760, 827666323, 390545796, 696779225, 516303821, 917279507, 428820547, 763608713, 37488673, 539914073, 532678656, 34026239, 213847769, 248692382, 17323496, 524771618, 746954212, 816046142, 825491930, 286100466, 570188808, 480824729, 22541905, 678454920, 621235586, 347827525, 222976564, 1832067, 103248706, 949379403, 312065913, 423074611, 322473094, 789582264, 286249707, 750506392, 871013352, 103231234, 215443852, 638238952, 86679787, 53378559, 365843584, 768345258, 651929658, 905105554, 391766980, 54507223, 145914734, 499749845, 541269561, 507977761, 675692806, 555624658, 256858644, 610149314, 168836714, 768816610, 78029519, 377335559, 422779401, 918408680, 920115737, 649710499, 133232657, 173525332, 22762104, 443096042, 545949835, 911534480, 19679073, 753327207, 95509604, 237924273, 322629146, 792472717, 440294010, 57541618, 388084820, 738510537, 448951563, 943501105, 726020008, 782072523, 351999724, 541433702, 290977402, 3215576, 244125352, 594802286, 420020280, 183038849, 493759736, 76279884, 245771616, 480331873, 849793150, 913252740, 428396619, 166229277, 639352316, 626481151, 31075169, 378869957, 537983567, 277661945, 869936308, 94292761, 763752167, 719126852, 230876230, 8706060, 400640973, 495007862, 870948284, 453772027, 869466812, 38384047, 240291287, 375155226, 104845345, 934499936, 367431367, 123249114, 734542187, 455330687, 990453805, 776292159, 90765782, 526495442, 421067506, 788357343, 446830606, 612567406, 308176577, 570177188, 283980013, 973839867, 737826359, 303970465, 592912564, 857177393, 994935123, 889960455, 436239294, 672452391, 24717660, 632888163, 469107029, 924926469, 472719115, 457482485, 950675481, 781531634, 818011847, 227588947, 331112445, 488680184, 325976118, 35852963, 38067661, 65022878, 450661541, 559179149, 310031833, 525272628, 109815491, 397011176, 454837477, 521590290, 561533381, 634097324, 701408912, 924268460, 879103737, 761758195, 858547522, 393516318, 361001908, 242942790, 792007336, 785044300, 515197892, 489489182, 703333372, 351656817, 972088642, 655941941, 284081280, 812355463, 514345125, 678128137, 398441560, 844700566, 76207142, 32387934, 820751215, 58628689, 773887099, 202591942, 962360247, 56656876, 63454777, 610509555, 932246509, 122043865, 103339604, 968910381, 487476638, 247047862, 330100595, 195251321, 159961103, 601391480, 829148626, 282187226, 517128522, 20265197, 596756219, 164985376, 675324354, 980689464, 188498925, 763473996, 430395862, 397829718, 988739244, 679486410, 760783677, 115045548, 311536374, 983801432, 175724709, 588808751, 82771707, 840262982, 987277766, 732096005, 642631760, 691042666, 893511911, 114285223, 662276842, 591472720, 8492192, 108228442, 9593712, 713892864, 337708144, 898900715, 405628231, 668493821, 650122754, 283661495, 929097792, 980675374, 219272415, 97424543, 929545781, 595519252, 951667749, 405487402, 866696560, 525916577, 431140071, 884249125, 324726929, 71909950, 710839617, 866057129, 342584937, 498364188, 667099665, 331462516, 595282507, 14076783, 34112924, 727766228, 911534635, 365348963, 74832712, 720118901, 392181680, 493847209, 418684938, 92058998, 755512247, 799044454, 323266438, 26102409, 64394298, 548110549, 836877878, 455481424, 153960257, 874343783, 791308578, 461320391, 339020569, 374908090, 848444009, 155996278, 816496317, 626295962, 388465426, 723796201, 393137205, 886621525, 379127656, 539753108, 336715057, 375176917, 583225158, 414999302, 451668129, 517916548, 989747495, 43338419, 726511608, 20336751, 316780285, 262815595, 876361378, 83875408, 34294752, 366004834, 410404463, 684349151, 451383856, 209281740, 128656084, 429365693, 907529951, 148526607, 912668941, 190380352, 510001637, 641050164, 296903956, 172795212, 612646416, 717392265, 738981343, 60471483, 361277893, 338214122, 879950265, 203151203, 279078425, 886476543, 429872333, 952631203, 75531631, 159225241, 584831733, 736390298, 298828481, 921866427, 22502600, 224934719, 999976596, 218097989, 997302738, 685949639, 254839014, 115809354, 341274651, 957634079, 970705556, 273699291, 786461059, 744773041, 768525543, 336426998, 509616805, 307479143, 957586650, 857267713, 752218759, 452835948, 812748050, 328803537, 51699366, 533265320, 201642841, 945262709, 435172274, 958284302, 974439811, 412651313, 458081674, 172225685, 442525721, 187544417, 516663444, 50667239, 574895984, 728722505, 986013415, 337595066, 761881149, 378180792, 36750685, 95950265, 980649163, 922667843, 816218861, 790905882, 26801027, 106161328, 651438902, 621130736, 654851618, 764065791, 668386377, 318789069, 603279732, 665171058, 487530689, 398964143, 904358912, 723967052, 280923321, 765758454, 118919544, 680618501, 386844255, 769332435, 768278037, 836652943, 63293971, 656968012, 397888138, 500069955, 806268246, 2137402, 668661276, 458442445, 153142553, 905269373, 132802892, 209035523, 131284007, 891665806, 500703472, 165836238, 339553982, 56399271, 47407922, 131151079, 314979925, 356777449, 627818750, 884480686, 861496386, 543130422, 758792478, 99648563, 905264902, 915119145, 99470380, 514182931, 861100081, 488159998, 627947789, 444951438, 267518172, 785208188, 140990057, 464606234, 79387884, 855053836, 303057250, 155465102, 316148336, 229312379, 340738506, 594207029, 465649141, 483174218, 894247567, 821204240, 576824211, 888343384, 349300619, 657112623, 125353615, 252672024, 196296435, 844637715, 697071040, 431737325, 379668833, 600172931, 361613429, 130382405, 954138727, 744944721, 121506967, 702799059, 705425059, 402718054, 231205333, 867938212, 173352501, 318163748, 254585258, 355686300, 507384020, 78249347, 991609830, 177176193, 480873666, 753564455, 621702404, 715583498, 460884111, 814355614, 44649550, 910490059, 484391309, 481755548, 210709824, 162069831, 606014913, 102836370, 364725884, 363841801, 458353559, 195710444, 83789169, 746797584, 162016885, 559773608, 779236566, 2614842, 865085233, 442927760, 731434431, 610879696, 326955125, 848929667, 191396232, 876321476, 976936282, 749824468, 721611275, 623993285, 674455428, 410165442, 495325771, 840801601, 679873044, 26038718, 116136742, 627567986, 984512922, 795580259, 420770636, 888443720, 831081496, 57962923, 897312611, 643011526, 522789030, 923868046, 535712540, 967146868, 847824903, 846479766, 828979946, 58644592, 548454887, 853999877, 306365878, 611944529, 780684660, 556989921, 773741441, 95246605, 619195810, 4672174, 412210420, 321255028, 691693217, 803194049, 265523394, 320424426, 375669844, 728645507, 286540251, 819016157, 352917118, 35591448, 549944389, 386742852, 408233586, 226594225, 963470569, 403825809, 4900608, 33525877, 603671985, 922577126, 123075464, 640781970, 158332166, 485621731, 615180999, 263658681, 182787697, 518254461, 164601207, 221898187, 871562446, 888352968, 687841376, 919379236, 77764498, 413652218, 874693440, 961718315, 614117085, 568562950, 33565287, 961969883, 385277115, 879643726, 749106083, 399747163, 380908322, 299636083, 501133771, 672949988, 521520448, 863660026, 973802590, 706264675, 803915849, 134050633, 518987891, 416530884, 437945720, 271141683, 107613114, 811731394, 733388594, 509584066, 406600921, 480385915, 115816325, 752488816, 828047095, 814503816, 973898889, 28820011, 453781326, 489389147, 837245878, 769024815, 304357649, 569691751, 186516826, 286365811, 258340292, 853429876, 593229145, 982225972, 260388371, 227963194, 898997408, 649934790, 202001662, 165249168, 948197927, 926316061, 115797909, 62189071, 932220982, 189730238, 358358992, 673975269, 518482169, 944927475, 239521369, 793505873, 485999454, 527355745, 662689284, 649030232, 425562861, 567253594, 689947842, 546473777, 135916914, 202859066, 313946167, 595008814, 660562362, 171606630, 164077488, 318772265, 607917946, 529433300, 618821628, 986689250, 816845968, 721875663, 352533642, 591095375, 125038243, 136477573, 336862330, 352493542, 528011262, 961209862, 699077641, 136107942, 809551068, 904233496, 925453452, 493620952, 78411824, 587710046, 415130752, 315766584, 327443229, 888161644, 846712838, 911536283, 852790640, 78967870, 202524407, 739076723, 911174566, 807871905, 546623288, 748165581, 239717789, 90176506, 827671165, 805099475, 388414930, 920341678, 593538609, 289303790, 115268798, 165752148, 499663181, 663074477, 466529359, 398647643, 74414771, 499074438, 168429800, 515867834, 733220912, 408772970, 546564628, 441907136, 886571735, 480855878, 375297038, 497380844, 852278668, 392012336, 228552222, 297647223, 686080486, 29220449, 104610727, 369416306, 789688218, 792456152, 681415264, 969623323, 678241968, 459353813, 86785311, 22698455, 70503081, 641034154, 923743253, 386144993, 500149799, 11273114, 578007081, 846723767, 687816006, 819685148, 444577570, 461701883, 601817556, 948307626, 887841186, 768283532, 827619133, 585799263, 12151110, 424878837, 188113240, 688376263, 659830854, 951782902, 846526810, 141389527, 637031578, 850099838, 590874722, 602253295, 332223363, 477442221, 509028265, 571780991, 225466927, 510304046, 386614213, 269614674, 671491613, 222647049, 985899837, 333272270, 760068366, 426352327, 268926351, 941091918, 908302126, 27791622, 899997091, 705154804, 904367477, 338892980, 672332448, 441961155, 959267795, 276467426, 433812748, 990420219, 645401459, 85272862, 252254207, 87382693, 441734943, 699100662, 546317472, 913206455, 192041127, 668018429, 961690741, 770612294, 880244828, 304464187, 371868843, 842367895, 189584677, 680764258, 64100779, 548305480, 294721353, 313807622, 223232412, 615770437, 95011348, 813910086, 796821838, 166381449, 193235821, 795319403, 614251030, 556293285, 715522128, 988095901, 5612498, 784998356, 744857748, 861847277, 69142570, 125646891, 818097532, 416380150, 464987498, 470078804, 623847354, 591777807, 575133466, 939167139, 725167338, 425740396, 248249668, 746413068, 174027241, 765574579, 432692752, 672295611, 776227770, 777783809, 742672342, 707639406, 135564406, 577175820, 554322411, 872374091, 195268123, 251125836, 613939715, 39668464, 790356660, 609399962, 50549366, 626133317, 856141946, 978179168, 238983555, 531009623, 55917675, 957961218, 777756124, 307738188, 77119160, 708582653, 458019444, 113314691, 315948617, 752320127, 527345606, 363431852, 781267597, 618399818, 594429931, 585874447, 335015549, 355804599, 751970480, 409035933, 300713032, 795557517, 209876167, 550740842, 602823515, 213640326, 262116087, 830932782, 506989899, 337061247, 941406811, 435721073, 987080466, 551484941, 732744670, 184444321, 823560397, 764174337, 272234025, 968470737, 697120058, 370801912, 536068124, 3853372, 836242594, 381436578, 908585712, 331686658, 941686360, 156704999, 181340853, 314921392, 211933925, 887851079, 82879134, 665598359, 817912434, 179435067, 428750257, 182785927, 753218898, 414391973, 968751537, 149857747, 613186031, 112042554, 566709570, 725669642, 737440558, 699380372, 190736936, 661995086, 792841598, 707490446, 463041504, 603901806, 979730118, 901609196, 690057729, 825524749, 249826616, 964336089, 323378734, 564500836, 267443794, 671585115, 496187133, 958559586, 740017312, 88641209, 14750203, 614937871, 691678610, 876307328, 953928132, 404958283, 462812063, 464663272, 148377240, 705497433, 574016460, 275859228, 453062567, 989308145, 602476887, 402072661, 49087215, 611106239, 79308376, 472131320, 430452414, 959112982, 463500480, 710059357, 704605741, 516781247, 215533777, 436810885, 113723000, 600204761, 800563536, 417468100, 959875793, 199990848, 767157550, 933049272, 618010487, 449256640, 388408717, 46382652, 47406481, 225641705, 39372398, 843817740, 560548273, 980998287, 903791187, 392307228, 80072829, 272077857, 571855128, 330209597, 427240342, 571039255, 64954042, 409540365, 459487890, 320273783, 409739517, 694063583, 466130729, 733670166, 256973428, 483645328, 35668674, 621729223, 949580639, 107361580, 661247026, 844264240, 213147787, 631101314, 836749284, 388654290, 24193595, 218424425, 440540073, 927990157, 883908370, 556816777, 469415282, 236858325, 727396671, 977446497, 111176100, 385093951, 802160440, 270489960, 304617384, 194501894, 853930043, 231681667, 603836310, 592776449, 376112497, 541818143, 902169917, 300417351, 674460022, 777510054, 781338232, 925810798, 290215387, 942360806, 53440334, 217621133, 115193065, 639241826, 379233428, 781543974, 209654779, 400334777, 383796995, 52052894, 229531644, 748091600, 200565218, 156742234, 106054403, 550832710, 34911681, 266166616, 547267576, 720000221, 935736058, 129358378, 712674112, 551031545, 178504579, 312668321, 100863243, 9592323, 383609481, 894538002, 914134591, 828240548, 571916834, 957033508, 586840700, 835093185, 524253514, 168727161, 367663794, 441336724, 114184231, 744459674, 313510977, 591698338, 97169815, 719033943, 19058154, 33595064, 936230210, 86707522, 237598228, 229717317, 381614421, 906453612, 717987303, 282861864, 505108484, 502310714, 808115343, 110345724, 137834819, 642194333, 783035764, 238536865, 187376393, 37237405, 210176196, 114914862, 82813504, 508316754, 96032840, 23848760, 197452557, 521024670, 530970342, 462749245, 570408026, 885942476, 823299225, 349605617, 77294351, 531397975, 483504930, 308910669, 284421389, 16531667, 566647510, 985625823, 241261359, 302425210, 934911631, 96486563, 1635060, 593710337, 737658759, 628031866, 928908044, 422324539, 398348162, 146289712, 594447705, 817176238, 394981477, 985930176, 868615758, 460896062, 891840332, 110950858, 96932640, 965500532, 848056777, 908133638, 804843425, 231132422, 5277964, 582532776, 989583181, 860913949, 233064759, 454495851, 405089733, 906693977, 838833666, 535410585, 940538453, 768359392, 420267602, 474378898, 395441792, 358815048, 781983809, 190045964, 988063692, 498309829, 426115430, 519636303, 584308846, 377340281, 651098911, 365786118, 93669092, 343937435, 654214644, 818531865, 909189157, 426921759, 895610208, 344937762, 885213758, 52712493, 663778081, 8697006, 963098044, 109157689, 825340238, 176381950, 538072409, 840910005, 120453110, 303390031, 592094386, 705204232, 330959628, 679552123, 253571928, 609192718, 812159947, 695667689, 843426033, 649444029, 835039095, 97676527, 479312902, 900275543, 964675824, 22914241, 291424402, 667310603, 557280845, 617239519, 70149823, 218106610, 760502665, 400824544, 130975318, 954084554, 272702423, 210606145, 190680891, 628469188, 251152701, 371914022, 508425205, 91527607, 367192960, 973391848, 648347832, 253642881, 231995480, 350360838, 903062717, 439755164, 874889322, 508994785, 279512991, 908248703, 146596828, 868730459, 930258946, 762412065, 935942859, 844998455, 613233854, 599837979, 948896994, 927557346, 413621187, 37857381, 697818036, 434243009, 469099729, 980672985, 807894232, 508300782, 222758706, 687290167, 392638684, 686016112, 401445295, 155375930, 569492400, 486899081, 100534813, 518827723, 987502839, 489034659, 65963789, 768825683, 270278606, 639972202, 852950991, 175858658, 768943269, 382603348, 84321419, 87950263, 261410379, 880995181, 227724103, 635107206, 882931848, 618071904, 618757246, 746449268, 312801889, 634278313, 478310421, 161049787, 111955425, 737928275, 59072810, 418788212, 345013521, 912215418, 580116195, 684040599, 947459321, 82226866, 728269313, 735996794, 872272230, 830841489, 728060540, 457705626, 2368159, 127371977, 53170475, 639644560, 394750495, 962255586, 72718915, 62340576, 520705755, 459013617, 315866481, 118206311, 596164048, 471035005, 558175559, 877740052, 222506892, 628266782, 99504598, 477535075, 433206415, 999468782, 803944237, 918217816, 58503617, 32352075, 211041692, 798071991, 760943972, 413086614, 938033994, 300370501, 253605089, 856437501, 936425556, 994655310, 372825584, 91464946, 597800758, 165445102, 86826428, 651321631, 324089035, 891567958, 154700231, 550721590, 993856744, 239089603, 702639855, 345222683, 861528611, 848752982, 551377976, 729453738, 628154662, 695465272, 998404492, 391856923, 985825019, 305877387, 828452309, 715463050, 227885112, 496251958, 335169910, 313359516, 757195156, 457648816, 581933215, 408746671, 204514721, 852525188, 666331689, 516319932, 18034408, 884943015, 178349256, 388019581, 820324395, 168711372, 22069341, 133382342, 134932784, 137879725, 973390579, 209312647, 200939892, 5984430, 376915808, 715875428, 6894505, 102491334, 259462403, 147115023, 279936965, 455900616, 737402307, 808110576, 207363566, 860625202, 29532331, 540739095, 948929246, 869035756, 33397862, 214942976, 744334093, 999586731, 905071065, 652093396, 494156435, 74564035, 245467168, 53612732, 342027959, 378742422, 262555650, 726368001, 845039149, 194096336, 360454482, 760970993, 460052972, 388090312, 633103480, 916063062, 755652849, 111175572, 970791118, 791446971, 701744764, 689451048, 779065202, 801977793, 898541363, 592106484, 83264729, 972538324, 778783104, 874605280, 564130325, 841127111, 236989144, 420266687, 477019707, 534751444, 239266215, 184607373, 353992130, 463497602, 533297146, 729049563, 516180714, 699121860, 174649858, 807132270, 591668510, 985778863, 655107111, 179399808, 20107262, 260741821, 26956113, 672432514, 644202735, 671720774, 692415985, 697176351, 778890891, 888411088, 817057347, 432210663, 11753247, 27549878, 555097611, 367428341, 355471126, 218067224, 24621846, 322135242, 416162867, 52889355, 101331701, 50670186, 651550545, 111708519, 820513775, 304911912, 296989773, 451265683, 270733206, 609817601, 178553858, 87072989, 139482140, 906420252, 302259003, 736025798, 543260376, 36181292, 648602777, 596899711, 651003533, 507503912, 733764983, 824364562, 163643543, 194647189, 927641139, 949875289, 954772807, 382101815, 424006370, 236036808, 359179005, 629596990, 463131672, 133961039, 112794475, 977927827, 408610323, 726562556, 911779038, 915798436, 695026381, 839710160, 396412779, 505408273, 674999908, 705330061, 592453980, 341938670, 800177938, 738652135, 399496845, 381245738, 184804958, 845311361, 177684148, 573520655, 475308667, 771537251, 538961130, 361180748, 420313672, 229187716, 567600568, 456827056, 402405373, 906272020, 596348819, 897560165, 260713840, 514045153, 464333165, 850092492, 756361939, 312204695, 190437314, 323022318, 407870476, 308813918, 199296431, 299205547, 977884503, 865124291, 783309798, 686166316, 27164832, 38685663, 167485272, 924378956, 351226793, 797359025, 295031911, 459409414, 434705889, 951163815, 42207324, 178419684, 558093301, 981866790, 365071315, 271839199, 224667846, 466393440, 830628492, 462727244, 1647737, 596356727, 689005958, 307466251, 352602060, 691926360, 268905976, 506421346, 130563274, 939749183, 624670952, 546807923, 86395026, 849742253, 302740895, 368484839, 833207581, 603409858, 26729203, 858021417, 336588552, 471758069, 508076441, 915092497, 823866076, 214409845, 922777300, 18696216, 86215638, 567116884, 153057611, 270477378, 243421709, 810343656, 730334798, 953421572, 558839288, 503939650, 330067654, 587342690, 192686643, 169907712, 285395902, 899799653, 867876580, 687048517, 53682011, 926506880, 201938982, 132024494, 378225154, 177816693, 976085929, 761142262, 595507438, 421210407, 825238976, 982313761, 454948744, 210992497, 66264201, 376930167, 563558817, 474211245, 416309842, 890956011, 676146186, 763800073, 836314344, 734189354, 359817475, 705202292, 899068362, 709036295, 412291106, 374644429, 149763054, 686161215, 883343631, 450788284, 894349305, 672818554, 692583482, 946714503, 891207084, 135181612, 730012063, 594059258, 807971767, 731805038, 207901266, 684243129, 312889417, 579121279, 326316529, 713673568, 763082641, 632938403, 373279616, 238462594, 339820837, 354117499, 319556417, 994048692, 242019812, 549486105, 872828079, 508268583, 629598307, 378503695, 302925513, 549538130, 76297475, 582657930, 68004403, 392151391, 996379346, 63788386, 164352733, 767932326, 625371968, 116415953, 280982098, 339112555, 162263016, 173945206, 654827488, 919664042, 790960868, 33925311, 146630453, 646883141, 974379266, 245797024, 309718414, 629372242, 539590039, 288282844, 176163438, 230352905, 198684952, 363339084, 224760051, 145130, 72976079, 517159548, 302530047, 420575534, 428856163, 47655015, 567120248, 963620943, 250637411, 138729905, 6546477, 86784558, 182518538, 899475745, 273412958, 584689749, 272632581, 955180886, 174687875, 313240001, 806018149, 689227311, 199779523, 407101181, 267111946, 21575390, 816795718, 366721334, 593477368, 291414920, 221857428, 90712253, 827122977, 235140278, 556708967, 929729172, 120465551, 375150948, 724508405, 830632981, 147365151, 745302019, 721200218, 396325813, 142016725, 67518644, 315168666, 263073588, 100119285, 34443305, 663746833, 810200618, 896173008, 570247102, 918163452, 999497169, 177588555, 44659478, 797921835, 422592167, 694505345, 132540055, 247541190, 995156667, 628921441, 84639242, 526404301, 170989805, 168562305, 305319704, 158587041, 426481373, 587678100, 550449373, 352886478, 714341214, 383813711, 173622707, 688352990, 53296576, 865218582, 342121845, 45812092, 41277128, 494005440, 608942680, 848915431, 427018806, 985055181, 806133537, 613553302, 395436796, 386536801, 992350410, 21975754, 269569954, 574679672, 98520810, 89242160, 609106317, 787786832, 417311576, 776707127, 917044588, 41979179, 986446365, 591068624, 968231937, 820085809, 735004651, 964801327, 930813298, 77959860, 55818929, 234713060, 297351609, 12649927, 643552694, 667979198, 890544212, 321778798, 623907791, 865865910, 174737049, 148112116, 755469375, 195509114, 584489344, 559254668, 699837108, 548662502, 398695965, 847114145, 948801602, 416570265, 77722439, 381629213, 135403705, 453679132, 255222434, 613744374, 481388448, 3713470, 474750, 624359941, 879352332, 128730099, 870775224, 304388753, 597986923, 396314814, 468171183, 15994957, 89773627, 940564107, 612074245, 422048185, 602384865, 879238075, 536324515, 193991686, 266490473, 62878663, 289677259, 650035927, 56460798, 678858486, 581185808, 245293144, 915563605, 130799635, 499397167, 112634565, 213914181, 205695340, 542367556, 763997571, 322444755, 328221971, 70085140, 271162220, 630281308, 923306326, 490302990, 945567210, 75193606, 5691232, 900665705, 641431362, 105558322, 420613050, 825985204, 330447144, 15491407, 477670797, 607684912, 247099599, 197265349, 326631037, 388106560, 425372751, 537916923, 440943908, 194507587, 590300317, 286649, 122913685, 214459740, 417393871, 55412409, 860812238, 128021100, 188198409, 242466685, 707524778, 790762392, 875361695, 968696226, 24818993, 824312629, 351136288, 488196370, 336337812, 911653585, 476423809, 30789402, 658354903, 946092430, 820374994, 598800000, 550350042, 812729415, 55812088, 947241318, 831386573, 768576343, 823859338, 3317964, 480041268, 825034647, 378804396, 10027254, 784148710, 269772344, 762016709, 798476318, 706621416, 386046057, 480733186, 98711915, 604582697, 272399048, 138090679, 274530354, 542915141, 55091346, 372918736, 77938166, 466159111, 958052910, 314097597, 345548844, 209194820, 101040770, 555345627, 939263140, 127163276, 527149336, 267375505, 477260583, 271212123, 48289363, 929163389, 419769702, 717860359, 203541454, 839766531, 606651187, 763679205, 295314793, 911520174, 53292250, 317210005, 382682978, 778690890, 319903483, 502946003, 406124593, 547329407, 965252297, 441573109, 683593465, 79850853, 907484196, 614623470, 781604312, 177720136, 937474114, 433190373, 38020617, 882912006, 380803582, 810636666, 585468872, 496531368, 455577613, 725742159, 615994579, 565772308, 471304047, 549386558, 212430937, 157334289, 396917364, 198673282, 277851395, 659038785, 306528716, 880024575, 637022902, 854295443, 783361641, 357233303, 427775505, 542756250, 533293553, 353511120, 220388183, 410935385, 376732083, 519846283, 159759403, 46270339, 269380224, 603729226, 18231654, 475501825, 254281519, 347899819, 433272325, 709598058, 575527073, 386588149, 67139046, 824668676, 397814862, 297915927, 439709773, 797427952, 926901272, 53710556, 483645701, 857218600, 930148935, 952668948, 240869880, 119880767, 972202510, 660834598, 498549672, 680027808, 169676728, 540150786, 110031091, 756229161, 18721277, 503008291, 753398334, 966155344, 805044503, 129276192, 726841531, 293010382, 988879190, 812911393, 255844018, 812347303, 346611640, 394978147, 389649349, 960763093, 260232912, 292452347, 3239107, 425654471, 232113734, 148653010, 70016966, 349326350, 379670080, 555545485, 139197639, 563025888, 80226438, 446117228, 475463073, 162781133, 827140474, 956733286, 765739200, 81529452, 695576745, 654431455, 810506865, 151376392, 496919299, 463364534, 181147232, 929146847, 291817817, 343350931, 900435877, 721261654, 225584647, 685861496, 737965135, 226309076, 877064599, 588286257, 545134561, 733391744, 142536558, 675386354, 605399849, 861382505, 286371709, 498632250, 62167596, 51085582, 749498733, 197205774, 92919270, 130913394, 71554977, 619534140, 633618149, 505411685, 895768824, 865505250, 231826136, 469132252, 671189019, 314774536, 582566117, 66418699, 375416964, 461906114, 703654234, 580768424, 132996634, 492386125, 236696830, 588282921, 715459519, 483459702, 194431138, 499768169, 903428576, 392198793, 562440636, 374308692, 651998424, 707099727, 632502344, 380271730, 74189941, 635035550, 622600437, 770402147, 852578304, 943610869, 726049170, 910072104, 586972879, 16787331, 255983521, 82132923, 331904488, 919305926, 865800332, 786228353, 821377484, 88247273, 739523584, 335113089, 597026345, 850415653, 55114665, 801808839, 866132288, 945346582, 81943339, 926205010, 311329641, 669354398, 862557333, 132186529, 821686342, 288769319, 675823234, 434263282, 703231161, 982375861, 324866206, 421136169, 147237847, 24199015, 273324738, 592114671, 926349853, 51012595, 328800880, 201270869, 34575992, 788628546, 39497531, 254871394, 599805494, 901423630, 442967589, 1976714, 934838540, 927015687, 13433940, 52857306, 21133350, 984024207, 944242097, 98279622, 424623525, 660748507, 246875327, 534249072, 379977802, 625725126, 500500866, 961299917, 80702804, 537763083, 543498286, 46558194, 262735677, 947393462, 128704917, 876927715, 497639035, 805466076, 772895001, 684724558, 155086959, 374388998, 948871461, 216004574, 956222457, 228311042, 831336372, 556078355, 918808473, 154210913, 801445406, 24016197, 770376981, 44589909, 717601142, 427553239, 341738469, 302596293, 793922277, 705666167, 308627750, 857907152, 645812875, 300797877, 687925819, 981529855, 448789567, 804677026, 474195320, 208118591, 440647537, 484525940, 304101103, 110095422, 383027474, 821594895, 242466287, 239640529, 5479971, 815315633, 217401687, 404864216, 330508233, 993853133, 504902073, 420201034, 453465654, 507934057, 116997873, 395476850, 796469304, 912824594, 760858623, 110840219, 319266029, 416487746, 664724564, 303810611, 540825445, 633679087, 92895209, 319037216, 228014357, 646811382, 254593189, 266692552, 653003222, 453036296, 693759028, 135734186, 36692915, 113505237, 512345155, 478128317, 113878192, 146955835, 995643979, 221922079, 731285633, 633151816, 438567230, 290654626, 61546177, 192793502, 190031823, 580273098, 698393702, 889917985, 191569062, 309449195, 420782963, 361184059, 748168394, 74101924, 54212728, 728921446, 792720092, 609570714, 480666994, 635093545, 4935243, 464467152, 365316488, 887633410, 926788956, 477675462, 176636387, 111868169, 780409936, 122062906, 427848803, 473233088, 228757740, 670956893, 419325562, 13688802, 194427889, 192923724, 636966039, 59406068, 618708966, 407075464, 98982610, 296245752, 744477430, 420685267, 212660142, 374704834, 815029862, 934470029, 365352698, 901076465, 449664878, 200383341, 211662988, 451205511, 678214255, 461782190, 742275833, 392298799, 913980247, 425015585, 29004225, 797878751, 290924701, 746315475, 487338887, 463737192, 591190311, 484905785, 337408113, 453980776, 788872288, 709768492, 211540330, 982899644, 928755120, 962451815, 367349880, 80251861, 717345088, 329864688, 46346287, 618735828, 100181318, 770578815, 48415239, 817816234, 707371543, 823864262, 938045014, 414013140, 889266188, 35294443, 413568070, 127902769, 595137852, 945436939, 754146058, 273765602, 40027066, 199102605, 48622808, 660864354, 418164843, 199272487, 740624360, 979426628, 422994851, 790242861, 425593282, 851528219, 830518668, 952448262, 402456923, 889500205, 173331223, 230366424, 471389797, 74746694, 368872528, 883120926, 534307020, 181512567, 94674800, 995845641, 482098723, 893638182, 872938160, 90070893, 287810162, 20081476, 149656461, 714184953, 544125006, 625829942, 188508001, 77472164, 935094901, 231489792, 914849538, 858246573, 38070352, 894839977, 229989780, 591140195, 816588944, 319608831, 409186247, 18419112, 767071155, 747395650, 220840302, 65884153, 798610705, 618197018, 102960039, 426514839, 949411379, 892103485, 919361978, 968773673, 917968522, 227215407, 724115154, 616118624, 731244554, 496188135, 764798317, 807726086, 39599332, 556782765, 499332172, 562245769, 21456521, 130843540, 121868610, 895170769, 245354091, 328208382, 184543364, 977659419, 846654529, 451889077, 871719745, 741684445, 22551221, 620898153, 474159038, 732452389, 803183426, 940588676, 703446687, 533182223, 891649518, 369197612, 444951100, 135777589, 29431864, 897001710, 347779918, 933747276, 412422499, 941432952, 521139655, 86065595, 302303318, 777007454, 111584450, 236026694, 883548195, 3005201, 154844853, 279088785, 397022114, 558116968, 170516664, 140370454, 342430937, 813436627, 785773772, 977724359, 880863530, 886256806, 469428792, 546887243, 795103955, 44344011, 729999496, 530343825, 302881346, 472642451, 411022900, 338101286, 736011026, 919767669, 517905085, 370770326, 349991804, 61001580, 661096235, 994123437, 578086647, 76621980, 969427745, 577451074, 397618640, 613150345, 839539525, 192196711, 481589010, 178406891, 779178296, 571285928, 536479432, 365020776, 702117023, 235965567, 957839078, 504136764, 156735507, 789899760, 417736661, 202268699, 461975461, 345518425, 212352744, 473973811, 286526116, 418632048, 84696197, 960498693, 263163237, 192738429, 130273642, 460570017, 518305802, 815252024, 703467243, 419463006, 472357715, 881338879, 726681645, 721990389, 638559688, 921947691, 100042568, 11321709, 68500969, 42184532, 490683731, 738318197, 658854480, 46615502, 590939690, 965090832, 638999890, 92157690, 521055217, 291688570, 156631227, 953874261, 935824358, 709749428, 634524919, 851337285, 496679651, 166664985, 856264126, 4799192, 989234780, 685702735, 557520187, 130317356, 473212633, 325983528, 792750262, 259946418, 740179262, 964147529, 238060730, 132290803, 855051787, 267187636, 243723091, 436547808, 719116072, 512339640, 637978036, 837446643, 129078089, 323966874, 253050778, 775159058, 276546406, 891311648, 882890413, 738414696, 377698668, 252896758, 238533160, 106421634, 902178775, 14866307, 994470846, 219909991, 440576008, 260808059, 607640722, 300153376, 610134521, 829368603, 705281648, 569766435, 165460055, 513082125, 260399858, 336560545, 996921723, 336088988, 288617094, 82638836, 809525874, 952069265, 545153778, 230457697, 679582135, 352853291, 561251647, 566004725, 463896584, 852725425, 540048846, 988224741, 387369041, 231025533, 667041196, 94189522, 569456438, 273086296, 420340190, 864553419, 134897929, 649389797, 540591444, 324172588, 774370085, 518424836, 827857687, 295149237, 769483665, 724971842, 558302463, 161574818, 33468397, 935714209, 691652646, 24610510, 487524840, 697657981, 621484180, 715443664, 52921869, 760693625, 185377499, 761712904, 527421321, 69960690, 758045189, 865846164, 96561553, 928423396, 585669310, 621653787, 850355078, 958829061, 845861281, 740797296, 204520024, 630694332, 452841177, 519913624, 381464307, 872861481, 274542092, 478581680, 306159095, 685589044, 657757190, 200182401, 155920524, 948585400, 329028362, 329959013, 197512856, 541724475, 293860052, 143030212, 210640778, 414954091, 947769170, 856753307, 578525394, 124018904, 486876201, 335428374, 741200373, 565842675, 909387209, 437463572, 573168747, 553008315, 363796927, 338672802, 842772234, 678114147, 861879642, 832469205, 503144262, 70312318, 293211705, 721979517, 130837271, 948622805, 480695031, 200891289, 853002483, 460056719, 518983585, 928106344, 619601326, 19298492, 536214214, 631955391, 659884139, 96040377, 604921253, 972029033, 59679401, 290297357, 581198372, 215137073, 542268436, 378795278, 910650525, 496239575, 765325231, 616681077, 910430446, 982792690, 449160428, 844342678, 903340804, 106158427, 391986023, 610992442, 255454771, 605047518, 509018896, 569716859, 808902587, 226046559, 675491099, 53090928, 954426694, 287261412, 287059760, 443585669, 409349274, 138520689, 658842960, 702202465, 386378194, 736219514, 443186047, 141684292, 100380448, 329483100, 543233107, 201221646, 248682308, 763097711, 295103151, 14826728, 445234169, 707887688, 238433084, 990389917, 29055409, 925857411, 169428061, 683949877, 46637906, 924563771, 429871981, 368138983, 293006441, 416108933, 809720409, 24977838, 739007739, 814350316, 818479744, 165249857, 636609952, 644562693, 18308731, 732009160, 485533981, 216018662, 763381360, 312588970, 425299929, 420511225, 957325949, 128172107, 200763191, 768513202, 705169126, 31154625, 376657955, 576170992, 525081303, 885649843, 812324897, 979104881, 53398690, 871043557, 552198100, 844858288, 155015291, 850298922, 958462234, 293840658, 237719879, 463568375, 439059764, 835343476, 387611520, 648968254, 509977699, 85016418, 484084030, 39125801, 489060073, 809071741, 714844136, 663674658, 60192559, 596577904, 526652786, 40093817, 585495614, 810509282, 531379591, 339044173, 45052058, 931449969, 858821221, 969135930, 513572752, 696929307, 374727524, 932381559, 194505664, 787359020, 671894182, 614636936, 371117893, 358973189, 55026482, 446097649, 289520406, 452528508, 536786461, 251659857, 286599855, 435173720, 287832862, 304513084, 516464970, 222601025, 841446679, 650505430, 856094771, 45209219, 377096866, 415363865, 739620310, 398024588, 795062275, 411988364, 728206634, 650640395, 685729986, 560976496, 459528731, 617029022, 635451052, 11677696, 856555492, 851182880, 876277328, 592955120, 944539992, 688623006, 329497451, 386408043, 14583808, 703769320, 573285755, 515584408, 209745617, 688789620, 638911749, 495685904, 983641329, 745786868, 18978514, 188072811, 232330548, 119135554, 333533998, 327068794, 849812478, 798648810, 524224972, 79960614, 96085499, 281384068, 913965244, 422165310, 676048937, 859291915, 45699505, 951819996, 774490098, 20770164, 906394431, 953360537, 575162238, 954178315, 680236586, 203986497, 305401811, 405961695, 90701999, 260026671, 468475799, 745805828, 372858970, 766700422, 994472876 ], 36156 ], "output": 10438785095133 }, { "input": [ [ 82466251, 792036411, 238315461, 862129799, 427868097, 460854185, 579648424, 345306034, 397016122, 612821671, 670435011, 615212150, 493657544, 486501087, 330934066, 896011950, 354917274, 129953182, 831982346, 236084623, 262748072, 645622431, 393323883, 329477622, 323446693, 413046212, 865879655, 801151805, 604380106, 587145521, 282648000, 411388545, 770895995, 668633774, 93050975, 694850467, 777008561, 659529054, 985161341, 714864544, 943871216, 711687538, 551395497, 680100022, 459868870, 563950724, 90955286, 964521489, 769140683, 207349786, 759439016, 861007908, 357259175, 389234474, 488471954, 15870500, 859700404, 829853232, 284193399, 739219153, 281809777, 325721312, 633861873, 276081366, 986234910, 946614656, 957421020, 134149690, 568611030, 303523124, 690647150, 188616981, 221702034, 596270960, 840344046, 33218327, 279916593, 673672450, 878813363, 639868674, 415688006, 727182671, 7390767, 957228861, 257574993, 695222508, 798599486, 119319409, 60681740, 930204651, 600585137, 682999691, 153908830, 134440944, 427463586, 855075931, 401457467, 575140638, 706012102, 719805872, 269926892, 324334045, 703352277, 916268754, 328517436, 846316857, 49466412, 801511150, 560703889, 961799493, 82453562, 579839050, 349490413, 641770159, 972109505, 969778519, 277535089, 967384712, 233135859, 465563216, 149210214, 415356875, 42657234, 526368377, 822768702, 228645813, 754482263, 756360628, 116143344, 69684009, 504951506, 600027512, 224466318, 945413345, 940522875, 817356513, 919085110, 23147686, 150789001, 857929322, 847268526, 600549986, 238180271, 512884697, 593919472, 740821338, 56291443, 17051410, 619874300, 559806497, 658619956, 956589391, 696173003, 677659795, 689834035, 824338319, 606228809, 946049869, 693159871, 942188400, 238901700, 71760060, 244802532, 138389499, 65726245, 75076463, 450709768, 352613275, 166016696, 108717777, 536295402, 26227186, 625619968, 453810149, 781507101, 716797016, 228997548, 635081916, 608582517, 961678186, 146192129, 857723109, 202729322, 429308675, 656419363, 489938559, 140702863, 447928303, 70118628, 492705362, 621203345, 967124941, 942645028, 715683416, 214651378, 992235166, 323329682, 142121658, 637563656, 390953068, 669803392, 313365210, 657877750, 532184467, 340329509, 281942390, 140053855, 53196887, 796520201, 260578369, 804582121, 714359378, 259397209, 97457518, 262969837, 516289563, 615754762, 297022431, 825276502, 307314280, 784780359, 901593150, 436731468, 375491550, 595374822, 286557767, 760170293, 419141300, 703894450, 391174777, 382995514, 59056639, 352972896, 770394964, 518803157, 636040365, 857100463, 132109867, 957407972, 61001980, 461422703, 641613687, 951765443, 166699609, 69533718, 429483748, 572678597, 284940669, 328741852, 751098991, 994641993, 134017846, 621417408, 475590416, 590214699, 112697473, 638728836, 176624738, 202805846, 452057053, 424883364, 934128385, 384765373, 160911414, 228294485, 272620318, 49868350, 662901012, 613430385, 899436307, 493158699, 235073706, 521401043, 311518692, 141399223, 71314236, 767272836, 842290745, 245234860, 534137370, 971790470, 782264609, 474748267, 303566160, 693109215, 631523497, 587366758, 737683338, 940275475, 964675315, 129715772, 730900533, 927312307, 627461710, 691295632, 883379017, 832972907, 4749060, 735468805, 434188653, 758014176, 333321605, 957809421, 985560542, 157444922, 816318385, 393005921, 721186829, 684925845, 618055685, 469209677, 989831624, 312082348, 391911902, 925310984, 279504895, 22821909, 670875713, 110772631, 943977919, 869350186, 302603491, 578359946, 273605123, 580280313, 788046875, 655835862, 347839896, 782642506, 827596411, 162633936, 417787413, 25909491, 516155318, 513331583, 424633559, 943433909, 549765199, 998264484, 157368598, 612788702, 238871657, 829759994, 197902677, 208781503, 505419177, 767529820, 169635948, 770095349, 743781370, 692219221, 170584664, 70219412, 169433947, 738654278, 477118680, 522005701, 714956121, 209697327, 535805030, 413433100, 563390938, 651504389, 742667533, 428256904, 704383875, 871693647, 42326077, 511899605, 746918278, 878453778, 637591956, 730951615, 590280645, 72357029, 638973817, 149216453, 899910565, 370654618, 498859465, 4192857, 956072321, 676086231, 380786763, 897525088, 959778225, 358286286, 154340598, 911477131, 594214197, 725027441, 239107270, 98068551, 915352824, 643169021, 248857194, 277310439, 268727287, 888066922, 349732591, 337501181, 632849890, 602355591, 495244940, 341516650, 257832955, 647249016, 771682440, 636320961, 149489264, 136351733, 226396054, 521259396, 846397933, 701730163, 745037168, 372224016, 462627775, 463803415, 428316433, 652727350, 834106741, 83244127, 782054089, 305718456, 780190025, 476037447, 697709686, 485297200, 728487029, 709307302, 169691730, 860756997, 268534366, 641802957, 190128376, 791658901, 18729391, 734667176, 164404724, 270748182, 87995673, 767003566, 820200395, 633347889, 811840114, 72860792, 768784636, 612741824, 376413466, 820095175, 492719412, 857197480, 844190056, 773553951, 466642625, 513002834, 753138335, 238628055, 666966896, 369148004, 471089529, 67174039, 49729437, 350097528, 970307631, 626233235, 345301639, 671433095, 809125814, 103226890, 732288411, 531046874, 970743209, 411405651, 66155669, 529050353, 687365622, 398071979, 442070040, 356688267, 314826767, 192581072, 518176560, 651086991, 179943367, 601493467, 669424670, 50609430, 192951638, 855340873, 174848632, 257374038, 22764544, 569715332, 456324278, 631154990, 134790673, 118525578, 422735391, 743723651, 760717667, 393343267, 161947863, 682941970, 432125551, 453730254, 872764801, 591594235, 100605546, 569417571, 441857128, 741070517, 395274483, 869024328, 658097001, 50148903, 534662531, 385028623, 443554838, 997807473, 686868495, 805170074, 164701259, 306233703, 78521291, 628547242, 282385506, 435992842, 822956334, 487385389, 947409554, 45635652, 600544701, 994431334, 542588581, 600568031, 160435695, 358653379, 742910931, 237616883, 670679563, 379197590, 943872471, 507832961, 437193443, 999334158, 274827395, 68005598, 642986337, 812327257, 168728464, 374992617, 969194614, 785298335, 955279003, 795314462, 734256189, 837501958, 147417097, 31176058, 394618941, 112021851, 804402296, 959113629, 141163673, 787572166, 609416624, 177506731, 799812236, 251100317, 117448367, 800666679, 798396118, 691966376, 207835151, 772702444, 701376876, 318285985, 132525374, 165314023, 227093011, 703784355, 620852547, 348684095, 186006173, 221713412, 14562644, 598177261, 374637459, 845763096, 649530247, 314059458, 298919140, 216715326, 91947474, 793457084, 349234159, 163875321, 328830334, 205016379, 853025338, 330245872, 207334296, 311058467, 915675421, 408200093, 450157482, 989480400, 578637840, 807603558, 820834783, 667998609, 564641613, 260608278, 607788257, 855444980, 383656363, 132239860, 657934110, 723477978, 746680059, 22465852, 717536076, 862111149, 732509875, 589556148, 644393655, 317908078, 117689973, 643110937, 364315048, 6255963, 103017156, 603689807, 7312996, 8581208, 649373079, 952233140, 639426812, 566897695, 788452739, 185431401, 290087448, 486300331, 997802610, 547128851, 921418806, 845247133, 194938374, 596409761, 935822950, 69514891, 123627282, 624462001, 622239710, 352577791, 718559412, 416063878, 241320054, 463216617, 921598691, 862956498, 368071097, 281976198, 66406554, 9773167, 571938458, 555099485, 5406026, 665175058, 292395189, 918668904, 653934798, 154129702, 125392815, 812419120, 219159894, 808507059, 991104982, 466145757, 686211998, 767387481, 589377536, 205099853, 955290922, 36040495, 803128657, 368094027, 30376110, 931621146, 973506729, 78619149, 505927721, 39453600, 931134405, 488908691, 212252325, 974062440, 566958033, 855780087, 949556697, 744757527, 942544284, 728158666, 750816407, 857999069, 319094660, 292558390, 247123499, 704795409, 800828754, 978693301, 490608689, 553340703, 915443339, 86559645, 274815903, 728126478, 16805603, 378303226, 589694534, 509776408, 601236293, 825056016, 694514994, 841603220, 831599010, 350112312, 257184574, 358477915, 5117618, 367248190, 18768144, 934838629, 895939501, 329303372, 115921056, 105699675, 866019740, 848872275, 447874355, 591953014, 735605955, 259553369, 316315149, 181361631, 822122442, 597486413, 17921764, 864192021, 731549423, 630217703, 909593534, 914158852, 910440879, 280228287, 412023736, 98616197, 312885601, 997840010, 385590165, 853817130, 817450186, 369410104, 813455682, 912021110, 699181466, 248176781, 640534588, 66877611, 979807939, 343494843, 977375954, 198392361, 199461858, 943939443, 414481373, 335556903, 505336474, 877924958, 860996966, 755291487, 763047726, 80574308, 55794197, 260210795, 312159182, 927390968, 313723504, 14664175, 700888044, 849279790, 826907834, 662067743, 783537545, 929412580, 66206051, 21317734, 49376964, 553644941, 823913106, 380215655, 952845508, 746110303, 633693384, 67475008, 856696126, 355304318, 224843606, 98040318, 238095191, 195380957, 525642349, 63408226, 269238373, 518483184, 720123056, 893195529, 206606252, 385241579, 753129742, 785940785, 689733302, 790292237, 794330049, 387728956, 506149014, 401474849, 280344429, 314401721, 854120514, 419806058, 685194762, 628568045, 8865946, 544040467, 925141307, 875868555, 942812190, 32894524, 873880509, 957728783, 174442242, 300301388, 793958193, 988695471, 185994206, 849556975, 830729791, 355378939, 283847973, 74129177, 235632619, 795453670, 87294059, 185344551, 884700046, 823847075, 428355250, 281980446, 822957182, 94170986, 982229665, 619759816, 806709066, 913982732, 297417606, 203158164, 201543641, 220748814, 473772642, 144348480, 17048296, 13066056, 583729285, 844475667, 700371489, 221501165, 837902483, 114170469, 221255889, 799159971, 963356708, 71282737, 922277760, 737511433, 135584627, 631741647, 658999925, 474494339, 682362339, 757809413, 827862978, 302867489, 615387040, 769046924, 935583018, 693244806, 349540707, 291350579, 868181680, 477439329, 288821577, 324972439, 954579868, 902102416, 936960608, 870224405, 201372929, 428418838, 118136816, 219557642, 268344898, 929300588, 891938490, 661838673, 205305977, 965735696, 484456673, 122353196, 535061107, 119237402, 838443955, 292957024, 913652146, 230890100, 473655105, 655152397, 291941440, 409155548, 878560883, 685897786, 433385536, 563267571, 103366244, 510608383, 401942702, 218744505, 389022833, 730679260, 684127196, 925479916, 30623741, 584186117, 839200663, 77051652, 535717061, 690058024, 615973275, 539764789, 584738207, 983155908, 394123863, 733050169, 219550368, 214521265, 117027819, 935186368, 665950631, 741190098, 101922195, 165017060, 863397042, 225867361, 702477876, 561392839, 730261991, 898688623, 521761066, 947463999, 536080407, 78007280, 901017112, 699411477, 535114338, 771913167, 516025397, 130333268, 322871923, 391171868, 229704350, 292126007, 777054028, 2882173, 856814576, 917399772, 674047119, 249558836, 313733553, 842204666, 459378184, 287692559, 44592170, 4645954, 865165581, 630772601, 220633293, 207345208, 42618343, 794682483, 884041295, 826691597, 295344276, 545884846, 670692191, 149534075, 761245443, 91775462, 274405178, 265698861, 179035602, 172028106, 37171249, 129010317, 422520109, 779379145, 34926327, 17218336, 784690862, 111863112, 159595766, 734259743, 771827075, 378628490, 566357557, 262266133, 577771284, 360010847, 937829758, 966532711, 281734966, 406042650, 316227778, 30377697, 896432933, 118452922, 353846462, 701047900, 479719141, 778536604, 538982582, 23087140, 713114517, 618406146, 177098801, 589121180, 975276890, 390959580, 277836347, 948086724, 167034999, 559724497, 949864869, 617992746, 125443344, 67156809, 333607089, 300129199, 688123336, 569808614, 771238948, 449756828, 735513341, 884411809, 214175277, 685924483, 521806365, 784514653, 370451022, 768794968, 445560903, 80920630, 699067866, 954883812, 362350957, 605148987, 662786281, 516988311, 373020835, 553414833, 34551378, 205512259, 883739928, 959069846, 223792327, 730761545, 677262279, 900784066, 86985523, 174272401, 414730357, 804347384, 523122548, 997810969, 666880881, 696324325, 546937593, 789116002, 823937473, 515173151, 105755286, 855568131, 849172299, 776548871, 790193661, 441867219, 201937294, 863377320, 302977304, 574529582, 58525674, 386585944, 998476041, 917226183, 76289386, 293949255, 353807289, 348135129, 844130998, 7814531, 940886812, 376051869, 344677411, 87885220, 606456505, 294600547, 102463106, 915637830, 325589651, 103490292, 201798401, 158203244, 62335880, 214817282, 866989272, 24072609, 715893954, 701563019, 188392767, 184029490, 796916960, 726066561, 268555571, 318818967, 639176800, 39953455, 402603928, 108498788, 576058604, 183513157, 779000709, 971749784, 462811832, 674374777, 752284156, 860854308, 670304317, 632432925, 846134797, 898471573, 116330842, 38349337, 309421333, 58959305, 965987983, 15177656, 342118716, 435304044, 649810571, 185674922, 804285762, 409399093, 891463504, 721245351, 979826561, 175306806, 453479803, 949396547, 19008951, 730030954, 351569737, 214817370, 770229484, 7156112, 574136059, 538161963, 617138705, 332991499, 228858228, 827523849, 530710175, 85513150, 198206436, 940889374, 909863596, 460975360, 572700970, 913268105, 764069666, 546914198, 660138687, 310727913, 436935778, 391416918, 620089136, 991842665, 345054410, 992833788, 848378564, 584779807, 357715884, 885280681, 776108033, 152073653, 328313695, 85398737, 94647779, 464496912, 365291405, 440825219, 163918073, 966684667, 486031678, 185618057, 834425418, 361357324, 317303520, 119577342, 166639234, 569384226, 594378862, 238915268, 845427701, 4040165, 63787399, 295326753, 619006901, 138514064, 407853585, 779295800, 369069795, 406046553, 557473434, 410610030, 471986934, 640829021, 91976028, 718341897, 737685856, 441901101, 879380824, 84625557, 991329209, 589931889, 759596756, 780388112, 109290596, 398354517, 308006468, 356745317, 698718358, 163918464, 890633360, 374769880, 777387182, 427550983, 810092609, 293697888, 229756311, 837131293, 139472723, 917366380, 483376700, 371465331, 263679273, 699077606, 108631794, 818478013, 938932605, 817548890, 861046318, 274915147, 53671446, 952334855, 764871199, 27524905, 574586481, 703882913, 99332247, 968327888, 729711827, 456247969, 732640891, 9301567, 206241248, 812577763, 89469195, 390665215, 87325829, 36290867, 432514505, 281721519, 474518995, 21357194, 430674119, 546566724, 166147422, 53349699, 64269192, 547756423, 492618375, 842833663, 34512998, 985588434, 284637796, 519407857, 209385933, 325106239, 349198300, 945956667, 311911645, 201675230, 118298019, 490524469, 966926620, 99811617, 410421143, 446333085, 109755441, 69964376, 414140865, 99663160, 80851608, 681514527, 404005244, 267234754, 7748795, 1798129, 494631872, 169993304, 150048141, 815827178, 634658740, 673548266, 580729455, 594009357, 922799449, 734679957, 372658716, 711848513, 77883606, 414834659, 819486744, 878952412, 193892139, 88786874, 139974497, 97943666, 481084284, 774478171, 720886111, 267268605, 655105060, 199381702, 834506038, 941146034, 491765191, 369724881, 876924641, 105661325, 356351987, 892140380, 170327578, 230746644, 61817924, 677753245, 313766492, 307992629, 654246685, 91302558, 905707885, 150199651, 174070424, 671342423, 657348924, 446503807, 370546088, 568828661, 989135313, 874370813, 792389451, 975127435, 799940234, 730899206, 833224029, 608175524, 215310015, 544271612, 442393791, 817610844, 8447865, 50646111, 692702068, 663984016, 461152137, 10236368, 682854202, 418289085, 467625856, 271223207, 120090656, 530734774, 306267541, 504158205, 54304583, 322250927, 298815125, 185761067, 676947017, 595267549, 881453383, 500576959, 697136944, 789329701, 963937905, 603673273, 493818177, 28501377, 723922109, 940974676, 91935859, 458030225, 683328514, 783700880, 579372435, 515454901, 478889952, 781175008, 988395666, 959227266, 62446258, 171270944, 637463716, 993459213, 795315416, 376136352, 794551643, 774374664, 887946236, 839896618, 902930517, 414656062, 78109711, 472364647, 432583202, 548787749, 862272111, 720803465, 450534104, 273702595, 39762682, 531519481, 247528308, 65596122, 420724040, 404864318, 175128562, 173356973, 65716798, 494061937, 577679164, 126059682, 296304920, 700438112, 185320690, 994639545, 957474468, 898955971, 640191782, 934233884, 95279617, 460140915, 944214985, 811363085, 753877001, 144634960, 709267523, 213684580, 662895404, 22840903, 446666968, 697136818, 140797614, 805829379, 789725160, 710134782, 116649778, 490458502, 882005738, 877830291, 526112873, 517493325, 62799700, 848787962, 692529599, 631324772, 577894517, 125143511, 661458834, 286628006, 700489587, 268920385, 674940595, 292661994, 543174851, 45133194, 41039946, 103938610, 662966423, 713396587, 660736168, 45304724, 120863791, 291661043, 506344515, 444863083, 120156050, 512170722, 723339035, 274651205, 182074430, 506347367, 75053233, 418830451, 241627276, 574724694, 392307867, 726566468, 294242305, 696214593, 258363432, 677344271, 668562174, 647791870, 965278822, 487315084, 82302525, 554402567, 400127597, 932781799, 44953008, 496020978, 964633619, 201831653, 91927814, 280731108, 369434678, 155549045, 253923968, 624888860, 53199694, 782536790, 870900009, 486601886, 493626640, 629785379, 607718977, 733020374, 886853982, 309141929, 141304840, 463921596, 87548237, 554018202, 425261013, 682792560, 590970898, 235123422, 623303385, 774956156, 130378943, 650862113, 670516494, 108775946, 337913690, 783126099, 873027807, 826526173, 623818887, 27967258, 249102847, 808416314, 174020510, 962398100, 668845094, 252154071, 641892498, 360278358, 273006124, 852641331, 465966485, 768473751, 733593622, 910319229, 346215631, 963181665, 560560600, 213025725, 723881705, 797656309, 391933660, 825940474, 291942098, 127586816, 646891550, 775739378, 53196735, 750194047, 317319951, 762910387, 50607336, 772420868, 888963866, 506076136, 909054437, 418515307, 588921475, 351758696, 24619881, 747412910, 479490239, 511878192, 644192611, 95514548, 994032789, 958759274, 947866368, 443491463, 77075294, 271707285, 438930819, 954954302, 129300693, 565906255, 670362964, 335491731, 476902211, 391969326, 262144131, 825875669, 73921463, 306678428, 155459056, 422997893, 846359313, 366137757, 847649845, 900493979, 47015019, 247920392, 378116811, 103968001, 445688093, 396093386, 94339005, 721396080, 277018104, 150089810, 378005517, 94282581, 874110333, 945033838, 687502706, 853670302, 929206714, 753885051, 82552727, 652104742, 349885863, 663587056, 839818272, 795505968, 901493040, 632463330, 292157161, 854338514, 470302880, 444248582, 145862168, 182906070, 959894753, 123198639, 745848858, 817992278, 450679898, 686751767, 162829879, 752718236, 56728336, 397709502, 136113170, 722556080, 290627449, 282985234, 228807171, 159960645, 851804530, 787556928, 302427551, 625169764, 803477843, 255317755, 276321120, 671169816, 642369383, 917909983, 612730955, 727041592, 83849887, 119159690, 7400119, 334631774, 521378910, 572280602, 413617730, 483640461, 343934649, 234609340, 671885387, 48757683, 508888506, 418177721, 352786204, 266038244, 685403974, 127701048, 271746015, 414777983, 325259137, 476906767, 693764158, 612304329, 831272448, 977172150, 153110100, 832858610, 612707284, 854140764, 754590513, 663004339, 329580281, 180395115, 787591692, 6282321, 545621462, 794165167, 72540925, 981608942, 628509235, 215185142, 795356827, 784562233, 768358526, 444527246, 815149756, 320197949, 429640771, 178288298, 516110030, 342213906, 845333902, 286428849, 229111183, 815821367, 838529192, 950156838, 87773305, 696465107, 246337230, 66474627, 657411843, 826554163, 928790786, 316541056, 957556557, 2796105, 2500486, 996674904, 805732223, 878646147, 273640075, 959139091, 126855991, 519370089, 75957028, 220142509, 530567247, 568909691, 353165037, 276854170, 338606282, 683534555, 104591575, 73275473, 126657654, 853752182, 774249454, 575119891, 526911055, 31681788, 819562272, 832908538, 256348604, 384703008, 944672110, 810916355, 608085850, 782902344, 747936503, 976170955, 224054605, 913343918, 992790532, 440749408, 290625966, 217130385, 867050368, 320290824, 380776017, 121284764, 598756678, 409841821, 837988977, 56679232, 952517633, 381447357, 363673744, 809032896, 773571632, 784867434, 281857597, 221525708, 545496151, 614525913, 170011058, 306217988, 666164640, 863940923, 52572502, 759972901, 595064455, 236643554, 888552356, 528096314, 899212382, 959318583, 841972038, 498950203, 746518591, 997613018, 248474627, 983574267, 319623196, 923696755, 22085764, 918772889, 882305791, 559455366, 592901701, 533150896, 423900708, 210933410, 587536283, 867101639, 330478739, 539403513, 143171783, 82764585, 460506980, 271791106, 972398194, 108671366, 306381403, 422714554, 611701241, 982935088, 611836983, 964005942, 609760284, 412418757, 508457322, 449008470, 270187178, 949134265, 682622973, 404698605, 834033903, 492342352, 842474975, 150147913, 728320160, 339330240, 9938480, 753238847, 283871140, 717820758, 634749872, 807836712, 623186182, 452281361, 412821613, 302605093, 46187138, 142978903, 612334271, 114743010, 328816732, 187785384, 475349353, 823080786, 179125123, 675572065, 27071983, 798009310, 122687458, 506107187, 62707436, 195367080, 851609832, 217204516, 966656416, 504756620, 592075557, 192074750, 996408759, 870371291, 189032788, 470105369, 832895166, 366894500, 188668476, 884480666, 768672400, 142753042, 354823559, 435916115, 671474144, 65899892, 103121620, 451094786, 399727336, 896593608, 331548173, 245103692, 356042008, 76546208, 672014043, 798762023, 909814418, 150808793, 929462182, 757828584, 476577050, 681478892, 665917920, 403577996, 873403535, 467271584, 466604109, 565464044, 992688419, 631322112, 154118035, 788543177, 873145155, 56946704, 675635414, 154572364, 396477074, 261828440, 551282319, 584862329, 138807415, 335956275, 781987968, 769759756, 608681873, 801336195, 467137757, 683094943, 366464569, 38335905, 14035153, 400644278, 508031957, 192173661, 681587653, 697746638, 914765657, 994256515, 710540176, 419996642, 609011686, 54770414, 172003024, 635113606, 644661038, 394427199, 407318158, 287354356, 137282800, 476334508, 780297558, 348187514, 795267314, 809817580, 398272317, 890101966, 589383223, 603445416, 201975254, 886211717, 639643160, 870774134, 796005584, 283993724, 699058859, 364612272, 686275952, 608573884, 843376123, 717382556, 324024768, 797112309, 273338806, 527584075, 669814039, 225884584, 13271519, 190235164, 126161152, 472550565, 62822289, 680784924, 312885198, 735358301, 599185771, 677781092, 149580473, 64564090, 87559176, 925394985, 668022294, 590488113, 595243986, 32671882, 582906824, 588173202, 268053482, 982808411, 169739504, 240902200, 674403919, 217434032, 87273343, 290384474, 119636267, 522459091, 985459321, 43433463, 43471026, 758701827, 532558679, 760837136, 288237562, 444024542, 580409889, 194308378, 795157831, 503601462, 234127967, 271669261, 620735801, 826343090, 231517168, 261239776, 365080031, 194764033, 156570649, 236779682, 45345314, 825587394, 667487725, 217687834, 449319507, 365827564, 162084896, 313929022, 769208760, 151541776, 690118827, 111450822, 320222351, 102786569, 120916279, 309696568, 648763780, 375281129, 322221138, 448352435, 940872979, 310214495, 473299248, 854166811, 248866531, 472086867, 569355927, 203064000, 962250471, 865157418, 968581090, 985496814, 997464367, 218935155, 869628498, 179003899, 283734002, 439266708, 965308686, 693606133, 662299977, 94529014, 411820617, 911267388, 681259527, 824830662, 329356583, 689187362, 11166096, 230665759, 731479418, 78856797, 882472452, 921995691, 976433936, 570628995, 322420776, 767769662, 600680213, 193476248, 989183040, 975122490, 71438596, 916202936, 688794515, 849004249, 742756026, 247814739, 631188241, 534213889, 486953909, 809742438, 511643619, 773182081, 332722811, 159114530, 480428938, 429139582, 810346822, 876932430, 927472251, 392160999, 513215618, 924718430, 589013683, 453282176, 623417089, 412420512, 796712809, 576289291, 148911252, 632040789, 675216414, 968501491, 921691840, 771758881, 214918247, 538721351, 648046962, 682305042, 834283443, 718978356, 158607575, 50273302, 32654927, 941033156, 883104097, 927669780, 842267809, 910337509, 836565462, 369740357, 452052275, 62315599, 837181643, 522135756, 97579722, 610349871, 547889583, 477908003, 625645669, 810179519, 13859857, 387974566, 619371292, 688508157, 743887326, 953087794, 477791876, 815590182, 24488039, 897601458, 908981822, 270129299, 97174392, 105893397, 96058980, 321928481, 668849775, 660076381, 963617725, 513707973, 637652405, 829512600, 248041349, 792849543, 894236237, 986377980, 929523184, 280999577, 80570282, 526918968, 116685978, 766828269, 90968508, 397402067, 928378711, 127078497, 107065406, 283678187, 193319819, 539189175, 213358308, 458040958, 100454007, 354231524, 175857027, 157509208, 866611011, 117503905, 132911724, 13177215, 931563695, 234623941, 470961203, 52187832, 457042694, 102329275, 399217093, 524837467, 710776779, 400877698, 504897089, 898758536, 607473680, 382461399, 274137889, 970014131, 846662718, 450147579, 470856991, 116576656, 215868608, 703283491, 488980472, 757248700, 106326648, 483197539, 578498859, 409901979, 281650131, 135597468, 820541924, 611720891, 90680005, 604467562, 702245754, 92151094, 581646349, 671820068, 996229505, 520829260, 771714338, 424715135, 895614042, 439462179, 356771073, 492421844, 630612266, 37912590, 335832888, 59548468, 276810246, 986667300, 438070567, 868256743, 453646994, 123370383, 322933259, 393234447, 542744893, 633149124, 279213470, 110250379, 61449027, 369545253, 36740228, 969051832, 388138681, 746215944, 555225484, 307098665, 941618362, 723613136, 884708969, 820420032, 551103090, 697280984, 234133354, 439786048, 43014300, 467281590, 545578847, 103707774, 307476506, 515330493, 575344349, 680837631, 304237080, 349148489, 239910761, 74708748, 566109962, 880678209, 341605696, 501611099, 102761625, 870586497, 618451370, 950491827, 650614278, 986096179, 654733782, 680514115, 968841805, 81973825, 815046764, 512694767, 668022515, 913561949, 48344329, 866846155, 974497975, 735602182, 72834801, 410211765, 727863348, 958286668, 914804469, 366290793, 814761637, 776094800, 801759083, 115733074, 993201583, 486667501, 636872647, 685614984, 238019872, 717605585, 321249588, 632038669, 193996123, 861683971, 568390214, 948190888, 307285765, 873871319, 323623661, 626204099, 67741155, 337453563, 21590254, 493293452, 698399599, 16052364, 806180994, 275094110, 148070983, 56490959, 322557361, 950477316, 585689376, 946016963, 688504190, 459426485, 226687964, 357649476, 553118861, 31159561, 238196686, 953731364, 125998551, 115310780, 247362206, 623938596, 184579253, 333893963, 27681852, 157212455, 506997412, 868626352, 167409940, 796295720, 705845535, 447778494, 465461059, 171411849, 676797883, 249740463, 64348006, 830828197, 824857654, 234924987, 328046354, 881000295, 345300747, 597889309, 899370322, 178396854, 878536639, 972574115, 764711696, 44725179, 440845156, 355429048, 669967954, 521016713, 126770746, 61156133, 32653261, 608929476, 506346853, 190892743, 15044494, 802674284, 542774990, 610368197, 647591175, 142245390, 662029671, 640921656, 756327739, 591585507, 827358334, 826355076, 951536736, 206242722, 662351246, 96491762, 544433691, 758076621, 593032217, 862654721, 764200933, 754207267, 734762616, 24184898, 198084211, 645023736, 102281431, 170970831, 671360779, 2509397, 562741458, 178013082, 991802621, 172066893, 320278774, 399346063, 505819013, 290437749, 917554829, 251042220, 804854845, 34191122, 933896276, 282152137, 307576958, 127364807, 971309610, 715790773, 966487564, 649490579, 851193885, 65715215, 112043843, 699762966, 376909984, 515755472, 406436585, 952996040, 55995582, 515502531, 467842090, 417507392, 468704905, 752545377, 850613516, 652765069, 49951875, 881209034, 817200024, 727238436, 894666224, 253387443, 197290213, 356209792, 976560950, 2585318, 2935311, 132317584, 479059728, 89915682, 709940224, 954354852, 960415728, 843608409, 542577795, 131639413, 872037293, 551875332, 767821863, 955489277, 503005416, 38674755, 219888779, 642146581, 778378956, 249149859, 411262885, 925626965, 441150848, 191046605, 133711404, 234285201, 72750818, 746268649, 636415919, 705649876, 203276146, 729020458, 899130869, 639516449, 725847052, 372875688, 980152676, 334363008, 169893008, 430867919, 1032293, 85814043, 900669741, 692691652, 530917967, 668719632, 317963123, 796398514, 985761113, 954962195, 624984303, 782891102, 646627336, 360600319, 568183827, 550009909, 94723250, 239412845, 87708744, 767574228, 571407879, 5032929, 295559556, 884248231, 457790941, 727324201, 338053629, 452089118, 472902525, 304373869, 47766227, 393967000, 416861155, 171689784, 107111404, 969977026, 696340829, 698930306, 401581564, 81315728, 231801905, 110631416, 998624935, 137224677, 215568008, 909698186, 569929066, 682859649, 976135081, 976208466, 602281802, 46941621, 647978521, 845076343, 254000114, 630195094, 772379573, 280484508, 2131901, 638704618, 603963092, 224523823, 6295948, 557937485, 587777510, 362991695, 75462129, 102915041, 126800543, 952866282, 397405890, 476557638, 556075576, 835185695, 66955943, 199064195, 607590441, 613270171, 9891318, 538562868, 870266209, 530238224, 214733435, 589513446, 371697361, 183951925, 460654348, 355209110, 962965446, 3878675, 314013752, 578983237, 36633547, 893729423, 712719135, 867010223, 564894246, 500689792, 732074480, 618926006, 671379813, 239266120, 59560944, 30471146, 532170183, 294834953, 516647839, 194469951, 186138834, 740263196, 906789141, 323175432, 545948386, 640920983, 824619149, 505141020, 256394670, 829592272, 487451964, 923378647, 960721740, 344629863, 236881249, 230587904, 39842567, 166274537, 611402797, 381983167, 913425658, 928890988, 325525441, 835247275, 828352002, 201512088, 404152652, 500111005, 112987915, 991736762, 194636251, 550462993, 91160258, 366723662, 790489685, 770225710, 418013340, 951984818, 20510866, 999427646, 995558610, 329762006, 932075935, 198112912, 430469189, 485849002, 197209718, 491539792, 696632920, 40644906, 559282250, 25159684, 83876709, 483783124, 902748750, 963214425, 379378814, 653587346, 818079714, 12182279, 940552420, 911791426, 762429035, 440749716, 756486993, 849631765, 635798372, 685324788, 796774354, 719632143, 777564289, 522847849, 495272852, 979390118, 106543594, 498350054, 834826783, 491218173, 915096141, 30275765, 355371147, 975189108, 696099944, 516785831, 832633728, 882732118, 419362663, 833671212, 234121613, 470877032, 609563079, 475119814, 976738422, 25713642, 750873453, 468525069, 673373029, 540581646, 343964618, 385646554, 25472609, 735626368, 965864287, 141193770, 292643000, 897114583, 843335917, 413852062, 78930242, 829031464, 120716710, 618647154, 542847308, 76347549, 57230107, 309752913, 173638735, 796309871, 904445006, 566548345, 274330306, 221944940, 277040487, 715550707, 680056991, 697092636, 581981733, 912870172, 841299936, 54737918, 165720591, 708382029, 239137212, 783005228, 424410632, 36667747, 659645386, 164971176, 717542946, 163487799, 355640195, 183934986, 417194672, 10519065, 425061889, 583042312, 996261380, 156335694, 981933787, 3716175, 276069738, 276713696, 135851719, 475823230, 153469282, 81873796, 319327588, 313059379, 667663376, 430957795, 505421947, 983800659, 169802630, 979281353, 33712407, 544130909, 998527758, 446796560, 230960701, 482086218, 875305559, 888086736, 65154508, 568459214, 920499548, 22254502, 607343515, 405848302, 260016201, 75734362, 875584954, 212567180, 680775702, 593749522, 51757903, 356216768, 787102885, 859911571, 644166564, 818205769, 467951328, 523880943, 949945653, 836293948, 491528792, 500672756, 11704895, 535536266, 21076951, 60806098, 661596170, 48418582, 510019077, 985333123, 331460879, 936151186, 33090018, 125273199, 891916483, 289430338, 823406358, 397516915, 742353882, 966749771, 614851863, 320801322, 921806703, 799266034, 29485007, 494194734, 789273756, 99349429, 322683790, 632033714, 268072667, 769478102, 871451406, 280447628, 513714771, 9185483, 876370138, 626744473, 938866267, 179814504, 692941649, 43850054, 375928181, 809646030, 131351765, 273982528, 912341333, 909019444, 244180153, 772074139, 609677706, 845925386, 586199738, 707322161, 40423159, 314541458, 777764283, 494336480, 817810005, 498279311, 617989714, 790082474, 470227424, 584204485, 871658459, 156870320, 618845211, 616879193, 775990599, 940283457, 347493390, 813416430, 476996120, 909724658, 158976904, 956310977, 27763881, 582378095, 272524224, 23941274, 600881162, 108492276, 334995686, 208536109, 96506710, 624070199, 615689690, 695006251, 852366600, 919371136, 537279993, 646937454, 156300752, 139916892, 327263477, 60700552, 321699093, 820805928, 39169259, 178581878, 244756308, 411496563, 87274172, 157069410, 795434625, 743053289, 923743605, 52767187, 191682958, 432369256, 445320810, 89488790, 833150885, 417809076, 364217620, 984171577, 107648525, 841076023, 311602035, 736920912, 559340696, 463835593, 412354639, 864246419, 78952440, 377614266, 131235469, 772862385, 372401697, 791233098, 433861, 46340537, 222573509, 495904415, 100498853, 823154135, 997375248, 429847787, 607696959, 12641908, 50810842, 867726671, 646603200, 738725539, 252292125, 397878096, 588777091, 298499657, 487474113, 520460923, 8797401, 322000877, 645425746, 941860750, 466433307, 375144017, 548878318, 181917330, 481068526, 818167568, 466108378, 318632670, 761751123, 37896850, 368494637, 805775931, 83410589, 744455263, 479123370, 306021290, 981798481, 445578407, 673086472, 822251780, 667247208, 991416229, 402223972, 292038568, 224765280, 463372112, 133005277, 197619192, 980932043, 977334655, 104337429, 182116389, 540270760, 616077482, 714762785, 766603926, 501179052, 42048705, 195579653, 383029033, 56851208, 899682425, 897275179, 254165367, 996064186, 318337949, 518667757, 28925449, 755986308, 168776621, 13770498, 429587355, 562170594, 308016771, 54779386, 288161021, 667181743, 536824247, 34723833, 672657796, 215409960, 980798966, 562922801, 459126832, 191717754, 721396407, 648329323, 696021776, 388495790, 304630906, 887783566, 584660614, 336680845, 508397544, 836119518, 476767978, 881287962, 10192402, 252387265, 450904214, 807840147, 560615933, 680403991, 639638588, 993489727, 788617139, 232359927, 217395358, 189127562, 945401812, 179429833, 583869472, 865940199, 433538645, 412329337, 961674525, 900765028, 985578109, 709106826, 39249194, 99021023, 753634561, 627800089, 670390348, 790079517, 281607701, 182421179, 446534711, 116187317, 584626196, 422251396, 197149743, 511784926, 106503221, 508689391, 667828348, 598207821, 209156512, 630516481, 851593588, 489242106, 529588435, 945158029, 565899430, 564217119, 815752709, 21820943, 707680108, 194500909, 889074655, 643773157, 72947686, 824124032, 255095502, 528864391, 455447684, 807572604, 896522858, 460854060, 700958302, 811212167, 209626724, 105334545, 528123270, 529356079, 835192286, 616442425, 504342129, 502770256, 49094429, 753717731, 133279229, 157855981, 415260937, 150796258, 968263345, 707038274, 62383308, 862297597, 775389702, 474388492, 405339259, 336348857, 167636713, 933541543, 498315479, 778878019, 773119508, 477926809, 828660948, 950069680, 88158130, 613186008, 62050173, 17158967, 995561705, 653890506, 219261716, 461027776, 456822171, 477306323, 556406353, 576517148, 799291356, 558841016, 11932903, 999363326, 830667968, 829059523, 662811536, 493478308, 873978727, 791376045, 862022684, 435250015, 504396631, 168962207, 477192435, 765062238, 255053813, 937485115, 441233033, 760783390, 651695827, 688376810, 422302295, 770490986, 602353433, 539765654, 30165543, 439474106, 737208738, 211042057, 679476009, 263484572, 218780952, 332801896, 742260207, 814390452, 965853552, 644114387, 517006058, 810168586, 223144298, 266522974, 488727232, 720115230, 149523958, 454663721, 907874511, 726879910, 696456239, 186791143, 957127796, 34837884, 924239054, 902689460, 887642493, 124968811, 103690618, 855416807, 492415595, 475110584, 301703595, 520613559, 382849239, 616528320, 371829158, 34702010, 569648767, 558522602, 486005742, 487424547, 226975747, 541516569, 714142326, 729287028, 504669630, 579312395, 794523988, 310653469, 911830101, 929740192, 688216249, 196853378, 85856660, 457904653, 925100917, 195875777, 876023003, 972980783, 238497963, 215202151, 88230594, 532982268, 768483130, 796798131, 890744309, 113017735, 422336893, 625454799, 58147521, 788768335, 291037648, 879200666, 374799104, 668387809, 993986750, 268438163, 383870273, 514316130, 180176463, 245965245, 700700457, 8102446, 842064395, 479794691, 624177966, 496432160, 750038614, 602186624, 405241611, 302808105, 829207150, 927215436, 904133705, 102283348, 862883184, 920257482, 910497084, 814945434, 499275172, 632269193, 766361357, 756031838, 507557626, 730109028, 558024159, 694874940, 326667417, 735399157, 248121455, 345469771, 80294224, 539107332, 606564713, 610634700, 327065828, 422622074, 89561274, 751409542, 59977386, 395510783, 416672499, 353324122, 884953315, 830962540, 247716250, 668800092, 220049322, 106902393, 875548352, 523793450, 636594869, 316389266, 860753121, 498701848, 427237781, 555223451, 859848125, 880316725, 729908617, 975364834, 553584344, 139594175, 917937208, 152953856, 257059258, 197490159, 862076848, 978768362, 111173429, 757644252, 785938792, 517518533, 49023258, 20560106, 974871724, 929865590, 968122636, 819254603, 711111098, 541828790, 303013463, 858747972, 81713343, 246315449, 222493252, 650785286, 699208751, 221208007, 441107865, 936688472, 590628997, 937951809, 108861704, 829207532, 834288106, 439230852, 506969832, 785296350, 725178188, 90292590, 60187253, 86221695, 471511367, 472745809, 863827887, 419038581, 718914289, 790402766, 233767768, 578883945, 158934005, 74148846, 584006563, 356312164, 383791594, 59228280, 23499709, 922248507, 897070878, 489878547, 846854975, 487212029, 78435724, 599693332, 109848683, 841687814, 276800492, 385100018, 501585926, 34842080, 981384366, 372963765, 297553838, 533411918, 213849617, 417064080, 297349436, 956075548, 654551755, 634938892, 262327625, 117134773, 981463055, 496092862, 114800137, 418779279, 518933812, 167852549, 974929114, 609791640, 162141328, 341644346, 99217117, 868000538, 341109579, 536199295, 340337383, 524642174, 140688473, 537888622, 812906922, 444070524, 180898923, 274192351, 182815843, 753980186, 287037621, 600347689, 233869015, 572500797, 325123777, 685704023, 71109150, 263643550, 291185292, 923071971, 18014006, 210275283, 396015054, 797937226, 878644629, 558124355, 152306172, 940255834, 993825094, 950473489, 928365852, 284836718, 433878971, 448421875, 213896463, 521979081, 152492857, 142100678, 190110941, 940043909, 843577865, 27116082, 657857883, 140285218, 181413576, 654354903, 414303000, 93710845, 270643118, 574627499, 706515441, 327232391, 752544678, 381909024, 643309517, 822860929, 850113641, 226175166, 550585706, 337096696, 65978187, 417021132, 994051244, 681988732, 813711301, 244695297, 149627789, 405015437, 592318951, 367629570, 177941054, 765107444, 362213552, 532721376, 769002684, 288430046, 789030022, 728765743, 691524350, 156027706, 495169238, 901640802, 41335358, 967260097, 288423483, 398021663, 654906710, 273242352, 70555195, 139331433, 314301784, 507392517, 798396467, 815271623, 264502041, 268820075, 387735046, 345411932, 122508918, 678656891, 764856087, 419628552, 967237401, 953961784, 940623369, 557452277, 563914941, 128039375, 114545917, 842918127, 133859652, 44598881, 282052623, 652098668, 904752888, 43076074, 275054182, 968755316, 253516264, 91473620, 664012558, 650991551, 416150293, 691308090, 656738502, 553723391, 241824761, 110620754, 923042221, 300376949, 793483410, 892089283, 151872682, 869543988, 8104306, 782499722, 262105797, 593841780, 121646367, 506068114, 29711445, 377139574, 483258022, 193645929, 994802703, 30944010, 313957114, 245237308, 234937887, 313672270, 752270217, 558596099, 558976273, 553000491, 399847747, 548360465, 669510474, 226511381, 315095836, 259415246, 862404741, 161390340, 250784837, 638962207, 986743387, 560493953, 641081535, 285399139, 774454808, 178227473, 299187635, 708829197, 315673451, 51692268, 379445443, 546557487, 960501615, 156507202, 559808969, 572490655, 752295409, 802010529, 627744197, 908846425, 127894200, 416260528, 936720896, 961571278, 382465180, 9225731, 82610380, 420757603, 221919673, 108532871, 190059317, 611455787, 332451828, 382651038, 278792028, 493183888, 711944407, 602403436, 921979813, 648989240, 550824111, 344419453, 533628359, 556281797, 885621857, 862165591, 377812955, 716603386, 639838163, 937446230, 789980989, 241487503, 585863879, 69739433, 885025760, 628187579, 775294866, 995835413, 705016269, 506376217, 714831043, 538315497, 624962857, 247048396, 205749163, 18386007, 251026375, 108768723, 882461849, 387549511, 81395384, 995307637, 973925665, 971771109, 789325772, 533780599, 375323578, 449835957, 251119190, 583825665, 202506543, 973081267, 43800806, 220949453, 3604954, 392745868, 209017644, 998940187, 467728840, 571986093, 387620529, 304234920, 89292585, 636337383, 778943667, 883252857, 746484297, 978343249, 36485978, 210096621, 806201525, 567148492, 266371204, 485146977, 414522156, 652130334, 170332704, 428976087, 991071424, 147700505, 962074862, 832254310, 707042436, 600091049, 323264723, 817153337, 732316383, 828302341, 837854423, 72340931, 325011145, 8084787, 221621725, 749328383, 685498206, 521734102, 975209812, 720113617, 391131019, 840089245, 224537397, 975345033, 784879365, 236133833, 355889813, 181545337, 338879141, 302871318, 125181567, 140989201, 808778393, 665690284, 828601554, 791959619, 29521730, 739699307, 511065244, 918405566, 900920542, 348075766, 939742498, 150313484, 630472467, 402345242, 402477737, 633221929, 174975024, 181998762, 324231419, 724511705, 273305928, 666623121, 506146139, 922153690, 770594304, 887852023, 516229352, 416057638, 301619552, 260811670, 397305094, 848079864, 416680722, 84604028, 167043625, 979079594, 410016494, 581945898, 872061379, 312777235, 160203523, 994885653, 488582298, 583825036, 291428833, 264989132, 911516267, 315799662, 819409431, 787989000, 146172890, 437666985, 697533475, 303697262, 492806081, 917035007, 434580261, 900760664, 819453986, 109804356, 850428927, 174105449, 490710361, 545603057, 678900037, 712899088, 313078841, 157296629, 471954859, 674542265, 26522480, 210807251, 923739974, 402743139, 168369732, 35577476, 738116409, 355834099, 127907373, 177788403, 983469040, 59034975, 98853946, 476853195, 907107079, 487328767, 810089321, 924676322, 89573873, 319644373, 388194963, 286871831, 608637071, 173412712, 535896097, 493294982, 230592656, 308745983, 914093321, 742788815, 288081300, 390594844, 55930105, 929063092, 351875189, 581766310, 375357465, 751398034, 540600278, 661931238, 742082849, 313234516, 197884225, 849396226, 301305005, 145877640, 772877285, 220795938, 254071100, 121318384, 974315142, 283675848, 506376411, 590698825, 614672624, 149207031, 464742002, 298190391, 152822217, 842154056, 828282004, 633310474, 863422818, 647120956, 520846598, 95148418, 274918249, 292929655, 34173745, 200484188, 792152115, 754246459, 482312628, 147793521, 17996705, 986123973, 726004179, 371827453, 449027256, 782812536, 239804661, 941240017, 246504256, 742649491, 219115086, 985845025, 841422684, 231734150, 116975203, 23227717, 473615749, 949878480, 302186540, 89702222, 293630918, 821624762, 24944655, 279399050, 873279765, 437088242, 147236121, 229053112, 769391859, 820769786, 435413973, 804054862, 342322796, 94588371, 190336261, 266452531, 29654684, 649765802, 671397463, 669554583, 416213123, 931095114, 127892549, 159467964, 293322902, 496433951, 811314877, 559354155, 874313142, 711827897, 890707915, 424416752, 151843709, 253676428, 741955582, 398270650, 493003610, 709054577, 924565439, 956261660, 501242845, 823871392, 466397295, 834424840, 975624058, 423993055, 717690512, 416042677, 817519088, 887066112, 232814238, 674205183, 187412437, 580531217, 154537763, 57238358, 585352844, 34634724, 536055474, 412944889, 855738990, 286367835, 892214364, 734874732, 75518685, 384109095, 448753386, 204076947, 220578594, 361584259, 173198185, 84890069, 969995966, 958128758, 404061273, 144343678, 332809262, 641775995, 883731082, 143430845, 101727632, 802989140, 835069627, 442752109, 7548438, 229820355, 19127878, 206562733, 519557913, 840613880, 430405050, 591881445, 515235959, 325265432, 882725236, 747762350, 161438597, 454984943, 512484362, 527731408, 800629109, 98886584, 584793204, 837515770, 362519900, 984157872, 474410975, 750527696, 719746559, 186829278, 270455019, 950079223, 550970815, 236567079, 453450620, 621868732, 6045743, 172481324, 66486317, 186204054, 894489338, 158651345, 204613600, 258574449, 124469083, 418945994, 643200414, 852568593, 508514801, 162045146, 368530823, 236328977, 858299770, 775752997, 208204465, 587619954, 732734814, 865770178, 748230675, 285378919, 898425924, 957496281, 655440100, 83287495, 561446533, 87774392, 206795760, 416364482, 584838643, 388509595, 132708892, 755056952, 143077320, 850380790, 102650945, 147936191, 11549278, 973604497, 491680339, 35779129, 979704752, 751027526, 509931480, 641316036, 956883273, 914157135, 457468242, 381627473, 229652379, 531309316, 600642425, 344850330, 517109521, 456320676, 414489021, 908370677, 886998545, 240463834, 726068633, 574035757, 582666172, 312206327, 580467433, 194542930, 466258432, 602439426, 708698837, 355549138, 658533525, 655623925, 101072634, 455685006, 591024375, 566364376, 462325871, 794017626, 846578168, 196458894, 975859108, 423948766, 452354544, 443324258, 159158143, 870745434, 775517575, 395906146, 313369241, 166703027, 448151265, 872572474, 681262582, 136325763, 80066727, 652012370, 878335140, 181771813, 744906243, 209925936, 457127110, 443069132, 502181285, 223328478, 808979959, 120248863, 620711386, 422122049, 140627849, 712547899, 173101395, 819382218, 286173609, 783754534, 295054711, 856553210, 993830624, 612090065, 477429588, 204411398, 932425247, 65068204, 163572595, 393870291, 901596023, 227135242, 57486463, 147762788, 48087056, 209019413, 791363734, 978795017, 953646004, 534128581, 115012770, 369972404, 165036487, 809465789, 195977699, 235171633, 194421127, 861616498, 75945620, 389969725, 311478419, 193989812, 502620566, 377859857, 319317641, 315163518, 24157385, 152652582, 24796124, 865705480, 909404527, 990486563, 816423905, 826957681, 316471377, 264338658, 705073592, 772122037, 455422376, 425351986, 703598124, 128252411, 811227566, 972182853, 762424561, 685190415, 18657374, 475968677, 786242585, 992180255, 366776727, 278329184, 899107546, 8466265, 191927826, 129733459, 13530037, 511704578, 577988711, 965883231, 371888037, 89440435, 774264179, 411265521, 205032227, 165130935, 28611081, 716748335, 462866451, 816054812, 739438754, 276273844, 406753929, 164494866, 905070754, 32566569, 920601892, 953856807, 302495346, 578552038, 556498449, 984535243, 771987314, 519185578, 688616952, 666424446, 591593504, 949022803, 919608733, 851669084, 563955720, 258595490, 811289123, 653919056, 665407591, 550789417, 892717678, 830265000, 768458754, 121743436, 482238777, 301675827, 372139587, 534127585, 388396665, 951995480, 310983480, 422164925, 3300581, 828737758, 233296632, 49655613, 126209162, 354502855, 318069572, 336398514, 774335074, 913192290, 293353692, 226982880, 327064056, 358178733, 358345776, 980905703, 896665545, 276821901, 242322110, 843819623, 636922210, 425193179, 176430248, 208172711, 143767978, 285380054, 779614065, 193319281, 219140741, 359923192, 466266036, 709713115, 444260171, 221468226, 880901555, 136605486, 418101265, 830944370, 481292204, 959460715, 613610426, 886429228, 399303133, 357770563, 527747448, 840130466, 813213331, 30855470, 72584961, 860197851, 611483473, 327421433, 559970968, 487588665, 690959501, 927965428, 848100676, 731225127, 977650910, 787843120, 884388910, 721099895, 889355005, 849783596, 762183167, 604489152, 497793042, 715045647, 694097015, 415899180, 826369306, 469384662, 940601224, 107421086, 604421417, 118413546, 594451796, 386280190, 452504965, 73332823, 33843684, 182308271, 358625921, 999134526, 58670666, 153137822, 540514221, 601921752, 244017219, 456442785, 38953003, 786413300, 14839191, 308211979, 680541720, 299022038, 167344400, 849050292, 122685089, 740491703, 755902082, 595032896, 732094069, 113010665, 964387938, 443223326, 903954479, 622905424, 552527643, 547080818, 743561986, 950288841, 904856881, 297195811, 910449318, 445656028, 618826897, 232643380, 808969994, 488346742, 166956689, 682928591, 693240704, 822291534, 622427630, 172338104, 14229675, 442988998, 479717757, 184317119, 474337386, 776976041, 25377519, 417232797, 208172451, 68240317, 795640535, 286419568, 454354546, 125583118, 795325326, 575452647, 929681699, 869466375, 738994821, 659532149, 611548457, 597193055, 496450479, 754752435, 155692516, 315122344, 386649162, 568959767, 323003597, 716525898, 511190076, 400291059, 697701361, 549912886, 947610927, 201187300, 173727032, 151029834, 842137394, 988716094, 913906742, 872464437, 248704437, 362819680, 394612198, 495102176, 822551099, 380746022, 77919937, 216714882, 466415163, 658429319, 55693401, 815133251, 602460025, 34710634, 209813540, 873495400, 581481484, 140835445, 921907614, 934820289, 532417885, 308745966, 589802578, 837500670, 682930020, 315037656, 322513007, 60606968, 988542299, 99197514, 639930391, 121232455, 206770559, 87609133, 582945851, 230018918, 160036840, 760609274, 458084167, 482343084, 207461791, 812578238, 560181739, 394585308, 52835505, 791699188, 759491730, 795676379, 47485253, 540463343, 392547261, 397030802, 506180044, 193659601, 116557066, 80230953, 400813165, 829201005, 517103974, 611747230, 844390259, 619286037, 512918090, 630981022, 82075751, 203239341, 494401817, 538301218, 748320679, 275955140, 269608738, 906656570, 465625080, 761358442, 301230724, 320416242, 811778404, 823324678, 592018436, 704949247, 325145440, 417027358, 408107265, 596430985, 538390402, 236847410, 31581336, 907270937, 13842498, 345502831, 360374917, 339385777, 61763420, 913656183, 997848803, 430917473, 969960958, 768763642, 885230904, 959753843, 240599159, 142439602, 477949844, 415399736, 736768258, 495712617, 525630785, 259200133, 863225100, 24189311, 468573633, 982583949, 871391942, 984369963, 234897695, 535010176, 382385741, 37581597, 374657239, 228528945, 507210543, 943065493, 457982833, 833959849, 467903537, 799626896, 294729067, 234132262, 119149862, 451089671, 414269356, 71437950, 895217423, 153697281, 290792563, 163413359, 272282996, 955009341, 160191522, 736362172, 37573749, 748100245, 761138819, 53781652, 900981022, 442719232, 491227048, 551792307, 651991590, 610909596, 928934486, 732428324, 847615224, 498055580, 846725086, 801412398, 609482039, 285354844, 562537510, 551241394, 404540111, 621470146, 95881974, 619388243, 10113115, 219586830, 689881139, 219283058, 565903190, 674441415, 594768466, 833151196, 874783811, 237932907, 221953036, 590830467, 490819014, 610561687, 842744099, 620636087, 193192253, 696805161, 804714399, 168928610, 872737849, 331798675, 310228032, 271056951, 716927466, 116845025, 724494362, 217321459, 912431032, 369962655, 557540443, 295318114, 376208560, 899913212, 322277644, 456945143, 259043625, 143969757, 703408950, 190739228, 891192773, 435351997, 104969964, 955028363, 648193833, 948823286, 728592090, 455034036, 229333555, 392486417, 902773155, 784564685, 764920168, 617794624, 796298540, 313507515, 885274353, 370883718, 2806393, 150860145, 387731170, 303434574, 612461107, 14120996, 345605015, 222116535, 255299670, 424926230, 314677805, 802955273, 346838658, 639803279, 858970828, 10931248, 831276107, 472134511, 997272091, 150330808, 796926675, 420451250, 577064383, 47927663, 191352149, 415784634, 25607531, 681923046, 885297681, 213724676, 942441615, 295745836, 832152959, 992442174, 19973040, 947790930, 906486412, 258857542, 151548631, 343439643, 442923426, 389565193, 360586890, 174685903, 819206264, 57018916, 132968263, 850323436, 46295274, 59969148, 712758562, 372550607, 944279643, 829945585, 325001812, 673936158, 320087046, 587432920, 29329604, 665275086, 978399457, 305920603, 102240865, 656793172, 226225751, 671464653, 150596332, 809520899, 334577818, 167350688, 106572097, 588206919, 301047489, 457627612, 898516178, 473009323, 434678602, 766544305, 787648424, 47303105, 78749319, 402750200, 37434315, 474586960, 525342802, 386660711, 196709377, 10443104, 761696479, 341411458, 269201263, 867298098, 13690641, 495145568, 851220701, 803156505, 505995166, 468083273, 220106039, 851624095, 413224273, 757076507, 688746479, 54006516, 480522144, 519790619, 992460881, 711380808, 770864791, 32612967, 770047840, 935970005, 379085903, 743841448, 504544233, 371506537, 512319183, 653348471, 413155146, 428553355, 785165599, 208583675, 888494861, 843966974, 529335092, 480878607, 152781033, 896200247, 301256608, 382887196, 630843721, 238843185, 113718068, 571724638, 183175499, 579725907, 747447273, 969444036, 317399151, 492439716, 288885120, 506825235, 430763172, 777275249, 902341993, 321318390, 673930929, 121759781, 305617791, 181965575, 845820251, 345778114, 547059094, 305011194, 289329127, 223478072, 234808612, 55302463, 182698022, 262296981, 797050018, 344671948, 655025156, 122693958, 108079242, 20225199, 638632148, 115654046, 753198029, 734235695, 932359902, 306206446, 766550076, 378206202, 807059725, 900730583, 565067309, 173430528, 674050641, 927983736, 861563536, 171779067, 556321330, 67575909, 89501695, 106183955, 961499867, 954055911, 53353517, 498511764, 854915508, 890170276, 303142859, 803930027, 333406560, 306570196, 509180791, 767977756, 385317436, 71268082, 990005461, 242043433, 547079901, 90659519, 909866853, 195817770, 554594887, 635593248, 463583631, 671717706, 121100530, 360311430, 715046225, 870435050, 521020990, 322043799, 414709577, 672719367, 682267005, 590616910, 927163202, 692352113, 123171454, 472231224, 137571190, 271542015, 354421859, 266355243, 192967026, 735169672, 599858402, 472342903, 891505800, 675677125, 779843266, 860987880, 69480457, 11171377, 840171176, 373889957, 677221672, 734729941, 526056894, 777231408, 875210485, 447704700, 361961446, 566543088, 105720490, 967886360, 855397436, 243676003, 432997947, 397462206, 633999051, 319405438, 755074097, 899691062, 884214803, 183948902, 810971877, 853300812, 864799025, 293214251, 280540605, 111405461, 255337443, 50457615, 569302998, 831605851, 342593543, 728100387, 877207852, 262486595, 89139094, 672136696, 849330361, 494997399, 186262189, 445182710, 873261431, 25056203, 825001306, 235799027, 820130338, 595044477, 441491025, 996857855, 635189714, 195786265, 187276955, 498578229, 337415395, 203113697, 623549663, 298108547, 175341466, 854405603, 124024454, 451570985, 399004615, 143379283, 841206497, 662723326, 755292084, 359969869, 147950611, 125907683, 12973985, 444729127, 420840054, 404974141, 610217246, 371976606, 387980608, 421175091, 395266767, 941190182, 506488520, 59793999, 718298869, 97849567, 985196237, 370818591, 472643420, 819293932, 52605890, 355157853, 3203851, 810032105, 493492159, 40305979, 783723001, 684004666, 989439204, 117900793, 668457543, 809575829, 84510608, 951339160, 204305665, 362692745, 599092368, 447141898, 375960439, 936509602, 877202593, 632899863, 93097131, 573445286, 648832003, 879400700, 615078126, 857300151, 5321115, 662401392, 83970573, 175788383, 594807345, 819384730, 801511063, 631881177, 943227295, 194580295, 318984802, 328398276, 810154993, 259659176, 219097912, 105878334, 638916175, 799675417, 811609284, 238334863, 317796433, 911448793, 139317971, 495034466, 980544523, 998731463, 349999808, 657133906, 528274055, 308933762, 586706825, 463551365, 134740582, 786593218, 252317743, 392310902, 168244021, 644078132, 540618603, 499083117, 319335401, 246553740, 521827987, 632063047, 969498348, 448283491, 658155296, 369563087, 882341475, 755816433, 109644569, 132889253, 564860458, 439951414, 782408687, 347699505, 609972108, 440649550, 786306047, 565931790, 633902018, 382368206, 64108466, 309086210, 997981859, 655670881, 869560302, 10916493, 119280151, 927757441, 216151833, 256214220, 787155261, 481231014, 318434447, 584384064, 619414442, 117722647, 169179329, 199587555, 477403958, 663804660, 627212551, 303814593, 314416298, 710248850, 207864513, 922290872, 234965031, 501583800, 824485964, 939637225, 72039128, 6640928, 770296134, 47999275, 72618041, 334859081, 313157278, 420576074, 445355624, 806499147, 105965914, 816260951, 418074678, 822678432, 373835612, 140130560, 113586657, 533938941, 364605781, 805324737, 683945589, 29281447, 616134419, 936881515, 520115651, 598758168, 328382699, 238016957, 786563546, 481742371, 591460945, 868998177, 955625939, 582554125, 679301352, 209005394, 692247002, 422692205, 78690247, 89183985, 517412560, 138344505, 574317877, 961660767, 168767077, 43322959, 937360916, 127605761, 417408364, 537460335, 6421146, 432125876, 310035425, 733897655, 968911341, 581336795, 68334942, 221834851, 894847354, 878718397, 876533305, 919490904, 260483056, 872968964, 692251087, 793398653, 382700845, 932330679, 93315989, 51079616, 985183360, 686783101, 638406343, 803849815, 98538369, 608452522, 586567594, 365287728, 255042757, 886067930, 291217773, 803892394, 453692044, 342840625, 827053759, 852230764, 397467503, 635824100, 357663144, 671423221, 66677715, 144451443, 807075173, 604410609, 118110712, 851502251, 835332699, 240895287, 910825397, 82429829, 684795252, 90653116, 818623918, 807081900, 838565664, 582301304, 682505400, 978822935, 743830165, 637825440, 53515791, 396626678, 233213804, 162414095, 274753268, 606714392, 689020309, 272416297, 442192668, 590925483, 167074047, 509011573, 618807264, 83139424, 874994361, 263291925, 206908410, 867554523, 279083393, 341915467, 945697278, 338346500, 269223601, 795704471, 782510531, 884290143, 146205178, 146797664, 224208566, 569579712, 804327874, 93200763, 542755813, 215854031, 27676628, 231518506, 555391390, 462373114, 216797757, 35564909, 892737731, 117070925, 438433416, 626049334, 239593417, 10968986, 518993304, 980033289, 998511697, 691062195, 5477122, 970339646, 596806441, 727350706, 299832628, 825880157, 35936929, 810130571, 923049290, 555731118, 990512161, 875865390, 119554779, 142132273, 195203494, 868926865, 753477884, 374864620, 476443361, 893425511, 833040210, 559076041, 423211005, 970146611, 809014657, 180629898, 360930790, 584880709, 714173716, 922359477, 511213810, 812845609, 412854703, 801375070, 331256906, 763067278, 656710303, 884636458, 531449867, 204811537, 509616985, 63683557, 95847622, 391324411, 222761696, 561998902, 444265502, 609790684, 471337692, 95141859, 117790863, 73162680, 9719384, 265193618, 971044191, 418131760, 92249347, 102075335, 833335360, 75063562, 965073482, 959304049, 70127664, 162962119, 512390436, 286320956, 86463246, 788408080, 1706627, 821799982, 931331148, 22291872, 158318172, 292745994, 869198811, 218217335, 551835392, 140098652, 541481476, 91298423, 324730684, 281289424, 819762958, 632898786, 17521916, 824885670, 132200804, 188419153, 734342200, 627923686, 951400606, 987681424, 365082886, 292148876, 264881231, 547878817, 345597161, 750586413, 443132485, 998648678, 244406482, 520865824, 245623941, 345662672, 36539096, 218782505, 196356400, 767514268, 167776029, 374597061, 859024195, 863805525, 250697657, 710293735, 300377011, 803086316, 322804435, 228728607, 238623102, 328396571, 421489289, 844771451, 588020982, 854888587, 691683832, 128693320, 187513183, 192413492, 450988053, 165626692, 454255380, 325917679, 954722829, 231605872, 77034602, 28180780, 770850973, 416742836, 312847133, 165246978, 897196149, 269908952, 70335457, 246525046, 280566379, 733588526, 43395692, 136587828, 101747286, 481283893, 505434689, 914911826, 998026428, 346153813, 105633641, 668093851, 54538411, 538890566, 489704356, 580664573, 222350858, 692368302, 744191380, 935810559, 423009082, 5098525, 362530285, 3489773, 225981026, 966984307, 494525991, 711645933, 143262247, 935378318, 954116673, 623662110, 85605717, 532740981, 101038267, 538774565, 484758222, 545861789, 917830667, 646421838, 20454778, 811668036, 474335497, 38343601, 660112395, 379150655, 700894117, 919911897, 777894480, 849625398, 954859398, 864600048, 259673998, 230909310, 29606739, 913366654, 427115478, 97547657, 443534688, 962691037, 720271271, 31938134, 697576228, 628269367, 892455435, 232126495, 771982215, 739662417, 762221984, 469568465, 757823073, 294481440, 663629804, 138051377, 557284658, 23026332, 955293296, 313520616, 295606611, 548819547, 462047060, 726827839, 343677121, 47493897, 588542379, 204741908, 165471252, 985767610, 616982344, 779930162, 689771716, 937715193, 133356563, 856512464, 716887053, 109066548, 279400375, 435865717, 58878236, 265485963, 446942295, 636032844, 961888555, 984765566, 558868538, 138947503, 920761314, 818905331, 572032314, 545399390, 409831847, 449442710, 141702361, 203716268, 759120936, 858820412, 350495618, 814612511, 895861562, 663138510, 777513903, 404728336, 230784011, 961493750, 352867999, 53986661, 685045308, 229449616, 340033205, 476775743, 747748411, 245929676, 852009812, 615488865, 504843902, 373024433, 719835320, 146951889, 535510156, 475276061, 145263985, 638693562, 629110340, 397217463, 756609514, 96978303, 630447104, 487072786, 112685139, 587350089, 742268898, 865976775, 941599467, 580069691, 994625960, 835939828, 572140279, 587768750, 760796338, 778493437, 955397406, 280942240, 324125066, 52156324, 798936630, 100547227, 791526127, 122983701, 410343027, 176879188, 644587562, 60874569, 927426590, 656581113, 604140284, 256488603, 979635466, 577164913, 293854590, 497240491, 554959348, 516575354, 668967798, 755027770, 556967372, 818346030, 430170733, 985312774, 535453455, 935904552, 309426167, 607336993, 496703650, 427894994, 26818638, 293810080, 959773034, 873623130, 472099243, 553866333, 251700193, 549171615, 749887628, 662649503, 974189994, 355574688, 655218109, 466134515, 626451363, 380068911, 806922246, 644184683, 9047657, 941779933, 177526144, 397023127, 598696235, 442210344, 782561437, 583740816, 9680017, 433515345, 720186772, 832851698, 269422452, 708481048, 369019622, 351197547, 757163857, 323681867, 393547869, 60309919, 415919066, 163421909, 381754349, 482325957, 589108011, 540105487, 185604595, 815330820, 500457937, 620596793, 426225203, 55907530, 35329487, 138688825, 826033236, 956319083, 444131826, 198724002, 771116985, 881235402, 554740521, 407780202, 747507493, 68921600, 583553375, 684980889, 240237221, 772955276, 998896264, 725070401, 670822551, 977520038, 815613044, 931071943, 284513824, 439211110, 557683269, 41143575, 184706512, 747689166, 714346300, 884564820, 129932650, 691098859, 636383932, 755555547, 718296534, 359532048, 384640970, 131287146, 934225441, 555109479, 817418117, 935245257, 30831665, 504146106, 660864460, 503874348, 573065196, 730982159, 932113193, 387744797, 8996936, 369734441, 63148772, 145232542, 657906007, 547669132, 180179182, 637930852, 71925930, 352837185, 119337663, 309790471, 523231753, 649760933, 58966745, 80974983, 602801249, 319962682, 65591494, 243482284, 633343320, 119857457, 539253907, 10305081, 256297530, 587921657, 396729250, 884415762, 625091385, 795367067, 22750003, 291694090, 631305916, 197615889, 128575580, 982212090, 596176977, 498377714, 370736407, 195557610, 12363868, 417989879, 602608971, 196690033, 330601710, 422364424, 69453771, 561243081, 324567437, 544235278, 105199009, 332381415, 601465743, 918440126, 37857959, 615700222, 239143374, 820423878, 392974752, 577449921, 473216601, 817092799, 559171656, 150983110, 839580538, 922954707, 127915860, 849799799, 908313791, 632884968, 746792855, 633401568, 805419133, 688468151, 855575882, 118754677, 623106648, 653740925, 389866341, 939572542, 216435735, 830096755, 166887334, 145892545, 170217952, 974628649, 293504028, 555092226, 627123697, 352894774, 50380980, 336932491, 375123973, 228931529, 22073120, 719186813, 888927733, 462837607, 612628618, 777407842, 981250658, 66108545, 859608959, 20499689, 508534061, 136381463, 505253507, 305226512, 695695930, 741999081, 505784771, 60401969, 248165596, 155109254, 858415678, 771396143, 173282735, 681597540, 544894555, 797583526, 182646609, 524716774, 339157290, 432364514, 613839176, 228504452, 330481592, 332745441, 905061550, 758067598, 356658874, 567802427, 328269725, 28408185, 762300275, 482231252, 703257865, 988677242, 957442799, 262440357, 776642739, 499835241, 97421821, 772786385, 158736181, 513893950, 810875496, 782407703, 284197653, 934346152, 941974909, 863773757, 253041284, 349654526, 405341819, 560860910, 861940366, 702615467, 425791234, 456753489, 525600346, 776874007, 102292194, 733913927, 213429670, 691948159, 846991425, 53574242, 976002321, 143476473, 540620202, 248022454, 104478492, 430522258, 900750410, 803168053, 897404887, 995079913, 952491104, 229564357, 169962142, 697729711, 482736160, 211276716, 990001459, 553946400, 552107955, 514085800, 851288357, 958978359, 123396789, 523293723, 237819575, 9637192, 643275374, 25980027, 3762529, 166518020, 754540216, 422693541, 325267314, 758629731, 628588644, 739488089, 193845006, 493687440, 915610426, 931143797, 523958118, 113060373, 534012181, 694565693, 293227233, 312735617, 320810710, 611527729, 954856083, 78004574, 847139856, 749111593, 95927144, 413137209, 729108766, 367530591, 15742865, 895894303, 149424759, 506380446, 927718073, 867253504, 696058612, 548679637, 86173678, 401270125, 574270213, 533848663, 438906185, 75394140, 888248383, 842213801, 68765585, 964912789, 950631388, 859317839, 391617418, 300637079, 609226246, 21769187, 714815433, 309535221, 608410389, 203906646, 225940749, 375281312, 9158161, 913404325, 981295191, 847137536, 133828, 180541883, 897346150, 644371519, 143671886, 737192427, 413161490, 688126336, 365574253, 308289201, 427384503, 364736001, 259663840, 910336524, 212906843, 250277489, 768000063, 969389565, 252867887, 708366020, 706326148, 839028639, 810487349, 663848133, 740428469, 732541564, 570951894, 192091352, 756592659, 513694164, 411612675, 873312377, 377785091, 347819404, 639693335, 668057720, 610126794, 709033265, 845722683, 761337032, 534874261, 505920126, 308557522, 117900744, 242296383, 480675371, 390312229, 636845834, 358601841, 253726165, 21726907, 692144631, 437279190, 751954056, 612851627, 478082276, 851558623, 316192128, 488206150, 644575888, 100168764, 854877265, 810323567, 317404664, 484621163, 635904656, 332387350, 699139537, 953475691, 857273244, 726454586, 222263041, 186440251, 451441825, 994389800, 537058584, 674730614, 117926396, 48069540, 22574671, 901802664, 495384316, 944616757, 113525039, 757048731, 726304973, 932028203, 669501774, 707957556, 286444704, 978679463, 459409061, 639851095, 185870354, 263558071, 913032643, 681825164, 712326657, 654235435, 491674146, 365147034, 547136446, 228031376, 26861459, 765117772, 254770408, 189775595, 769791768, 3920141, 132931455, 595681226, 611168705, 160144646, 268337834, 266201389, 869572992, 651330173, 168787703, 720448790, 705544712, 216611156, 803431255, 42153585, 806036071, 349642998, 502931127, 748706851, 420955586, 411035905, 336452686, 551728026, 399146989, 148947865, 340075937, 970185890, 892399334, 671016260, 331686019, 915730442, 926711118, 770779219, 74159697, 467307614, 481670342, 56661164, 187600347, 103009751, 723527119, 75057447, 955059645, 511194135, 38242278, 587500509, 985052566, 650936797, 25699677, 373758072, 882186058, 964362756, 823176769, 550068477, 569022750, 892762114, 831146921, 377175477, 627729073, 821333000, 772653213, 243428567, 655782208, 755840838, 661066421, 673241659, 5008201, 110300286, 41095541, 278111831, 331915887, 458508502, 237942397, 92926078, 80240258, 999384727, 31105826, 55831631, 629027102, 724250915, 461447849, 832630477, 319930858, 731403251, 813374832, 691024637, 662070487, 46503722, 499594867, 918711387, 893417521, 15830248, 958066637, 588452718, 928039600, 175831641, 621709345, 371486795, 926511089, 147516530, 431634658, 748998545, 682756386, 395696174, 346601026, 131709142, 777546950, 887566959, 512224377, 189792032, 331415514, 148132040, 120356595, 263161704, 118818383, 682024964, 671492001, 11724017, 449108342, 526941515, 146535980, 958177476, 352842694, 765513641, 401101332, 384958060, 545393119, 808528042, 777666805, 390090504, 777724750, 249308122, 555655439, 744333781, 436479321, 580709084, 291716018, 207457394, 224665912, 634545839, 859647139, 528716089, 607329189, 408866950, 825018405, 720875991, 646672873, 545711829, 988693367, 474945565, 161989107, 753091704, 535490413, 973473453, 42018720, 746042011, 744687284, 534086498, 125563615, 524162943, 909304360, 716837206, 23828279, 558395764, 624983410, 882500946, 772467285, 114784441, 93354377, 712327479, 804248460, 853393549, 289189670, 348787330, 796184868, 97432818, 229060846, 366188200, 408429103, 202444424, 515435971, 5346250, 486409209, 402528681, 367510540, 622350285, 311080514, 961190057, 691983140, 784960375, 169845221, 432622793, 529256683, 632221521, 631010613, 998367106, 491267592, 52378702, 162156975, 417537601, 503245095, 179643256, 149413192, 650755248, 513316734, 167493369, 134998225, 890450276, 292796482, 819124446, 35582014, 944386163, 798251449, 793315469, 800477418, 102132641, 440085456, 702473718, 469637917, 143282870, 228923774, 503489874, 430516013, 189839512, 681515538, 546545026, 831005538, 607034715, 798334551, 117973938, 37153481, 687132238, 175241846, 167380991, 263749192, 980489299, 587416669, 960529643, 337483703, 119894191, 184973428, 343410667, 92926890, 721212530, 120863744, 620016959, 202251643, 359927567, 269696340, 38392574, 384475855, 227672647, 872310861, 559959131, 566798698, 341654361, 31898806, 498857073, 84563095, 363100329, 78377765, 717370359, 367104080, 156165084, 325173230, 999045854, 772523367, 246357536, 69758702, 30933855, 807573310, 736522876, 880025692, 651147167, 849803005, 213473696, 190962822, 570785191, 173964955, 259426574, 250524325, 833851088, 18128305, 260871444, 686995717, 871356822, 215825029, 821681151, 438380604, 809358681, 800669288, 766416485, 838723274, 408872032, 139574179, 286740926, 442749096, 324969263, 252838851, 576126229, 366900227, 473367329, 320604187, 597579381, 26503106, 802659559, 860267410, 566772590, 153078482, 907486380, 416310050, 641413706, 449103129, 401876637, 76656218, 201017500, 552885910, 929828074, 804333386, 49333096, 615136971, 649252846, 702783853, 625611421, 428723991, 475495913, 590126570, 524496519, 338808651, 808492100, 458454038, 31052060, 638697125, 620104494, 754991534, 208915433, 203513669, 2875644, 487985663, 698844946, 122973673, 423081023, 739537669, 348755475, 192397739, 533566984, 541263134, 64359535, 399432434, 801031104, 353364503, 626394012, 207422377, 315256696, 999395157, 95998588, 863667412, 862849040, 511120737, 17274659, 931037642, 520391924, 609081273, 998764336, 331678153, 150750756, 797489519, 408420838, 9200835, 992733139, 327791439, 421225360, 888091173, 65951454, 690800919, 342189282, 639805500, 234257344, 931767317, 104858545, 649323909, 596843633, 606858973, 409118799, 158943705, 819572276, 46514354, 406148769, 890005228, 687207189, 354486796, 672538959, 479106279, 54227184, 358278333, 384291132, 496244507, 32187008, 640337654, 718382691, 264835826, 575505521, 953391852, 360528522, 805785448, 725074183, 9674450, 547457169, 547031500, 656406084, 564893295, 668456736, 586858354, 811734014, 305674403, 788605163, 946791603, 443200007, 201160135, 152985562, 936064337, 522443134, 968738567, 189840993, 579020043, 896101651, 232084391, 120407182, 873714594, 742161252, 689634287, 341258583, 119144785, 868360302, 843619146, 782759894, 754268175, 109818836, 303191213, 545777569, 796990724, 77328690, 229591687, 696073995, 243664768, 279249237, 478538315, 857966134, 853593237, 148817325, 474781141, 639932145, 387872141, 451124741, 967816041, 324946532, 225124121, 288825587, 874077832, 852476312, 928210885, 108586420, 558096318, 27053565, 82043352, 641703265, 218473721, 901123100, 287119918, 846464586, 900210607, 553515550, 438798555, 477307831, 483149582, 653628362, 756370631, 184226875, 137751919, 723337157, 526998932, 217842175, 520236522, 340107154, 122607713, 559377851, 741488428, 8118562, 326930881, 887302803, 786452251, 400640512, 84783217, 170780149, 348143968, 596046254, 26692695, 668262022, 773102268, 922344429, 664499330, 385976437, 682860182, 743279205, 479836739, 273815083, 633677250, 258492596, 80345212, 640592348, 370102667, 890392867, 513036250, 170971694, 611466170, 692418811, 237970298, 641266908, 561291184, 318792939, 328471506, 837622774, 893598702, 438073054, 967787406, 870698231, 249361848, 6767182, 358302950, 579947173, 540040209, 811535383, 954159737, 957853261, 426157038, 821777410, 854233387, 658855959, 373015553, 480216250, 560327652, 45726932, 26442943, 187645785, 554009660, 993355934, 998359370, 50343228, 525248153, 196207943, 605231656, 14211182, 249997359, 669620092, 366352429, 949188299, 917841300, 403800938, 208315240, 62008814, 189101648, 296946431, 342762088, 89063668, 351587602, 206466093, 682626989, 604067965, 623622066, 934861623, 217061315, 525107843, 100296058, 204919351, 525596595, 177427926, 141480479, 431792655, 523453029, 928244630, 943025691, 396663306, 478483881, 643175318, 713585972, 894466299, 201408162, 966164510, 494233082, 954759986, 689662125, 947828772, 467815458, 4783246, 891590263, 556403696, 734463558, 377247872, 396485020, 412333977, 642491782, 709999879, 500842768, 642565007, 803090271, 331662880, 548336413, 743950636, 446921409, 70712550, 977937128, 998350658, 458444216, 51418938, 210868884, 949596821, 521505409, 13335337, 448293102, 978435865, 588580559, 771505506, 359983036, 335310980, 606640964, 531359612, 483479619, 58284629, 547321240, 462119574, 592799686, 670067107, 235621300, 396763415, 19840096, 576397980, 985295685, 542181599, 236373131, 988592842, 884959712, 608202337, 178768449, 227543400, 974826938, 517176779, 543761012, 381124330, 53495817, 501412561, 64835974, 514056976, 199214005, 690949688, 269273693, 687499518, 834010572, 214243161, 83665602, 65337166, 152658395, 920271013, 783144285, 45191757, 742121537, 527135649, 197484764, 580307169, 902323068, 788468462, 401700312, 267750565, 176809501, 426424657, 303930464, 856488669, 141522751, 263145604, 911960512, 469671859, 378033261, 793202059, 468480365, 260104452, 576196903, 706602305, 579332079, 827152530, 690768242, 496992771, 995224741, 450062851, 274749609, 400537720, 726026988, 409798543, 245200098, 491546933, 438558255, 274019469, 114106827, 364302840, 421864341, 411379577, 499940348, 535889816, 780754864, 775264641, 230459474, 250953167, 360195003, 678677410, 829773643, 85443635, 588124913, 400220655, 969914492, 867220160, 272819641, 377668935, 737434329, 677071786, 81267368, 482007313, 996406132, 32407092, 903902664, 483836855, 391026738, 124452703, 502543918, 348676200, 920381972, 275660905, 207339139, 747025753, 40514616, 773351934, 247709545, 786657714, 720310186, 852234752, 689971354, 255356470, 482187662, 519137772, 973526793, 560196053, 920853825, 179913876, 7011338, 77184105, 285868287, 741325961, 544484554, 808552193, 670438201, 922216003, 267370029, 683475492, 81532472, 174761181, 42680492, 920194664, 299352456, 913661358, 33159970, 741314602, 890076751, 170906782, 958618301, 984677156, 665637413, 240669533, 466146865, 697787429, 780268783, 880167264, 692493026, 500416394, 10931823, 506789109, 865443800, 267879255, 382349362, 510002417, 293636470, 723945745, 405462151, 682636668, 768658797, 267022537, 868753412, 172702625, 820378993, 214323624, 341417121, 243426291, 924159003, 923966360, 429758277, 930056836, 545610040, 440239206, 447623921, 98510595, 386970182, 897632196, 242936060, 880119580, 871285109, 639663462, 63889058, 705910835, 161142155, 115860181, 535523737, 691823665, 208606214, 219332499, 654277448, 827719091, 495694281, 862819255, 995471154, 34272680, 124864440, 151354464, 639753221, 130929770, 530076885, 548499988, 203879492, 474995658, 344876532, 722348260, 753728767, 563770381, 195118276, 210781791, 461075808, 430894700, 107489526, 52000878, 220239192, 980035211, 764094741, 878964364, 840661886, 586695394, 125882308, 694496728, 214176851, 617380638, 639098481, 82815047, 598142730, 584770573, 956683642, 587562021, 55425967, 67904762, 920871563, 163125171, 822308227, 896373014, 823651908, 307908034, 769073956, 8835474, 779654463, 471262490, 794310054, 653489647, 495842323, 366365491, 369249139, 376012885, 230546711, 195901746, 310472292, 393609709, 355694881, 840768794, 328853044, 816263461, 168757863, 205096261, 70986307, 321332092, 318416979, 102215301, 430348358, 789938442, 898741416, 56475421, 224916720, 706574614, 411255800, 679095985, 237565574, 382905333, 360139324, 414525483, 695002619, 270064101, 219736377, 811699701, 55559420, 84531802, 192404894, 391640664, 826010029, 626761237, 245417253, 701589521, 781094138, 543533516, 811576463, 425603326, 415661364, 83923952, 442507665, 82540828, 687299941, 276000588, 718848461, 363359348, 796068826, 39461600, 702234379, 700291439, 321215524, 968651215, 672701694, 52438183, 206235553, 740064927, 964707511, 589443408, 652224756, 488422550, 927557151, 885898341, 679043954, 845153508, 393688310, 409139179, 543282017, 466600171, 841910184, 372682606, 497028262, 926579215, 36966678, 442664741, 419704430, 248656333, 2424884, 803445397, 405259755, 709180333, 509589189, 691946983, 894104978, 187409752, 813344250, 741944260, 458780831, 145314445, 815692576, 368875745, 297696266, 728857905, 247141379, 359275829, 350024248, 590957983, 801895472, 182471424, 26319432, 629048404, 183517053, 436728013, 5704865, 709530623, 891253069, 393802811, 973355579, 205963400, 73142842, 14075615, 92032278, 265156782, 584253524, 2653404, 313369503, 556116671, 683671399, 404085641, 201724820, 159499482, 198003222, 104237636, 631873414, 996986819, 491944566, 963340367, 313653009, 387320012, 496721784, 608638994, 191968627, 424932068, 627780258, 88841819, 588786279, 73946371, 714635399, 791061690, 883078886, 408756050, 746278023, 331964958, 694973604, 98604819, 62951575, 516388389, 560728416, 889916646, 703490285, 804986678, 17609212, 356417120, 207756044, 207787677, 756849031, 821551737, 525989355, 271528980, 562269502, 260455851, 573123939, 19117704, 976341373, 546072829, 732442091, 544542932, 756439812, 765436616, 722817363, 599240015, 310713120, 511636123, 42187142, 874440191, 646650847, 12504581, 495403041, 223135696, 748033215, 741284223, 997809695, 210579152, 858668138, 259612228, 388212042, 515997646, 460406345, 561732855, 637339565, 353002835, 201951959, 818219188, 792800214, 692485271, 346214392, 374570584, 407190561, 370842957, 366977285, 787133869, 800030515, 553653717, 277512365, 147520524, 566303987, 881753549, 398974647, 460061291, 623002363, 355533895, 847516976, 519531655, 600833730, 728097972, 548452704, 421035876, 192749341, 410761064, 863771822, 750055886, 882276844, 845664430, 981555925, 69638754, 566130916, 333610437, 429492290, 540088806, 208945650, 28373002, 317042944, 740353144, 827133804, 452003613, 512870629, 496520955, 982565530, 234635793, 785677918, 604169376, 477669397, 997089307, 535930, 955232768, 746778727, 647492969, 242713840, 189208885, 310961839, 951142122, 647679049, 814458109, 192603439, 120411312, 75665169, 239964409, 581543218, 813861183, 740775977, 586940172, 604154855, 242950864, 362206100, 958948967, 617611568, 566701458, 779066873, 192095787, 304241932, 423008788, 227544510, 481268284, 584646050, 23583053, 63380138, 435182358, 84745446, 296119927, 733277039, 412722631, 436199670, 462869200, 381501582, 718162190, 691991956, 984711811, 29920585, 845213948, 792417816, 591456498, 282401095, 23494985, 696635848, 811693996, 902782889, 122807637, 552729740, 477208361, 853559528, 903222177, 195801407, 235000326, 195051513, 693468179, 320384016, 924761596, 764042978, 495523634, 721393578, 691635015, 445942687, 801479604, 141778928, 670299237, 991481062, 197557174, 331659498, 841175985, 380606271, 664395799, 897834745, 626212086, 822469576, 110405396, 518812505, 944510180, 846043296, 706623306, 981023539, 125260817, 733816711, 78300079, 770478870, 918664251, 12619444, 521444752, 854107237, 28647821, 174723775, 421075801, 608599051, 317801435, 267918470, 82800602, 954232903, 316265880, 51612733, 388825898, 28558409, 788423087, 168701826, 758955073, 660687475, 984997892, 473310195, 623365120, 942127101, 894082159, 185288281, 554404821, 238185073, 651477246, 4641679, 989229251, 321102899, 321932940, 128816497, 979834865, 169072311, 1177657, 524753740, 533019378, 829413200, 496632021, 552197671, 499675041, 236194899, 210246234, 727120811, 294370038, 913825653, 710091966, 939371851, 366677311, 427673790, 21313868, 810610453, 583945917, 455816540, 156475093, 108194264, 117791066, 522566146, 78951564, 264407050, 946242703, 286756727, 596356049, 92732544, 299468608, 89973240, 93679989, 140157117, 315636537, 930630023, 86982648, 819704090, 235731125, 677401569, 93941995, 421493471, 889270993, 475817380, 438375325, 12561611, 967602691, 230345819, 668472265, 965309325, 63760152, 435451261, 20354662, 248139124, 620203597, 722765310, 906122061, 792114017, 18740652, 644613224, 206681715, 906071152, 512317790, 471824561, 466360231, 12627359, 469370655, 728778963, 614401651, 257908267, 529569650, 809478905, 552119708, 457129671, 327993298, 726098696, 136176124, 144455646, 803885382, 999028094, 386946801, 409506964, 271417192, 730760307, 604913414, 790978402, 686678776, 660845395, 216534323, 470158944, 950973537, 131816071, 645844376, 433090516, 516261300, 221543302, 875578211, 201417166, 460260176, 410243344, 172708942, 832634189, 361332597, 880790929, 851062138, 2068874, 860623232, 932452327, 860790084, 141927719, 609384815, 95796880, 114619202, 851308299, 446623247, 93184866, 164056986, 600657168, 403810375, 770460579, 892106389, 233708824, 958709846, 693165151, 152126633, 859546304, 558981909, 229450659, 792781483, 155998709, 607536377, 742498820, 131949068, 797231474, 983854682, 778417685, 112405783, 636644726, 363687875, 380421425, 531222194, 336507377, 856465877, 866702558, 113745164, 820151946, 685619129, 763834968, 149164899, 16092829, 594376615, 293974446, 324988250, 362797835, 356688693, 781133580, 525417378, 712917947, 488492656, 553656341, 996428896, 109392319, 863658970, 289963810, 324731372, 316704748, 542918618, 69071479, 179609909, 775117608, 941460936, 113363557, 352394396, 357868751, 460418989, 663641355, 628507292, 563861488, 283315909, 756710503, 617304214, 679089735, 481524358, 986127491, 271244865, 664688247, 263270949, 916115828, 720877324, 223170973, 800484550, 956665277, 859461173, 965374516, 154205232, 309736715, 572228657, 947705932, 621656687, 377880892, 912540271, 50085332, 824043811, 955655760, 779794955, 997203435, 604679096, 699525353, 496178839, 71181524, 788891583, 123834290, 536896005, 964262439, 849778372, 729328311, 608866904, 385999273, 510853455, 920051494, 177702301, 558654984, 527493809, 762475003, 118157884, 441306809, 378736696, 406236440, 8594317, 470690864, 472567786, 1885197, 339551555, 755510472, 159284755, 351993167, 37800532, 444705850, 283191890, 238657804, 128181375, 838425053, 387272836, 939260106, 458421287, 211007398, 837572487, 685612107, 748179089, 703355497, 900428382, 417004916, 110634657, 411554160, 543653495, 845165441, 846229056, 684961677, 729024158, 691091921, 886800899, 148523115, 945242934, 561999752, 574713128, 80461376, 102124304, 572529527, 87441285, 969152054, 761600024, 851863293, 19842434, 837943186, 569426558, 567020317, 708775334, 689883905, 382150332, 926664706, 378246873, 79753409, 585426331, 598378549, 652946123, 632890835, 629704187, 91671369, 359234388, 316850832, 45457575, 96542334, 434408595, 771434704, 836006534, 555902137, 503624823, 224170903, 345318685, 157062577, 520964741, 633009884, 768172104, 810882579, 925808800, 447210487, 473069233, 152741195, 393107621, 656739855, 863480657, 299951428, 256819153, 495422854, 603951731, 515027523, 576443620, 962810219, 39757420, 177947479, 501167829, 989899235, 77269684, 327256052, 689598366, 894660875, 306853184, 220268787, 718204135, 504884442, 386512080, 26943610, 480258256, 815036619, 994969059, 200993992, 342943745, 572014868, 90079052, 673317617, 388453780, 707860195, 91153616, 102820217, 509237775, 120158525, 585573701, 480207345, 739456760, 994630210, 17313320, 72045601, 149610865, 614455301, 354582287, 996736875, 82079195, 134900443, 297162431, 799414933, 823351629, 11997689, 3136720, 290059612, 131200437, 812332226, 165442925, 928730298, 84819581, 702097357, 968786360, 60411144, 359134336, 349704673, 645570459, 382003256, 248925024, 388162206, 733132663, 478969235, 570658471, 361181229, 88143308, 81974460, 485601, 775733764, 570124775, 203865990, 222947605, 769312274, 1689879, 445576515, 296004894, 876841031, 488421455, 742888433, 396289096, 827204469, 51258005, 583830728, 981252796, 947565846, 979868098, 279454528, 676454144, 524601305, 546055574, 886786550, 868743812, 745547958, 45610013, 522498771, 695523479, 69685182, 927280593, 169962542, 623482980, 887804855, 983980908, 471779927, 489853208, 796237188, 725151880, 416458479, 535240486, 312416824, 597141120, 121923329, 957332955, 383387906, 316043907, 265148706, 565122457, 929855045, 228453057, 703454507, 556729178, 405530300, 360609376, 955779648, 969543608, 933787560, 955118454, 526539818, 275112329, 28080772, 507465845, 804031000, 566565036, 360322557, 849199656, 215881129, 851909800, 578526590, 447129301, 106340076, 169499362, 578048871, 6432864, 477677943, 850365750, 369481331, 378223550, 344417318, 950421383, 898358227, 525730994, 108173604, 499227893, 256614596, 628655252, 372082296, 385709221, 552585778, 490667122, 759310974, 731432394, 407842598, 109673706, 229773297, 299466509, 530674662, 210504572, 273286099, 774823316, 619324527, 704707611, 513158748, 940696322, 215757738, 448394339, 150750926, 3206481, 446854076, 141185695, 480151633, 766713744, 947139925, 949204880, 239702129, 85546691, 354461208, 309825305, 629921458, 97339340, 664571409, 604185869, 575900399, 53747896, 771983055, 328560538, 802531859, 998964633, 539577321, 466146936, 578769531, 357459888, 958007386, 441579237, 393116464, 300891605, 547448585, 96827392, 14871918, 171281768, 827027926, 974957383, 594044373, 521729833, 640896789, 549879353, 210874862, 118521854, 932341924, 658668535, 777703339, 834958195, 229308999, 522291558, 437075836, 286173406, 513175077, 901392201, 111862726, 186580002, 720952400, 124973908, 971809294, 838840028, 754739760, 824544875, 690170967, 21849005, 200792735, 246844456, 957036333, 135904302, 117688276, 620130045, 80051951, 372522517, 175761364, 414542297, 270448748, 285626718, 797502023, 286815708, 903463246, 23884104, 421846240, 319761680, 44857114, 916288304, 33792796, 149620167, 276634324, 259220479, 146652015, 908580726, 426280542, 714375684, 42198691, 321899535, 849707355, 293564651, 979160469, 797261445, 330571665, 870544466, 111646378, 283784322, 671871626, 677872799, 530114963, 413548622, 356093071, 908110698, 703038423, 239584838, 164371230, 270802904, 669075007, 60264545, 861862174, 437042378, 819052323, 258160782, 645698253, 247858863, 359534171, 402745143, 472159377, 606027368, 749995097, 109304135, 554000673, 945683107, 99780226, 618130707, 272126798, 741872999, 948337103, 461442420, 914585927, 583944133, 307383431, 642701487, 743173931, 396347625, 513701381, 805810177, 225116917, 539174713, 587142275, 120558041, 918392025, 716587479, 866129076, 251857216, 822531247, 999091303, 393154479, 410732639, 35302449, 392784259, 138224520, 507205278, 809077431, 993405024, 593246424, 471589686, 28055261, 565102835, 634373102, 225138590, 72639780, 612756727, 952558457, 319963225, 561355735, 149891574, 622619456, 869084146, 119537338, 70149494, 266292329, 352696940, 399034287, 521464067, 512421118, 404519943, 611548982, 301869016, 338115489, 114009047, 102550496, 736562029, 535440111, 247681912, 824509055, 574143914, 320600050, 86494718, 715087543, 501477266, 346189890, 310762920, 723107492, 547808226, 684852925, 273183308, 362258557, 428496381, 125152798, 935753075, 387971678, 806803809, 864105636, 517122916, 932014883, 200741149, 20708147, 162717713, 528407258, 63929478, 93676459, 8193856, 572454132, 39798023, 413177339, 830801766, 931704262, 763385549, 149451264, 459536499, 60208639, 104844197, 946681648, 643679001, 518149448, 982366483, 616441420, 217162983, 489219349, 876733172, 94932646, 893507342, 572626554, 970222426, 551405705, 798918665, 630453791, 198548632, 472289070, 188482352, 945492405, 935710749, 705138533, 958394618, 707085030, 166348286, 846529857, 769211169, 365851708, 644728603, 40438327, 28826474, 358258457, 118327183, 652342581, 56646106, 268745750, 829333826, 305117427, 623599831, 750112414, 490406788, 467382329, 70197421, 387843698, 794674606, 387953582, 376225426, 79986864, 592264700, 267354367, 807002086, 105625793, 420494841, 83483503, 591415707, 950862529, 443585844, 390614480, 269121982, 907856377, 660398030, 383054053, 539792235, 262535933, 925085634, 598802339, 505083088, 372767373, 833007247, 494031520, 85235982, 515019715, 481116045, 47761766, 185551253, 751063090, 673019934, 292429998, 74215049, 303532143, 96345559, 845364362, 323756755, 901935613, 15297442, 989940301, 399803027, 595722284, 944107691, 307872914, 63249370, 592189244, 51835878, 617221639, 946265768, 452626985, 83739301, 856907203, 10290192, 291309793, 343314517, 715478394, 504615033, 249360769, 931565833, 405682384, 585903446, 845449788, 620102675, 888147550, 952903988, 834674625, 937213477, 675833492, 802247395, 751191887, 978083216, 976316770, 89653325, 803605120, 548342433, 886670973, 444040861, 761190967, 875343378, 202780176, 913276623, 656640539, 631932917, 906882344, 812519514, 114088789, 194702269, 966580325, 976930898, 471464782, 818409600, 116241774, 566174511, 365566770, 613483057, 630318146, 767696261, 140052977, 790014571, 432627713, 628220772, 307718988, 814776885, 253926202, 226352988, 207227049, 168493804, 291029089, 504937923, 205499093, 704215572, 468513854, 412354120, 849018424, 315562996, 349523840, 241942085, 980189106, 47104775, 948836990, 170035691, 265459210, 906488867, 215603340, 639708803, 595318584, 645643786, 619139936, 430722997, 22662572, 955560266, 368137824, 308243917, 581225861, 374999313, 920875888, 674911120, 782554765, 397994598, 483731772, 810165678, 921888414, 731809439, 227065744, 640530316, 617279909, 733473056, 120393973, 60331677, 790071772, 327900802, 782454577, 327233402, 743823674, 350028157, 965618559, 754631836, 677762014, 282811933, 725175749, 689820671, 497720977, 494083364, 925021743, 170194220, 699595833, 482105364, 963723427, 410889433, 268209343, 814486234, 925834820, 494257837, 120791308, 28458213, 366524842, 734757733, 566984789, 26228956, 894790138, 532612523, 394289658, 382384541, 819627130, 164733209, 18005875, 500109061, 367362015, 356860172, 807904854, 75887890, 291123894, 391685218, 203859992, 860149682, 290591461, 241708869, 478771405, 400485921, 565877614, 128856959, 206147710, 860036724, 526066765, 315629743, 656892391, 321909055, 689060536, 160372115, 854738202, 912324455, 761429086, 802711360, 704999232, 500670666, 671074661, 780433479, 17747927, 905475774, 600385205, 788499742, 965931975, 675139952, 421786946, 623255607, 996215736, 675025060, 482745713, 160145466, 421776924, 236296216, 883096254, 431566811, 698987637, 136699757, 167923439, 901275615, 942935103, 425345437, 730236031, 362229018, 533402699, 573740228, 103582412, 884735045, 571909816, 157977024, 319861487, 663170945, 642557136, 27297573, 85143535, 931540834, 134391493, 271127946, 105327465, 918855873, 748874380, 908161716, 850406516, 159046974, 539018352, 531231626, 55728236, 191542011, 725532633, 914810208, 505495042, 8996071, 57264068, 639039337, 207497591, 693595478, 167723287, 645956299, 469770192, 999359419, 723283687, 262446419, 612029727, 464022822, 482888624, 509901635, 674352739, 670736720, 21570269, 246221528, 18026909, 809485651, 935640524, 442460861, 256645400, 899922802, 763217286, 467019969, 547340995, 765159439, 654337931, 478495770, 161147130, 963396300, 279058430, 68123045, 893345936, 777147117, 766116633, 961882079, 485509805, 241908440, 901482750, 718608864, 541791994, 956749311, 590134496, 171029629, 212471583, 198432403, 909155939, 194910622, 475001430, 464297887, 29938187, 315617917, 166492124, 704104562, 666314866, 947377722, 109605502, 496169304, 226111368, 244226520, 691002493, 976546434, 121530422, 477356094, 966897136, 505000150, 693658215, 361612290, 903409360, 171635814, 921320270, 563477598, 589464921, 213047212, 69329221, 780240645, 708485416, 193834042, 728558653, 139224230, 697377111, 923970503, 504680497, 601429851, 886243784, 844830436, 746051826, 871597196, 70200152, 631048021, 29922811, 711910363, 845111855, 179673314, 610729098, 349500284, 376716726, 727692622, 44398835, 342585047, 32392795, 714642877, 64909596, 833193421, 935805867, 323744664, 640853923, 399211506, 327516583, 396310117, 543667971, 697723843, 911099125, 518395174, 99170671, 810502928, 674146641, 806316499, 775166604, 934265047, 828174976, 169419486, 411630674, 208046063, 769887996, 720708672, 272201735, 44537692, 331070301, 45851615, 182629119, 466745508, 407686486, 47273706, 365377771, 79334960, 313538451, 844648595, 190347352, 802674344, 340659778, 698316496, 549298249, 983286665, 993296192, 624716146, 172953433, 784831002, 120125729, 550759212, 784630946, 634572398, 119802272, 943859721, 23345463, 232453442, 272561522, 414819462, 659747556, 93121358, 623674130, 36195292, 669740918, 387777754, 127530981, 389942374, 23006750, 340211149, 261967089, 566003278, 790276853, 135355327, 784507814, 368345883, 647318220, 349076103, 88294838, 711656101, 999976295, 719212874, 418842436, 705895900, 200979651, 306473357, 120030751, 303582873, 545944834, 491178459, 446333933, 967122797, 232357641, 194211326, 321570519, 867793439, 282138355, 377257061, 314627570, 392414891, 241680852, 896089625, 485682946, 909343591, 932668143, 797676869, 727919624, 587137732, 760011037, 4338385, 536457664, 82867827, 804209839, 643426714, 817273046, 478426848, 950861362, 715225736, 544044203, 683072682, 90526335, 1017090, 863196184, 338453111, 62304420, 670941402, 882495781, 739580303, 360176133, 323265057, 28348727, 387651592, 688899734, 258933130, 978927337, 454687912, 25264859, 289079886, 680933973, 711074363, 978683557, 39363256, 310282869, 805299944, 151737325, 728230963, 504409673, 294154466, 995344087, 560658111, 779862146, 575673901, 522620665, 211136034, 115442361, 162920290, 373132072, 104760472, 700006404, 745766746, 640562235, 13840114, 502458342, 752206228, 71350130, 109482448, 294224119, 233305788, 284922362, 394321642, 535981997, 396669617, 902749900, 978633325, 402608486, 543254434, 421989560, 442919667, 426261176, 202087663, 953681673, 851869126, 702143729, 293249875, 221630744, 699781187, 679171051, 120412378, 538536146, 958717177, 630757572, 100795487, 351438458, 345304681, 500615024, 310680074, 765732764, 574633076, 863990084, 846290451, 725880175, 844708875, 129154978, 104817119, 289653795, 642040364, 644775083, 421548370, 412468001, 71081313, 597458741, 281026393, 924590752, 743933465, 66753414, 707917373, 67954337, 423031852, 145209317, 601833173, 4788529, 124481435, 329741076, 438333104, 483408121, 251606880, 494993516, 80996019, 651280747, 304285250, 11390338, 548854445, 180497132, 563964324, 210969214, 881395569, 544985287, 388845608, 590092113, 763132192, 445640902, 980951116, 125076235, 844845312, 554588747, 694498567, 836250304, 610394509, 581973173, 562772270, 802708305, 700536477, 759970061, 743527582, 718856921, 263611056, 988942209, 221610524, 942435065, 213767393, 753898082, 413376312, 944666710, 532738587, 238221288, 365883140, 106261363, 961127959, 726311536, 222848505, 428309346, 300018044, 792980756, 435078398, 411949127, 943371313, 490380076, 196866892, 652346801, 557760444, 618027434, 926630184, 169400327, 892822070, 183863600, 976506524, 691221340, 113817314, 399570976, 36382848, 705100105, 276816639, 49237353, 760263473, 996691410, 362349390, 239210476, 272271, 655414550, 707764227, 125438010, 820063093, 32145980, 835616081, 455595588, 576010733, 269778846, 235022814, 415096122, 699240769, 829522356, 126746147, 666537333, 557378343, 395673142, 891413810, 219270639, 587112979, 614995161, 887296548, 803175633, 851233926, 796840921, 3415376, 461629838, 37844474, 896311168, 186821296, 283993820, 435765475, 167027195, 854511042, 774966365, 392390526, 105433640, 517124545, 984364706, 604391003, 254258900, 145652619, 185594209, 203591411, 520554566, 249037183, 177648075, 10542226, 340275838, 843594184, 102691062, 269280697, 768668252, 393462715, 556188897, 964930195, 115916341, 769677999, 287264979, 263368351, 997662576, 398684475, 477526386, 932273803, 682332723, 960196331, 665315909, 106084339, 346676977, 813889415, 574983303, 942404639, 776473756, 664574243, 397690027, 661630093, 660666585, 740061113, 966753087, 786792711, 123421416, 304638623, 385432957, 984535520, 697433863, 800061748, 539475020, 824873136, 513309441, 682984646, 812395603, 197254498, 600770982, 605050579, 608434864, 308870962, 690399194, 579638460, 199922294, 971977525, 277307682, 612180965, 186489155, 895018830, 42824946, 213196494, 99682317, 375581794, 243757398, 734743947, 298737054, 124402653, 978733055, 53881449, 866752325, 816974185, 477657545, 678129368, 749661262, 190191029, 90720904, 929767330, 538784857, 869524378, 252259099, 333499302, 229408841, 920312389, 65413350, 687259816, 856398447, 885055808, 718108420, 950876798, 804546494, 638520448, 636351630, 290971021, 35829799, 581093590, 744791121, 367082120, 757127462, 878065607, 446055152, 542142289, 819530335, 208749115, 853889151, 902958398, 830840763, 700477937, 451767820, 378684463, 951187102, 474195786, 657870507, 163488772, 91810531, 928726757, 129881498, 34789780, 630731206, 983579927, 44091631, 981216593, 771822725, 984825819, 865695210, 668866513, 334312484, 518878109, 372171206, 926422473, 365882584, 823630057, 553605605, 931454915, 780959502, 869414110, 768925268, 656578256, 580515641, 674762652, 932575038, 961250870, 405586735, 509250321, 363596721, 451276228, 549802261, 974834852, 185957674, 483553142, 976288886, 912709872, 788704049, 116993396, 755958221, 455680205, 519753791, 931931901, 632069294, 20786384, 424537507, 9763988, 927149776, 362203768, 163185109, 845943198, 993064115, 93386506, 654240130, 745486825, 863853570, 161777641, 26212810, 427043082, 688018688, 994274390, 907321992, 286976093, 853394479, 458406280, 35852803, 36546535, 987023142, 242071470, 970483863, 94884935, 257379123, 930630969, 650632415, 420514087, 838937296, 668408519, 228996804, 144969656, 656127841, 993495174, 65515898, 770345195, 915207738, 299408579, 325450115, 62509836, 473737863, 307332088, 546632193, 799705993, 811839105, 219903154, 407395448, 554578984, 49617607, 795260800, 715723594, 867486468, 725911561, 515334107, 301474815, 996672458, 791658734, 259529674, 442444057, 102473557, 238343878, 519692920, 925699632, 478352426, 273480011, 695250360, 446704429, 670662448, 802856713, 192136747, 499323935, 523216600, 5661385, 376207057, 93209981, 892059590, 933250192, 112396192, 483292570, 817135271, 327013642, 228105975, 138580630, 377716933, 472910594, 668136791, 676317169, 132243355, 481376114, 191987163, 86483584, 588190618, 196675094, 524044552, 526613643, 967304065, 791662829, 825199128, 91980266, 235878202, 162444014, 190898377, 84092902, 911108385, 734233030, 191142203, 516563957, 654040246, 359468945, 633534441, 980432191, 943445766, 970059656, 75554821, 526677213, 812683871, 721691062, 115678012, 265281051, 920914414, 788786511, 490898396, 786089608, 472468630, 922947649, 61777198, 796896677, 904964312, 299327214, 162666468, 206698382, 502858529, 902432986, 216081595, 586695669, 34958462, 644144242, 531106773, 306951148, 364201713, 112836585, 306407740, 437124005, 240035549, 104109490, 23075321, 878847662, 407746966, 414068893, 310296206, 908237148, 268823087, 965705804, 480806095, 253781357, 253403733, 471304, 245000525, 960296093, 572688072, 113553962, 963180716, 592238312, 6036629, 59536609, 396662615, 3819263, 774501330, 64368113, 246376931, 410999570, 588561141, 901487088, 928458920, 395143721, 371992112, 387359689, 405800772, 566522571, 625532999, 823778251, 787724559, 464317158, 398461122, 384165510, 304782740, 265719517, 940327883, 902007222, 450111734, 103543608, 254770618, 907552799, 290427141, 612412259, 451559064, 245995013, 262867833, 705116890, 348989009, 734217951, 812162723, 223143024, 378889315, 707978558, 492560587, 347505267, 160448262, 13623575, 885399560, 435672183, 624193675, 550778996, 313478379, 676314944, 42359174, 652815138, 237877847, 710146608, 65229088, 767138468, 348401596, 598409425, 481669600, 722395105, 83752502, 268693079, 255079891, 941104197, 588935194, 142770721, 994986836, 301737980, 239148591, 521425203, 182117819, 941989189, 259280834, 915427209, 387476332, 320065073, 123921041, 177695533, 719920962, 635069050, 567815187, 727196727, 359798837, 341435124, 957225209, 451998219, 685115817, 242818727, 854201824, 955325633, 781637095, 931138815, 742210773, 791724384, 737139743, 913294559, 829114844, 418491043, 425726616, 417035358, 352052535, 819421708, 665775373, 857552552, 800258239, 883196902, 685210788, 329662236, 153284171, 293868117, 46991185, 633778976, 454883366, 110990746, 152164265, 718859730, 430132394, 274314659, 257729045, 738595421, 726095586, 919429283, 37753961, 511107748, 902731951, 15400776, 482232629, 761291921, 21091847, 428643911, 336363689, 231234036, 667333074, 256438945, 245503497, 252966116, 137403175, 624903266, 725094344, 703792078, 652877613, 563705144, 954241476, 634659043, 748126353, 723447506, 806694116, 313856407, 72121498, 675096587, 459072269, 671708714, 299461807, 592789775, 684286114, 210226392, 861916107, 548972803, 797431460, 319585263, 392095077, 175227952, 820014264, 569915192, 708673958, 306966319, 191765018, 63915219, 534460764, 819237578, 538085985, 627482749, 293962858, 672867209, 469298073, 489776869, 336403170, 855528700, 27645413, 324571869, 351322052, 780256110, 175663667, 635085314, 624710327, 581250978, 241742216, 674878147, 505603919, 78321944, 950376178, 391918103, 465022206, 731398876, 263082352, 217275726, 664512156, 194021316, 937673863, 110241078, 904170750, 163902285, 802178390, 780025471, 901233296, 68464810, 179841786, 696958217, 631472323, 957540620, 886249931, 321462650, 404555901, 251648819, 447831801, 725702798, 364704393, 411822351, 93846376, 800314080, 464568373, 737136999, 459197812, 167129246, 406797202, 644578427, 882555890, 601805090, 962675349, 885888205, 875234149, 900421715, 641180063, 313573897, 948724013, 594149991, 979327382, 583332902, 777742180, 658565643, 219723501, 451918823, 130138503, 545534940, 27078203, 553201603, 38494548, 689445181, 691657924, 154047122, 87200540, 295467187, 705993405, 443110540, 171310876, 960847325, 127579404, 638708995, 169652694, 351627917, 838809118, 282552416, 801532415, 764870764, 118130133, 287249383, 379195539, 219708620, 476339816, 169905918, 157651787, 73874657, 97698080, 420897453, 468007256, 78276930, 439750249, 558087367, 423797094, 379709107, 432890734, 841439205, 10512218, 831620792, 47758296, 934619658, 201184709, 661447432, 665661862, 279705746, 58330636, 964111558, 670072306, 415700263, 430836647, 615627843, 636988637, 134072767, 745164559, 286970532, 920608262, 742935335, 395317246, 828771112, 412779384, 285315497, 804598617, 143326712, 32539204, 854117919, 590790604, 989452178, 963905922, 321598750, 515629108, 799015852, 266277190, 579838551, 796304152, 397916596, 800189738, 815112635, 494823936, 687769743, 770625538, 174812350, 507091416, 788397976, 230042464, 408281218, 423447922, 931431326, 90024092, 140259117, 248369637, 470977041, 556009778, 61652498, 576680794, 903166531, 465999174, 87090732, 236009691, 440500135, 310595195, 241933853, 714431143, 347238456, 62403310, 92449364, 379322934, 389861678, 39199930, 867424889, 997908256, 43978319, 581934526, 714321912, 888317698, 496157, 235233303, 481981605, 209169348, 507068922, 974226685, 292568210, 53995020, 874969109, 258323751, 923728560, 927984595, 646494185, 31515569, 188729938, 15513649, 628321421, 354412231, 520282021, 912509105, 229422439, 443511363, 260967320, 938134583, 818882350, 205163515, 435386687, 800197080, 260859825, 323953785, 46045881, 917140547, 394712147, 740251274, 861226908, 597758383, 139427222, 747813588, 768038063, 894268926, 607110444, 721388433, 99142637, 673300257, 203755540, 144341584, 988680745, 797553347, 657698836, 378979142, 607246313, 362976855, 392422687, 44783425, 764990494, 640621376, 379990408, 799853772, 67787984, 345563567, 187717029, 986448259, 145605021, 526887416, 258549231, 390952001, 712454672, 431938412, 912857664, 918540428, 162011642, 704022627, 748324172, 8695923, 992682, 654297806, 834164311, 741271967, 307745334, 645273262, 522558275, 746717397, 363957650, 270588243, 498607044, 73669719, 408088040, 825277627, 119654052, 93102297, 699507698, 886568562, 114894307, 458794972, 639493347, 6157544, 621874387, 145106280, 810365328, 123116140, 919060788, 811840543, 801206105, 522361502, 205137047, 256953487, 875660221, 725878689, 907133206, 97010917, 362057538, 107540482, 353175138, 127040254, 464600578, 363805710, 868054902, 732551979, 655754935, 371154190, 847262041, 506660039, 54480500, 423770247, 170983844, 365968053, 65589767, 986267800, 178529900, 319197056, 447900423, 775925007, 176938642, 777021157, 380805632, 918215622, 108470124, 426154510, 580810672, 454492735, 934355723, 759631849, 559043229, 495432765, 67483226, 460488473, 745991900, 18172652, 489900225, 450553253, 79861026, 892018064, 881255642, 764818367, 926257225, 850953814, 911201083, 701093388, 709674400, 520031709, 108027089, 459147470, 661782866, 905359168, 254878629, 811560128, 457230443, 665443952, 728074338, 270094882, 444316586, 79828608, 580854408, 916101039, 381528588, 231533184, 410472460, 424515810, 7688390, 364382901, 764211743, 730528754, 996240164, 966105198, 721842512, 662932448, 183041191, 752856085, 225442906, 961339507, 996337586, 827443165, 288448959, 720229042, 976779027, 540783401, 261365382, 754348554, 342319657, 77767919, 267306017, 786577329, 557796950, 869696, 566890115, 885478260, 708436389, 936037206, 855009290, 553645250, 544630012, 96104757, 647077583, 557959010, 8450329, 292933494, 919697107, 121713878, 104939530, 438385311, 333973662, 438798637, 428690121, 525858925, 956557166, 726110954, 235046284, 580307390, 714099844, 828824040, 446757803, 184512889, 525173857, 145934716, 789829513, 762251352, 662017369, 787633574, 484520039, 454556284, 311626868, 182151698, 719889400, 565969243, 84606859, 866921224, 304320958, 554889405, 445655225, 152594891, 47580499, 212470349, 538358238, 548407704, 234176811, 716171943, 206342970, 750231816, 281543620, 60447667, 130017256, 478754481, 605146552, 251089441, 951989599, 675176161, 795462583, 937265760, 349677660, 476557923, 423275650, 12891540, 16782277, 262846838, 135434314, 960140219, 770114047, 263345004, 608636874, 843519910, 438343671, 336050571, 262906760, 200992133, 9158776, 510673375, 872283608, 104589737, 470282975, 168069017, 513946983, 556202169, 29639291, 550405828, 651079714, 646168226, 820034390, 196367845, 195896579, 202255603, 867280596, 677470270, 182394770, 584958696, 437175849, 742788418, 461627521, 974938790, 247573659, 471597121, 435394618, 39899201, 261129558, 482150182, 73873996, 598861598, 801513024, 186442549, 346940491, 157878774, 60083883, 681857556, 865649770, 952818398, 570994543, 867966471, 418674134, 240636029, 339083082, 363511899, 20244483, 631361889, 97201544, 560411404, 587217813, 246772627, 255722183, 846901145, 532914058, 436864656, 567640877, 83795592, 479117117, 341267332, 330631094, 785631837, 960729110, 424170016, 140663526, 272501205, 814721805, 473125218, 71494217, 379719910, 993780201, 500730458, 174382367, 406496170, 467780125, 900945278, 280044877, 157334745, 545425984, 408150065, 24676173, 800708414, 663569591, 819163751, 690000858, 444011515, 838398249, 347218205, 760588305, 704872629, 528134238, 850681010, 978998659, 544343438, 490584476, 807670483, 91676834, 291659564, 292392183, 82156307, 476340650, 823797812, 592895890, 516494346, 958469494, 424289407, 220776438, 755123463, 57060214, 51615546, 748268975, 458137239, 264602180, 356275955, 791554769, 234663646, 784890399, 756106912, 670514792, 581695945, 162472030, 143328928, 881224927, 99532042, 538092740, 686084099, 740718618, 265232910, 666213424, 217662591, 999632356, 357458823, 371386135, 974254741, 620188119, 286097387, 585931190, 386611581, 97889910, 992379940, 554061002, 751838292, 635816549, 508424330, 681752338, 755073872, 272512192, 960487972, 75798150, 655701602, 815806528, 463816882, 731463128, 153466128, 711731126, 776195140, 558080240, 912436514, 425033951, 505128620, 684185799, 948807246, 765200827, 377769533, 227511877, 535554725, 330505848, 623998519, 425484615, 131667255, 46187676, 965742439, 907648203, 864742667, 601108141, 683797471, 15287245, 468613164, 779356521, 312264007, 468073857, 85217826, 808321446, 734625068, 333447213, 994904967, 142846432, 408299182, 271004001, 945838062, 138989078, 573185753, 27545982, 111913254, 834500020, 578107418, 36061002, 13081638, 754302631, 235362896, 589666771, 565409172, 729570421, 756283669, 491381315, 28755296, 219197789, 356641363, 701860678, 22245880, 526483895, 737570741, 247480094, 972783645, 983725668, 916531749, 682620757, 770061161, 501183161, 462758720, 635599504, 652585331, 809267813, 439587120, 973614438, 278889557, 749516449, 843886479, 581215784, 637258779, 402721089, 667454674, 270415011, 819769299, 429123713, 806670021, 446113623, 518105659, 154502101, 442708641, 391371213, 558934389, 665798689, 527339004, 693212501, 693807646, 192787451, 233413396, 586165521, 89059124, 798849283, 644529903, 701459920, 305717014, 710087724, 739369643, 206569916, 14900314, 775951093, 981245438, 108429951, 589812539, 54610340, 703197976, 359936595, 961957859, 836064401, 54096287, 708198804, 533428531, 836746324, 404102721, 533047714, 109018302, 538541666, 582179865, 745583065, 274559967, 4001349, 707935664, 450785672, 105482588, 28609646, 293903810, 359652102, 488832685, 470313176, 788218374, 703010204, 110909195, 768589058, 893771896, 584167425, 862108866, 181436039, 947211239, 95172643, 944046878, 937168776, 185002906, 447015627, 760746760, 388084754, 591863738, 990860049, 875027393, 911931039, 481813200, 405072504, 269816592, 680119832, 871350759, 785337371, 476120120, 475983959, 878350424, 866171955, 760120989, 110246837, 245463573, 553527845, 210724157, 126075753, 297184711, 867314206, 237812074, 684690629, 534762170, 779931507, 426944592, 776757794, 226605393, 541685654, 515046988, 802820326, 688169911, 284683727, 399285454, 376066743, 483704541, 620832859, 932021433, 496712542, 496815811, 584140243, 758860724, 551177541, 601807210, 864039679, 270760872, 157766833, 891791291, 170926612, 492345732, 550779667, 531216987, 114702326, 679272401, 325029452, 668126394, 96809211, 372704168, 46569481, 834811114, 334574094, 665200728, 61420855, 520542689, 995533589, 35190099, 382390063, 528941452, 35204727, 635945189, 645497725, 983449424, 5416779, 977203376, 123028081, 87088372, 719981622, 703370819, 923693761, 126150054, 490215635, 143675347, 813983888, 866668836, 7394316, 493281125, 921845097, 130385636, 252498390, 937294910, 692383249, 89559557, 624481392, 761452277, 94470942, 421921862, 760857837, 277256298, 466808678, 729734451, 188654167, 22946199, 528743816, 584065020, 437779816, 606055327, 321763554, 504343757, 560199685, 846094846, 94440409, 383267696, 638228360, 223787426, 923332934, 960605999, 260360874, 801768777, 629354668, 90379924, 737951087, 578873521, 372932389, 338564379, 909167655, 785457318, 370616130, 875233865, 778341238, 799403814, 7969149, 976732709, 388523756, 153723751, 848710160, 748065111, 116059411, 456144917, 730381661, 8036560, 450387393, 840927526, 531116171, 896714583, 785523728, 395348999, 284629515, 350253886, 270115567, 28717633, 8624574, 602290870, 287541949, 753925650, 209156845, 80091222, 601229650, 610914882, 621857238, 556498496, 153096867, 888312242, 316535638, 89601804, 114068269, 484529329, 526338865, 904625450, 933114675, 637918920, 942307965, 218958283, 638304395, 231365101, 958364049, 209295732, 758379117, 723297366, 340285536, 115379333, 924084324, 862728191, 428998323, 225423157, 255289923, 915237180, 135174967, 994883045, 505054192, 402571485, 472895462, 240700393, 798942889, 720436615, 185032189, 929122162, 86077270, 601477753, 685928531, 866122291, 986478917, 737581448, 61551261, 729999856, 496119929, 309216592, 495738913, 514637983, 831059465, 547694788, 263999699, 586479250, 832921910, 2717536, 85648829, 592783558, 642973800, 79688033, 102708679, 593292612, 603790572, 81649490, 663056521, 958226924, 854435367, 465370257, 499928524, 626352884, 559581048, 934218811, 446962566, 519015419, 548775700, 785894344, 836391739, 974175790, 452673982, 773223397, 2983489, 987471220, 158101271, 364420662, 712503808, 959615079, 626335923, 383160906, 869434444, 178165870, 491328373, 364875319, 786756865, 342249883, 971194210, 969118187, 990324433, 490513752, 967384711, 956390543, 311259625, 629939185, 372201224, 520950891, 594467078, 149233183, 363332484, 488583437, 280135938, 929810024, 642981313, 287310105, 299218052, 389054100, 139020895, 761808709, 403295432, 54306498, 918329237, 465450340, 500026997, 515321731, 412243596, 81123440, 90249942, 761396664, 943431155, 385151399, 661099922, 964764047, 564586722, 21192954, 45572436, 240349454, 782470426, 670663969, 616316833, 432032529, 861626881, 409952476, 37603264, 652469948, 667833186, 557622508, 578770318, 91291098, 578685598, 565937828, 813747710, 59229963, 305991199, 995711542, 651103494, 239588448, 782576594, 384425046, 458502581, 864668279, 847424225, 138744670, 665812103, 504856256, 986200716, 772941651, 393648321, 867980333, 322973509, 200644851, 403141995, 179447265, 838648272, 659147971, 725129632, 716556868, 243416955, 364066099, 916140151, 306539751, 173880256, 756625547, 729771039, 911853362, 388074247, 982631868, 70808702, 958060077, 506083855, 693094558, 897254468, 959858900, 241476314, 909046973, 706206227, 789349271, 51932280, 160093180, 300426722, 211380925, 33134298, 934849724, 475845347, 759057249, 395140056, 573273502, 85426490, 214490418, 559079200, 862379663, 726617938, 223206875, 881428216, 673075928, 90007795, 50172351, 12446734, 53798293, 373195896, 533477989, 532506662, 352139594, 242663076, 345313075, 681955052, 290623753, 881969995, 736233362, 195398781, 787672767, 829284795, 867651310, 825576287, 334203389, 721177469, 362076478, 456491852, 158546194, 402310308, 451557881, 741788679, 259891469, 527677749, 547253474, 801103643, 853933228, 437029956, 533743494, 98652535, 552191323, 574748033, 733960079, 42641434, 946981706, 852323272, 177110980, 974504621, 970056194, 842580467, 690468772, 432861507, 950996326, 888353657, 815519273, 594482065, 241925754, 716865824, 609385605, 361428337, 491347365, 15716418, 78498830, 359321180, 556984002, 933469089, 690695073, 297226162, 847605047, 343042547, 71848232, 156026500, 129887677, 983939159, 196997792, 552685157, 26764959, 8596126, 816970687, 260114531, 685291974, 578147685, 783818516, 716087824, 289578613, 664303895, 765225165, 885582238, 897276920, 540903046, 615535599, 880519271, 97733461, 876026971, 232172056, 210187037, 885035582, 648509492, 419260271, 396415482, 230710605, 409981981, 956717344, 634076, 634941808, 135231669, 16220732, 553808750, 860095460, 464014054, 947728516, 542415949, 921180015, 212175796, 59720880, 976991785, 113976107, 175537122, 583861802, 231809146, 860268707, 610235636, 491694821, 102192923, 556914389, 830079988, 508258617, 887844479, 498745669, 308235471, 430274269, 102646339, 875882296, 73327445, 27651468, 571272077, 556283812, 415493402, 282242063, 251069305, 259747299, 83368306, 463973155, 807353433, 16232336, 199660429, 198232133, 109548014, 490251280, 286495312, 843418551, 285333455, 461727337, 931402398, 740357939, 903842942, 433654460, 76253514, 895480050, 454345685, 465935364, 555432733, 41209846, 481343170, 740493202, 247989435, 170397544, 394437090, 678165889, 27047726, 731476191, 108341287, 2916697, 527466301, 307688780, 879139106, 558575214, 73807089, 36875041, 719830285, 936195410, 210592428, 178402167, 440983853, 303884656, 471506793, 527731832, 897769528, 790497780, 768449794, 795672888, 978125271, 403151300, 948938319, 505122388, 216981581, 30763886, 442862240, 530167064, 835545229, 671564285, 681043172, 321241403, 205140225, 825911871, 867234126, 549767813, 43165286, 678206788, 893460388, 582965469, 859382924, 187973238, 792243707, 68693057, 951344771, 83517908, 258134873, 634907159, 571388550, 168877194, 760715060, 186366769, 632160738, 374480242, 823742038, 805949815, 96609390, 487550392, 299389691, 738898491, 223354922, 748063711, 101998308, 845260835, 721064932, 580554292, 397124670, 487422523, 275558671, 23355266, 860496158, 247351992, 400557956, 510350735, 493586449, 582720407, 367544705, 820278812, 105267591, 961961497, 953016153, 159300067, 532795589, 565818346, 442121592, 752701310, 997403070, 142577583, 419369240, 731041262, 704533395, 388096566, 106847650, 847483971, 504478701, 348656928, 822742825, 452614896, 842574049, 418301593, 823849443, 921395348, 488093268, 128239671, 356496492, 491114629, 959031516, 520298741, 921921525, 319062217, 874705995, 950539693, 459504929, 573722081, 101841548, 542340071, 642203794, 95375031, 333702983, 200470649, 273709986, 45238964, 947070324, 877671364, 218151168, 21747481, 609320588, 994497498, 220928585, 308433594, 6601132, 342177691, 716743712, 272221470, 707152179, 120538727, 913873053, 868842800, 686982575, 403397594, 907965363, 737276273, 762273766, 941006680, 512264578, 571231371, 157193783, 202949530, 528145720, 692575315, 587319680, 9496160, 471335933, 584910160, 413577173, 592732411, 561136464, 53904242, 808257809, 855494442, 405250935, 909876470, 233573286, 936294297, 809293629, 629069470, 593487273, 297445141, 678148889, 421588039, 789712842, 770894943, 611195703, 479662144, 873328882, 984395792, 60227535, 791601332, 119817941, 565290213, 235983080, 665372340, 510844436, 902542402, 153322568, 734292703, 629311002, 875592974, 791733619, 548621385, 140097747, 334749451, 571763715, 78549969, 940289369, 673983576, 544801435, 458257742, 548788797, 33367543, 314278879, 821900984, 303236468, 404528115, 104295279, 328472969, 862061572, 212545929, 546304919, 711792353, 177691716, 622365231, 976464091, 912524117, 532579069, 484972142, 883210034, 98600448, 810944983, 649648041, 273300104, 233987114, 307887439, 309796294, 759054441, 627442296, 38513772, 712166970, 817775248, 348066779, 601457365, 666014972, 791734928, 345012346, 509249881, 953516060, 32941739, 791105120, 540011146, 158236395, 636109417, 772383046, 775373310, 923312984, 824942477, 262628938, 508654142, 252408354, 807877686, 663265513, 418671086, 168587776, 203408640, 160294798, 535608454, 354474901, 971541827, 420544337, 516833265, 86166730, 75209757, 631499891, 68325943, 48174902, 294161817, 407643515, 69204393, 130283173, 19143271, 446436266, 483666882, 245905908, 451229251, 59487488, 581822754, 652802847, 874536437, 696568489, 739943128, 806504918, 448934507, 66158013, 154637600, 897977954, 214166915, 79797359, 444921433, 851909808, 814065698, 937474390, 738782340, 756162619, 888542989, 372608764, 15669847, 349915748, 461126118, 886612309, 555838296, 290348838, 367372402, 54626290, 791719373, 347501586, 626441210, 356245283, 68887421, 736304182, 819284686, 654207177, 393930540, 369814055, 903450178, 215942709, 948971878, 948076366, 693782331, 351500797, 340608098, 934747713, 410933214, 218519959, 629370911, 479580496, 981722775, 413647941, 578005153, 149481509, 562874857, 998802379, 777049339, 216099089, 986807062, 585236337, 536255781, 753872325, 901384342, 823582252, 400929573, 643244185, 557124354, 832475625, 380956458, 701534822, 988680354, 12490151, 976933866, 690027679, 601114362, 243608907, 389273921, 728942179, 969071600, 888215016, 116032719, 216775352, 276858079, 467873492, 59756336, 714364680, 933698631, 347189406, 380473710, 862783109, 616594548, 489015460, 890857051, 312610658, 165053341, 191626101, 491182210, 850534942, 645690081, 427279414, 448387041, 524553809, 365100684, 204351448, 943478203, 597508256, 481882524, 15844301, 448770457, 219946055, 524322019, 941870619, 30405430, 331906079, 143454520, 888286039, 820528728, 549359776, 563291582, 324009891, 18354744, 31514727, 388744006, 789950308, 203150343, 347379973, 237672205, 575693437, 499521147, 288580968, 109408038, 13475603, 666722414, 818920539, 873847002, 516591585, 432212864, 591964833, 200881370, 353748627, 148795815, 916893376, 144358088, 365328137, 834329658, 229116770, 856048594, 594873722, 82689759, 540806499, 614379403, 492577307, 446670008, 270909810, 285796181, 925688430, 391377237, 171791241, 753672806, 843925688, 280174999, 222264831, 684424149, 587171427, 477951244, 3800363, 16197911, 889218434, 444522844, 228148161, 585600400, 341286985, 39634388, 682755523, 297985946, 773761639, 823933710, 452469634, 730560325, 493334023, 195848190, 999324010, 61683707, 141057348, 391118288, 762957813, 180291694, 322572276, 958964031, 617436569, 459615046, 51700416, 314217406, 916640747, 361944711, 405530898, 705941568, 627213294, 42088745, 66955491, 780318097, 373771947, 213412264, 160177274, 180498465, 176758543, 478356278, 291059559, 483347681, 290058986, 798932772, 376245047, 890751552, 507920027, 431617672, 465886302, 200325537, 531086394, 183287417, 559692957, 11472090, 725226552, 816931914, 71719890, 707184859, 373250851, 753032677, 274699277, 134068756, 506783809, 51613476, 870056386, 454533560, 588506938, 594216105, 411253683, 544055885, 286483998, 101850366, 860503250, 122222753, 466222154, 448614818, 816804822, 478853915, 102325514, 938597773, 140307070, 659200674, 301099663, 901871822, 648944160, 812915162, 656210475, 553186620, 264726789, 309871546, 630093180, 324076096, 70476072, 892416675, 829985171, 639328874, 899644742, 514839814, 417882750, 893704626, 495130218, 428480588, 6211451, 129529056, 500787354, 569053562, 397126804, 155510330, 462542430, 147573227, 623905469, 999262017, 487234430, 932585526, 798177643, 132654677, 694091600, 198229168, 415876587, 735793144, 327640120, 110146344, 543265250, 753737121, 117300840, 385882519, 208018716, 558937380, 980772016, 79612797, 854650956, 957966665, 518028997, 808731714, 360856193, 518521560, 913820328, 158703665, 448242491, 227894086, 681861112, 242593987, 533132748, 635183117, 439632637, 886979659, 289165224, 505836637, 783736713, 526957461, 79306678, 985302145, 813162155, 798235590, 354977309, 404785906, 770652979, 744879986, 193763596, 697670848, 243460475, 867564181, 108000998, 537151859, 901107625, 75537868, 746975310, 484914360, 100286734, 576868035, 824690258, 114909488, 959417907, 898615524, 707089650, 897585117, 979095540, 799058876, 431050906, 745972784, 526848863, 769044000, 688266190, 329054188, 966070391, 704030634, 327975078, 992458693, 180088227, 343209599, 266079937, 581173984, 102014546, 591450219, 632948120, 725893331, 816989961, 743377763, 470448382, 273523715, 201168035, 947101043, 253705415, 323853746, 255318886, 719771043, 432212802, 809711941, 62805446, 75795625, 143077927, 506831181, 265169083, 377780769, 398252614, 506037136, 761540929, 495768041, 665852978, 62914717, 644685383, 22942364, 214990944, 43423313, 230676163, 441529527, 270918049, 90452686, 156320304, 571654440, 504615958, 356490407, 86523508, 496428965, 53307132, 989988122, 176106939, 443417836, 950589324, 891930858, 868705693, 938677073, 637295717, 80621249, 841170435, 111719838, 545927087, 67563541, 661929401, 744524686, 129972627, 924794539, 32404862, 973750789, 501822668, 664123053, 45608016, 871337319, 762574941, 11116351, 378646174, 901003261, 722542835, 358533208, 647373661, 685831026, 711740588, 829081709, 932429576, 499827, 122401968, 351434539, 838503613, 255283085, 571105526, 14575746, 394574118, 122842558, 128656195, 176596557, 224187959, 303532861, 417862840, 833362233, 730411862, 539932351, 204008731, 507552816, 252748145, 811383335, 680520994, 226147529, 636889766, 476826594, 171846668, 335392260, 278048439, 190583714, 344888153, 719484100, 638194755, 206978412, 876759189, 218551975, 549243210, 347782565, 462210843, 743776974, 358342052, 770012569, 408274303, 329565075, 118710606, 325841264, 18655491, 157034780, 368728260, 404252365, 882691801, 222281921, 897809912, 900865300, 923459982, 281008529, 387419226, 400069465, 846953488, 19282020, 817125577, 586094898, 271561419, 789015989, 556977886, 767069605, 866174987, 208230506, 932580516, 861301786, 618892755, 316036774, 989878948, 928630168, 113677567, 164140567, 951642532, 879638038, 355736682, 99845568, 70152179, 933558463, 48631011, 87223217, 168048828, 651861982, 450940208, 793337765, 362006753, 727070733, 936144423, 278878330, 190871344, 977551516, 671953175, 186289637, 951643093, 531012224, 354531206, 906289021, 834822306, 940876502, 405239109, 144461588, 863364152, 816806545, 159093415, 212153360, 387755124, 970851069, 953811432, 415885776, 62935882, 357608705, 937769926, 389864221, 611948355, 406049019, 591795913, 842920504, 433149530, 487089002, 559404798, 18955053, 276155225, 309893640, 650908113, 948489670, 700194750, 215546896, 309218090, 781911453, 921797643, 408735298, 307300405, 81330203, 842640709, 168290677, 302028056, 438892582, 290373043, 23661852, 866074692, 810324695, 299832548, 303286955, 141508074, 14321432, 255895578, 627540596, 539302321, 184124667, 137107944, 929280721, 379548007, 974084862, 41065306, 250976966, 512949357, 868351874, 835483442, 146556981, 80307634, 922178674, 316656166, 722356403, 369108640, 394402177, 599922956, 645477970, 809910660, 356737416, 761392518, 330567070, 710372549, 407486650, 543976892, 571803576, 399873605, 689423045, 406330480, 33533467, 600088937, 398507309, 13689223, 731541396, 695072067, 327794093, 718177937, 388009465, 841960203, 181541046, 844416456, 119034379, 638942865, 10731173, 861003523, 189100509, 19632831, 925239762, 531882187, 363291462, 238539677, 530985878, 483463002, 360443570, 258194750, 768162599, 685910903, 128365601, 907429953, 188965994, 128783567, 991701926, 912348025, 595856856, 221056109, 419104828, 863484761, 355392958, 823116837, 588932766, 228445576, 299365958, 53990819, 441004994, 132259, 548323423, 547537901, 967517861, 282892664, 394314223, 903398153, 660482538, 467959566, 532236212, 837904817, 641741676, 444089730, 580029145, 92657558, 870518275, 893347491, 451719734, 521183654, 560462627, 886827384, 923913222, 55876158, 795641587, 422034856, 71945090, 833995366, 619374743, 71305972, 994941019, 111810592, 687710015, 128892348, 619702991, 963385474, 321826576, 848918362, 444264070, 860854832, 844947246, 737575066, 264960201, 214674790, 946911314, 760180224, 29639503, 680541273, 248512739, 54151998, 481977550, 939680217, 19266728, 438876894, 816804276, 752108316, 655332794, 860717784, 771831128, 525156302, 637644324, 508435439, 38575882, 563900862, 698787802, 816259201, 305983522, 601713446, 110494413, 279777029, 86587648, 85379439, 520154574, 881116587, 578121631, 417424000, 968479228, 680603715, 66936266, 866939885, 422155958, 412571953, 627939802, 826850714, 114271949, 542059594, 55730168, 434488077, 212917238, 908412974, 333800855, 816175664, 523970806, 517073210, 538190463, 712769675, 20202795, 890720835, 805427529, 638335476, 253610020, 542473803, 7672838, 218507905, 575085069, 453720676, 656575183, 361736513, 353778962, 346190150, 358874947, 702231722, 631735049, 69292159, 631988557, 526491669, 119775844, 744885760, 195985337, 294662391, 228484469, 824817622, 455153838, 922602952, 464469688, 552084477, 105810252, 425003332, 576071429, 790467517, 886923423, 116547897, 569545802, 476486429, 968833536, 873263098, 589287095, 448950872, 813799271, 336632984, 676562717, 535042170, 320219342, 948934187, 215880820, 719126561, 129095372, 387250320, 687042733, 982908313, 487502828, 283730061, 9028015, 14581416, 278223970, 373079333, 933047774, 449983168, 800671761, 668439919, 105993433, 728963507, 561532162, 38251214, 150702555, 764753917, 652377549, 970995141, 765263062, 21280834, 796758998, 179532812, 126243935, 299797228, 530128542, 816225209, 654182816, 332206680, 685632068, 683291386, 64422529, 544718901, 670774201, 522181405, 930921803, 693830428, 984503964, 214078512, 297674270, 996911124, 356034808, 48130453, 938726174, 961176921, 3323051, 215691871, 971784914, 858234315, 503903651, 561390082, 756754172, 989301014, 845917630, 983407012, 889773354, 85630126, 189248379, 618495048, 300050392, 31880537, 23014274, 104007127, 788512373, 990255342, 643174325, 275642906, 253802306, 294649724, 200848947, 347174101, 52894865, 321930968, 607909064, 685648554, 768019526, 428783314, 300977248, 740997146, 432623222, 738911190, 27332187, 245295397, 696922164, 390760757, 10441699, 506180039, 123835934, 423113136, 563354359, 902888693, 542782676, 682266086, 767052936, 134629082, 647133145, 536046467, 35289743, 24895214, 926314463, 894801588, 195519764, 146436546, 704089687, 452399178, 626829670, 567554389, 735883699, 629066773, 268634531, 364927438, 188348653, 593331680, 929628156, 515087685, 91680238, 389819049, 257928164, 193573978, 333120622, 683303153, 877626580, 497848248, 923368967, 649395470, 607292088, 557376339, 674441046, 236447183, 476623785, 406406834, 594581056, 949892586, 539026961, 890134413, 326440035, 25949573, 403049652, 785012594, 473857091, 915721736, 740854656, 96082668, 840873926, 215752880, 523348122, 30027184, 265899684, 540589410, 691046675, 871181218, 179623776, 315055915, 737042786, 956419643, 643790702, 764898423, 211485648, 33587976, 144334371, 616468704, 135397880, 132002013, 803671226, 847214560, 71230379, 32642908, 290520167, 250100912, 887381956, 921340330, 673329021, 29483961, 454676573, 133668228, 376743408, 84348315, 263426812, 633947375, 855042131, 179758857, 615252052, 842344909, 437863762, 983314175, 569737956, 261423163, 26079653, 84615521, 27329211, 379205925, 890966676, 869931264, 597109468, 96170966, 401621234, 324394509, 120877254, 956697405, 783133899, 862664869, 995029068, 819950941, 290955165, 90529246, 777573079, 963450915, 179443451, 691576049, 489164598, 323919031, 774478485, 505570893, 995873089, 627883222, 379271365, 85525926, 414358623, 513612936, 746393581, 881153651, 652364829, 811856767, 478772039, 437811171, 737200497, 341144963, 358091135, 772441911, 176627190, 691893150, 813509349, 723625828, 529533588, 373330507, 713376255, 706111124, 615858205, 411057540, 712795529, 821606976, 90567233, 690062050, 419463730, 730552213, 242108701, 783088459, 478756267, 317922356, 706176943, 988713796, 661364059, 71871018, 8312387, 719672042, 749712672, 664166828, 541242788, 493153434, 485379767, 164324454, 688022414, 301124003, 801492814, 227511252, 177462465, 782565172, 749902280, 145478827, 285437239, 471775543, 66271808, 280716513, 553062157, 825222016, 375941385, 74121627, 167433826, 356523444, 256405408, 597471927, 243000412, 103842466, 870666626, 754905624, 673181001, 247437962, 9485008, 182871362, 700202672, 695870082, 807318134, 653274257, 374494442, 870984355, 47935781, 493134289, 821011094, 393326842, 95737039, 682576354, 253182457, 13040129, 159840816, 102669172, 262847682, 862272249, 108024197, 60738788, 347258258, 936116824, 644421103, 284614522, 42080351, 730399402, 714832803, 561035739, 537564221, 583980387, 779070489, 90403555, 822418943, 927444075, 362895656, 16316912, 702385695, 389826972, 635666296, 966888117, 800102170, 557533806, 201282332, 36797848, 461475704, 545275584, 185061105, 45129354, 605274925, 445602267, 312837696, 468526141, 643408055, 350448900, 570083897, 210340201, 887571971, 702071154, 270836581, 683583779, 420724796, 83638514, 857123078, 230796956, 175894498, 220743059, 375054789, 376365222, 856241249, 831561801, 610210998, 765793627, 395713203, 836162191, 893115301, 257637343, 971056033, 723351191, 529923530, 669171080, 395294404, 769957431, 318274947, 511178102, 314061024, 370716697, 682750102, 997905834, 270522668, 922952428, 88758464, 983316833, 243485838, 561518408, 334829527, 812041418, 285299717, 226890998, 513940140, 516434102, 782116432, 385544999, 34236381, 315456441, 12315443, 431524623, 240648250, 950660591, 900053372, 876761543, 303574242, 43127040, 186125732, 186453001, 368554815, 354311056, 677945853, 80036217, 168923846, 141836879, 713436308, 730925821, 691304311, 688884097, 853569695, 518096479, 282774329, 325547884, 962556899, 234724146, 901358605, 392518218, 888773434, 395978513, 600009118, 573688514, 740801414, 387018292, 250293390, 210851432, 334055455, 879970614, 45592878, 631730775, 317286619, 495158266, 405269646, 199849206, 891875438, 838287732, 529495864, 856667499, 153671952, 259616498, 49054051, 184353493, 838260185, 529370978, 604393667, 833266139, 656318189, 871306936, 303583979, 413031203, 602226346, 422825584, 1386916, 254812470, 711882188, 4305714, 376262384, 265883720, 581601380, 231939514, 651184606, 946387373, 226976245, 779866399, 575995018, 360168652, 407442912, 247627054, 832926837, 39973219, 249605451, 215836630, 809838433, 201998312, 715324845, 420202088, 798951525, 946148501, 453634069, 669945427, 662911968, 437954799, 638412199, 965416369, 350241777, 49052717, 732167266, 358705548, 264554824, 879999325, 152040993, 176249405, 590933423, 85149582, 897011802, 756624853, 941246624, 811721788, 360167074, 344415402, 232912273, 385542007, 521798999, 304896877, 774565400, 425692893, 328319521, 283063000, 608460914, 898122589, 70342823, 927531888, 773255997, 499462099, 367524666, 573198872, 530368285, 833539482, 517479090, 795914540, 326068342, 46782227, 712072280, 836330488, 205681307, 9313579, 929585313, 440670254, 122797048, 440223806, 124884691, 772392187, 102593875, 213078892, 834614085, 364670356, 335870007, 899086548, 54603970, 701738443, 738484072, 846144924, 899561432, 772967144, 930353263, 506976769, 175063254, 564208385, 158127364, 229842173, 147900644, 592682920, 790447121, 838599542, 919623802, 663459314, 892514591, 999696928, 917372053, 378512849, 957039380, 817120371, 152303081, 891855403, 503855446, 102683907, 246096549, 105462347, 128409542, 403175248, 865130906, 610450657, 328763072, 607334814, 707718088, 859830127, 293659257, 845204450, 509811085, 519439799, 49948825, 39490939, 432201308, 753641117, 586122350, 853461185, 736654508, 795369918, 371640677, 627829760, 403014869, 521284832, 158871053, 242361977, 207696297, 463306658, 114603541, 317681393, 160409629, 831289255, 113180954, 537395425, 201621122, 461785240, 811960568, 617289950, 427945287, 894353705, 355847046, 671130533, 72799843, 470415940, 967687544, 776776789, 127932928, 304065295, 32827077, 214980200, 293293034, 453940187, 358963959, 416056067, 992152215, 44529469, 921408611, 183190678, 743110182, 195956616, 769574769, 646427782, 689291641, 417077458, 105721624, 201390536, 357470468, 359780878, 543948229, 814205090, 334216597, 9533062, 666346548, 143905892, 941347746, 20868091, 331810763, 442503606, 125103088, 988640010, 311178458, 323832326, 500419021, 461686145, 597038679, 263963458, 835082149, 270371924, 518797652, 415881063, 396641142, 305111989, 211458173, 55742274, 478131249, 383809975, 692636282, 741376000, 836800768, 949883109, 446721291, 231476487, 392143188, 261217238, 560350618, 655583194, 494141447, 849150341, 944616804, 302273145, 276133556, 723233416, 103155516, 590073197, 600933153, 457432941, 667363477, 908741120, 120131648, 330510840, 308517159, 475702499, 950648752, 779603338, 991716355, 196188058, 763618760, 342444549, 577869603, 308814990, 391101448, 644691244, 583588452, 225871858, 288162017, 571794377, 416818838, 852883974, 714486390, 737619223, 105720014, 528381145, 730907523, 369497463, 798600931, 875575016, 399109613, 37548602, 820911333, 817613186, 979155636, 917987658, 276624054, 685956953, 732814827, 771454837, 67142557, 942761798, 921670859, 228981051, 176723694, 544648758, 87496506, 213201441, 94794776, 774377128, 702484513, 273370478, 20516923, 61429774, 824141480, 694912277, 89287194, 506357721, 460973559, 46735723, 523886718, 521395335, 51122761, 694235109, 811613133, 938439991, 829222577, 46544710, 502195265, 460990872, 505166526, 105704229, 414372428, 707856862, 897917539, 887766563, 323791417, 476110977, 421194125, 59446170, 32646754, 591292081, 384071269, 568753884, 385394862, 627947033, 749147256, 293609375, 325982278, 816289511, 514766227, 415159244, 733313409, 656363862, 63980578, 701119913, 69453069, 95698934, 554207474, 288573191, 494718611, 206636174, 280158250, 30232313, 124696530, 543956268, 526917362, 830851811, 904607090, 41525238, 368552010, 287791000, 543728957, 41634531, 258685775, 642887467, 121644908, 634059546, 879283918, 926545547, 554868998, 780983784, 417885516, 845579317, 529507782, 960264639, 178306103, 667730684, 495890265, 31049114, 958715035, 630383753, 466922117, 930061194, 218068122, 170461353, 639840153, 390101478, 717410895, 187210154, 856061284, 757476011, 976878996, 257234936, 886310848, 218202994, 386179137, 31740504, 744051983, 755488445, 484624647, 606594370, 853406385, 136043840, 858400551, 486058665, 725637930, 386772269, 207806986, 759327818, 687160470, 547278795, 632633101, 667678525, 340635152, 186543165, 569421741, 929633568, 609950142, 764603324, 333481099, 461020306, 851435747, 405354329, 160929033, 256455166, 615568862, 16951327, 721276194, 911729072, 686246847, 227104832, 274026317, 144734491, 265990996, 514018088, 310278200, 719343221, 996008664, 464534557, 241664342, 693178238, 792999363, 67619287, 137733745, 589308013, 547027506, 1032468, 111235552, 657746002, 50086641, 868366898, 551618628, 620876150, 253968006, 594531551, 636840781, 381005252, 807151951, 901585290, 404052679, 17424606, 158647642, 697662149, 663124344, 686946853, 443035080, 905585621, 864200356, 131427727, 70919719, 954745238, 777755669, 985293936, 192295297, 687463797, 190536497, 348280145, 293365990, 479996078, 858052605, 350198615, 868713923, 587034878, 175947920, 422675624, 81820107, 447175006, 639913197, 542139269, 41181681, 830824085, 619917880, 467199523, 589951708, 438261394, 75779581, 920221655, 268139686, 928775191, 578534254, 839002805, 923632303, 726240048, 164402541, 639231736, 138868003, 486543147, 679638691, 572728061, 469948498, 70327818, 844522405, 920737732, 800916288, 529637112, 125745294, 352172442, 447513313, 430720844, 761287207, 616894586, 60567027, 946390741, 731239138, 486171472, 291440243, 324305475, 444478191, 419177334, 805578714, 146165359, 207137337, 857103478, 333212391, 546202411, 833571562, 618333059, 653788700, 755292463, 90789779, 627552983, 135865122, 77677923, 255798915, 974216575, 219989104, 113575741, 445295447, 922763274, 874638665, 13964394, 215037931, 360626149, 256567632, 256760123, 730630476, 141433957, 599970138, 809982284, 243086357, 671239464, 115548496, 2161874, 704163225, 207187166, 796188685, 162399038, 71169293, 208482346, 456949319, 5148707, 64242175, 11702616, 233506038, 767360907, 683021347, 20119437, 418778289, 274618459, 193253298, 695528796, 389896838, 292098429, 737289216, 507869801, 166294558, 440711477, 923043539, 149132475, 812808144, 946915368, 412553261, 459009345, 784686818, 724442007, 834277746, 192012589, 962043673, 208591962, 193513049, 987558101, 870355663, 121628491, 96001705, 337457718, 803016827, 143345915, 997583046, 733655654, 937879025, 948129291, 547686968, 652324402, 896601257, 706883644, 695161816, 391550643, 664546967, 571437530, 533748349, 142497259, 478888193, 957864304, 61394307, 488542089, 717110079, 791106630, 659743594, 826090627, 354011374, 516123524, 184072457, 902747627, 917863102, 903773060, 10048832, 469912954, 123558605, 745659163, 139250652, 502304849, 642671693, 391266977, 818751269, 489803864, 126619755, 434530819, 872896649, 953270545, 441995191, 150715833, 712656514, 772150620, 16063251, 656126654, 118112135, 330852480, 968599808, 878808398, 181876136, 69372062, 920402295, 148839376, 501840294, 208391232, 200956036, 111886226, 778480376, 522921488, 489907671, 90512, 687873671, 567773979, 654489957, 182995199, 273102916, 134860472, 127118024, 243780905, 93857211, 548645883, 773742193, 554790550, 363016813, 119465095, 328132675, 433247500, 210727498, 155567943, 416893316, 987105693, 578905121, 161847470, 96713133, 889554790, 292662805, 820724408, 143382970, 51544835, 367646823, 723498090, 394422753, 729516005, 703469653, 580601895, 782945798, 364708640, 490731814, 662094194, 868110910, 577587303, 937931646, 442675862, 491782197, 539595229, 867043198, 871043562, 669784863, 490617855, 901913246, 840278543, 734728142, 714177926, 480416029, 334766955, 356475201, 261225001, 820924358, 30754684, 999576279, 247854716, 904513334, 486211723, 834410443, 649335697, 728199315, 678224974, 952975553, 217976701, 552127529, 714601105, 670934407, 164393639, 853978726, 926304262, 976894063, 162729864, 580133203, 953703806, 762779674, 957968859, 595311177, 188170309, 709522080, 133588900, 648658219, 68616270, 776502958, 143279356, 792445005, 9643511, 436397002, 431315175, 244073598, 908881868, 997668566, 670848876, 239677886, 135672994, 285714523, 910173624, 691944323, 974176902, 512273582, 924920798, 123941676, 356166669, 185270776, 117822087, 187356202, 107867430, 659096771, 935261525, 252060108, 25923436, 357607113, 565506476, 203768591, 244268746, 116188890, 427800659, 700844199, 375942766, 40161951, 21270242, 513379030, 911488016, 380467961, 94272382, 317747523, 680785509, 382104277, 877044246, 392411574, 906366629, 513599073, 175745250, 992832483, 122938061, 803457962, 498940337, 515534233, 94839944, 916876886, 422085276, 354624393, 368507135, 41331957, 296686204, 103102536, 831851658, 377435696, 243122880, 99246724, 341069157, 321942023, 389380030, 910786519, 513919150, 790917315, 881089748, 630742309, 22827541, 378962975, 639734578, 220918603, 730942366, 842763119, 591025645, 467867163, 673406152, 983675627, 915196814, 382241030, 41471090, 554282834, 273066868, 531130754, 822713397, 585750436, 856994780, 752367878, 801575506, 692839506, 183868366, 886047994, 596719919, 729038644, 412892700, 203302985, 365106613, 335980624, 224924109, 780439293, 143495181, 971611369, 869695925, 520373684, 906760817, 373637522, 13168541, 28610650, 842321743, 363027133, 138213627, 464589327, 266781468, 956959168, 632947457, 819140418, 935453581, 72488040, 488877195, 147918922, 214122775, 960167006, 722778259, 328082571, 615138696, 611940767, 509016170, 266299207, 788545990, 307895685, 399218129, 183586682, 709533779, 575336989, 563566360, 501191433, 80794657, 206599168, 547879993, 449612671, 441880973, 575392138, 143644765, 48710485, 453029301, 448695519, 278533011, 872602012, 472845956, 740178282, 768601215, 484464662, 224280228, 165297325, 712429977, 287793739, 281375635, 34379554, 773621737, 240281649, 648828344, 738939228, 333760136, 537846671, 860200231, 86326761, 337530307, 837494458, 101960947, 218898635, 570184197, 608581222, 743669657, 104162306, 496888290, 963604024, 641693835, 883538176, 228249855, 886947943, 847406364, 692086234, 483308536, 938352398, 938595080, 396618881, 582554336, 178438808, 300296380, 603350142, 278413490, 830042244, 251958985, 3248242, 813749355, 865730217, 677365370, 584566476, 151079769, 824035478, 697429592, 61723481, 595198855, 774895464, 972202400, 751479635, 522431087, 840551709, 955720761, 837036110, 541655811, 463414498, 898731069, 47332166, 10238670, 236216549, 714789377, 261172362, 209411520, 513114735, 931041512, 868761999, 904838331, 345216531, 380211131, 368865489, 174966223, 930169592, 358238667, 46264643, 883346928, 352965370, 809849217, 539723027, 139563047, 206402663, 304466171, 635055043, 568827413, 476451844, 297345087, 344220374, 72546874, 644706431, 855912023, 462379217, 777932672, 727675324, 972940267, 967519856, 738017967, 553292522, 594223288, 72409606, 730479636, 169646633, 20336331, 488475373, 628073544, 118900715, 644712854, 911157150, 653117781, 26680922, 75531227, 591569913, 705715501, 564159170, 437876316, 91600983, 476991491, 348313719, 675870614, 602539157, 290563262, 448698516, 273537972, 518633517, 245900239, 552095510, 776716175, 545526056, 56608711, 920037832, 339293115, 460535943, 484644251, 363350370, 111655715, 437866715, 530111995, 6210462, 164508481, 196076176, 72570559, 740387593, 729968813, 221232155, 505439781, 486665709, 874304993, 737054137, 899459730, 128759986, 867762416, 381557783, 246853234, 27646945, 851057884, 148118433, 198861265, 249029202, 736399100, 956094288, 246536501, 182386115, 333863506, 769270573, 728024264, 325465611, 130535807, 60624794, 31219849, 306291756, 507230671, 853631428, 149328421, 626715261, 817381737, 457304058, 41820314, 998056833, 423893785, 417225385, 79212769, 337738021, 10234409, 405630506, 977453797, 278776189, 320416842, 88770757, 920414003, 886898388, 773987768, 850144367, 450028619, 637417558, 611048712, 887792456, 795819337, 545780902, 704777394, 570958298, 132596722, 230983322, 592941571, 371482038, 101091655, 128499790, 300478715, 472642535, 845437412, 128440265, 490987642, 19295082, 911629091, 838943951, 994674103, 771346184, 17290606, 161470398, 526499202, 676289876, 593271624, 310215169, 402815442, 54311145, 540081147, 857962520, 317949766, 976298918, 957906012, 427700916, 204829599, 249680544, 531169122, 503306227, 94264412, 563057897, 886569260, 449428984, 532193152, 225314312, 787328185, 581896225, 32318837, 116197737, 285868636, 853169443, 808841064, 136110544, 856080494, 938884412, 295659833, 370958204, 935376694, 420482062, 235656124, 647055611, 567504866, 336561139, 114801019, 519564213, 142278867, 699682570, 891580495, 417248441, 348041934, 117375069, 647148206, 703125794, 497860513, 938739823, 136336236, 325264030, 843660375, 98383737, 997788201, 824870665, 819803577, 643446737, 760786437, 487788987, 129003000, 95004328, 144251935, 467964587, 212468741, 886887967, 206369840, 149398304, 457351975, 899130904, 906475605, 219025263, 188604658, 824773837, 679289480, 578895036, 248370884, 694540936, 709135434, 221821641, 846639649, 889599195, 414364930, 865140223, 995179241, 466916097, 9436789, 785584119, 579521587, 681385084, 803935687, 709741981, 895270951, 163818748, 207719105, 135024272, 23961176, 525241843, 833675914, 977842102, 39653743, 971569662, 482329949, 317179511, 444267156, 246395064, 187147123, 40812622, 707050088, 989221400, 947435173, 473921079, 94107821, 119834902, 115659409, 754303722, 789689558, 490414878, 250939976, 793198642, 78122098, 59256897, 616890630, 554842844, 883680149, 8421255, 157225520, 979574234, 618995331, 360847365, 58174751, 523284979, 205988608, 417963345, 553040068, 208610196, 75114413, 564738254, 891593361, 498854288, 464291452, 262738702, 807709965, 802575717, 772536817, 827536240, 642538867, 962380748, 481571611, 133535689, 117773967, 827103072, 290068263, 154286250, 222665801, 258732338, 864556817, 267761650, 286966318, 321549409, 330984738, 781181293, 558953754, 869876648, 486068115, 380521490, 659979733, 173864986, 473230137, 667858811, 349319192, 312333129, 709910919, 802185096, 293597634, 384421859, 868490277, 498068237, 231025602, 520573343, 410138683, 625007637, 910452052, 229794980, 456831366, 924930446, 574479056, 821803755, 737891776, 109040324, 693198375, 792167410, 636805385, 15143290, 529217155, 869204399, 464409295, 503364069, 942490122, 934952112, 653278238, 443256193, 305485912, 240146530, 757530200, 794567114, 631169785, 263701552, 809473218, 566502565, 29806774, 454504112, 871616436, 828493959, 809775389, 815599455, 640915590, 437900590, 421752629, 879379523, 835087685, 357340671, 758129911, 101631245, 530993192, 451123442, 27176843, 495946733, 908957074, 147798814, 899511412, 801826427, 318487567, 275826192, 211941920, 682712750, 496977117, 374866499, 515330257, 98337720, 814888194, 85131437, 342762903, 638648577, 681749863, 39945696, 214129492, 698401412, 610918152, 458800320, 602812571, 968822214, 794673018, 417205526, 908746519, 647750354, 566238156, 448617661, 608429223, 393593904, 63237348, 393429335, 878538710, 479302063, 647878809, 894968271, 568272928, 13990920, 910084924, 931101059, 926339679, 256596211, 890434348, 754704011, 542441848, 811278489, 644023869, 36077197, 283785002, 820393146, 250659249, 621228737, 700570754, 115471863, 981886253, 582269795, 667774188, 726756583, 197991268, 228539531, 894157626, 17446756, 147816082, 129631356, 449171776, 538695870, 670856132, 707233826, 466268827, 345414234, 134703038, 956396543, 264385769, 573322744, 824620741, 841657401, 87840141, 594785209, 108224552, 218410654, 801274591, 207973564, 846281473, 163145521, 315629831, 914819027, 61212897, 391785090, 934796341, 649380219, 930131965, 126056243, 352068171, 257923061, 587732149, 88951274, 256647065, 979844771, 630995241, 616683453, 923567155, 80227012, 622227994, 78409995, 14254598, 184151128, 642013036, 472602219, 88981943, 222986740, 563303003, 818789354, 295323498, 952208869, 553541691, 3541659, 936564904, 574533663, 726248156, 58227682, 950821009, 261172309, 33472115, 786882460, 579807861, 527942879, 888674349, 395700399, 718966470, 32243595, 27054543, 109209441, 594349221, 180109184, 956539374, 837516000, 117118858, 725757719, 670672806, 794177979, 581585478, 90161081, 399044431, 463568506, 549879896, 390003573, 373941306, 771455464, 2971660, 523279180, 830340907, 820913965, 20427955, 772128906, 31445989, 686973492, 953721418, 999737310, 978424817, 46395394, 228510218, 931150723, 866049747, 391790192, 538577034, 559359345, 546053995, 52973614, 917146418, 670253696, 634567976, 738185314, 985090360, 718478801, 946710642, 394804508, 818402546, 237578873, 483389072, 930504679, 781624136, 861080752, 973607595, 703038703, 838926867, 265784370, 705929027, 88694912, 554797001, 646011666, 484821192, 77724670, 214203367, 435798792, 136988323, 924551810, 40112878, 532132568, 456893596, 437183237, 710869173, 115819361, 168817908, 704331832, 292441648, 562749357, 631613286, 169367477, 349103706, 3054182, 162763740, 419731007, 533445565, 765095996, 600149772, 644568535, 996526168, 245197697, 680969626, 987213517, 301717670, 359286361, 121727507, 134543601, 953701401, 519522650, 95804026, 10036629, 783544648, 74936735, 519032379, 26524219, 481927690, 319032906, 432319509, 897776077, 205833563, 681945611, 841977639, 625869677, 873769898, 391909588, 189470993, 595747278, 987382686, 43424784, 470896304, 564386393, 375882804, 891272466, 257111369, 875695460, 266350120, 444599780, 55056452, 991867279, 552741956, 637129244, 392324736, 914633144, 289054718, 369675508, 73608594, 36902264, 641830733, 819081794, 421725898, 360785754, 867662222, 726862576, 755412346, 728658981, 458595302, 29893236, 573601595, 99651678, 588431996, 355036689, 533393852, 902881937, 376238786, 883681564, 859622440, 392172627, 344737917, 513227866, 770909718, 575809072, 512192632, 802204007, 761104861, 634364929, 171018197, 845712790, 49409234, 607215548, 846853113, 902282844, 479368491, 30443720, 539327567, 842412829, 198552553, 455420472, 479839336, 110692600, 48883956, 599027417, 402992855, 791085724, 605853354, 818308016, 58145210, 826595908, 218957439, 556195172, 474289819, 985162351, 725935135, 933946940, 406006060, 945769475, 170616926, 370956829, 397764418, 737471041, 51900387, 910487137, 705502784, 17187408, 430998838, 383695391, 811213440, 495336377, 50268566, 6284522, 578012142, 554319773, 653402099, 1254334, 129217814, 431854993, 569385145, 679113221, 274617107, 593681690, 666782378, 953575678, 990638620, 621604978, 646685910, 4965962, 397062973, 58726349, 804446022, 632148685, 654483513, 558725838, 252385143, 277319465, 7513415, 413827453, 808992095, 887133357, 719712688, 906101420, 128710403, 710176499, 581269002, 316173348, 792642547, 754133444, 634347785, 216154578, 754000278, 445610153, 308433197, 201054706, 488661930, 989104367, 526839823, 746499339, 926477507, 415875882, 699562574, 504785423, 552619801, 872673148, 262183104, 228890977, 585625797, 205268245, 416621585, 560091205, 963837263, 691653592, 42097057, 958673495, 180894589, 344815714, 421792987, 324772756, 56696797, 888274630, 291610501, 873643401, 346615367, 225283553, 164440740, 524413992, 712735081, 408724572, 426003956, 480786204, 354437949, 834129226, 426495310, 517584743, 855342816, 915449407, 60182946, 868234303, 758436432, 844574022, 80404845, 492383656, 537811860, 854560325, 356051082, 12073575, 67281775, 817719284, 930836486, 363149347, 828683777, 272078886, 52625083, 106755781, 414497009, 893485837, 652009271, 93163509, 676438409, 323843945, 627723300, 169396945, 781465379, 750974829, 665951386, 744629066, 677145576, 508613748, 92840516, 552089486, 904776554, 595964695, 979596520, 665981706, 858357007, 306807201, 37333777, 6489536, 735350856, 919412125, 254125318, 853019719, 213204335, 49609422, 342383459, 87151641, 167097249, 411342502, 515056865, 966609320, 760019958, 949196857, 31445279, 508335479, 835561833, 204151906, 705745821, 541711093, 529620540, 346283089, 244447367, 875077181, 39680703, 250063904, 139866275, 198276096, 57179011, 940576788, 748730467, 961166771, 575853187, 464773696, 921264486, 750573192, 906903809, 803466868, 467665944, 823211926, 44455496, 171788068, 762197246, 228930876, 561076743, 374550862, 6104393, 277571921, 735746834, 791800723, 936475393, 11252310, 103525168, 888075992, 808969527, 319327081, 246119587, 426712046, 811864337, 184378945, 675307113, 360332724, 57999148, 201634681, 89764870, 811531645, 421923336, 260826824, 539026632, 556886016, 877695292, 128203805, 330502294, 597498888, 549691779, 790249316, 538018530, 535204331, 67587719, 521234759, 368635206, 220104607, 7173426, 448176246, 867000011, 751775315, 103141169, 838223405, 894798101, 701785602, 329858737, 705777197, 128620391, 186515198, 50998479, 190620738, 218468259, 500275444, 454515385, 677992839, 98578172, 575159062, 868268115, 214295845, 172862719, 322460499, 964038733, 200498004, 743595129, 313528610, 493513829, 464886262, 625871619, 261814428, 968922694, 537492115, 731764117, 922788612, 704489329, 803114401, 505421478, 419824989, 550060452, 483264975, 445070089, 429138715, 687771379, 240316654, 602423319, 298818804, 299807778, 836620557, 373979804, 450074015, 138860956, 851652850, 526792423, 789039429, 124172447, 94157564, 785143336, 573181405, 181859426, 213441005, 931045554, 284035345, 28782429, 431256564, 384170855, 179463972, 763072599, 632945739, 851398325, 932605074, 526147464, 895267644, 505275951, 445642616, 910892953, 944522967, 932727650, 829852700, 931763122, 216453675, 389654973, 633249244, 144116809, 545361897, 757370896, 527993697, 348534930, 794119988, 877669270, 500004468, 368907831, 491017004, 313742647, 152049089, 261730520, 495692560, 861495121, 188975681, 96216682, 764736117, 698689274, 122959739, 391276292, 820262332, 879788612, 890130431, 454098069, 449437745, 569125399, 469180029, 956763351, 956501995, 989071207, 882296461, 613888096, 475678663, 255217790, 211162278, 317290885, 715164083, 522631730, 415538622, 909020670, 900822097, 734709266, 135209438, 928010323, 23289682, 498571132, 229539729, 837926463, 919074585, 503175651, 461170821, 918702550, 204356502, 650473973, 851588763, 217143313, 530796412, 399730481, 432519913, 821682145, 260072332, 330434965, 350961811, 538820708, 345285330, 686673031, 959282454, 910218336, 253421560, 504023674, 456030344, 101837290, 458118043, 314284, 842568464, 821619489, 207307237, 354165071, 859992844, 136051186, 749605924, 588237034, 755906033, 248065258, 982895003, 964945123, 885906068, 326418583, 939672697, 323695469, 969703359, 510578537, 559195649, 228056110, 490956294, 895051504, 935138714, 701049222, 807533081, 967644748, 247364110, 912738467, 225922725, 785861128, 361111525, 376386649, 220480048, 139144760, 780116389, 24105477, 822165005, 526599831, 14477655, 589114911, 983809775, 598315641, 808465080, 67681220, 845970042, 31443933, 529122007, 411621012, 693653133, 105545991, 90967980, 901444802, 550647969, 709454220, 530368187, 305319884, 847293307, 572525609, 226457784, 327202771, 459325288, 606828974, 718435568, 521564623, 655715923, 968589797, 145742175, 741956484, 451813881, 485664904, 95046642, 779402664, 696113143, 620015255, 465602810, 894844971, 489451555, 204043131, 794701274, 70046263, 314631317, 443114484, 343247141, 311024080, 516281430, 652873011, 803386317, 770739495, 147653746, 644692708, 517580010, 591551441, 944141309, 901988441, 328499258, 997334380, 419501344, 330693693, 988561291, 378758466, 170581180, 520341392, 302453772, 773693967, 149479747, 804699789, 459715310, 649784273, 696918236, 334653244, 18656182, 811156779, 551008102, 464356514, 259967550, 251153206, 92490140, 71671608, 630855915, 901343710, 874384202, 346257324, 580176016, 726103673, 270065111, 563746975, 708755121, 393546936, 13540198, 81054076, 927345002, 319040144, 429871783, 590300205, 137095695, 480381258, 939283672, 133644522, 446435906, 259485413, 594841441, 410107223, 387918829, 286396227, 698025007, 782750289, 5083997, 540886110, 723229657, 878354869, 234906384, 82118075, 371619413, 465561248, 474492492, 426409742, 888852738, 653708745, 982371081, 523690158, 996291532, 650417534, 171109803, 891519859, 986514936, 947533396, 982444390, 180150381, 574316630, 853254466, 753951512, 640046442, 743863947, 436792175, 320867374, 516166663, 523251046, 875957194, 103470864, 905725689, 664236071, 220334241, 317129217, 811842626, 826973067, 491477952, 258222863, 290903656, 661659731, 353956752, 137363421, 577972430, 213687758, 517744546, 207989625, 973446217, 570965044, 225990854, 475375467, 513559007, 267538365, 998972589, 352301557, 661697548, 187356818, 339442352, 677789591, 585696885, 543678357, 864773482, 641967678, 956624887, 628144686, 914715274, 962819094, 531066126, 2472615, 583779365, 994261472, 55911689, 59162818, 4326330, 668791597, 492399855, 681956297, 591349208, 169818119, 149625610, 586880032, 85479108, 421775344, 930770150, 919391741, 348746597, 966920143, 105225232, 988717944, 846514340, 467324624, 168704335, 647785545, 536272254, 233839831, 365407020, 852601851, 33718257, 779020113, 910345421, 171462145, 812374186, 802543396, 523585081, 136830606, 618875557, 444993854, 540085049, 441065577, 881990362, 896836887, 743494817, 364411446, 781492221, 78901032, 391755807, 811869563, 471007007, 435605699, 101509777, 219269729, 548454621, 212850883, 611671914, 49227475, 858865782, 918323085, 913265466, 258536496, 698557360, 202539083, 172114212, 916058623, 46456531, 505262749, 644236404, 307066503, 525660969, 5283306, 915294658, 830536546, 345930443, 834147589, 28541383, 824266055, 587672305, 15206639, 967110571, 440318988, 918235018, 302873574, 5319160, 887373640, 29619224, 488943043, 379574083, 719208121, 827969010, 319089714, 448749871, 512965505, 847483132, 341507633, 331761403, 64944695, 4714408, 888714064, 54864174, 111954716, 124429287, 334402256, 592451802, 105898982, 85584164, 104498332, 159651356, 482151012, 954719441, 103448532, 95738942, 331731226, 448215502, 542567696, 304207268, 607274418, 36275038, 53057953, 663116323, 130902076, 902412115, 343903777, 461449434, 89751907, 599603073, 420949810, 342070180, 504938721, 46750848, 24552199, 320680669, 567540210, 504044310, 128545599, 58626105, 782817280, 514359048, 29539914, 450664829, 626414281, 705540583, 388045751, 960974047, 914856786, 987046613, 957110070, 861894449, 403953225, 697382432, 943248803, 195503457, 658825928, 219022468, 535446434, 144150800, 176718372, 367358922, 869734829, 746893505, 396226515, 365086180, 439004610, 192141905, 967440138, 165084334, 523131955, 161070519, 357093825, 840971473, 194098139, 112474808, 589438066, 583397471, 568965313, 599223581, 750183988, 987280083, 23625877, 546810474, 543285023, 555665961, 961420242, 528960349, 931043896, 975700084, 191210578, 120552662, 714147912, 448248812, 673393412, 196912452, 591417289, 732143043, 620200029, 490284550, 670510544, 770446346, 529267917, 59756084, 666163882, 276872351, 542056865, 124376914, 824746126, 19805141, 53683132, 576623323, 487421026, 502905795, 891925753, 138189744, 323227371, 207104917, 18404673, 493236218, 12870955, 410332835, 269119429, 545195859, 514911679, 345570207, 340704914, 249990917, 756104184, 562183384, 456330700, 512194429, 783271260, 46586579, 681644811, 168238056, 300967596, 150130138, 182775890, 927539049, 979621818, 350823506, 830486266, 726459337, 593734646, 688131524, 705603238, 484636408, 272761955, 959971909, 249314120, 230485824, 165211738, 266090374, 720903527, 654727976, 564269311, 548348524, 750731250, 221213702, 179753638, 463151321, 884948179, 509666647, 175562215, 958244211, 304574328, 843053458, 393683991, 947807587, 121777017, 907452568, 214597513, 228675063, 610870476, 268621399, 649751007, 332506666, 906408883, 816595555, 232361508, 373866408, 965112065, 251806795, 826419855, 413678208, 405170617, 816079311, 681912569, 537504243, 51212021, 434791683, 886804979, 542599112, 631575894, 459885118, 32443511, 254176346, 345394753, 79175308, 407629720, 694397706, 727376511, 142552863, 618867679, 649894974, 868926638, 807786103, 93433893, 639137467, 184429248, 439364314, 122500544, 823106301, 61909632, 549748061, 651298867, 85844080, 204572271, 572211557, 369534039, 623561662, 733310569, 237078980, 910547790, 481439193, 997416173, 921677254, 790906323, 475604385, 925154992, 731048422, 619388002, 210274351, 687936279, 660342926, 368390828, 165721693, 296919096, 755977750, 537079324, 716127481, 253043109, 4914349, 535341071, 80802974, 587355929, 903961205, 559846661, 527243527, 808283859, 734948071, 644309889, 459260757, 849448131, 496849582, 422058663, 718469109, 76622072, 404795009, 294398640, 47207609, 879943195, 984862964, 221094302, 611340697, 373432945, 933357077, 774334734, 483483648, 860794134, 841454504, 161649965, 772712641, 541550158, 440165696, 754719714, 111045020, 591568483, 737921543, 780643661, 570339554, 567976417, 842774875, 734425618, 434549294, 507756563, 579738641, 328736844, 432186268, 566005088, 180482376, 323021447, 945446855, 887358392, 178962539, 645638957, 394877240, 18018794, 334949521, 583443486, 85280395, 182023924, 748120952, 675487377, 821915497, 593768008, 721895099, 913351545, 170342699, 428805754, 161864741, 484790962, 892333505, 240441113, 585147741, 669343639, 747732948, 534943987, 705021501, 70906112, 430852512, 527012374, 221059670, 188629529, 503310421, 964247969, 403519296, 224716454, 77084627, 623792899, 685716104, 957172276, 260966603, 219093586, 286248479, 979212923, 154787867, 213786136, 740707213, 483768096, 860101473, 63298597, 625764113, 745287247, 851144724, 627073401, 174324539, 179628039, 904430108, 871738009, 294675981, 428138277, 402200329, 487095456, 247708589, 279970835, 346575522, 964910656, 393635882, 196237089, 430007239, 102244734, 186365975, 795778962, 993638589, 605729523, 395580575, 192116359, 356417461, 506659592, 863810081, 368956618, 959539775, 768483522, 881685528, 316681769, 809683073, 287688404, 546695128, 548627185, 930411334, 459036760, 791830960, 335399382, 185685150, 648858285, 765622462, 840789215, 828161150, 59780719, 370034675, 394455492, 325569586, 274941488, 814887606, 213869893, 713382058, 906170679, 234187055, 761090719, 992664466, 881333223, 408954871, 94378865, 111924345, 376918384, 30238485, 259607422, 491178388, 729774123, 429616139, 676818918, 839709348, 681595745, 627799023, 448526152, 915625307, 511125928, 598765058, 274206154, 856963609, 493565159, 554884923, 278935450, 594353338, 435413882, 233771679, 524314127, 909458489, 388591757, 228252049, 395544024, 921601975, 447026703, 71081650, 531933035, 112195581, 860421994, 649543227, 834170524, 576371679, 379845034, 943247720, 622716515, 508233505, 35143095, 554371599, 770333825, 873122598, 541645283, 182211017, 218457365, 199056424, 592056801, 153567801, 44455481, 322963856, 701777073, 413895611, 72940350, 692455956, 391780626, 940169461, 718344556, 306034420, 107022493, 662077220, 581526469, 444798533, 325675234, 150053530, 202573270, 739664955, 283716744, 870912910, 520240048, 926656256, 939327923, 977091637, 650149163, 247277101, 531088641, 659463823, 430887688, 235016693, 993689095, 534989103, 513952117, 847793712, 359544801, 678735238, 712493567, 461987433, 830391491, 314582915, 145938065, 967363879, 441721553, 916916999, 85291315, 424449176, 407349286, 318180667, 362102884, 152501650, 324576511, 641418610, 36588537, 697796909, 992512037, 25769241, 260068822, 80196482, 376427692, 164911102, 875888508, 929796979, 408617470, 33402905, 844805664, 294086960, 427958311, 166975814, 915836352, 348124414, 437671318, 607819431, 923970428, 644482012, 322290896, 261667423, 38167452, 159570348, 310700741, 795907629, 414233415, 594171903, 119532657, 272640667, 597335680, 695140027, 445185240, 656523128, 801366272 ], 12724 ], "output": 3761531150043 }, { "input": [ [ 19363302, 364981564, 707374791, 626308398, 513308428, 771159494, 990353886, 423062786, 857000322, 790013853, 735742206, 795652027, 227957976, 5538513, 81514389, 591412758, 315972910, 809704975, 203267341, 434929150, 803386835, 791378863, 248094723, 232250675, 761919129, 153545845, 590310051, 225022386, 50789516, 30685521, 11651275, 257419450, 788408579, 578546594, 925058842, 323791121, 53756373, 822411171, 202706933, 851610614, 74716827, 834470888, 227433546, 868522328, 434049881, 446398821, 83413621, 18490260, 514689198, 367549587, 906686245, 556016754, 531404109, 278972067, 595058524, 574801122, 732769946, 800653260, 465545823, 431683170, 546624158, 393274669, 173632699, 923068325, 888654850, 342440462, 467048904, 666608894, 152173814, 159502900, 853794015, 470554151, 113499513, 345007508, 539430588, 458913853, 531238961, 648637037, 492415795, 810898548, 431214169, 335679373, 146042742, 447680211, 307301927, 894878463, 252476066, 690341500, 117137145, 957585019, 401522737, 721421380, 980498181, 889153307, 811655394, 160661972, 913020273, 173129408, 699501855, 575503830, 637068529, 631790982, 735839595, 550119648, 329007635, 680338770, 821370173, 436970683, 67314330, 432433787, 545983969, 356674139, 400833892, 227383421, 515279860, 173846493, 287010996, 261434235, 309243093, 640868484, 885012515, 680324024, 924546664, 246207235, 583295018, 351708176, 432597540, 19163691, 106080379, 259481025, 812599477, 905690587, 810082358, 907177759, 171334520, 673439122, 765950496, 293315217, 129876530, 798093071, 135942628, 662115147, 769863228, 860409911, 591650224, 245869381, 585226075, 655941875, 304425566, 41175992, 836120497, 853263105, 367958740, 68196114, 566103603, 960690103, 671527401, 86727897, 739883663, 947329936, 552099782, 898564801, 621910938, 734758676, 57018910, 457019381, 96552550, 723363326, 474478346, 320573765, 915193254, 715808225, 57508984, 216207580, 217119411, 90359435, 394861353, 318282554, 564688593, 839402542, 967865245, 888764268, 97290184, 802764304, 40731846, 65827236, 572125155, 550803772, 124680381, 39332550, 204219689, 323425202, 161316144, 53611110, 71225300, 268555962, 838923924, 795954818, 290033437, 708166980, 109809943, 47080255, 402491791, 59608950, 623975383, 537293617, 213441841, 28053410, 237470434, 724370187, 893702500, 892839076, 932593701, 104839939, 580876791, 270239669, 387546131, 338679692, 500602472, 320142545, 263571136, 170707019, 807214679, 167592399, 354422350, 48893473, 343965929, 168382291, 357319759, 772625542, 308895322, 420708921, 438551290, 838239710, 236389226, 259421970, 339403091, 546025262, 634998501, 836026803, 59529737, 351657394, 31195677, 772034711, 367171636, 269004768, 288192377, 739394127, 12236053, 199272136, 762659350, 633223958, 367402912, 551632689, 361754911, 730646108, 512443887, 468066580, 978129085, 45927876, 260380119, 485305558, 269110325, 992178356, 767304705, 787119057, 724096395, 486478094, 294592975, 800095146, 732036441, 62269203, 326926029, 358221339, 141950705, 89690018, 142916797, 311977764, 823552864, 887735253, 844419609, 415845430, 569825481, 680975674, 538255526, 345618864, 784833573, 78380014, 42606817, 508602789, 822743547, 942760082, 982816400, 154901181, 552332619, 680687874, 360273984, 549197186, 660815118, 792517276, 683291609, 390419831, 945069467, 151748792, 607907011, 289569717, 73323906, 637060755, 651211789, 310758937, 552016120, 200323755, 514974038, 466087616, 564413284, 911803020, 741852170, 565251841, 514433892, 159861317, 650842422, 352080656, 774270134, 51477405, 862350745, 259743548, 257973893, 933434060, 241048756, 228353522, 882114847, 411177705, 689147021, 163461667, 690316978, 379722940, 898766058, 424107540, 379994580, 672425519, 500785229, 43682992, 160362185, 732089036, 682529355, 147068810, 304268508, 31116643, 681045172, 217887788, 688587872, 712526670, 941403930, 81223344, 306118543, 751346593, 729288364, 5093264, 382882918, 991575203, 425039472, 620431073, 407941997, 769460166, 331857556, 787198658, 24712723, 303090303, 865351855, 123020691, 597282265, 16924547, 362997647, 803483933, 919843872, 992718498, 416809855, 754304742, 877389950, 786835623, 393828123, 710253456, 415318408, 373156304, 709321037, 33294544, 281212867, 784143591, 464638733, 632481831, 477777248, 360417433, 240018479, 45425321, 301030157, 686388318, 603911021, 595617442, 608328622, 807660272, 718037046, 71214385, 615399212, 399682075, 166035151, 550039332, 914683049, 642472609, 359119713, 278904485, 736001945, 728971819, 344854700, 176108267, 353562313, 726518967, 858423516, 482762319, 644624074, 829772214, 479043145, 450537417, 427162115, 816797715, 241084965, 533800113, 651763522, 869304409, 681504455, 975006162, 746233713, 671344953, 77703853, 243427821, 808913218, 139609716, 297738928, 624057326, 234830909, 310289777, 686496739, 899736520, 136258223, 190769022, 692661433, 537645591, 786176252, 710906685, 305492695, 147753146, 569993006, 731284988, 841443163, 522523824, 419449975, 486111828, 735053813, 483083630, 271866810, 504122935, 820149696, 609213051, 598371235, 169273726, 246334433, 42671955, 230138354, 516935203, 654100363, 214390768, 932371145, 85787845, 631244397, 249754448, 990703977, 604427412, 285356616, 403193999, 967217676, 19814112, 511961486, 431755042, 831394826, 873844111, 520341551, 877877578, 326075647, 278563197, 622451074, 787632978, 24080361, 245512463, 967810972, 248032910, 814189916, 210558848, 578887563, 486899128, 460740172, 440708587, 847247361, 372463131, 828771402, 898486162, 613924761, 757402362, 872211585, 488500561, 916906217, 977594731, 512984108, 600670465, 746211954, 746407367, 869388557, 17160673, 847292918, 152047749, 155081054, 322617585, 545041407, 180473193, 751206685, 102015585, 63308458, 916483294, 605672440, 793184375, 183610262, 60919584, 944776907, 436897338, 828219634, 815546794, 512480748, 297363216, 764561206, 156039631, 23123711, 825417436, 55823826, 954263754, 563627675, 748718494, 731264564, 568096588, 646695143, 792764113, 215923984, 685172342, 511605343, 491148931, 952197008, 311490919, 756970355, 965365907, 350297099, 757497016, 776704805, 188070057, 116470149, 258086601, 177186698, 678624201, 288658996, 194276844, 999851591, 130346390, 573828589, 424415606, 898475879, 44443399, 316450076, 550518672, 246655405, 837619075, 443867090, 473337265, 501889815, 420779400, 586623178, 306781731, 638843962, 57703765, 466985112, 289342894, 631213193, 362931520, 311784188, 274320865, 803973644, 592834607, 762830698, 264333301, 689884822, 155290317, 83379896, 647819897, 299448127, 645387227, 741948143, 145113823, 89379500, 551216186, 950275578, 703646113, 179705600, 892984657, 591417615, 604780710, 799281542, 33625445, 575469494, 343401420, 650380690, 385886332, 531700385, 464347785, 737152884, 60088694, 523988314, 858918418, 429756238, 351478232, 739477095, 178360130, 738415948, 472386507, 193873901, 882577354, 520734049, 572363359, 939470749, 905396410, 474211083, 933822122, 607469523, 735000999, 877142625, 749834734, 215697161, 200091484, 929456666, 648248436, 319007475, 112116950, 775223914, 897517891, 381354529, 993239438, 807378978, 878725472, 935153098, 505833644, 683123945, 734115275, 226042271, 569492235, 766152272, 408597347, 13094249, 589372499, 933782222, 241904696, 408587206, 624954432, 25862773, 239420397, 871793323, 187092128, 474400149, 109663488, 736146549, 266236174, 657627498, 491725145, 104724745, 828243731, 465149008, 990853983, 840410618, 34125242, 238024663, 753384492, 323710401, 979802804, 674825446, 42072416, 157929248, 20816089, 874090281, 815313671, 746361660, 253627110, 437849368, 849366494, 239456208, 116315182, 662996612, 279020363, 896450519, 698729480, 404564769, 477369615, 133819423, 922112868, 434506430, 80323105, 839400848, 727536171, 403607748, 809211904, 994669141, 83991929, 584018900, 187754008, 663012975, 119611949, 697656359, 552707112, 389721591, 833786037, 349518202, 962071363, 481813783, 333197842, 203835452, 867489792, 811057389, 424502885, 102015553, 421188835, 171665877, 406017861, 254385460, 80634449, 843424131, 366693008, 392898646, 871966603, 560202960, 634104150, 433368860, 202864889, 738994721, 421671969, 373508731, 973198735, 74272513, 36181109, 600102681, 480423225, 129271184, 433000965, 462846582, 571265623, 523311266, 144832363, 213007714, 71854972, 57913946, 540397843, 68178766, 942307376, 254172401, 514276913, 48849438, 378389952, 127511773, 406948655, 863996462, 597475821, 666631356, 923891401, 628220438, 830007016, 117415636, 369886266, 607076620, 703181950, 135382720, 538502367, 568374160, 62219053, 185899241, 840749471, 818821096, 715853861, 801278963, 391104428, 33308044, 612967010, 233142333, 615653390, 745011309, 120393306, 228445560, 223190216, 55489197, 278731748, 833196064, 838292610, 567467985, 274551252, 760419167, 996591449, 985323842, 789589939, 185899904, 229476401, 394098558, 851013379, 605068522, 577070700, 447024808, 397188310, 508746075, 356027801, 329915431, 527211286, 321207076, 717101696, 875005754, 71306485, 512921125, 415441822, 722980732, 255398446, 785375462, 510064968, 220397312, 823888259, 624589630, 937518324, 645160384, 707568010, 731682467, 503913968, 433715697, 828895244, 695944578, 322525187, 174073820, 880284599, 441413836, 820415181, 167699761, 862349506, 634669671, 743072847, 667616905, 352066640, 723739203, 810523020, 706720536, 782626516, 869810369, 733044120, 242460967, 441233156, 787127725, 162621631, 689416389, 504241673, 524862081, 259491875, 576497218, 506968350, 394432342, 260191087, 8823064, 241585071, 790435255, 898362487, 513785259, 425436344, 318427001, 852894946, 16401892, 932214116, 498191598, 245101388, 621139141, 224215395, 969746768, 601092234, 37450068, 321768215, 184328585, 276926495, 599549577, 870749435, 826962769, 290314094, 797788136, 806707214, 287163073, 903600563, 680616558, 611392776, 248164862, 205132551, 608557810, 258892753, 718881917, 814127266, 483264211, 925272177, 667845213, 638341784, 971033108, 463849943, 706239758, 792553896, 955816206, 364164915, 131029401, 806217770, 628114652, 250702274, 356796426, 670262413, 21260168, 901885142, 472283178, 587013611, 897054396, 594231461, 708121222, 994279684, 850980041, 343480350, 822448881, 340186283, 150446245, 997299506, 490008136, 607880899, 279755851, 640031967, 62232696, 388417411, 662756197, 43184793, 961092339, 382542818, 62380626, 644873353, 240268862, 332127948, 256225905, 903715650, 353811703, 222102018, 81730825, 809494815, 342598120, 116837427, 349715439, 795983164, 624737399, 388629725, 540698431, 782218267, 853571157, 662126247, 298281876, 216362, 294084780, 676460303, 29501095, 671104430, 217103916, 261140591, 619687443, 728444396, 460916893, 180217030, 308057290, 50173454, 107408117, 573454321, 965748768, 106107616, 205827949, 263391593, 666870348, 160736429, 335281744, 135530688, 464943949, 778444392, 793133043, 89151166, 956592290, 581497681, 951473776, 279759482, 795224400, 202606755, 73767391, 140969408, 44029167, 710478365, 470458779, 462897509, 734386907, 703521818, 439537521, 435682403, 869961730, 308674349, 371615258, 311789076, 816304107, 288398587, 966764053, 519929660, 753617026, 427494085, 512941996, 572777373, 569175495, 795238423, 982742037, 303141151, 980356355, 574550560, 210017467, 548867276, 670288645, 882250845, 466038895, 825852359, 723393138, 660046469, 41359635, 555818995, 103000032, 274737175, 10715046, 110891657, 731816490, 789943958, 149390265, 485682475, 880938635, 251802635, 127984687, 690052770, 394441754, 77733219, 525388260, 260416165, 350716147, 394115358, 211301748, 569613166, 518400584, 854844983, 929144483, 270174689, 344784373, 181526462, 664683908, 965970088, 153856901, 948217863, 866061019, 727654748, 297314025, 691134429, 618674898, 59562787, 507785061, 608999012, 991453128, 173617791, 749855985, 958288662, 102509374, 547113569, 625183441, 645063692, 511607795, 604611181, 215469803, 346864431, 844115535, 932502062, 766335670, 236219493, 893289884, 116043354, 578492574, 286139908, 276944541, 926896389, 643595685, 419985922, 259169764, 143107805, 871169256, 939799726, 404026138, 403110020, 236044791, 625809564, 886877819, 98360560, 602767925, 492547567, 332417631, 347582800, 933347988, 92209675, 314223284, 884399974, 726393899, 674780355, 972331716, 531393619, 378575074, 766251501, 511896019, 710501277, 753640180, 481842407, 140143584, 722858955, 137752215, 9073978, 522007425, 687613859, 640250881, 972620950, 819872000, 58667635, 402111652, 262114772, 916399940, 52293130, 456078896, 474019303, 890758682, 612622014, 284527126, 759590446, 330482557, 509546163, 921783698, 388418061, 888939151, 102350181, 524290637, 722295436, 104762321, 68273386, 107414082, 466274060, 55732985, 544998451, 272551160, 796305794, 289307024, 244006633, 137140142, 912203617, 290567691, 758856448, 439395720, 275287089, 421923543, 135988916, 62321881, 939099033, 617681873, 15167320, 554551611, 983345282, 212450511, 564431858, 680690938, 872101424, 776021806, 449962926, 838995446, 779923050, 815760827, 795216734, 660949709, 460563046, 999808526, 79976783, 949404724, 645027975, 597964540, 416432829, 869711860, 811598259, 663697234, 270991040, 381524564, 606185818, 696280351, 198199400, 963622269, 72468641, 371593867, 742038870, 182540090, 695711558, 870520703, 506978421, 514457562, 33527912, 992712035, 51420353, 765549747, 763513094, 899279482, 112865351, 754097932, 409614105, 776496522, 603155781, 62722197, 495268771, 228871154, 223788396, 359265123, 624430675, 803434222, 621721744, 392286631, 23166155, 932301284, 511244326, 782579242, 438572252, 600379351, 197950164, 312889439, 586305325, 233336866, 993805008, 699360994, 202132300, 868861780, 777542288, 462112230, 37124218, 645484514, 967616042, 314552524, 862994130, 196655832, 572525073, 533238832, 369448309, 663849102, 745584614, 567882961, 246285827, 771077846, 439460193, 661054083, 615878642, 204396576, 504463902, 70761835, 161883858, 388699448, 291128293, 612043672, 237508650, 909944951, 233867423, 46749872, 238754116, 89420451, 317133718, 813610299, 56983693, 859733901, 68115871, 144811519, 426792038, 126120997, 895486117, 419825323, 168129502, 427538216, 730310484, 46265488, 97860188, 599785036, 374045199, 947917441, 980083019, 223684958, 35999043, 643317080, 438095385, 467936020, 149607854, 643951460, 636985727, 589198307, 560087129, 646694286, 495743786, 254861332, 534165033, 605693942, 586972646, 957028129, 920984267, 992136066, 46616078, 324025818, 784742769, 178151364, 204439429, 502294546, 113384596, 6139177, 9707087, 291910416, 38597150, 253519366, 836422423, 779076797, 527475187, 851338953, 212859541, 781992051, 392147459, 214869905, 175583203, 148765607, 642624768, 746450619, 63720539, 305138170, 203910343, 382930634, 948648277, 574111418, 714799853, 948641802, 184874978, 630172068, 652635013, 442209250, 794856481, 204363674, 763422520, 931094942, 316274993, 496456084, 673778248, 201754052, 308682672, 464920169, 30497575, 229147690, 249389895, 82896186, 615694527, 224301478, 578997087, 50797945, 175990465, 81189718, 388706953, 603670026, 170413102, 917119726, 768906518, 25254691, 331341686, 826150372, 964868581, 444628074, 994766901, 651735709, 966003195, 377122152, 93904802, 924560685, 537863567, 661161094, 978782749, 809825773, 54117821, 385336076, 138049481, 482125581, 239246966, 31148523, 190731777, 221058625, 330630532, 56669561, 856823364, 426393564, 863614601, 711193188, 572091071, 544123703, 395871586, 646981152, 235150785, 438859372, 797900935, 101781530, 16539112, 506605895, 119307558, 611295644, 542774058, 921534533, 251338941, 75908899, 85906067, 994120555, 40032506, 89338467, 596144186, 718753240, 911001318, 498182997, 667552181, 671436495, 262744872, 945469045, 157751821, 173522114, 10052622, 476088764, 618042947, 358277711, 316190830, 68480988, 135775690, 139750691, 790717910, 445907146, 250370571, 1684925, 673710880, 710583644, 681841507, 387315513, 459060430, 262902710, 518103026, 383367591, 833132503, 2239664, 449600456, 593760499, 872085085, 914939309, 380687998, 916461264, 687140636, 795423367, 63812088, 403481052, 534656817, 245517523, 428548152, 17300942, 506756418, 964626511, 693677706, 546430241, 362245769, 890205562, 845489028, 434048930, 87374283, 231079599, 713137586, 796008707, 427640219, 263983507, 58046451, 947747141, 671903483, 380181558, 206458434, 77768695, 18199934, 688813012, 892111047, 119939294, 469321547, 716345165, 832529929, 684496341, 682052570, 63314737, 20448040, 358752335, 610623192, 514778360, 721994479, 62901174, 17268241, 351129285, 329198496, 604263920, 12768448, 563951988, 223642375, 970147252, 729288527, 318760220, 368690482, 805035294, 820629755, 869464895, 574211632, 877692481, 878812731, 955181876, 16208505, 668793219, 118165600, 318323737, 29242060, 597260051, 949526277, 730023419, 685975620, 43848012, 991282087, 465689900, 665233997, 828772395, 589174791, 439549077, 902462307, 856635419, 216065309, 501157500, 864082614, 682508089, 365910562, 451358060, 878020173, 734110488, 737487531, 280342110, 974655762, 197557222, 226801961, 325457419, 755657312, 556707612, 798439478, 635670511, 29287044, 564816035, 600657157, 249425618, 933635377, 65041926, 265905562, 439401114, 719394556, 378796423, 610037162, 132491388, 335551037, 538861039, 406769727, 773281113, 502333100, 85676522, 274505102, 914797699, 62800974, 54374806, 972796277, 129361248, 33268201, 589192319, 30581884, 439661463, 94312198, 730091277, 86817231, 673678365, 407945413, 466633539, 694074530, 133289324, 566069134, 342079445, 991385083, 251620282, 43007709, 246921115, 560842800, 30821207, 853029037, 344277547, 240062565, 608338980, 873464811, 681902968, 773433334, 750697131, 609700907, 825631636, 560925929, 892161011, 972751327, 86667772, 267536659, 63065363, 620571283, 214463423, 125720820, 621778680, 717322742, 922125689, 298450170, 87421336, 528480333, 783827397, 882285064, 153077537, 720128303, 498346376, 957854956, 438280760, 346600016, 294814679, 870979272, 170075078, 741772832, 693383009, 784325840, 106380151, 735877911, 658703092, 81982186, 679582070, 383878988, 935346376, 997336092, 939109325, 933599209, 159943757, 301547975, 867631893, 469523068, 421172072, 35891547, 749668900, 543147996, 760921550, 827595706, 192200344, 848562857, 949208170, 834269940, 64061835, 153848566, 560483486, 96624952, 458184979, 202411477, 753122665, 935275052, 55471598, 622821187, 340506977, 866467714, 686606072, 899265902, 307534532, 314863959, 810871870, 711215086, 300867361, 674088876, 149484650, 512516495, 844860835, 858628217, 754912492, 903361559, 429799647, 888228032, 666858223, 906345586, 934725361, 840772898, 190427031, 928824090, 729433745, 728471668, 960350262, 706057241, 115787434, 328845185, 354286815, 511520656, 863085642, 65053445, 917598729, 206968851, 725088736, 336046075, 878115388, 462348247, 227058841, 758808538, 476107105, 459488850, 394948540, 436275385, 353161229, 617027247, 825904379, 710921886, 98687934, 864622580, 359518128, 666206428, 519855940, 433017633, 383639890, 655629543, 382835405, 974970537, 278787845, 20591309, 583731481, 13260607, 584151990, 591973230, 748184223, 671040569, 415270237, 624950095, 564512108, 759141542, 588753148, 97443465, 335230175, 609036545, 810146284, 46582275, 581023593, 21952840, 81359576, 140144603, 493765094, 176635283, 153254562, 240149086, 671877372, 928210329, 107934482, 881150793, 754092152, 484837211, 237808622, 900220406, 304783190, 566742017, 854125976, 942024070, 656461019, 106175929, 736851041, 54235061, 588399787, 487736298, 535396273, 329790858, 700366727, 90568661, 852078754, 373231696, 867094364, 268344983, 322934849, 902750649, 738428165, 910619984, 873377412, 142317142, 372462598, 844390680, 718946364, 874322975, 41901556, 497400820, 95145666, 681961415, 926777115, 566190520, 611124644, 422313141, 556678698, 523086655, 13050866, 579718133, 891879031, 261253348, 986643486, 575056460, 394778612, 873982211, 329430492, 647788611, 288315328, 701938842, 420832435, 303625693, 50586713, 799482571, 562112518, 589849768, 41875716, 156109981, 124686124, 471400142, 34971416, 974857621, 440136423, 633174627, 325315468, 180615720, 209426902, 318981782, 254844243, 808442832, 113235734, 718371848, 924260927, 561199951, 275329545, 939839617, 156785726, 527016453, 939281770, 379172936, 158215123, 41210161, 938700983, 775618620, 73210455, 494009378, 676568133, 276865050, 382746517, 231962170, 278255486, 111025041, 344258275, 575091263, 837690230, 492754103, 373575920, 892100838, 878215555, 24115421, 427562697, 370288016, 927832316, 884886721, 604593666, 160008729, 850325208, 134499676, 976899457, 960961745, 92845747, 899419780, 640860630, 394746850, 348946577, 269074383, 655951078, 494604910, 164046572, 998382673, 929538924, 666522744, 736476456, 567247928, 882449582, 914669669, 767760870, 285266415, 314580092, 745110221, 450201595, 282447619, 584850688, 869352933, 999987413, 655712162, 468364812, 827620584, 159437645, 368729047, 358326682, 658934881, 394594187, 795814379, 408681609, 855495891, 800806297, 741174998, 670065073, 305955636, 190206394, 173703780, 730208081, 382157764, 63651882, 655578798, 837944621, 111784487, 341212948, 46704431, 131003438, 633868945, 266667857, 448467177, 160616094, 757416452, 649147618, 187989688, 587077298, 937875064, 777077907, 888149495, 139229925, 159405199, 847308215, 910938142, 248555723, 29179168, 470288674, 938016834, 798923045, 935178277, 29421546, 263415634, 734506737, 310054899, 69272446, 332273360, 549486763, 867488125, 479121496, 760555817, 68241226, 823397404, 681639592, 953530713, 144861683, 517798420, 837641790, 974907006, 327631479, 117357216, 106871185, 320167358, 905336424, 106346354, 155929651, 937080970, 736159697, 549316025, 43971800, 566705590, 541640354, 900603669, 699686290, 62630377, 177372744, 169676284, 472349873, 96499450, 248553474, 994005452, 968380593, 940712618, 412278783, 743440524, 835750210, 334527253, 20342606, 155401875, 923665597, 731613215, 317560106, 213611799, 735390417, 410149435, 422529358, 329834688, 112670051, 340435673, 790192055, 55134223, 802008384, 909054168, 249600499, 66907005, 981488680, 645235486, 691137702, 353922680, 987626664, 304625366, 562971898, 167596410, 649345042, 747011362, 973337986, 840395746, 450596308, 748774803, 551720444, 690283968, 842224456, 10252733, 608421240, 205361492, 429338822, 951785618, 373387991, 750512517, 418557082, 514936088, 967049350, 921572623, 597144037, 601768887, 235164417, 537199819, 256310131, 165267910, 229193218, 896412610, 645730102, 650716213, 140694873, 65566759, 24916357, 333964128, 824270077, 848783370, 557076380, 529611746, 401444991, 435302617, 986204650, 323792662, 38957752, 199560507, 923166975, 831724772, 355298035, 705616462, 480588704, 513712363, 702121906, 468035408, 323273270, 744057842, 554808284, 769688273, 93486389, 180971459, 393049855, 830344068, 71407963, 118790415, 945035462, 326202037, 440698909, 99764742, 518477133, 440449970, 444587930, 671824956, 631385835, 492152161, 610046552, 917550245, 573902810, 300644181, 739667493, 268283061, 455004551, 196134774, 742298439, 392128484, 297414653, 183859807, 548516, 188529768, 459702786, 749577167, 537407614, 680434120, 88450122, 990715503, 533770023, 626225277, 710279223, 356212100, 833733307, 819721698, 789240924, 255754162, 949988260, 391506753, 287133179, 707858360, 910663735, 283542174, 958292873, 697329220, 409797669, 270637600, 629356032, 915266202, 372865623, 681113987, 442199607, 499045003, 363478721, 201243836, 737395652, 626373102, 773053503, 897981547, 297915082, 5727708, 426791447, 839525808, 981475512, 29401708, 287707445, 330515474, 389810817, 344509083, 383160458, 747381247, 423613934, 438317896, 787400802, 387771493, 665441594, 791427536, 918769187, 144821513, 683018893, 820005933, 313189978, 353624435, 730163580, 636198083, 655416880, 15064424, 206828529, 310683632, 257816301, 502522935, 608209907, 768129264, 898454435, 396544040, 966394312, 824162411, 929639072, 69786265, 877292100, 142082938, 738848720, 72856639, 115804452, 932548549, 642865545, 252841357, 599449025, 423702935, 973589119, 776610446, 134919056, 340229233, 939594751, 787663059, 474756749, 936929834, 986914357, 564153239, 283137500, 879987214, 145987670, 489318697, 411365301, 142006049, 706546105, 636883660, 870220825, 444866699, 443543987, 981867153, 386265866, 396086233, 764485100, 570823475, 389451544, 722976672, 818200393, 532722896, 309039908, 379224197, 917152441, 851683754, 802700538, 223641275, 39714670, 693409576, 57364905, 595590237, 598545080, 904072631, 475230245, 232855687, 226731419, 473951979, 397017068, 382231625, 257290266, 376304115, 72257691, 307941201, 470170155, 754920410, 902018708, 681282987, 45471501, 629205584, 318032726, 926431404, 41697427, 903728323, 834167252, 383185465, 115621913, 979766354, 115801739, 680633150, 738705412, 201192755, 672438016, 348615200, 565212738, 202256696, 868324008, 133862850, 353733125, 643866704, 18370414, 51841998, 519955620, 17236435, 986147210, 415504259, 511354173, 884129510, 972449429, 783655625, 845547729, 21443584, 11271523, 170584214, 810170483, 155532471, 292507859, 785388437, 726694844, 974741729, 494766513, 957305927, 45185899, 715337575, 772424640, 966281029, 435565576, 538261249, 744679488, 349575902, 378140447, 61665163, 320585369, 795071044, 894766797, 321494873, 577384562, 125176409, 830248894, 716668585, 385379582, 318953710, 668895588, 698708067, 45093555, 230819670, 554412381, 23266775, 142307156, 385416882, 204127645, 739413612, 442095236, 951685826, 46344424, 370891991, 597163266, 718289462, 94516477, 416989609, 860355041, 520006558, 906762935, 980433907, 2953806, 540723287, 180934570, 939155942, 607518925, 777627734, 635923830, 243626607, 521503330, 240605238, 880803470, 502734436, 888766370, 172351340, 385785291, 198474656, 442503231, 826548082, 268387814, 857801941, 256969744, 706610675, 248626074, 145211666, 461696966, 140124981, 508295878, 45392940, 478545751, 668627361, 658746874, 740856137, 355228223, 587197099, 504789345, 17171637, 232726942, 709894651, 297186523, 228197499, 631737587, 743610363, 596257337, 689098768, 138624580, 400192477, 318998240, 417509950, 104914434, 218645533, 401101871, 74933883, 177318483, 412962712, 975873647, 924300881, 152506480, 41243337, 8427535, 274627334, 926698665, 917819895, 998526339, 821241899, 263624098, 495803602, 138548388, 980413567, 890240940, 167180314, 52663651, 436140982, 473153157, 941960640, 423359626, 764791172, 404424325, 510857379, 185591700, 158151061, 736362181, 127452131, 525098655, 837097417, 667108593, 151843922, 683351620, 791189836, 695309954, 411054906, 971431253, 61868127, 375330413, 743412451, 47527239, 686332789, 322039922, 810338633, 6870724, 236093073, 788946649, 67367364, 518346046, 809776940, 797948835, 302317902, 984469129, 538200787, 854088735, 632877014, 575710283, 703375920, 866343125, 767918859, 722165106, 817026827, 899191499, 81551554, 740847134, 935601905, 917811326, 29822371, 973926190, 712670915, 161154193, 896038605, 312889714, 553655752, 956539541, 884681748, 275595789, 233843534, 754753010, 315032916, 632178655, 812382472, 39922068, 363723759, 526131024, 977068307, 464488585, 458635891, 660561485, 177387464, 120039447, 535985295, 156999579, 583812844, 395677026, 570397870, 249186641, 794424333, 410177435, 250731524, 990142670, 826953879, 303162719, 620744188, 234729125, 764051214, 183735407, 619502051, 547852108, 414050508, 934373082, 526520108, 624178123, 915999189, 265626213, 851440527, 660147601, 698428829, 339262550, 722642467, 634862444, 543243842, 703794072, 933631462, 234046224, 745658561, 713386032, 204810393, 767554468, 71907509, 48817019, 734136541, 50147151, 488138529, 509534079, 333336873, 99613132, 54723264, 894230779, 252058704, 373032703, 897081925, 527582410, 417211833, 984748435, 850228300, 331142676, 464451355, 933642228, 773346635, 666096157, 982960354, 882543642, 135553759, 533540763, 781741090, 61225534, 469288286, 440493826, 517643048, 65468625, 732380067, 243113667, 764999779, 125053200, 736301301, 96199397, 364133507, 4450781, 60120378, 341224308, 267753311, 241036920, 627585375, 985421987, 717504119, 515453024, 975565803, 355292930, 248364871, 360461076, 251368266, 735201759, 923328554, 2309426, 395016215, 784977333, 657039950, 991916231, 929584784, 672555496, 715742888, 132369492, 569293243, 356270954, 865136800, 224693740, 458011727, 796289654, 155900925, 8519357, 583934737, 682669590, 258232015, 840347384, 578447707, 35375306, 822949454, 916684583, 433293409, 36926218, 371616097, 110778008, 864898781, 443104745, 999516756, 867950274, 761604710, 267606492, 302344600, 575575042, 667836065, 505280684, 979207251, 245781797, 144546174, 410580185, 243663690, 491770847, 650604891, 941045227, 132508299, 28571, 158635293, 866525451, 848834775, 802706778, 449360589, 338135735, 231042112, 150150982, 550459404, 977310915, 396195960, 8883727, 653892513, 45313044, 862819366, 403018188, 233035308, 557718098, 864125069, 2004442, 17434329, 775963624, 590415378, 677522287, 724617352, 809649217, 793260035, 348615185, 246765031, 79700807, 940268725, 770907343, 3286664, 868735720, 642998347, 889504398, 531051829, 747973614, 323835724, 936062421, 187429212, 1033205, 197842300, 35787873, 948012519, 589646334, 711574652, 645712247, 19100238, 382366386, 13820571, 854490371, 331433093, 915823280, 512312367, 700197827, 199737991, 24131635, 597797360, 27986014, 200130650, 728796701, 861729904, 586600497, 755501960, 131451157, 863740286, 534208253, 648659719, 54920214, 682776548, 255575271, 683736855, 780522864, 60275767, 634347964, 402963632, 396333034, 645755591, 57480503, 107478881, 427219113, 67613595, 808811509, 103222431, 974512662, 703837539, 736419745, 32491020, 611854607, 13959608, 23119530, 264335339, 751222381, 541221733, 985007951, 539534271, 470994454, 302121191, 195882071, 434933157, 126463106, 207525347, 340133511, 599507974, 583639358, 780165249, 613327252, 64048382, 112802488, 704828882, 362986830, 887436891, 348633906, 552863020, 693633573, 556806692, 3846319, 699542794, 330253404, 144383954, 986861569, 550826630, 891017031, 301529651, 541016223, 714619946, 91408249, 698053060, 269371323, 933516619, 872749697, 854844950, 195923454, 791173611, 741602937, 967287295, 910810004, 660441598, 417829860, 790874834, 632461312, 873965499, 358937168, 730511345, 485650835, 530817747, 236525020, 280882397, 33321497, 823783429, 301311415, 137481145, 822092139, 587251522, 905465571, 783915921, 273825027, 114609492, 664568413, 977527436, 988009178, 209774246, 299646829, 692012163, 713573201, 592031655, 626826901, 417914611, 580960404, 207072914, 670167067, 990147613, 69938717, 662684125, 582352859, 851824804, 715308710, 414709272, 495506166, 672636918, 980273535, 26473744, 189372421, 455508047, 613828817, 83763086, 329565566, 904579373, 447904572, 712236628, 849749316, 897206458, 820385285, 701566342, 189143205, 806107350, 152242572, 829134147, 69665472, 602485458, 160210089, 689223750, 174205393, 891002495, 728136373, 3900786, 852266167, 917517007, 111721400, 768727538, 713013951, 140269682, 304747711, 634247828, 282256955, 238203851, 358520987, 165028513, 25199031, 365109062, 656760874, 768725972, 311327180, 658169143, 599457590, 715750401, 116006825, 303810230, 901085351, 488588564, 401602029, 112637217, 690772918, 308165752, 536570955, 454467154, 824096393, 293117048, 379166803, 333592374, 755246086, 502928372, 626250477, 681751505, 432568618, 70409616, 258739053, 79420943, 490977001, 661421523, 244667101, 327675778, 98814801, 462394892, 944660747, 827405407, 894423294, 234399325, 101970584, 231566778, 918187650, 43855675, 785753916, 198055932, 148378378, 738232577, 951206530, 381239151, 264360358, 223941436, 572224711, 497361535, 94105441, 46692003, 931013607, 842551411, 189123114, 104925172, 632074680, 116911487, 546406183, 233545818, 317443359, 96983420, 892690061, 486207614, 262800917, 992578957, 167665621, 117809048, 772146214, 201453585, 639543668, 972950127, 242124681, 730849538, 63340822, 548168157, 299219150, 934370154, 868104750, 381873578, 485700711, 59092731, 978638559, 422061210, 958701510, 823526955, 986647815, 314722827, 572945779, 115368349, 874133232, 591704348, 975621166, 641410119, 951072680, 591539065, 144340669, 278259540, 172790234, 933728412, 206321349, 165641216, 142527321, 319221274, 657725280, 280642408, 719043708, 267092135, 879252376, 118183836, 182895990, 176584234, 760022847, 675493331, 163775723, 108110886, 802622893, 559803244, 134654272, 136521738, 207906049, 808671649, 462679058, 217042353, 646611630, 126981918, 197711920, 967936415, 138549299, 680291748, 631768974, 734909849, 324971136, 271417577, 378743203, 789329473, 246308885, 633563768, 539376783, 653315235, 917406392, 369173862, 895795659, 139550965, 342543240, 412345098, 902498078, 695297872, 219107470, 465371977, 796195307, 92803923, 743984516, 616410550, 515861028, 482189830, 965954935, 915438887, 224443501, 857512810, 476866789, 222239173, 738335177, 678277758, 803007150, 658712861, 975350962, 924044086, 888079972, 724097327, 566662293, 65892535, 104641818, 186838490, 496395123, 606699671, 327874928, 39361650, 924777502, 344939246, 479951595, 258530224, 728741493, 683599518, 491410061, 211561803, 665076778, 261209502, 452261478, 221382608, 876632164, 27160114, 575718665, 544672692, 57667910, 639296812, 318073699, 859650259, 97929498, 363328397, 714638604, 396273718, 812122515, 961001500, 893066154, 807236336, 740598163, 241197519, 223296929, 303779055, 889491355, 867280602, 566711812, 465852656, 785034397, 238292205, 46750275, 516558056, 422420402, 234543617, 984184828, 581988633, 165238433, 855738316, 195695231, 265507328, 589548877, 861838642, 30675230, 758425528, 235436160, 833182299, 466218756, 376200098, 173227373, 456921955, 604965532, 729276826, 128235331, 652415297, 431240187, 172105802, 936083879, 551192611, 162006354, 521097382, 214708841, 883916181, 376679524, 623459056, 532270886, 241578741, 224854724, 686068017, 306228365, 805173657, 283121644, 264562577, 787836528, 263944837, 242778525, 940561570, 486213788, 641266304, 574560413, 44903610, 38522276, 504130494, 424779933, 539114519, 506491503, 733129487, 439114251, 353770686, 950663498, 793648107, 662269780, 199332720, 856290557, 156344505, 248026126, 287427261, 503377680, 840950406, 579959932, 810650601, 582332964, 948208151, 850001432, 995848497, 482120310, 648523442, 82890048, 322837381, 497248018, 468517731, 66990765, 827638417, 502264550, 491206066, 133609022, 510508905, 760451419, 940962923, 654071948, 757382840, 585895073, 565933701, 153411708, 950722290, 868719816, 157192890, 864328802, 821826310, 765704186, 889350741, 912559440, 338038860, 273759659, 504344594, 220536665, 269722960, 996855146, 81817650, 265177024, 646877419, 785030908, 787506090, 391445163, 337690445, 68847021, 103298011, 392531088, 300984381, 938016065, 408032841, 418803805, 776647295, 698081175, 878060154, 71872640, 985648074, 755947255, 857093368, 887019191, 311662079, 97349426, 962581867, 818028111, 902788031, 39472217, 191807627, 688032629, 624814797, 749395865, 673439355, 701275763, 491608905, 882560528, 175366154, 191121468, 632742873, 519148304, 830860181, 577634599, 518457089, 882439052, 442068133, 131284712, 568203192, 410489024, 18563745, 320846091, 938762211, 578168213, 87060032, 217924663, 556633474, 607429517, 865132889, 839951857, 378126078, 42205838, 446637285, 49217985, 589925895, 9402569, 51955289, 640400857, 18199924, 823322795, 979899298, 807663839, 341635417, 359953369, 716338052, 299727264, 861797254, 254879796, 402923552, 948922907, 404181328, 222451859, 470577132, 501571558, 285773158, 713975926, 354494373, 739499225, 373351161, 589193043, 876023831, 186191559, 75312303, 756102844, 479205690, 940909298, 114808531, 858247407, 107282644, 554029400, 811003265, 360211944, 189098629, 961460584, 868265000, 395354127, 909909522, 645567913, 965222996, 651089205, 603087967, 198524170, 399166620, 883154415, 603970334, 455762192, 174465339, 75978697, 830792279, 774748870, 309468384, 426487161, 484618446, 323447425, 731113591, 841549650, 372536679, 260291495, 85784209, 672666681, 9227140, 181212291, 511943037, 185217712, 775229305, 596941962, 420946651, 447170954, 1214032, 863166770, 218585941, 728559602, 721822716, 577783901, 951160197, 875417910, 803798671, 462011548, 671228441, 674057902, 21504358, 93834224, 78690437, 65685607, 444446141, 619267941, 755222179, 179119010, 429543416, 67577373, 848216391, 427059738, 486231829, 305013416, 83006600, 585505409, 283140404, 695823503, 308906176, 766318095, 81355124, 830562290, 439472500, 985287122, 359511875, 651568008, 692784234, 84060384, 139889591, 608114740, 137715341, 323522972, 573294442, 194436349, 809515458, 471415897, 259773664, 548122984, 563571412, 426800738, 968310895, 689200048, 44059603, 245764250, 843203523, 498597253, 209214866, 678005496, 897189231, 2996537, 861649671, 227922131, 13652899, 907825796, 360986364, 459436364, 459538426, 657073525, 916003250, 470254972, 812324268, 923463329, 345049308, 316903917, 713505453, 948631828, 881029926, 785742149, 777009521, 411155639, 20959408, 332201409, 672251044, 629326219, 773747277, 144275912, 826292400, 150122300, 901013258, 463688414, 237034879, 50137825, 290196109, 763630124, 134185440, 60152924, 780044432, 498824723, 558917478, 560606960, 805008796, 689775160, 768819962, 13595459, 826325775, 27134720, 586803355, 495110770, 282347252, 833431923, 207719104, 803952891, 816099364, 708521992, 984053951, 277312206, 723891331, 839705384, 329215973, 303133544, 495436786, 414572490, 35984932, 156158560, 446429733, 33059203, 126543078, 202457962, 976503547, 570374430, 515924965, 484596470, 720831143, 611636108, 40159194, 499147312, 145817639, 478700480, 697803506, 928746790, 451931495, 342287087, 874494029, 840882699, 104916742, 354896902, 726346800, 308411967, 228034001, 584881594, 274982426, 930893257, 174714937, 600100973, 944240602, 218579482, 829845858, 246584823, 142607414, 534194140, 15342838, 73125510, 214809406, 156211340, 411915034, 509769135, 132332340, 497498829, 508167110, 930668906, 279897501, 99567906, 85554798, 144297004, 922178109, 155670029, 393158497, 223251640, 561267642, 16475107, 151595692, 823723603, 421497189, 688930055, 458432731, 866230219, 590385539, 416661102, 586776467, 95668111, 556846596, 36738000, 779530449, 368423455, 157000028, 627809633, 737511704, 687479804, 820439524, 931626988, 938475980, 851045967, 476621729, 143736232, 841670097, 420602491, 319972937, 153780090, 156134056, 639852256, 442827306, 157961544, 720470361, 349742471, 335457751, 945852299, 184094003, 752838650, 964772110, 334186471, 991174982, 610963861, 136336781, 422352230, 220824678, 609195373, 960742284, 194327062, 129143983, 420278297, 733080771, 902844434, 845342833, 972690183, 306324723, 245518751, 479253207, 19220523, 340512650, 854867294, 635075915, 443072379, 919848799, 862296608, 790784746, 272019919, 31378977, 353335427, 404372306, 790068689, 515672002, 739244485, 205505193, 875423966, 639007552, 585587935, 821791985, 668874980, 138004758, 553731166, 209605390, 611662643, 190312675, 869215888, 123960063, 309048359, 487202987, 218919608, 838357810, 402482224, 194101767, 429888609, 269021432, 646648373, 457962556, 612692721, 457548088, 639510284, 595806135, 988756581, 997936510, 562195843, 308655512, 804103815, 892033907, 86631806, 113925496, 924484140, 570449230, 724896128, 947603473, 325847297, 165233429, 856598665, 483905104, 963514464, 608896442, 765493949, 739944403, 381323353, 869312494, 755736026, 428295987, 69818181, 617563994, 746830690, 667790273, 139081391, 54078555, 591002933, 916399350, 167339303, 388011086, 846561942, 758516478, 507003081, 605589740, 121790954, 388955828, 742888143, 938205332, 331957150, 420894002, 90056319, 781204243, 749203720, 702918115, 669106878, 249120911, 524738900, 993525317, 916314924, 526232231, 228089903, 131551694, 292187958, 829136305, 367968275, 877484339, 490845088, 987113150, 435463584, 692251837, 648542073, 961123481, 610097871, 212313583, 404738416, 324109101, 178690794, 540273877, 135806392, 676101213, 212384476, 954132631, 743609220, 549905995, 812701406, 706083556, 389165339, 565272414, 729485426, 810549049, 627329519, 816678318, 232138402, 630674656, 609664812, 526735737, 661746260, 183181873, 763415854, 592017192, 657455745, 435898378, 479067469, 450774290, 712403827, 985911669, 818397620, 186265856, 894833876, 258899695, 315387536, 355507107, 26778889, 755184670, 194548400, 921984912, 985503765, 114631173, 840267933, 244061779, 909112290, 271141549, 787830461, 978419036, 748394529, 340027747, 588291188, 309820230, 41933467, 423990977, 745196118, 899624760, 392472157, 802071805, 700608614, 863210756, 345258718, 47131047, 368429509, 349974629, 714938013, 76336221, 573158049, 683216985, 213291593, 990225597, 23381966, 246294691, 445671047, 261727553, 840381568, 685958302, 233461311, 194947952, 766087546, 738097752, 693856512, 135862882, 256796392, 298651124, 893505640, 736199930, 387043108, 91455877, 750921753, 634059429, 969275498, 130838342, 36707709, 429185070, 543016179, 682048825, 947935900, 494600072, 176283154, 269370489, 966814936, 397369980, 174217529, 756898921, 356602715, 72937080, 795298723, 575555341, 825652515, 591205405, 500739385, 583871625, 35547225, 855864568, 130215060, 114131863, 203721318, 716792041, 433101509, 240828093, 6418913, 784850963, 782967192, 977522208, 269210578, 38268977, 979966220, 896122387, 398437839, 900691390, 727092678, 337175215, 485197110, 975064890, 583749866, 148848258, 378454244, 98273707, 228408089, 368382280, 615271028, 320255635, 957490267, 401924968, 796399327, 211546080, 337485629, 698088896, 665129138, 775234900, 461073233, 76516813, 845707792, 484061456, 472173217, 204438162, 98410739, 446283151, 982110347, 419520888, 604225516, 315299977, 661753267, 544132020, 817275158, 879694198, 885508810, 53247995, 755812685, 238987902, 908971429, 827793091, 660975170, 202528576, 945223726, 869140498, 57444205, 539895140, 958777387, 819391002, 531560687, 637148019, 727103969, 19236920, 674033178, 360133055, 143183099, 22094709, 875785180, 610102879, 73913731, 118376867, 983625335, 941191445, 30892722, 814053817, 494150182, 245341334, 727816574, 661105814, 417475080, 520531307, 233635370, 204877286, 25610172, 95273452, 829105447, 221359347, 894430681, 178051261, 412065680, 546096387, 578929042, 820577769, 771306994, 90340602, 460567688, 604842026, 465178317, 256280509, 481146853, 830232742, 478077236, 370269807, 506443104, 468250310, 348558761, 817847916, 449593176, 328804766, 98188850, 964824433, 720405385, 475044761, 111280122, 928309823, 501153971, 864126343, 376485412, 940671640, 864974178, 894878795, 116176387, 417080720, 113862942, 928251942, 643545473, 460136312, 218179630, 503634709, 932562702, 939088521, 830724927, 280664586, 63338828, 736445581, 484616020, 646161747, 557056383, 904037677, 550796419, 868899511, 167455145, 365007358, 27748118, 467922008, 993502044, 905878162, 956740759, 326699414, 105585231, 40366327, 215439328, 703028119, 976313109, 172650779, 174207368, 244768672, 712385426, 865607337, 746979982, 120920379, 290713452, 586183197, 225063065, 951894381, 397760393, 187451105, 46362180, 232048252, 229000716, 13203017, 92093894, 392905255, 289658519, 727998519, 159909748, 567169759, 13968536, 926918310, 989984203, 256791981, 70232327, 83930526, 627150373, 655786804, 705053130, 981421637, 362624669, 775403918, 456051578, 137183463, 752333651, 76411763, 955346277, 374538514, 94723344, 203453566, 260776050, 45164340, 989606165, 990066607, 869331713, 390657432, 605730223, 234786867, 105282183, 331722582, 838019868, 592199856, 784413466, 765929060, 361590626, 563576414, 491952352, 606098915, 571988083, 724066651, 797031934, 433868933, 889978136, 3740158, 241092564, 918101973, 855667449, 253793441, 98516491, 941177252, 427025635, 961955849, 368088615, 969559415, 925459460, 299196456, 499201476, 947777149, 476027201, 562292745, 172063328, 60822103, 148040962, 745788157, 922865091, 8736677, 530792665, 532207865, 31454776, 722561466, 493450474, 315504622, 31330447, 559597326, 535420889, 730605636, 923912629, 427351535, 405706243, 330607502, 385463584, 206224813, 431795342, 427814970, 513637648, 714622640, 751021931, 784138777, 275965851, 300700757, 433080224, 395244469, 3203085, 904903799, 828975705, 646502783, 296126447, 207422254, 290531986, 609961023, 159995396, 304952090, 869834991, 21072867, 232027123, 421133205, 525391298, 984305422, 899856450, 10176604, 397831859, 202291525, 136671467, 966873606, 980298902, 658838520, 617960420, 399757329, 348756299, 160156747, 557349883, 188360680, 253963159, 654369772, 291561738, 807530580, 647120352, 940945620, 146232823, 362315359, 444061697, 254187034, 155827682, 391224177, 853946010, 202428371, 170057406, 945506609, 607390444, 985293418, 959943500, 525278344, 313700588, 235900399, 273477597, 663931269, 358119449, 164789575, 246944344, 761488075, 813905682, 738276703, 168574566, 88073812, 382180156, 109197420, 261169786, 830453096, 405545576, 329166320, 217839288, 656479365, 582531226, 588431828, 490349825, 71693978, 586138276, 766809160, 646025791, 280620397, 833218458, 523508684, 827335102, 693197142, 870009581, 529046613, 196331747, 383528346, 544834974, 537805312, 646432623, 879623486, 295431168, 44274024, 758050553, 152487703, 589568489, 154825374, 808188609, 122459491, 528302362, 329368716, 27588140, 25633832, 877586692, 98780864, 279280539, 819083158, 24882101, 999288491, 598912293, 489178043, 391399475, 312270942, 74649383, 347763528, 938744035, 381640494, 368009676, 760181536, 500758644, 42719077, 628002795, 285717859, 487221622, 413849474, 611015618, 584022284, 170141755, 720648443, 728449528, 579555239, 827999454, 875136622, 201221094, 848233781, 567678604, 144663451, 202907419, 104071190, 871801939, 318194688, 572659247, 129848147, 836621256, 922839407, 207432776, 294354079, 291332146, 476602520, 378595983, 57545498, 82193031, 289668784, 760600873, 666218442, 377130017, 883957242, 653578161, 1647676, 115623600, 236495073, 226370460, 489953224, 166163911, 118094197, 828194210, 211781231, 315695561, 830973497, 508803786, 309806472, 486008701, 364773600, 402868303, 110777649, 657183034, 997222297, 908758506, 328261981, 365232892, 665568744, 450531106, 341283395, 664585389, 555566405, 547902459, 38642464, 821310273, 204431783, 765796094, 130026525, 294338260, 957513565, 394499137, 266877940, 186420553, 617863520, 346863131, 941114559, 705616854, 719122035, 672271246, 651706572, 249768635, 696751771, 142145810, 964735066, 457406387, 44661497, 605734541, 929083910, 287490812, 350775195, 18739222, 131716571, 230630758, 145354382, 839782885, 490977296, 456586963, 861411270, 305722518, 37962981, 156475344, 221458670, 766048554, 848411581, 496637429, 314390163, 711768513, 102403714, 600105657, 78450262, 35707987, 623833127, 963842918, 345018465, 509429786, 129539154, 792952529, 127132559, 26662355, 455711666, 852704875, 164666155, 510559466, 529251504, 878705011, 435374518, 811535661, 441143325, 732364584, 347075991, 47050634, 361775228, 89084076, 498264545, 181651592, 728768964, 999225640, 320191229, 845910352, 183946213, 892274777, 65482709, 231472670, 144878971, 767792088, 805621349, 737215567, 238119639, 742408426, 421000551, 167595067, 126126411, 108319283, 537691449, 888403757, 244641686, 307794341, 340463455, 632044921, 953839113, 184498092, 297179566, 162058523, 104598399, 965556320, 715437585, 679174262, 355740634, 254513746, 86172291, 595199694, 988813542, 772965451, 416447995, 826060045, 510546882, 786082395, 679950210, 308695922, 193776518, 82431367, 633775934, 179497703, 95115129, 383974177, 511034507, 172596534, 452035752, 783923123, 633466045, 788353239, 393199503, 203918902, 711227041, 125168036, 342362554, 250839269, 323730851, 639852696, 756868555, 353425892, 644511997, 492878588, 75720384, 413632502, 89139121, 405880926, 530284957, 900372595, 426373571, 420947274, 337866010, 796618215, 35990225, 610340542, 311329557, 736555173, 188831610, 252294627, 422313146, 203873926, 619022631, 753158670, 196554751, 315596929, 244120493, 670059109, 140142235, 941742173, 288735438, 124838702, 777310502, 198706258, 114897665, 268320718, 851723141, 626396278, 786425505, 596599253, 859220661, 449416811, 121657371, 940207383, 657191475, 665576490, 819862701, 153179565, 777413453, 942247696, 681813035, 719413741, 789483856, 361239382, 336843744, 672313498, 92650332, 536075261, 70264601, 223421355, 935574783, 101747991, 10292539, 238693040, 978870666, 449576484, 159375671, 915770409, 553067817, 520115348, 528350598, 501223195, 226796676, 56964605, 880694865, 16466931, 76594648, 888521246, 909814336, 842705424, 791805596, 805198888, 44642755, 826104302, 524145768, 879356022, 715668090, 573158940, 729554794, 597301258, 704787865, 135733115, 399206704, 210667498, 162330633, 601115353, 287878856, 254386439, 88635107, 980677802, 349872532, 548635761, 562347529, 512676348, 394399735, 327449133, 342115935, 147315562, 503546953, 709673624, 87936402, 598066504, 53241165, 234737896, 579182432, 788865721, 482091096, 225065861, 52180996, 188382726, 535454442, 701173620, 148253590, 588083971, 41004872, 773473421, 309361354, 617736971, 200496594, 260768950, 73977232, 383384272, 582441206, 663953883, 876353875, 329705420, 600223673, 956017622, 693856765, 888633700, 524915951, 559474386, 786871105, 969999727, 746930408, 905837493, 385188507, 817004544, 398863639, 889864473, 725940948, 186756563, 40470978, 520258307, 501415978, 831830954, 348663770, 130888583, 257232170, 35236693, 561656942, 605504867, 803524734, 750634195, 742339898, 59939643, 261188546, 478253392, 984519561, 21263721, 537851574, 662902310, 954593291, 395896564, 467753168, 621630776, 213631601, 230292760, 695975708, 179620525, 555550258, 812499507, 231427888, 427888816, 503721163, 111267104, 300826760, 264125025, 64928301, 81196437, 939132416, 49275071, 896718132, 296934019, 226161336, 225343800, 772782014, 620771543, 298453554, 511796488, 97526131, 704464393, 79470198, 562723084, 108357606, 448379129, 97635271, 734676682, 256012633, 807351461, 146604878, 376584893, 756187189, 460170281, 451546026, 657575207, 342614588, 359197161, 726499170, 465371845, 93581224, 517433164, 64764919, 349939608, 581729941, 48984769, 494632449, 380190103, 129662997, 683131443, 226947247, 524308283, 760009698, 794239997, 585056177, 42276573, 577580866, 972073877, 713217391, 292268650, 184545483, 976321380, 145837321, 558052041, 245368978, 415640456, 373504470, 952609944, 704308756, 624591643, 733976719, 118870935, 818350419, 486180463, 995531862, 400260590, 536425844, 597552165, 753314809, 42833233, 171036114, 720494421, 403905325, 764085371, 503377825, 184730881, 571762762, 82181558, 146902232, 840952922, 660822442, 336288803, 141527142, 195837653, 437123491, 493196048, 935069391, 130758527, 845473750, 406479597, 242228660, 345826272, 506450928, 633168504, 399307066, 945116859, 794031683, 244016853, 91154194, 684563105, 348594196, 349043083, 915969950, 566980416, 303965706, 971907060, 524621544, 245701360, 371848067, 996921036, 419212595, 371043397, 77741959, 406220437, 942261342, 666530945, 965762640, 968636195, 434351383, 27560907, 723181632, 751286062, 649151030, 237833228, 632761262, 70589986, 142072030, 673116646, 912099896, 912242861, 146999110, 680656166, 643232486, 174811174, 946229059, 155896823, 185330913, 281798243, 739807974, 499087138, 620768779, 323137584, 347130478, 928362113, 921836708, 933170794, 149952220, 103518966, 690155118, 999148224, 446740609, 246119149, 417224192, 525285663, 253091070, 95744066, 82024519, 193744269, 286892746, 430973408, 70460284, 938913526, 440233899, 616427779, 79671524, 784117275, 195547832, 307343774, 772811271, 490630401, 764366510, 654364009, 212650288, 966806464, 874331028, 568519039, 68884525, 823515629, 521053124, 681555922, 338235523, 102670043, 962787112, 514881252, 9122302, 592468123, 937705620, 695154844, 814528449, 84310697, 723106938, 227876971, 709414554, 926887439, 192187954, 554136072, 511093124, 304865447, 114849029, 650895258, 766448429, 22820462, 368190350, 460645455, 541431057, 992420210, 836469749, 242624956, 965532343, 798833453, 879904573, 168024411, 945191438, 123499270, 495623216, 286159565, 791888260, 537041612, 936312723, 762239578, 89666837, 699462027, 866582432, 589754961, 387880654, 847925493, 215145758, 839179365, 901847903, 485200013, 664954320, 220760960, 561552967, 101892166, 459574428, 248029199, 643246828, 468860374, 456984645, 425035481, 695023792, 574189170, 98876981, 645605663, 768474307, 767038071, 639674404, 485746213, 826534811, 25910224, 353789791, 979780595, 759648178, 488542057, 402746202, 77396820, 553053275, 944621772, 292061160, 758102691, 678500459, 634596329, 78031952, 582045212, 974237878, 473791914, 557411475, 765428986, 932680199, 259500609, 463665729, 489253871, 852119735, 336666804, 331698239, 193949284, 545591677, 206909299, 997975962, 75458162, 326209406, 497220079, 19941829, 997810279, 252367904, 589013235, 671958385, 755515497, 169210879, 599053146, 799049572, 915555884, 189453353, 296179117, 795219611, 687959375, 229741478, 43760774, 988248303, 550058119, 853629867, 766468204, 547263297, 969984443, 172844548, 824339540, 622948953, 75993029, 353989796, 556090888, 701637991, 962287295, 923252794, 142719324, 938036525, 152388933, 636087264, 60171971, 516868893, 248192003, 649281884, 316498280, 511282699, 756964367, 563404755, 220967041, 873783543, 23719614, 806273289, 47413234, 188091079, 534405061, 197970199, 112904424, 643188253, 700865797, 90386692, 42142244, 202634000, 754126081, 767036323, 570711040, 847985596, 314424649, 436607327, 667805977, 816935376, 855396814, 479655268, 731981566, 590787725, 602556333, 154484445, 524715181, 175192658, 396235899, 795403213, 190076290, 248282413, 834933363, 683423440, 273631538, 79181252, 262851790, 763277840, 329686882, 385813976, 317970077, 96608043, 422506134, 472445136, 357846189, 288439650, 110278718, 426040678, 462880863, 312975291, 737515195, 412562991, 297037287, 236377336, 934374989, 599958605, 327622066, 501018163, 756005002, 344663053, 748789924, 629637653, 88155471, 536067612, 319014641, 495197772, 973432057, 320675749, 231253553, 178911391, 572036278, 124559511, 660686810, 229214437, 794365829, 933533804, 454862324, 950346348, 240476783, 850326949, 94878577, 77782967, 207981467, 503432235, 265424498, 886528129, 529748111, 638852982, 716676491, 609253987, 394483043, 731474381, 824518386, 24088349, 82556343, 606708333, 44925018, 609283278, 264886369, 745973740, 523058977, 750720709, 510430436, 135387028, 81351068, 576787735, 375765069, 719944927, 804019145, 787838671, 455825472, 163454213, 573366804, 288332444, 126460731, 17668332, 616362602, 517706548, 66480584, 729780513, 454634590, 432606150, 139014689, 914623429, 613435823, 914497541, 866906546, 357962883, 164257201, 755397417, 455733096, 533762374, 308562115, 710732214, 990927451, 682845334, 237388170, 606329853, 101442043, 13665647, 835817340, 695920468, 867218579, 310035251, 275066093, 641337972, 723257256, 596390829, 665710002, 268581381, 343924876, 20053565, 908365656, 271540213, 134575266, 481247035, 759057235, 590999710, 992788416, 980383442, 428348374, 571063379, 811004486, 846682704, 885047808, 293898282, 11390509, 750630170, 618898402, 936616730, 951805620, 194268412, 576660706, 109054866, 658672852, 388668316, 359370007, 771176896, 555674783, 723442919, 939515714, 651520475, 713659544, 673600689, 406972716, 93823903, 852388724, 453766552, 962297407, 772480268, 637940156, 960503960, 116513923, 43063146, 15140751, 265916738, 120082153, 346414817, 965221406, 413015316, 193572114, 631549970, 707012349, 237244079, 76411433, 823906280, 38362616, 102574336, 279743251, 377799032, 192474875, 746116863, 107033567, 38824406, 89754655, 485957085, 942439112, 216770385, 267937173, 665200680, 969045118, 582451695, 211950022, 24490432, 151934503, 354572998, 212461365, 307272199, 534960009, 69080170, 939767768, 35582542, 374806270, 213319489, 324709376, 258431568, 120659585, 771949356, 776021694, 159611778, 864668561, 315080963, 764386790, 959083855, 369715511, 413873863, 4988167, 57357418, 605484214, 883354161, 625649557, 474523056, 976377730, 849027277, 694563410, 755994735, 256883118, 15073097, 8119853, 273956952, 248715939, 914019991, 358927914, 75451484, 668447844, 19446661, 669249360, 269974589, 843217147, 21364110, 364318001, 836845411, 938061191, 750897948, 932168516, 579612357, 208801957, 568844553, 389164413, 370678771, 209215695, 190740457, 356132789, 890083642, 896637215, 132438091, 209873093, 93590584, 610363622, 260733610, 260279358, 736514908, 424002582, 517807930, 712711944, 716040802, 357426672, 30517873, 773589581, 440967496, 885803099, 78224707, 342160883, 191393114, 12744209, 62644619, 417176220, 554005424, 741341247, 605929879, 404306359, 439970388, 350687858, 493110795, 857951985, 333718292, 630849200, 816989938, 386876757, 823387306, 132005449, 390875215, 858497772, 863999777, 611183136, 958391480, 461266904, 219852985, 973412067, 246671066, 676886066, 893684533, 765694398, 492928034, 553869289, 222980624, 421541886, 352688865, 521596834, 357034077, 119275144, 572686426, 839927273, 185929253, 958948314, 982617138, 800167567, 133358712, 254294060, 877224292, 515051640, 448871828, 673812777, 620438773, 542089371, 909628159, 753878580, 614758974, 208301724, 571588510, 971656777, 186100232, 518951933, 812869148, 523370255, 711955582, 344675862, 79518540, 468254994, 140700931, 381835703, 31558434, 22209770, 728040988, 221664480, 787756727, 279447649, 436479336, 412747411, 142359612, 584748276, 743397487, 736645167, 755802217, 300120197, 902622643, 459807449, 956372599, 344138612, 686534807, 790866239, 401344463, 502701890, 314859541, 53729575, 925520309, 291682417, 492809880, 204348785, 416833065, 459870761, 33515685, 166487570, 19365417, 146639693, 605503550, 661864305, 114476099, 242590113, 889876758, 729763446, 520723650, 439563552, 563993082, 670607306, 264158010, 923386590, 836358091, 244275828, 544798027, 626548352, 242364337, 851973233, 610442018, 391341283, 998057958, 878262624, 809973852, 553326442, 110293870, 955249624, 385066801, 732001235, 286033773, 793022914, 774610369, 723980998, 20323183, 119617037, 393546941, 624107327, 105567038, 466054010, 318638979, 11369871, 758236208, 769003419, 451878352, 532831357, 534658495, 82372170, 343891330, 43494474, 219754506, 511580298, 383332126, 909408897, 73828400, 6014270, 402114408, 356638015, 766050445, 339465327, 170955488, 76053828, 734053867, 12105407, 385871893, 182736071, 548130614, 867115895, 712129836, 883692619, 77092070, 220370463, 813625737, 526290171, 703719405, 293963406, 577311609, 927993598, 768150151, 930990255, 553647864, 801934301, 846458636, 242731955, 932317446, 421506457, 402054767, 268410970, 646770416, 404159641, 954466995, 811184085, 858626582, 806799156, 881170554, 996708128, 949941295, 481981515, 494599271, 247207184, 730086065, 698959285, 257820765, 35900178, 234775518, 153377492, 32475925, 279822326, 789554599, 941217230, 376935294, 951767317, 761758417, 917027500, 544331061, 262561569, 870019770, 861569960, 167896325, 626791303, 837772516, 594192851, 812750466, 549419015, 561283653, 810821146, 612481856, 835078104, 683553141, 617740966, 800649966, 314667916, 352589862, 699973046, 114294616, 252702378, 500990675, 319824131, 167551006, 861660572, 393135139, 557971989, 425161293, 404093325, 790051163, 270324891, 141123993, 172949718, 550269600, 513825668, 394238329, 87725818, 192187716, 283375538, 336942843, 241038523, 94974419, 757116685, 393428259, 162043830, 77371815, 266614259, 6743929, 319186633, 213407006, 632724055, 908467695, 203376461, 570880986, 981773919, 644326067, 253830074, 415531774, 903840835, 246406600, 953799185, 456240713, 337402123, 56000937, 579193089, 904570904, 414173568, 958563681, 363602055, 2164731, 135795408, 453856071, 509578215, 688486220, 332064147, 781367109, 683076316, 218580001, 495427313, 672383662, 359955530, 563128636, 69495845, 792272059, 668778468, 410477769, 173105638, 809381626, 35287989, 464655857, 996237705, 411442680, 908399655, 824991396, 129340095, 140524978, 250232014, 416620966, 94631339, 972118919, 186101268, 245878220, 801630636, 134276121, 865865787, 726340566, 741607491, 170500530, 706823714, 279968209, 85537475, 564240870, 369713357, 905828770, 971382943, 671228707, 235093430, 770117510, 724307492, 17140384, 287334088, 452262686, 158132297, 700867219, 97303302, 365560986, 773973440, 502886026, 531495646, 56014939, 25797763, 761770470, 741408119, 532419164, 434063051, 458418058, 185813005, 465999830, 781794499, 234874325, 453936142, 368535453, 768557825, 481300034, 394603789, 692498346, 279030223, 97136930, 192983339, 538062366, 822396680, 880979377, 368433105, 18130729, 97355057, 563959540, 161244507, 672241841, 186563584, 94012273, 499117293, 3755627, 991924074, 790438338, 334395600, 803810764, 78302886, 659232628, 954927313, 531522002, 769829767, 650214972, 969944878, 55341505, 691612446, 377961357, 666158751, 782949148, 295436172, 835721557, 663822634, 122413277, 648917155, 544817470, 837498189, 291858842, 728209220, 963017389, 805145284, 612199141, 896388537, 237947134, 716858242, 149830556, 879655180, 7314325, 271136921, 920807226, 78479492, 428582138, 722056450, 238712899, 429522724, 868710428, 496794670, 85397854, 536658321, 204843430, 607998335, 615601676, 163097600, 538963611, 703287293, 329388504, 540207813, 259319717, 345358749, 612393295, 992420049, 979680874, 952448214, 593799281, 150223085, 594513139, 616237529, 547188876, 166318634, 135214010, 563755265, 797103550, 926236411, 392041294, 686443788, 807552175, 556287120, 932467503, 397763485, 465586734, 567488372, 834322455, 302856937, 944490155, 779277765, 638004155, 201232987, 481601184, 617664413, 739535614, 402743881, 212387316, 141918141, 513405022, 476466727, 81212599, 972144887, 599299363, 103672444, 893197011, 661667114, 932712689, 935829337, 613916152, 919474477, 213373789, 164407478, 196179315, 89281607, 61047192, 199398300, 572314739, 34187536, 928252689, 769982493, 103393591, 412165972, 733361116, 148144781, 482284203, 792555144, 641951682, 210335376, 244764735, 536959971, 116886950, 941910233, 744930012, 253363761, 711803765, 3812274, 980638613, 861100579, 781440299, 592669285, 150505016, 858541879, 559964073, 114251778, 622019250, 510664597, 506055165, 444856138, 350859408, 384226809, 861578131, 381899288, 711483852, 227862067, 492008216, 744090217, 536761016, 470568510, 360268399, 816891849, 344968740, 63815655, 396176650, 229308948, 351095553, 972294527, 934016274, 182329042, 223383880, 474050689, 15010221, 668541377, 551649169, 357838479, 666279908, 621218112, 403444917, 79100994, 280949424, 986391168, 855347949, 680490673, 81718059, 216739368, 169789442, 914761158, 657997621, 257188399, 77784167, 715576687, 956239672, 798606502, 280310007, 91516596, 662650218, 34072220, 332170095, 855301205, 467104762, 350920523, 746174557, 661374170, 79997525, 567248490, 83000674, 192661591, 723559741, 692260599, 235039079, 394023715, 959191306, 928286561, 98879202, 697282526, 905722381, 257985830, 808747683, 169154107, 775587405, 846898217, 180699403, 118663467, 611163338, 956183982, 683540401, 543555861, 658148064, 288224962, 271166223, 222740197, 844930967, 583585293, 354305017, 264649324, 649600300, 663885723, 915876394, 315573036, 995994636, 871258283, 167302596, 284302591, 570096435, 198262695, 274495315, 888282225, 497406325, 231533681, 379576058, 655139385, 403381457, 394395164, 730240357, 801396435, 429681842, 769612911, 826108676, 141329675, 124609822, 485828135, 468858888, 911698971, 211899236, 710056950, 254476926, 556327928, 573975295, 371466630, 538220576, 529848912, 441333935, 129469760, 226060768, 245915856, 913342238, 225165335, 812276339, 323936924, 481345501, 694726923, 764581144, 990484020, 574046136, 672222339, 381674286, 982767512, 216551663, 823271320, 137758444, 980871983, 35588001, 75185670, 235058401, 675712465, 951485956, 249654745, 678865793, 400877398, 100813129, 866491365, 610838816, 403595709, 589997690, 830065176, 602640537, 391900681, 553055943, 228660326, 962002042, 994936256, 339057509, 588958545, 381858532, 549427073, 225409759, 47054635, 206457532, 451948127, 967312456, 833311280, 152849865, 533588390, 411038262, 125776895, 905078180, 778614689, 572311941, 479470195, 658436937, 990736134, 255226296, 855266497, 855567084, 444650629, 436241246, 699549995, 405264472, 47260075, 425868394, 887970297, 691784872, 698225020, 100292261, 598049520, 265286019, 739211195, 509292740, 398669086, 123550193, 4177009, 867275200, 920186962, 560812821, 702761413, 876343679, 972205359, 837216242, 846851276, 694933335, 851849446, 955444944, 169424751, 500715230, 58012409, 320884628, 207640796, 434421872, 609626927, 454023095, 592169346, 817616734, 186711111, 146672690, 171453417, 588532766, 536759112, 61396729, 997946843, 180328256, 949298727, 182456913, 84016071, 216091642, 785048368, 631961788, 834265928, 718668046, 913060499, 850162321, 184484305, 571641784, 637494710, 25271895, 872845558, 211635177, 1914711, 873051685, 520647111, 829501934, 725648009, 498123168, 285093185, 160613809, 142240100, 595106355, 148758458, 522282517, 542821751, 35028109, 416650672, 876223688, 737037378, 710863780, 471437476, 379901473, 911576921, 526278489, 561503705, 5493218, 330749883, 602920612, 368139454, 915511952, 695466232, 162888374, 158776504, 810348380, 434383232, 826251005, 664239568, 499130575, 114333121, 833811422, 628748808, 337035284, 852012466, 407430314, 683943380, 64865491, 659652083, 920589866, 754331460, 395464691, 950025302, 193407992, 677550540, 283293861, 183148936, 898540558, 626227708, 774020825, 197972448, 217157699, 168900297, 773306757, 674825840, 950458588, 643007841, 981384568, 94195842, 875456472, 646058263, 182898994, 160802909, 522690055, 198960728, 341067681, 661648242, 627988094, 298919681, 103506998, 525960905, 698666427, 139789717, 239729157, 651404331, 247749826, 132932964, 888027082, 237109327, 60817732, 221054077, 693759121, 595914892, 783607929, 352289130, 487041171, 190273966, 617594344, 701870560, 175553452, 496551565, 644700285, 602877135, 234433438, 724493084, 141034299, 308525746, 253930713, 644001346, 399027508, 950770422, 309458320, 908299326, 257733701, 158669578, 56997539, 907119190, 902032309, 16105259, 108477724, 624043439, 764410247, 771855112, 185786641, 363927159, 299282897, 398964236, 951748682, 426075232, 505001836, 717028618, 971706428, 128069952, 236872258, 879461457, 302472167, 87163619, 909812761, 339870597, 569599419, 992131709, 604933566, 705351021, 733120079, 340633604, 304542650, 706121555, 996991508, 711414397, 239604793, 332842633, 25474119, 249295333, 279751895, 44561442, 688624927, 616494701, 209650557, 268130889, 825871753, 221305194, 57679514, 466585643, 62390689, 279456451, 185380268, 348793263, 436937373, 492568497, 462119402, 699990664, 495872391, 334422323, 855242326, 354584976, 175420481, 346990974, 65546059, 213369857, 864993079, 632625788, 213254058, 566393884, 922233550, 154885700, 817490820, 22973705, 277489413, 309926265, 827212842, 462184623, 54959343, 873059880, 218212982, 993983485, 838067305, 35559359, 607934592, 602095504, 129011317, 759968769, 749254247, 182306912, 955615882, 490559552, 367718790, 317963878, 351472275, 435199829, 382646943, 166882527, 250952095, 10458651, 382847991, 465004061, 466309638, 698311742, 201609730, 907699158, 406179879, 745724921, 544668994, 476373068, 378728876, 420497591, 235828343, 323131159, 351332392, 546255920, 35151699, 378324565, 262071688, 292186833, 42390445, 89479379, 797118472, 527090652, 26310208, 560845840, 498521928, 261610871, 389046287, 636194764, 752887832, 133738854, 85147710, 833073005, 739596878, 495636280, 448046658, 325269135, 527661477, 865946674, 876338459, 987129188, 890269929, 374472280, 829154568, 931396765, 406116873, 262766921, 517709603, 672100944, 644613595, 74222061, 584998422, 503874166, 538456608, 891825550, 350161251, 65528873, 4080023, 605106196, 508306066, 7414385, 284169235, 861785260, 579025345, 591159998, 776364193, 531384377, 977003436, 355007813, 587932723, 703461870, 392536752, 605441621, 64587470, 949292829, 34590720, 864219919, 521620465, 617996059, 680774546, 604331784, 644148456, 179395214, 365201365, 326090781, 798959454, 293319912, 526523967, 278763269, 68623695, 5936192, 806283308, 920976637, 14904780, 497170349, 183215619, 644924518, 857752902, 210746700, 380834758, 123435471, 817110416, 420893078, 793730801, 421753011, 184739505, 18289440, 413987012, 285480118, 169917099, 501569600, 674712670, 798644802, 267665730, 481805266, 870876300, 274499333, 704280730, 815156438, 373179399, 62813940, 141065044, 431913283, 598316634, 695964562, 25475584, 644275957, 536904635, 208600781, 857330844, 525007843, 196730279, 410081103, 831871939, 993097252, 137365539, 829044031, 278728778, 780866674, 885101385, 723969803, 309330100, 921753170, 273171316, 957057402, 45003397, 879549756, 403621886, 523772337, 709228068, 308836507, 309671061, 462817582, 614968644, 848628622, 947906024, 698804004, 11518768, 908072656, 972353676, 543660681, 826470359, 556189351, 831089456, 74829339, 493052155, 71839877, 632669040, 114324263, 782594366, 546370848, 527680341, 650111246, 65375862, 303632787, 110191363, 497332945, 353496340, 717535173, 546401483, 922472913, 697063104, 639297647, 273342458, 477334462, 693959136, 114989609, 543384854, 152198843, 751950718, 633442268, 333772347, 604674637, 235965853, 275724695, 822061276, 549433014, 726598177, 651983356, 45733799, 424933013, 496887225, 664680151, 104628247, 63686473, 567848178, 547942249, 647963290, 688486481, 92198353, 643421976, 76236052, 846090046, 558159712, 264678323, 781156816, 820234151, 359808831, 739671265, 478611602, 515936351, 190106322, 570089784, 985688119, 559555844, 19430404, 364658731, 984778254, 513684517, 139215249, 809661746, 938632322, 728010970, 227983369, 428410060, 594209952, 19998025, 501651679, 209360256, 763162108, 212399214, 113940669, 677367370, 967977598, 956004071, 506105476, 425779608, 828006813, 521405442, 606714022, 974650188, 308407020, 883744789, 949192175, 644389354, 272863941, 839002415, 510804779, 589980321, 791012949, 84101744, 568349327, 791626388, 41450979, 226016210, 570542687, 52534489, 125230812, 263251254, 44039722, 517254470, 37476490, 671200100, 43625898, 230430690, 495526210, 670567525, 813969844, 871171059, 64240795, 815299124, 412245023, 341916246, 525160753, 48623897, 657450879, 663617876, 843248811, 488487854, 113811360, 59193733, 985732023, 266823911, 384822607, 614967583, 673110337, 118159663, 130285507, 560555248, 241763051, 920271110, 913845549, 594426431, 270701053, 687445505, 305858688, 202197484, 265606369, 335685534, 539182257, 855030189, 20029051, 46683202, 230773380, 108039514, 572175688, 331626560, 500188536, 281045619, 42873120, 653518295, 576912246, 568388061, 998802398, 367839395, 718058323, 78222506, 453166647, 207969764, 972749511, 258232023, 503741559, 869626051, 844814702, 409001403, 253955311, 247337983, 423536915, 976553868, 906260806, 664385596, 50328782, 563323935, 587433375, 401990121, 4320826, 930587738, 94284414, 247552324, 404692884, 574524560, 646587071, 813009507, 392866462, 81286145, 182251030, 774048911, 719130075, 193260132, 798387586, 136048235, 233308824, 454752388, 961335410, 885744301, 505797998, 788126051, 260760582, 19697999, 739875558, 335780239, 708224365, 510601812, 603893940, 679427048, 347787498, 466091209, 514488992, 767257, 692611561, 13073691, 415875614, 362776890, 762188943, 580916807, 291635470, 168799912, 467989190, 522820585, 398251463, 822613550, 913852597, 357327973, 790744243, 873939363, 192185379, 537948286, 539804932, 464156957, 164728889, 793079578, 165504429, 298940002, 813677204, 748547891, 736429829, 326337518, 639927314, 104580344, 771685088, 156453998, 846178938, 821316077, 273671219, 118447138, 46877969, 421319119, 672373804, 930290249, 94441896, 620941828, 677389636, 326964751, 595675083, 726738982, 433396491, 525281226, 196563461, 684710761, 676331966, 991683296, 735960734, 315923739, 526781545, 323946802, 333445679, 553665023, 490682387, 170668185, 982229985, 11297264, 743645282, 403814217, 890280788, 71818429, 694867551, 712651982, 564295806, 446950366, 788050630, 682077748, 823389324, 982786893, 319696156, 40327392, 831586187, 645769523, 651419233, 430175867, 189245370, 945689439, 344011727, 357441954, 506518016, 936471636, 773706798, 202747652, 941146637, 324264563, 287618064, 720524678, 217986893, 860518600, 676344920, 389049160, 128108126, 435781985, 309249000, 234965625, 659201209, 445081015, 450644438, 872256752, 605440781, 184659331, 769519219, 655613839, 274044484, 68595369, 154153122, 995089859, 757940686, 581924405, 720887726, 403448716, 540129470, 688906657, 611043259, 956502952, 187036541, 648934296, 596844628, 579601378, 618311924, 602964743, 594400475, 843522607, 533188041, 461105015, 589636211, 443658628, 614972413, 509660848, 595699035, 305963310, 285893655, 593879040, 588381229, 891716358, 105290216, 639057271, 785216123, 814056087, 880475146, 413758019, 156690461, 144879781, 683766010, 869432523, 243308362, 531885637, 331218015, 926712415, 572628306, 288513881, 175459942, 949058770, 353208078, 859002142, 376245411, 510365091, 272746211, 70885218, 364111890, 222598582, 97092595, 81219054, 636892446, 797630365, 432590792, 521892027, 938772153, 97272208, 121626823, 703586348, 373368136, 458706230, 661100653, 780279286, 215448968, 132521438, 543010083, 891247018, 171411985, 134893571, 395521978, 464049797, 136102109, 753408405, 131941989, 300294155, 811034521, 226778920, 256282354, 461058956, 120008578, 235292875, 962521400, 81396765, 811119848, 268153961, 764489466, 833255086, 161209589, 614687917, 104037554, 58418012, 321096229, 316341405, 82401856, 514384470, 483632321, 339455282, 436860840, 168546823, 719800006, 578323131, 156985523, 955171102, 319152017, 930649518, 575020640, 236931873, 9862920, 227896890, 169559902, 928230766, 290885674, 466306470, 884320027, 148288921, 462804809, 58216555, 687187416, 636856539, 753459592, 353210827, 800430624, 419989307, 413412901, 641026803, 620950715, 365303838, 685256424, 445366667, 837392795, 972592815, 777400994, 672491934, 746648399, 281063024, 511099119, 363139579, 863403336, 744984277, 386793023, 259212593, 987512638, 413200960, 807559163, 194669525, 779711014, 517895285, 862912601, 625691419, 837213989, 358682087, 415896886, 592073785, 442121777, 857867236, 448531895, 876120393, 518713847, 550783056, 133935526, 909584727, 735631564, 246096470, 713408129, 875931781, 411018029, 607767712, 714023625, 680963862, 479676395, 369648521, 198524419, 498138770, 961391028, 711119539, 893177205, 356525608, 816047073, 600603119, 769332844, 109558282, 757136187, 216056481, 733912905, 53081711, 414216181, 490361249, 530883676, 304222061, 310706111, 253461930, 15305117, 556692611, 9143369, 793908319, 502864651, 292243697, 634281767, 863926466, 926518994, 766121994, 844014129, 119812699, 667793403, 496292148, 456685971, 346804781, 30988953, 641276806, 478665298, 4047519, 518799630, 221718338, 118717841, 282366331, 943400478, 319565756, 139430581, 869539873, 370747995, 845395109, 441173376, 866715639, 357920238, 829535491, 759965310, 600412704, 25634649, 246604513, 847997420, 208177186, 342496430, 84795282, 915349878, 409534224, 997453702, 189447341, 736678641, 637171613, 806532988, 504742651, 196683175, 798638611, 130061470, 447646960, 723716489, 852335761, 850352074, 206537156, 939568463, 48870578, 925745930, 877979534, 189502870, 859185976, 439175681, 631952980, 775032193, 886529282, 781036862, 31568422, 740469206, 614310563, 597116651, 746736704, 78736264, 65792382, 460909630, 208168099, 2979050, 564284414, 546659741, 631862732, 24851484, 556936697, 518936052, 122470116, 970335076, 652658160, 154214235, 532601318, 30641258, 688645965, 807477993, 414555161, 7270203, 920793977, 169505676, 194138513, 974213750, 214380620, 517421854, 560071663, 390320349, 366564530, 91869011, 590766246, 904141713, 914309389, 111891384, 508461765, 107250805, 296279864, 365290973, 49987341, 850652435, 981995011, 319699810, 830967048, 30882420, 137001140, 7268873, 974301462, 709233992, 144449208, 977853756, 862948116, 952384869, 281053761, 501698247, 507096005, 771020549, 479790535, 111704720, 998708753, 792529461, 60551690, 918537898, 615325779, 286770145, 171383411, 527446439, 216213921, 36385592, 598662618, 752883232, 797223174, 105965439, 482839384, 330301903, 197853606, 979687035, 41071904, 859161965, 223871887, 965552188, 842485317, 237265909, 813803159, 814063162, 533180641, 187640529, 645222183, 210596176, 241008019, 733868138, 984266594, 846458525, 861411057, 778188834, 990190688, 878288693, 199451193, 427072393, 218398860, 223188414, 304447897, 83536900, 879509949, 443919376, 578067697, 188901625, 363387616, 873628791, 577049631, 324514422, 87715048, 268920426, 670501737, 250910878, 864176699, 61718530, 416294307, 147454889, 948853019, 284735173, 919793628, 613881154, 556973681, 496717934, 626911823, 301569849, 577781823, 736990020, 283087767, 600080656, 438055062, 575562273, 804614776, 497376285, 185386665, 445918721, 691363286, 172368759, 627795595, 179787533, 391341962, 764918599, 393261562, 407467165, 286558782, 166792509, 773060469, 40671031, 251255833, 549251539, 392584976, 51871319, 394257014, 557392707, 818517177, 13522283, 487786615, 108679663, 92198705, 472867136, 251535122, 849821539, 380665563, 424563748, 418132917, 553064913, 706643462, 884571854, 381520271, 636417531, 509485601, 690023784, 231933421, 676673749, 51571159, 513273895, 535994650, 959756132, 469746437, 945846751, 32848894, 343242361, 764198831, 682524550, 574751252, 798286899, 626793709, 651599851, 454441951, 882932772, 144361040, 193587650, 282862817, 815922121, 660141095, 540566346, 478674740, 593285696, 906888157, 870562213, 938136786, 932882910, 216291082, 478582568, 126378247, 483786237, 470349394, 399935287, 623285453, 737199942, 295898174, 970624948, 864610757, 514688934, 48522707, 909947220, 949604149, 114371875, 783082651, 929102310, 137670316, 742103689, 84481199, 37923788, 277853921, 447411770, 891295005, 658277566, 586243110, 770152264, 665751464, 240242066, 19021001, 621010187, 177592445, 388934517, 347949888, 792271760, 6481248, 234692887, 17990495, 104387116, 146446408, 228237685, 680798733, 753226805, 465441765, 547629267, 969462087, 97849583, 837209095, 414494558, 597997820, 491132393, 163119922, 608382731, 585871431, 197709158, 874054651, 826134353, 543715623, 998426410, 151496163, 489031777, 66468542, 302254369, 936177803, 635734930, 118151470, 537596463, 684122056, 397237268, 730633830, 563793200, 714987067, 806043887, 340178181, 393269670, 614716588, 379195093, 174070120, 915634890, 776887048, 953021091, 889757331, 457376033, 380182879, 617500596, 674579415, 406374811, 96073917, 823923537, 523592251, 598119063, 609807840, 540173465, 369063985, 230553401, 130427705, 541133551, 65581248, 841250171, 713684613, 327658517, 324039134, 784964940, 941964643, 731512449, 504016180, 922856403, 918374993, 681181803, 871450490, 410016352, 851365704, 419938238, 793317003, 711800663, 309801030, 823288542, 42561338, 511375239, 139552239, 554050684, 655868360, 250879321, 962651631, 765438433, 972732619, 304172811, 849883725, 107679798, 832865067, 439712358, 756119671, 728919137, 412272496, 454580655, 893657534, 684133219, 179573905, 119365953, 875181258, 163877718, 263368509, 358492785, 112579655, 505684208, 583123959, 898601836, 216180192, 335212, 890657479, 557461442, 250896746, 97734401, 541264909, 572119421, 282203252, 820913536, 332302411, 611440898, 221377706, 523913934, 931463766, 228775371, 737509025, 609936955, 538134753, 31365766, 377700552, 946194863, 645939978, 979668795, 440789001, 863650057, 823353232, 384200589, 828847622, 104034080, 720460931, 456952396, 552259074, 7495469, 524765944, 45485955, 276515593, 367984559, 203484745, 345633225, 669979894, 853056210, 297245408, 974413683, 821547270, 505448419, 804741515, 140048747, 420829222, 898373287, 92821605, 66081092, 318336564, 234188493, 755067844, 757216301, 805822964, 38241432, 637485753, 802111107, 651776598, 250376334, 524483506, 124197334, 190574119, 379063732, 658623262, 166841994, 50642371, 541349696, 809596313, 404657646, 846730667, 405287435, 882392887, 748668628, 949107168, 222295761, 340426118, 214093758, 195109973, 35257916, 632611773, 308942714, 247451661, 449868845, 502971009, 356317205, 742459574, 137666758, 571003502, 223709462, 50550197, 620969396, 176037652, 843685927, 601504611, 832534937, 569477294, 61067141, 743708201, 659336626, 71059007, 216648891, 134313012, 133507153, 246133772, 988457936, 892241959, 295958427, 189361203, 973524393, 386607735, 106338714, 863409624, 701597236, 1465345, 92340686, 917543534, 906597646, 330464781, 644913423, 624108892, 711447556, 364010296, 244246573, 720735674, 576849786, 603082060, 584220280, 455834783, 797664297, 802327161, 614445195, 771314770, 261567500, 991118032, 885320504, 178009344, 971764057, 975049288, 461843406, 983068536, 847866522, 242865816, 736135890, 441446151, 695217643, 826148285, 283685667, 276262162, 757336486, 628174133, 10027532, 473045211, 588116369, 60169062, 626724753, 119504044, 931949983, 92771570, 852847155, 70227967, 31020161, 712514188, 193521469, 178571261, 769977598, 958957384, 238925279, 802834288, 887564475, 621569591, 649863834, 684283743, 970270930, 332041167, 549857322, 152566869, 275068464, 628689736, 132195913, 969354854, 855460844, 564308271, 543230305, 391776024, 708558101, 266519795, 516775770, 273716660, 113374284, 20810367, 780968626, 678868586, 869354811, 325194562, 555582319, 513931619, 778513341, 558217254, 219564872, 755411976, 291897956, 723812987, 900341242, 127619814, 710678189, 840980772, 997292859, 823038181, 900809609, 588746423, 840897336, 702669111, 190425080, 499175669, 246301323, 738241627, 389782998, 754326837, 196710733, 98524650, 908031287, 243032255, 333064425, 86660027, 372380268, 861567647, 563194304, 677852047, 250907239, 667511530, 765969505, 843549923, 560170165, 358003041, 488183597, 915977918, 1177757, 66249908, 931054741, 389459926, 142773344, 80688648, 113754948, 662783752, 253379499, 645794198, 856734565, 39032130, 62751309, 226070814, 834192638, 81334105, 496653881, 298615838, 843017424, 168102083, 288223124, 332536592, 402868743, 431647075, 939809783, 99564843, 569479258, 458593133, 465897774, 79602679, 142460680, 975208423, 260977250, 352863129, 888751449, 177222410, 226289609, 847848409, 496339730, 194276792, 967089092, 121281429, 912772262, 70970292, 430055040, 279031136, 48114886, 437181794, 709165642, 84814833, 914653410, 816880697, 295412053, 156096963, 436521254, 437822270, 902948695, 597230159, 550071194, 56215721, 134404499, 613990221, 282499072, 905657319, 298750687, 283036567, 691576136, 813824801, 331433160, 488931194, 933918461, 554512657, 181055826, 897583732, 930567474, 181035696, 260595083, 634206302, 24346693, 177334043, 116884253, 51897188, 826182844, 96266764, 94823127, 531660903, 317843374, 523150813, 986777137, 889113898, 188107341, 895237064, 607672750, 960300138, 186084477, 40413995, 646675652, 453140074, 330887651, 584996255, 890942665, 104998114, 749342353, 422337482, 462870158, 642554899, 19763781, 677734980, 796777048, 114244684, 718494492, 346754962, 85439297, 832203245, 939253009, 941665276, 230510146, 992036622, 541982508, 401453258, 81813691, 533164336, 917869646, 683361110, 521148060, 720296537, 318581985, 652050308, 374210826, 93619990, 906763821, 771048639, 748809157, 258139337, 659311524, 185147889, 24456881, 53864968, 387052714, 591543129, 738814579, 658645830, 135171706, 345312676, 671477300, 421977293, 215098396, 236286229, 342461409, 605002901, 885058446, 920084160, 41893357, 479029903, 90094522, 422173173, 709926595, 703680902, 309036334, 111813359, 731405322, 1818203, 883025156, 219601296, 157299313, 362307750, 761281031, 205109613, 879691427, 556845583, 985469268, 463461191, 505495757, 824180967, 859884143, 767891078, 937881783, 753148108, 212548567, 541071276, 527075875, 183037262, 188249329, 230871782, 84576079, 351451028, 19200717, 853628620, 964215689, 908605296, 105194742, 633970094, 305238015, 132350066, 365843927, 704460325, 79313090, 464876568, 633323051, 690691585, 815061999, 69543955, 650078600, 321823931, 921374653, 170512872, 420006011, 737593367, 182675076, 991025298, 108810647, 895756671, 312056554, 782968851, 74447637, 407582557, 90795277, 119543689, 704847517, 129560111, 552114269, 550883251, 367204955, 681707701, 683683750, 53021470, 587496902, 457920146, 262557008, 236304405, 468535485, 628787929, 30982096, 125941266, 9053608, 476801410, 921993967, 214935743, 751170654, 894871053, 500658813, 869960754, 176805588, 188638971, 954834909, 57850485, 14210888, 871660210, 265078454, 337277484, 555694463, 439262622, 195296569, 306149271, 151761407, 552685572, 887867921, 353725778, 622417664, 64880841, 8217391, 215690940, 473826033, 827939059, 714775181, 892512517, 996145159, 607764053, 388831473, 173029567, 454145637, 967211406, 308705483, 659441352, 723745291, 621227815, 975207868, 331417026, 89356355, 683038676, 411780222, 622183712, 227826664, 835965760, 789037028, 29481503, 931379010, 473956931, 207992080, 824016541, 465849139, 622980395, 224281779, 164694297, 377357390, 569643370, 485975883, 455273458, 628471932, 28609171, 885912640, 807979305, 906840554, 163858079, 71585341, 933025339, 373631611, 736002155, 295402381, 458060642, 288191636, 434878882, 538766601, 393706461, 837641575, 446978250, 243352752, 624386571, 910409548, 447203903, 836871167, 536530528, 178657678, 59381826, 803338922, 356027839, 323542237, 494612373, 963805733, 547058725, 246630241, 122556409, 53934431, 834479184, 337656207, 971045400, 23241139, 166287371, 382446653, 336186177, 492495888, 202542127, 930785693, 111277253, 85083587, 463679121, 606916214, 364761217, 51981226, 796451097, 122312674, 150805270, 901907186, 681519689, 535128307, 463792914, 961224423, 277084743, 394164720, 295131463, 814839432, 589894549, 986408069, 431422856, 223352189, 460866635, 218357473, 470933628, 887457678, 392246880, 494719071, 870320649, 627973264, 509164555, 875458659, 944570665, 667461879, 67560988, 969368393, 936324839, 284060419, 24099580, 311691433, 491946788, 247539123, 832487157, 962368372, 884853844, 246350968, 340119065, 617108492, 760972095, 358548816, 72341373, 204703844, 773383344, 297882647, 548811148, 153461289, 80132165, 875168838, 271732142, 44077432, 267338759, 391577986, 725246240, 808181177, 508128514, 343442016, 225827122, 380579493, 189991766, 396965640, 578954164, 856474299, 807144550, 936577744, 972296350, 34440775, 708660270, 155502683, 64317683, 180783007, 738853148, 75020608, 342132939, 646792489, 345988054, 479551187, 426951483, 976925197, 669121845, 493674702, 977543686, 833433860, 319188557, 861545416, 632634777, 218434618, 249694059, 438939430, 772348567, 832851913, 534919699, 556135035, 186548173, 606241202, 712225016, 827681667, 883610584, 577466342, 78802730, 632852883, 275649830, 139789430, 397863233, 757904726, 758201659, 720089364, 193484771, 550020920, 3160399, 917910507, 32364249, 988933862, 251838274, 357297069, 819427468, 837436185, 645213988, 254791032, 174889102, 800437329, 146327587, 468929721, 439827679, 17472661, 417787885, 732943366, 192999998, 637212736, 988731387, 108970759, 627613313, 716428898, 381193709, 416155289, 785014175, 107532589, 830771533, 641260038, 316312404, 356185960, 277107295, 296387961, 958170243, 968914607, 312342846, 198463949, 989006884, 523834507, 53937822, 812158340, 328487769, 242577460, 65686287, 556744386, 443086961, 322515911, 450221986, 851286722, 607539641, 609305187, 642737821, 388341047, 739490929, 943091092, 77220503, 51948295, 714167686, 51470654, 551946605, 579346993, 166622207, 480062948, 431694362, 413206786, 102685906, 413084531, 147121605, 449622718, 839177433, 985830821, 585867507, 765410537, 274284779, 36093668, 124021416, 267769423, 199944145, 343741865, 503611252, 936211618, 295216518, 994829770, 885050752, 182350283, 174397944, 754142135, 969634618, 958030085, 586356700, 112243617, 607932353, 6708664, 27249177, 841417156, 238413152, 443978597, 945774301, 948788672, 105959908, 909667848, 655817987, 263543652, 945113604, 31479611, 151580912, 297500903, 95198264, 749769422, 270515880, 328892141, 466191508, 884120319, 1821405, 235370220, 10808339, 914607228, 820703821, 104544652, 607007410, 641051247, 175870992, 190942681, 98968333, 540007819, 752753531, 901364664, 973280233, 707064331, 566998004, 207361628, 838377521, 148360563, 186874503, 767673684, 560881944, 919856350, 347106871, 440519992, 422336431, 611079011, 812159890, 393445396, 385116286, 550072159, 957632468, 603401249, 11772296, 665746155, 326672836, 407257356, 233200710, 399883485, 450613365, 23102077, 261641839, 8031971, 466618275, 542014968, 921521408, 755163809, 283850182, 552760396, 966281072, 383525526, 536349437, 159208369, 721650871, 159132628, 161520205, 682923687, 915267069, 512532824, 469865509, 416685981, 94460087, 502071210, 81480410, 953192153, 434132984, 872853482, 433136332, 468815386, 954323907, 111911113, 353067753, 654240503, 530733898, 718068526, 3060835, 379675887, 476932861, 503251879, 419760433, 182760095, 591527928, 145506215, 120839523, 322909076, 146491452, 55911384, 279601782, 737929595, 843543404, 363467328, 704331617, 821143656, 814732728, 978217451, 44735544, 539286317, 524180874, 848898152, 326093993, 797941958, 534609902, 756988239, 347015793, 299896546, 334723672, 645252235, 934925903, 490716743, 324389826, 265729305, 472190839, 544033234, 324888868, 81871249, 473672976, 249965410, 342106560, 548545190, 440465160, 935128053, 846590582, 698933441, 784170874, 914288634, 65077949, 976440174, 946088654, 468354055, 344642060, 451686700, 178383107, 689615807, 559137912, 919642853, 186434303, 196428105, 780471176, 796960873, 415111412, 396730761, 103739307, 931196805, 598586675, 689719314, 565777361, 896399665, 87891064, 717022676, 848798275, 803516803, 130472847, 117362338, 55478402, 274018924, 782549178, 490007900, 774372738, 481997432, 413503329, 70165040, 674784779, 836759604, 532631970, 201216962, 139529049, 394635160, 33217583, 727294510, 199247607, 983641276, 840615606, 292910204, 496124296, 681462398, 742365387, 952736102, 211373763, 160132640, 435127672, 478133299, 130710418, 788117670, 819411387, 834168899, 562494430, 669364535, 757335813, 229228457, 919171539, 900443904, 103034804, 501472223, 950277128, 282206727, 869884617, 393858058, 368805796, 510803987, 21869805, 258380733, 553009701, 910485423, 95209577, 581251393, 879468252, 91057114, 69619182, 332859315, 689256333, 110756184, 309887250, 704725530, 691894222, 780967629, 775839227, 954686886, 283652184, 136999943, 229398450, 866624616, 820259377, 212602422, 157491518, 624345453, 647084551, 271737312, 695548591, 153950709, 642212178, 493845550, 503333479, 953498876, 60902627, 211128340, 79896701, 687938314, 84888757, 74946258, 728620263, 877012985, 652156553, 518837076, 288028413, 764557850, 390331126, 462890370, 933233067, 755658106, 723846048, 118023491, 948191746, 376387670, 790303750, 934375731, 3826963, 653269140, 894216211, 815500199, 138903910, 140266577, 227187855, 352252502, 241756483, 131134986, 794973075, 1325099, 727687145, 862292306, 944734795, 707296567, 344973629, 103948881, 296262690, 918452498, 717236572, 753739550, 640444844, 820221614, 59794970, 308403141, 685244198, 795703880, 59182686, 381129221, 590594407, 36571386, 196669302, 849913758, 533555112, 555527420, 820446389, 774765693, 915104715, 864675538, 605843921, 43597108, 306503692, 796089836, 789334114, 686252432, 878821052, 465484369, 932816371, 203543177, 508262252, 520288446, 841904844, 653950039, 919583595, 373661039, 552930148, 658008815, 102050533, 433533729, 779584547, 275776331, 722965802, 714062642, 671699862, 318536586, 327610370, 817845678, 898647940, 634351960, 400565921, 194361713, 1979291, 299886415, 375480553, 703312131, 685678579, 942442603, 702587832, 141396776, 493193863, 229487070, 843658040, 975405286, 307702695, 847265374, 297393600, 607859354, 164436493, 238944388, 948733493, 660460358, 13004335, 11776831, 617797171, 90741742, 251954626, 423906407, 998685102, 249706008, 925248421, 445060128, 837115787, 91580097, 492895884, 924782457, 348132867, 383360572, 750311041, 252388902, 815276663, 253024595, 647996401, 958516093, 16707199, 811201811, 275065305, 66249804, 898138113, 83466961, 399126483, 485765650, 176287047, 100109983, 337714285, 965454592, 125629740, 668224254, 684343394, 190882139, 706888800, 348355517, 574105899, 375878002, 674478028, 354313807, 797981964, 512315097, 71288161, 948124985, 931812567, 264740802, 708434399, 81890888, 278634389, 819095118, 508453651, 516528135, 344132127, 4615858, 342343847, 697131778, 148480284, 695977182, 76157503, 473941811, 982394588, 99035752, 550067777, 422516723, 613080098, 520430124, 500123524, 330630349, 323611925, 11063262, 986870124, 418652760, 110116184, 351316215, 130011502, 598424766, 509981558, 355340872, 521626454, 196802882, 634412170, 525327712, 779789741, 8590684, 529213138, 356754524, 6717936, 550895342, 959607693, 361012251, 422250160, 561454059, 920180287, 238596448, 12484692, 898738563, 86008264, 794015766, 639742191, 577369223, 300141562, 651610232, 844853581, 791499434, 369411420, 128176053, 230839522, 255520963, 418681378, 58036803, 666439785, 890833947, 648848889, 69735882, 364443349, 924736947, 492335067, 210874511, 487201251, 703511579, 650399334, 729438646, 26427433, 612138022, 363780258, 583041529, 304286343, 783719813, 247064051, 495749531, 296671828, 869832543, 368878910, 639782749, 357746584, 694730892, 212930172, 103396656, 682439023, 982466835, 605130531, 417780976, 788631544, 700911678, 415791640, 361782263, 683201635, 359050769, 417175028, 555296908, 186754856, 404950125, 961794408, 948041705, 798856036, 609415942, 338936034, 555578615, 989318415, 524369762, 64104983, 653898758, 218579008, 640133132, 705605690, 396071530, 115577986, 278522996, 654937197, 784407857, 470205815, 726714343, 489905539, 534939409, 936700494, 431063255, 330594188, 276213041, 707217664, 981570789, 745433633, 851041769, 270467931, 338493463, 581652255, 558011249, 988002727, 810806908, 361227293, 413901203, 529633881, 501052346, 9604449, 998481934, 891618594, 938713943, 474869652, 827834520, 450677737, 334981693, 545079706, 124406274, 977265823, 833130162, 9587581, 37845087, 493973115, 834446620, 657263110, 808108383, 662003515, 673483440, 874975525, 600266122, 705255263, 448515904, 413584298, 63870805, 343021033, 714284618, 482863289, 638198443, 391694318, 416376713, 138742892, 880972731, 992994699, 700116279, 585392418, 671085200, 300754158, 718605908, 55840246, 571237037, 842902558, 633094782, 491578087, 760858064, 624100394, 455202539, 10082704, 638728949, 748282308, 407857115, 728771995, 822158666, 971643979, 957998572, 941712657, 628895124, 537569794, 311080992, 744802152, 289346804, 481764360, 142348781, 636249951, 139307129, 574914697, 767633390, 121381698, 523824784, 72199105, 243565205, 620734770, 169916377, 627249709, 777183394, 603542775, 46840387, 983136384, 53797782, 456054986, 473980345, 495050473, 243071057, 824590349, 372357946, 96177371, 83431813, 185819841, 71314462, 717213245, 766281821, 870520808, 94836719, 188243303, 286865947, 631569822, 513137047, 347029418, 145363392, 154073076, 410660781, 36766293, 295956187, 567140808, 567404245, 787442694, 131844245, 969996550, 630236363, 8853095, 205565022, 106355792, 392334174, 42214341, 959215348, 607589503, 460743355, 348299561, 266858143, 340733720, 7658440, 29766806, 545313882, 772453732, 968452143, 226830621, 329424105, 317032625, 821400109, 138839712, 301536420, 458734524, 889088319, 877387638, 302547470, 197066717, 735393027, 513478063, 991778171, 176419098, 352975150, 240992736, 772840294, 333858217, 401012215, 43598438, 991671906, 511943870, 980861837, 958186470, 879108220, 913854614, 955964855, 886237641, 604354228, 158589026, 817129583, 478912690, 174622417, 126337109, 379694074, 35268450, 893174824, 580795250, 718810000, 378729685, 997598822, 302498928, 485967779, 476379118, 713633077, 606089337, 21991641, 664253438, 118735564, 130126193, 936511415, 425922742, 554138206, 263738702, 796168433, 941610264, 268904388, 30210300, 280918931, 620292586, 891792470, 489387338, 717244540, 385820676, 305544905, 318340888, 429154945, 475582098, 457926778, 674362121, 325826498, 497382550, 122523844, 17866807, 82313884, 328046395, 444228859, 502423053, 391555228, 131849119, 688009665, 224904726, 178707215, 715387165, 591000310, 513837155, 92842290, 776209491, 647247431, 258215386, 40668091, 577263560, 618135678, 471396668, 486199156, 396995895, 187080567, 149124308, 662670463, 567660528, 890972645, 731259496, 325580674, 871583163, 589210922, 995742040, 304408668, 773557372, 44835946, 307509652, 331586383, 180420132, 113841803, 816411101, 607672369, 689883647, 668029835, 786111509, 52440358, 477565162, 258955263, 226937558, 987707521, 558193687, 786391020, 710564339, 205728013, 216133688, 779092003, 910986998, 67753867, 746864846, 234815504, 664150372, 828266134, 378355485, 565102577, 478720022, 463626483, 390593492, 171743220, 668678610, 274721181, 742986407, 949958982, 955967743, 106821451, 170265011, 405985066, 69644463, 595641299, 429499150, 792304055, 557188597, 982726487, 990371341, 232459451, 599840789, 67502212, 240320161, 7001636, 637857915, 686739268, 278462736, 820276094, 923166525, 383598213, 342243270, 537982279, 917996282, 371698578, 270481594, 13510176, 477506060, 290279073, 854710621, 62977390, 705455614, 372274312, 373758823, 292204213, 26662199, 823431353, 22051073, 404885438, 593504594, 406266649, 461881902, 972642753, 713802715, 208203048, 553899345, 784198762, 977491782, 152870194, 851216981, 599973748, 86534726, 375125423, 198467120, 663930982, 343650354, 165120078, 628728010, 604442834, 579014851, 728639556, 496505799, 65213142, 513526550, 58092495, 967283666, 937983927, 700885672, 26586726, 52347961, 839154167, 883856179, 837159171, 607786542, 995492322, 396572697, 858696189, 962546799, 582110274, 963480522, 921919665, 770697610, 191637572, 223522718, 828543603, 983195531, 714321366, 868312452, 891802633, 131785216, 392668336, 514802139, 544386821, 605210870, 729504082, 782419347, 781855045, 299176394, 457823446, 972736030, 573625775, 627246015, 94348095, 291408984, 498442384, 944388829, 175935897, 541422547, 499664671, 912453986, 962545892, 753441531, 72340067, 970901606, 180695771, 371122503, 460099598, 125024497, 406078904, 561884807, 522814814, 667148901, 777319779, 230028300, 550083692, 962230946, 450678746, 461947133, 205042210, 659046842, 647171329, 931001695, 531352357, 232732634, 771981252, 948415752, 906868297, 570310754, 984220307, 498951525, 241544156, 418907145, 101271909, 508086876, 164471922, 494578303, 144196026, 36349433, 293206623, 439242929, 689723440, 304889631, 820857979, 896637692, 258307849, 572165378, 690462004, 431440074, 680245291, 939666612, 584086657, 212554910, 694746236, 954241895, 601193445, 216869443, 607178435, 721988899, 766600889, 225179806, 612693784, 235146209, 254707082, 702155009, 308762920, 948523325, 412942890, 570505099, 15697211, 533541148, 403759025, 423210012, 787552778, 462177696, 944708968, 927846946, 20826210, 347398065, 750065906, 954347300, 809553745, 181082652, 352929215, 507432387, 314259659, 162906262, 1961245, 272286803, 375614904, 283589228, 620325913, 176391344, 276371211, 439835636, 46326349, 794164674, 241509898, 403868054, 119005409, 688412161, 711983503, 441336220, 481903539, 721537549, 375292138, 656920941, 589466031, 391854059, 118195346, 844189915, 757691084, 394612826, 883419956, 662958865, 221505320, 419071829, 864332646, 79319171, 283813489, 211721135, 311433988, 551547153, 650666156, 768438594, 186781421, 815915401, 923744219, 56713345, 431362684, 962027399, 950415591, 169428067, 290740434, 899047829, 145159276, 504338325, 945151751, 676926860, 424701278, 122752210, 418983928, 573781379, 214838304, 805418668, 603482426, 585017284, 462951260, 633061887, 507125193, 564679218, 729679470, 444849526, 575683756, 738554333, 767471195, 239258944, 730477005, 205792047, 187638331, 767464842, 348822669, 558261429, 24623383, 107061727, 383774702, 887949835, 159871944, 480521186, 619856111, 998967343, 284796698, 608414654, 502494424, 406320824, 782881829, 404526785, 606715323, 955215409, 241780697, 533696300, 772291282, 734631941, 604349625, 669847184, 922739154, 772586820, 632989818, 645710716, 485256860, 998491375, 124362330, 912837909, 889189946, 49825626, 763688940, 155155587, 370607083, 625830515, 657369873, 358195211, 137529546, 304617493, 751183688, 945946533, 174081497, 746279274, 524049932, 149666675, 23381445, 608407155, 71515473, 226018575, 401186784, 668370599, 688507800, 597828874, 61924250, 524321805, 570851589, 514280433, 605026614, 390020721, 598057836, 399413119, 759515409, 327184609, 658657355, 328879199, 100954536, 421023407, 565128186, 230850708, 665900398, 264182727, 867277893, 208644581, 135432241, 129334931, 834868755, 668633889, 126341528, 709511722, 209239584, 674914725, 193359902, 719742590, 129883573, 140030015, 42430568, 216454724, 909473941, 285697998, 524873893, 891699042, 292441886, 955729032, 18364956, 348748883, 72722542, 403210390, 602247415, 136660674, 269589089, 2510240, 57823289, 401693523, 389155654, 72244315, 270108821, 857715428, 565633318, 699959907, 122609992, 762165478, 749381504, 381239989, 287938419, 867453886, 53262565, 187159304, 184152478, 870094009, 94458621, 101102047, 576729014, 681156705, 407204200, 358874060, 142511098, 57631391, 80765681, 417430026, 219134170, 198709842, 233712846, 456727177, 295161907, 85129797, 373068921, 309469564, 643337112, 593605298, 63016000, 291147181, 291056574, 577153399, 566976212, 759595505, 444397755, 863854662, 535767242, 960770260, 391018680, 62559916, 527281221, 244699864, 363423069, 655734196, 181564323, 392239442, 972921688, 175898845, 249573964, 209672639, 490870935, 734044363, 990882119, 427858702, 80359183, 51068302, 530090527, 680616830, 244964285, 533769999, 898656151, 516108557, 567727782, 93486195, 330523239, 62148580, 813433275, 752958278, 766234939, 232177621, 923590913, 946355223, 32086780, 371844409, 767268190, 317950550, 4914138, 412781097, 547265686, 619891474, 484354566, 507411291, 906723656, 165541028, 22433275, 426753666, 5936853, 875646851, 38162835, 585287306, 178366442, 129057915, 877581393, 921973107, 254856102, 79220239, 635132, 905155700, 368457268, 993331430, 503591551, 482882818, 38738263, 655257267, 621670104, 151084498, 905803832, 222480864, 344764032, 465111810, 606929216, 53146208, 291914513, 510968445, 972449893, 82120736, 207552039, 999300821, 242825336, 815258529, 495883833, 715233341, 41043575, 719166090, 534353708, 373494996, 272893798, 893095473, 353020506, 220033821, 378502372, 833740380, 216396664, 816882177, 593854061, 825709602, 93738002, 851023417, 286975922, 755332558, 564044495, 864291825, 17958243, 505217071, 424525630, 505204491, 31172404, 550598161, 811856881, 564461135, 596661057, 10957210, 884708478, 929567961, 407620423, 901132218, 667242536, 511948941, 104064245, 391158566, 534257300, 228953275, 376991749, 425452918, 413189386, 390758861, 594915634, 186657003, 280910209, 320309928, 94813623, 469982421, 330879122, 704679613, 217033832, 823905137, 272223815, 675379293, 726218013, 76650265, 471706985, 230821601, 822186896, 339714736, 161518272, 561945895, 23382633, 37708035, 174689680, 50774485, 501343551, 385150644, 994626344, 220192440, 933395869, 475103546, 11954412, 808379, 397907180, 823411971, 229525823, 64521867, 699526764, 71898344, 12586108, 500891447, 961213405, 240519098, 899542291, 289814840, 50546655, 91546428, 719303427, 650692365, 284837012, 331780638, 883526453, 767496819, 592786450, 576135962, 724271664, 711355367, 170181875, 762831902, 199077442, 597203644, 501476858, 807933656, 331511636, 888370763, 502940197, 681552391, 970145802, 646255490, 806894782, 299443203, 972081128, 511419430, 729542974, 933536671, 368606691, 618395505, 619358012, 194986925, 125036959, 169346314, 343756397, 747352350, 746952243, 113607203, 868587284, 166263737, 1320393, 277032613, 102070407, 321916358, 478648895, 883179147, 581233949, 528499280, 95486320, 791436712, 453815809, 577209524, 479428385, 441112214, 803419522, 986191606, 227918965, 170256680, 704145456, 886512645, 391317259, 287762476, 560504786, 883246147, 599594103, 284296492, 313741503, 927950373, 467420689, 478190546, 522451948, 920986004, 703486464, 560992251, 841229186, 659316169, 514766807, 228958011, 62497917, 664809556, 259592387, 314940175, 894918696, 447828815, 374324354, 994331660, 440898499, 283015994, 59235670, 984305153, 180398082, 585534311, 532739892, 21278521, 735425969, 61485851, 80466885, 271514718, 359413423, 976896711, 267701950, 914617821, 80251925, 798109747, 150154457, 297182122, 511862040, 327915354, 498719359, 130303686, 153384238, 507598419, 121281520, 275484444, 501571100, 462276718, 663843583, 328584899, 422558327, 519552189, 414673823, 475489556, 50150057, 900535033, 641134232, 806900452, 596329735, 454587043, 456466818, 751145283, 419751219, 139167741, 490639580, 24908874, 987259729, 660682170, 289670664, 812110889, 899340247, 60258292, 981508279, 94311763, 787992917, 757494828, 168834640, 930351872, 537381075, 630967116, 49719314, 169212737, 127021564, 403500419, 936879495, 274306364, 805865287, 813591257, 978419732, 265885623, 936317945, 957417728, 79903633, 736647887, 426663809, 840810016, 673853031, 928535206, 228193086, 761256923, 831154484, 197551018, 174428068, 561774692, 177780551, 565257870, 85338487, 264438854, 87596473, 704113453, 737766035, 396045899, 561279956, 839417364, 6229099, 654073443, 188325475, 179023125, 806942707, 740644721, 189913877, 633872898, 955830105, 771625916, 9720927, 295635686, 6242552, 891735262, 695570656, 242437868, 119799205, 695820285, 310469771, 455563992, 490530853, 240784137, 517792920, 241506294, 372008689, 311384411, 796358326, 334156613, 196769468, 471227746, 708898152, 959676844, 348426927, 453537448, 146716194, 443961427, 184588615, 823844787, 60740923, 935896130, 925637798, 93431600, 566043910, 115075859, 227388560, 366559052, 982850626, 618787670, 746142995, 99261294, 439670737, 194495778, 744796432, 529316892, 851528394, 950311427, 399226821, 757273618, 174601616, 865473226, 110156166, 703432851, 115027475, 386010733, 487507916, 933806203, 987784782, 293977069, 722642614, 69692174, 544070397, 828409401, 95958508, 901630200, 200035554, 310623361, 905157473, 909905455, 532864201, 240539964, 8713240, 106436734, 912055752, 216087816, 253316594, 562711866, 604191756, 746816050, 457990126, 665803412, 52238698, 995144029, 101927022, 831641391, 83349721, 739869252, 756483266, 729280880, 948763842, 536303445, 792352684, 818706417, 857191082, 353239360, 420401135, 984604840, 115894455, 326718470, 329916090, 383149124, 722507865, 167121230, 741198419, 240743615, 250455343, 584012340, 577467358, 426063250, 489531313, 236907762, 137104377, 529480548, 346165224, 143889727, 800062114, 497879038, 186299270, 280925121, 730616365, 287590096, 883759600, 910393530, 435205110, 464119215, 607995447, 439184407, 337431893, 928166342, 30776132, 392209480, 49396653, 54222693, 78992708, 322661285, 22646991, 791154658, 164287480, 756244049, 296333682, 432981516, 199683170, 323064369, 642176183, 891047003, 337383374, 262324800, 924189859, 983978314, 897231870, 904876194, 5027974, 245717394, 676509775, 421688892, 311726515, 659161571, 340327530, 522535342, 380078041, 952557313, 498672852, 545721256, 135856599, 748684076, 160656339, 785871371, 295285216, 541891810, 756719777, 102358511, 481194153, 564504867, 177686772, 770915150, 126848035, 265658770, 662531438, 462960221, 76606755, 54993919, 351723552, 811407393, 280790574, 308639835, 912946214, 559137336, 509136946, 593837654, 199303860, 648471339, 105441968, 303348675, 200100540, 88357388, 351954591, 641495577, 814443235, 357456886, 364107947, 344572626, 74805013, 497450817, 59948895, 151004656, 699064556, 984346312, 163329062, 348261937, 216052234, 312378809, 959247093, 202304711, 957270073, 766216079, 212861485, 787004700, 501545958, 645961965, 921318282, 744770925, 655314768, 440661054, 399208465, 4599543, 966083286, 782795310, 358857405, 679165196, 243370038, 919104922, 92905551, 401812723, 338738063, 992512233, 800117114, 90861967, 560266669, 608220058, 286173377, 884675916, 925016267, 310131954, 952517377, 688264697, 748838838, 124869112, 325216366, 214763389, 181421260, 719674998, 10915039, 181968783, 140265786, 305978969, 137147947, 381857894, 642496614, 861136917, 944687598, 149388598, 171325270, 570434446, 677231058, 385279267, 399872324, 416235082, 383245826, 532497290, 776196474, 330890803, 937044938, 980627854, 616410928, 938155575, 674554201, 963358619, 404577334, 924392977, 793836373, 625137628, 869801268, 816106850, 565134006, 738621391, 190333878, 51939116, 611166857, 200099113, 625745490, 195865121, 688354039, 204284095, 909381159, 481015576, 63840860, 794414903, 788501651, 92935678, 192741079, 713136741, 700342310, 404654372, 525105513, 55396748, 451999867, 831034978, 899719699, 897107972, 78273155, 498008130, 807511832, 451822378, 782870189, 752422931, 636140955, 275490308, 677501773, 873372775, 45590145, 317896027, 443285881, 325056797, 935854989, 86880181, 20695046, 812310397, 116133347, 147478117, 164211817, 207253913, 680865693, 382118786, 379283074, 922148633, 474666435, 628423579, 192274112, 22664695, 842317979, 197226200, 175600017, 814749313, 738006544, 140315639, 669380166, 144890232, 201599794, 122152362, 96907790, 523093372, 746975503, 652161494, 851456479, 49727027, 505142313, 299018183, 443694302, 33882941, 420772944, 214315236, 431926579, 583239565, 357739957, 926248928, 672171860, 36914571, 182688583, 799159073, 427310570, 421887075, 225639202, 761041818, 704435828, 764977554, 972382831, 38343876, 955350678, 251782754, 53123996, 813659685, 738342732, 840112128, 662585580, 745270142, 523028022, 392730915, 764340356, 661858067, 226559171, 431730788, 235176269, 728867767, 423617486, 689918142, 863114864, 850200219, 914329401, 908798877, 877204246, 198843905, 51343889, 234833003, 192995840, 147605778, 484855301, 175206055, 197151154, 960382845, 861166409, 844427774, 35396285, 727561034, 383413613, 889571072, 794563805, 986486268, 851182592, 458799702, 80086953, 474108014, 246884866, 62296244, 771436835, 392485163, 866701885, 769862676, 302547446, 187678952, 917774497, 508714001, 592620035, 84505093, 675478667, 589038378, 518212414, 743739585, 836200839, 567918734, 963711418, 671161086, 216331868, 394894677, 493888158, 760131612, 169761160, 518027104, 10348493, 99991857, 326158983, 253304663, 384745860, 356758517, 855890162, 897593095, 896663085, 233599954, 23665287, 62196193, 425927155, 691993455, 379359432, 294891544, 955254757, 597876403, 778485067, 563312651, 927987298, 653957505, 266137632, 290881149, 842823639, 953785041, 500854154, 766854171, 473487126, 897238497, 396419529, 968476053, 261451447, 991507003, 659400514, 409036974, 199419314, 431666691, 48649463, 408131817, 673206473, 625939848, 6006336, 303426957, 257724069, 834159228, 328236398, 176109636, 942047861, 245825132, 597302815, 617451051, 643467435, 551470613, 391001207, 442605198, 543215893, 487255829, 326736046, 641163518, 994993268, 494538882, 717339706, 25187197, 408438143, 899059918, 85956990, 300713733, 759518065, 385199041, 679756230, 393845037, 915787716, 174732979, 570834854, 763501529, 430205640, 603519635, 139425083, 489800106, 719229591, 19328538, 144651508, 764360936, 668967436, 393464538, 169421620, 434917306, 363735380, 961675968, 275354754, 829982792, 371673347, 339092545, 440391202, 531343863, 578826873, 227388241, 699923323, 359821295, 302661185, 320854827, 876041889, 358118137, 724617182, 123914990, 934791064, 864690588, 56589468, 464896500, 138791806, 466110363, 665855216, 441028881, 868111094, 136975470, 777095071, 751918883, 40593731, 144162362, 301896869, 971259508, 863310217, 624870935, 348398257, 549293740, 966589894, 160012535, 347973826, 971872442, 132138359, 463472159, 972911668, 613594398, 188207467, 389352380, 587069316, 633285074, 536691548, 190113092, 418409655, 337379635, 929309412, 225618331, 874496540, 712124449, 105760710, 867048307, 103820541, 133549889, 502275992, 150247990, 50824581, 226196103, 160722380, 406278775, 410438166, 582631770, 865227612, 810668661, 610140141, 321932952, 952055953, 959706799, 897061070, 163970104, 49606541, 613286625, 381332365, 614950467, 483554089, 738508860, 548703107, 440280049, 843502950, 90324973, 735154418, 953172622, 838716925, 27748170, 740410074, 357175837, 400436984, 498294202, 731637728, 824104397, 430238803, 738326843, 127883604, 941903539, 750895473, 811344165, 810166312, 756254145, 48427656, 292090984, 842332538, 317576425, 369125241, 587442726, 370683691, 949941231, 144942400, 526156217, 517774410, 99982546, 711442601, 268609496, 494073384, 798703182, 183476980, 415672960, 230676648, 857429903, 408082020, 576868131, 856023614, 374138776, 901822190, 619770729, 877246868, 993777417, 624853975, 926507384, 610995377, 68190746, 555829294, 319980683, 354315249, 542787528, 965554238, 775935659, 93699817, 284779125, 685721942, 627605313, 168698962, 38090656, 195861403, 980987350, 404097907, 764527135, 310785586, 43476433, 9078529, 382528829, 654305945, 571966647, 840414705, 606528216, 138498166, 421928116, 971778592, 305777606, 182178642, 830615713, 908421340, 841631606, 111861087, 179602758, 586881380, 571523566, 368592015, 284044448, 168161014, 715374562, 867524922, 951921658, 690754800, 372144252, 942584732, 748546326, 245002348, 862531661, 909325926, 377359681, 371385415, 667163185, 182183792, 535660135, 940440662, 791869906, 491696552, 746655475, 15604151, 840553572, 286924922, 323919839, 609967698, 181273845, 88169022, 649666286, 512453381, 272293008, 628340998, 376251205, 890485166, 39339275, 925421232, 959501635, 853533483, 106047229, 972107329, 778467785, 189740986, 45914467, 171275558, 257805754, 44035204, 901248250, 968870834, 587654090, 45737957, 803660603, 112588991, 688343603, 757601245, 402154033, 871798099, 259082273, 847253431, 510308400, 908621619, 684039018, 964621895, 951745108, 54003227, 992235596, 637348574, 572860493, 750944178, 573278863, 904282033, 687686129, 736450810, 232146492, 237140, 22091457, 532029980, 817517118, 538360790, 396280152, 964635317, 811079525, 330587308, 67636780, 439335051, 158863574, 832814330, 270422514, 836128309, 322047603, 213077817, 308514141, 313464688, 97035140, 45089166, 465481522, 663744138, 424930237, 973971319, 850077763, 361070380, 754007393, 592554928, 568669178, 726760042, 48040747, 791918565, 72469209, 108887665, 249364891, 868245699, 622950125, 975045713, 812197898, 402184370, 575809579, 327603252, 823855222, 730826555, 527708385, 694376312, 945762394, 295144796, 821168907, 474144784, 16157376, 864784636, 398820056, 107729256, 446028861, 266725864, 542405022, 85294118, 704498725, 229261177, 515481989, 702665688, 556673151, 895010010, 549630698, 974874894, 635932314, 638694540, 564900082, 960130059, 537571731, 324213894, 223919609, 718809870, 264931402, 32780678, 465849217, 56803508, 851300977, 968842316, 780635285, 862445830, 298292760, 249433265, 764577948, 109776503, 582075876, 70571411, 62190567, 39074727, 489366460, 223101677, 691200218, 383761194, 31556867, 407003915, 793499974, 986239079, 198015471, 219733939, 854539622, 466365707, 933762708, 877074228, 591770496, 85549999, 663685629, 785046448, 863075021, 618812045, 392371245, 778269752, 576926902, 225579676, 982229324, 762753321, 914938757, 423741771, 504268407, 740745825, 666169637, 48603758, 203205096, 269621701, 754877885, 103963607, 691819395, 122890306, 407738677, 264900701, 980393068, 411139558, 20691361, 742235081, 34034165, 168022057, 819737823, 63388865, 810424451, 357377701, 257101137, 937333734, 267871273, 61514425, 688416231, 436181566, 148544763, 952709699, 533386799, 192077082, 299841365, 781879089, 66528588, 411540140, 586906087, 160027733, 257843749, 717934597, 733704571, 715014604, 559502269, 340895051, 272540415, 906157588, 341057059, 968867940, 741100446, 53853246, 501501267, 703061149, 335253839, 942628770, 296251072, 797251883, 544583279, 687778905, 716906315, 335302924, 558440557, 462656601, 51503982, 908477327, 348270075, 242364378, 38672934, 193560808, 286302674, 116477680, 836948877, 137822422, 820515414, 100015435, 432218488, 211232837, 553281604, 92692162, 216366223, 6928183, 731856916, 803237756, 346214948, 115806430, 791968338, 457850555, 587240862, 519993226, 947767895, 374289518, 479164632, 102147800, 580038630, 544039742, 612357544, 630283355, 729232085, 389478149, 32819700, 955297002, 311582913, 34756541, 412797343, 821942866, 382511404, 278172891, 924325188, 474771658, 350986936, 608239591, 626856963, 452977587, 860614433, 30126851, 967049307, 58931401, 619806802, 583299999, 666861337, 493140764, 147549060, 990937064, 568784289, 807081419, 97983306, 823401738, 468291324, 452027394, 988464808, 681652948, 732444187, 472378605, 590357439, 57034886, 99734595, 11951931, 289193376, 697731270, 165485136, 374114740, 772926454, 384169348, 902185473, 544277735, 373385274, 85412233, 923599129, 830757116, 966422271, 135931847, 971728235, 133983449, 202299805, 552860104, 373322898, 216284462, 566802679, 950404342, 165756193, 896158589, 311387462, 787020333, 337907084, 746993794, 452941054, 114565070, 348494393, 206170625, 409367317, 341800448, 400699855, 250466708, 154171224, 325893133, 394509283, 6502906, 351897968, 38923770, 130086076, 455672657, 489301546, 756658457, 51811297, 50738703, 587767536, 471987088, 384703879, 820342759, 796600229, 731454569, 726616606, 800489668, 279757415, 907276478, 45555784, 474843765, 753884837, 405035264, 351304880, 761465358, 39972040, 219271992, 888607994, 417386734, 684724493, 91462582, 739268826, 101507947, 996247600, 637684848, 107099996, 106603842, 721167788, 565980238, 836666313, 843664344, 165114128, 129247469, 313104934, 519371921, 649911888, 930796918, 510624220, 408706640, 762873788, 970641648, 830009747, 726930234, 287991692, 989547165, 676192103, 148459336, 828947002, 675496857, 923592646, 475272142, 922742562, 207434984, 998406310, 61106990, 906321036, 501179863, 386701263, 574193255, 511985411, 663653231, 821572185, 937143729, 78986341, 644903499, 706806757, 97831726, 20091057, 891688162, 629286447, 683955490, 912629329, 901634960, 101212606, 521102899, 261969695, 973433517, 564999057, 213795711, 628169480, 829324462, 560330811, 366913690, 803886106, 340714208, 520074781, 228763894, 205357097, 551473279, 36743968, 811984321, 125037713, 953855038, 272305514, 411060791, 918728085, 151147947, 241767638, 255052989, 51041918, 907561684, 150608857, 115428310, 96664742, 580022216, 540298487, 442090329, 932920989, 882203069, 584942211, 269433622, 848947552, 302123719, 378774196, 710499913, 94173414, 238131142, 376905833, 634053581, 517007387, 923747106, 48126412, 922967542, 451828964, 730858905, 377624542, 624360863, 523748726, 508866600, 175477102, 741572898, 106026837, 636852063, 774852407, 406317721, 146659507, 767207266, 609795660, 718645755, 792240930, 636188711, 781148747, 886147446, 261413047, 906226376, 339219718, 542792278, 181051404, 265222694, 921721651, 351747379, 237489760, 939236218, 780058957, 117941272, 944591817, 357191472, 971026447, 2042149, 829428310, 903604472, 836022582, 97409813, 822532718, 497193121, 967209268, 792825698, 703359239, 742327082, 326749035, 337284915, 179454073, 37174092, 829104001, 486668689, 926322729, 687638542, 104696700, 476821083, 297529201, 451854112, 500429868, 581658941, 269361888, 22819639, 452770417, 884952279, 756350940, 251542991, 993720076, 642815608, 401707486, 908750522, 567967939, 240347031, 843978626, 436963339, 921062067, 555184291, 814159310, 274629167, 586553028, 446383150, 377005386, 713599202, 955768229, 697515670, 610212304, 609995648, 615922616, 567210998, 959606332, 811144641, 452752491, 637483947, 109037003, 725963651, 985141189, 497313138, 14807601, 425645671, 771052438, 922934316, 646281366, 29887164, 873670644, 735653916, 775369011, 137872643, 538087377, 339896232, 855678999, 918648, 648305067, 479960000, 143737535, 884549638, 53953672, 805454302, 666100005, 53891760, 698810104, 397750913, 519499204, 11438755, 898909102, 858717750, 957069406, 726823204, 869629822, 57687529, 375842039, 589888174, 452370936, 400062698, 898749281, 185668412, 490141784, 107117010, 327335523, 797060532, 283161684, 78454904, 537860312, 796441131, 960596053, 325623558, 522418377, 757815945, 141170213, 907495837, 702074135, 383762536, 95584929, 468889879, 573759661, 843762548, 397201237, 927199363, 233100697, 452388743, 327007229, 434364720, 124372457, 87989865, 258053903, 226651355, 573239581, 313896238, 450338713, 540703604, 975569686, 203432468, 221804341, 250289636, 946797699, 110918028, 985416127, 377328138, 18351192, 213718272, 646135102, 634077036, 725720592, 863618728, 365628542, 677440494, 981054903, 947621345, 751015900, 332048166, 92116359, 899253625, 400086945, 939366298, 794332551, 915227084, 556366151, 430431449, 252555699, 79006080, 938325238, 597383743, 988166031, 973934689, 777149927, 510556307, 859645018, 296543456, 434726025, 536633217, 291768568, 791706045, 546054698, 134058002, 695951057, 44948186, 248028722, 749654939, 786108516, 212352862, 890515265, 167518049, 669531331, 921221856, 688669994, 424882295, 187558135, 281871063, 525434692, 978542318, 421867838, 162263253, 970483388, 28197956, 304126445, 79718085, 431958778, 163424122, 730738241, 532650539, 698787664, 481273398, 231193694, 134291279, 738829064, 999227962, 768502989, 550168378, 46378571, 606374696, 540280168, 533595612, 813560797, 502946138, 399746008, 16092053, 152114120, 959023221, 93536544, 463190573, 102723022, 896519919, 203144042, 968634042, 961888701, 176497227, 219788955, 551740609, 234130668, 809450623, 800400853, 910039067, 136128009, 6112324, 7560885, 526608314, 184284187, 650973479, 38330212, 37629557, 355379561, 354644108, 294063061, 57708859, 485445674, 923447641, 164103457, 386419063, 473307333, 58401846, 229037800, 485636606, 961677190, 127957810, 513779335, 878954772, 780005901, 28268113, 93530346, 127807651, 748667943, 11670121, 626887747, 816413195, 769922704, 465990244, 794630245, 450868678, 762361358, 625891397, 203272874, 151234935, 97134325, 233176253, 271960126, 723539867, 370501197, 57901953, 184940380, 54285470, 309272584, 813567072, 628632318, 776250655, 513117345, 889827854, 867478375, 870105490, 228169242, 153754386, 483427173, 405445306, 215877125, 459951754, 888302982, 861484936, 570718910, 947874971, 440118084, 346692462, 965483352, 708598772, 23900723, 369335787, 57480994, 383229036, 357861310, 819004906, 317575123, 475313438, 364043246, 127644686, 207635474, 181704078, 855245155, 965055588, 870223399, 845831375, 65685749, 997340168, 282415381, 61218820, 185180416, 571586351, 545921637, 964347712, 182493071, 323217743, 334478642, 423843406, 741602358, 648775740, 642387261, 770999664, 275341914, 756977538, 683907999, 938014169, 579021252, 894046912, 795796333, 563128778, 596611799, 170295392, 577552612, 726873597, 953243143, 186505274, 592849732, 640013641, 874481255, 470791686, 859110898, 132974150, 470356102, 772705083, 414931195, 164200453, 407700918, 549777085, 433802859, 648179332, 899515189, 169932197, 886181721, 21365652, 479411549, 571674878, 433534233, 257910803, 427843658, 510775357, 479840990, 165589419, 194812295, 383057546, 592134971, 88814212, 908263356, 99484316, 512183595, 70368986, 691842119, 900881929, 229162935, 684900230, 783857803, 323614356, 464160954, 677921115, 748849930, 799717435, 828744146, 484218447, 15497214, 124790497, 726867504, 715623501, 324693313, 582306613, 542906078, 325649419, 575746934, 441735995, 317253265, 567832845, 564487989, 911074569, 786219736, 766023166, 16222761, 735379508, 730916858, 877978900, 613762092, 967878586, 694272505, 326054808, 731259341, 662538299, 264605534, 160970739, 200215174, 875875360, 524681508, 448639927, 486746412, 742436017, 586281445, 34198166, 222899880, 487612696, 888211123, 217402448, 428284958, 479153261, 748585039, 693905488, 325689818, 902238676, 539129541, 240441285, 278000325, 222519962, 269083529, 476328568, 623421359, 262031457, 308135000, 530823089, 996451951, 587866866, 488232759, 981487651, 703319882, 227321305, 449100970, 649046943, 964994122, 342366140, 665234282, 53793021, 891047572, 466299203, 292027964, 480404939, 598175016, 556363043, 183798862, 375308722, 884654911, 473784906, 180128408, 598084373, 288508207, 773296364, 45962042, 560470599, 640309850, 539749571, 936083453, 230412684, 390129859, 687669281, 221535619, 99621132, 810845910, 710438834, 60826883, 459543890, 513305345, 334825696, 183672114, 747586452, 822913005, 107719491, 549190142, 945934120, 434142125, 647660795, 119063017, 650923398, 104325381, 876090067, 161540491, 778061120, 242259112, 490574464, 67491020, 906019766, 982176951, 34650819, 75014700, 346058553, 506861771, 323380154, 721489650, 30370060, 752348735, 843853901, 504528822, 70191401, 395815580, 779083703, 543385623, 274101572, 669322168, 407731279, 133237829, 454859061, 903887370, 900541884, 35398077, 207223997, 124449929, 880632862, 863478110, 172736525, 572214885, 390652040, 441494330, 48816371, 597028710, 500277844, 925284259, 84082950, 349716010, 27098427, 785078148, 380484908, 132624258, 638222098, 801439816, 353140876, 414597227, 968576604, 829829483, 865738415, 352439621, 7363061, 582727074, 895823725, 455748900, 373880639, 507319691, 136015283, 256410864, 129916521, 460935248, 187268045, 341185900, 428978480, 714502199, 850657228, 452207729, 869688896, 371538071, 827058183, 1012115, 293616214, 434904538, 946687846, 410036718, 330978407, 845952813, 432631912, 150222982, 617140959, 78752981, 125449536, 803221933, 438338439, 931662729, 786392696, 615122186, 441994574, 47396014, 281666482, 35599087, 543626632, 429556649, 30765027, 994921324, 563517907, 55446370, 372866455, 904198793, 164082066, 864511545, 488908854, 906608388, 77550073, 787519542, 487360327, 699890311, 664322838, 782960719, 256768513, 428834412, 812789234, 653428227, 777460679, 111039367, 832345942, 797991603, 9445286, 446625667, 335187481, 503779071, 355976324, 731723024, 367499169, 714416669, 719068496, 845215346, 977598660, 42940899, 978633077, 491683384, 527861494, 430968335, 395017512, 968797827, 144009688, 490959476, 198426972, 270875005, 535416976, 273657302, 991638411, 646900363, 70736673, 667585805, 407480753, 915257145, 51775821, 565979703, 953210612, 913303431, 8800725, 972568048, 47317685, 281287449, 631742701, 240630859, 64895751, 746064319, 188279498, 867223866, 754003470, 840362919, 692992498, 273335582, 890511742, 159130414, 611061122, 865778915, 286182498, 386307771, 590687349, 589684416, 95532970, 233578344, 373057079, 921954141, 456463169, 798131233, 166711085, 26646909, 662494570, 698814961, 502517799, 816761170, 41106616, 710075977, 327591282, 82344905, 564444193, 347784593, 409209618, 922689380, 222891633, 947048724, 441235852, 214629567, 809851754, 447843696, 320273250, 85954810, 580635673, 562344563, 599416187, 857828897, 758525950, 418743749, 459956612, 403644923, 225683320, 506162363, 932002227, 131331244, 555444617, 63534434, 960628799, 806833786, 884443972, 679067530, 189718427, 779236672, 595371710, 928720614, 645930443, 984729512, 458914752, 892833643, 752528485, 161144377, 87006225, 423318183, 451365953, 623863132, 34283484, 880052230, 851221406, 856171275, 762127025, 290466986, 203837256, 157172284, 428080408, 554044248, 626025414, 690113905, 839247737, 269593118, 297121981, 746881114, 665645555, 309561602, 617763918, 39190085, 623501939, 726163129, 32744618, 731126530, 357012204, 973445699, 666663747, 793619416, 176567879, 770357129, 918458992, 129852252, 544551079, 880477071, 219224743, 322654481, 517912148, 551570889, 642419315, 795813463, 855177163, 860063775, 191219882, 125275942, 508445124, 529251723, 480290001, 567151466, 941553489, 937495723, 725101041, 524155611, 178553149, 800940103, 119569836, 124878149, 737310418, 837279464, 114695961, 335584405, 303334426, 465186574, 792349657, 496061249, 257209896, 391162138, 401531644, 845566114, 3965903, 781802258, 525231178, 384025310, 156377750, 530970600, 902851495, 609961254, 365181845, 899619993, 466622549, 861113687, 217363406, 866682477, 687954910, 629619725, 197315711, 990527103, 984095517, 873212980, 439894990, 658615131, 409911253, 378742472, 154225575, 499660806, 70211125, 801219739, 111427656, 39417323, 183854634, 370677664, 712601070, 959249156, 217051251, 188138126, 309685258, 572824069, 703084919, 370166490, 68818241, 581625275, 400845253, 70625354, 275671820, 468998772, 783689314, 261384222, 133382307, 424718079, 680098521, 242192674, 238710812, 760898901, 222963556, 164180519, 592199472, 461371193, 382116055, 411587706, 890479960, 487114319, 509428169, 318572721, 177636338, 552323383, 570050885, 764241764, 815588531, 378473730, 297192087, 449380818, 179915438, 428886034, 680517531, 101769265, 867551492, 577171211, 673775424, 620048447, 95823136, 227217702, 690034847, 557105546, 959625933, 509543926, 289421837, 179796095, 42456223, 463454857, 291846338, 642604656, 867813973, 185213112, 474371268, 141638468, 771833202, 580607965, 430943074, 374145587, 808893721, 127350000, 115014828, 428531677, 446355476, 104740949, 85148517, 224386531, 215557731, 949917793, 366454667, 771678383, 310872063, 999990226, 744492812, 749647422, 380257156, 597515242, 728452354, 312526307, 620008715, 326427661, 124451307, 157392122, 100830664, 22586198, 411009260, 386563858, 539364049, 966435378, 827619982, 880334830, 594103395, 849134699, 815697276, 696555223, 8752556, 479513145, 428182764, 864629845, 975503905, 662319981, 18325379, 427956393, 272268843, 732292828, 877521352, 348968475, 854350266, 834634050, 240356359, 593104513, 187232959, 440100670, 818719656, 71591102, 941252959, 881471301, 702746003, 626877223, 104564166, 911102480, 662234908, 565041736, 347852026, 113759808, 921017726, 703125546, 396912732, 428488826, 900431640, 113473919, 135457171, 893113358, 49081060, 222209309, 940172571, 207388801, 249689223, 204723126, 488981347, 378308905, 401269009, 672287674, 532385749, 596954469, 865542835, 790114290, 516254808, 133006756, 55566374, 758520872, 837186094, 922705264, 460180335, 766534896, 682847235, 108423506, 192769173, 216737248, 841379201, 962216357, 578177591, 644059722, 668693309, 472905467, 563146536, 364316002, 152505023, 229517820, 267770070, 659173090, 269278190, 413418880, 23041910, 711139164, 532891778, 572972817, 418229119, 675476378, 914511939, 976640896, 832359123, 194060374, 121788716, 61978983, 157822862, 735903140, 734289860, 307763493, 550230455, 546226818, 702072409, 657715629, 500523859, 551784139, 450370827, 442613129, 719776291, 686423426, 592671959, 315085583, 209098058, 391591825, 49830044, 734416511, 609894318, 487209949, 198091189, 414050977, 361819087, 5048368, 434354226, 281820759, 640554295, 619116848, 392930995, 802658996, 644433866, 22228236, 156786590, 237404797, 702330096, 311049744, 728981490, 301594449, 53163302, 604575114, 647433173, 560216946, 872003193, 583037881, 698980624, 419612417, 752683424, 668372231, 903479706, 804889030, 710962157, 708395512, 384622916, 455027259, 14004029, 486162182, 774607761, 826818315, 973830513, 83754650, 222975774, 757882417, 495351894, 408045416, 740184972, 641274532, 118706116, 191902082, 960533984, 684878802, 131180543, 962583510, 856631095, 327978409, 542524435, 227665378, 531733099, 849918700, 138104478, 365899737, 685521665, 59310497, 981903517, 540014663, 137971349, 226207301, 246147138, 953778351, 547185146, 399538883, 413788585, 400824337, 806042439, 691947908, 7499293, 143653692, 232553384, 791183634, 49039405, 527945007, 593706970, 825666338, 300873202, 29036799, 107001331, 61752318, 922950113, 495493199, 841255135, 768925041, 353134725, 893833099, 365119140, 78425373, 922141484, 221754935, 415384805, 528358960, 108095181, 916151810, 429603341, 626749700, 50940405, 81171984, 700163178, 873062360, 142207422, 816040499, 640006519, 107780771, 372077697, 428367328, 126575038, 456356251, 129737018, 364706984, 742746954, 858065484, 30759393, 882126471, 183837972, 906417353, 248706522, 51933491, 990725129, 116132031, 39665523, 975225224, 678641773, 354198977, 776300203, 333192651, 227384911, 688471338, 886797054, 197519091, 629602610, 121568074, 306632592, 342910145, 767185214, 567411034, 916995893, 347859683, 917075355, 151848239, 964899904, 168418246, 79402219, 647730591, 258215922, 680529353, 227993811, 112810939, 730507196, 779535847, 363402422, 362646454, 321667880, 518197266, 932380556, 729009127, 905740939, 636922839, 361261414, 958906273, 141359680, 994159881, 744882283, 501247475, 171829423, 847518143, 614665864, 808011791, 162400893, 530585387, 595925257, 319954666, 647699251, 759342408, 367450413, 285965303 ], 11421 ], "output": 3039496035262 }, { "input": [ [ 103116390, 857510213, 705099371, 409512036, 603574566, 965440029, 912345264, 93912734, 944664524, 470357688, 660864225, 583395078, 817609422, 954268655, 136685373, 917444755, 461630632, 884363059, 228675492, 685087508, 727839757, 204217129, 847006974, 800735623, 128757423, 413617033, 322255001, 594586721, 377972561, 815085165, 416701269, 28576430, 757518972, 514622257, 55149642, 697741460, 409879305, 551342713, 76252632, 228393656, 868779332, 545053177, 767178056, 607698736, 566722047, 741708326, 48640237, 673710544, 754839754, 549693208, 302873612, 402817060, 17568471, 36443394, 154653723, 341604667, 5014110, 769921521, 2945920, 869609623, 307553825, 625235070, 974737991, 626062405, 494544946, 955210315, 724607019, 746636909, 832944178, 459282317, 186240498, 220865700, 428698152, 560921640, 574604010, 315522388, 204278741, 362271956, 825246574, 919566810, 949758251, 501470970, 19765202, 814745968, 603786955, 158781499, 721528374, 973180352, 236737306, 406393326, 516896856, 356659549, 773237617, 170411128, 320645998, 362715933, 245830155, 498789387, 189563963, 327868329, 136102868, 92096930, 505613189, 796527772, 444228866, 408270683, 638259505, 326985429, 786986283, 32676899, 563105951, 877065881, 666339277, 884124997, 342446160, 249652221, 463413578, 719121103, 898530011, 514163938, 108671267, 168091242, 585315169, 88080140, 277097274, 163101903, 845646521, 329330027, 980048587, 998719184, 67428996, 10954764, 334434475, 990834313, 194668249, 996545659, 668282276, 507705157, 969460868, 831399463, 461040453, 930232245, 196910425, 946971235, 320976579, 803872018, 328166386, 455937151, 193164476, 673794045, 371030342, 25473307, 836816916, 26366788, 127496469, 94694857, 22282774, 558935735, 439733504, 234341972, 310369169, 125482543, 321764577, 970373488, 99161171, 107079203, 44469507, 470531966, 293273563, 46980356, 682488144, 164822520, 351315047, 636142049, 201674904, 143862596, 925815365, 372389438, 969829697, 604155683, 907122966, 359075263, 474183218, 761386444, 617749870, 60043182, 346960215, 587106260, 771575576, 689650890, 254205495, 339082141, 804014845, 188535712, 570913437, 18196350, 406154354, 133142298, 840876430, 38074283, 773975137, 712196215, 838615753, 870600256, 939417839, 659889669, 477762659, 307552482, 467693992, 93392537, 693795869, 504032313, 961395374, 82024874, 59308123, 454059212, 372515578, 527163885, 160794117, 420321692, 616719035, 523744117, 973908740, 971052748, 114012028, 958842965, 603017839, 331546127, 557710485, 922903844, 89649064, 940052167, 999325158, 163006395, 317518967, 129649055, 61020037, 636180330, 488686503, 364774713, 255876945, 105823705, 786810413, 189280303, 734426286, 70829060, 111854327, 932360604, 198162257, 471936644, 526925983, 983895558, 402488674, 823328749, 456247690, 136244080, 546902307, 842722488, 774087437, 211296014, 256404807, 930272874, 777316259, 708324194, 885815648, 338243663, 570783271, 664337653, 622161148, 221514276, 920411765, 982352768, 181770221, 282569949, 220633376, 564038071, 365181514, 79744958, 972477980, 755060881, 749920608, 122503712, 836301616, 205474001, 677831948, 26722151, 428128858, 582648787, 610760671, 786847948, 674716846, 110280906, 833532239, 695457344, 872443522, 668082909, 496350988, 800568714, 406729808, 842927682, 23807058, 490475026, 691617604, 563939175, 419451549, 189751961, 633446457, 14789112, 712201147, 5501280, 255632066, 244344546, 438068650, 582350541, 853285632, 402266153, 361101297, 984405360, 690401388, 112547885, 79172685, 479305521, 830447368, 397624945, 333052669, 532836318, 578574359, 59436324, 134631567, 225375463, 880019072, 109722483, 312062609, 847061986, 307830639, 364075788, 553542076, 173813361, 445552845, 285068741, 850546020, 895965472, 896517185, 367657203, 572197136, 398384310, 602835112, 67228742, 295732014, 456028594, 860007642, 62997266, 359361448, 836754322, 980616605, 884381853, 589856810, 103064683, 268234469, 148974057, 306381623, 925181846, 495978387, 256971296, 28002312, 343335297, 36270056, 705789940, 954400411, 461401161, 924219682, 250465433, 561700113, 330919854, 781663133, 307207382, 137032378, 285543125, 953710388, 295757489, 89070189, 764033848, 552566422, 212435393, 728297817, 274582789, 688479232, 377557846, 366982641, 728099056, 120390972, 877530739, 765527057, 998714108, 25786526, 78649173, 7973875, 152235798, 61492615, 387591754, 4506641, 70600591, 533827561, 926941067, 510012076, 60027050, 239222073, 636136138, 416219285, 504060154, 237023188, 612776105, 275550195, 852827537, 172580240, 306266190, 712828943, 84066983, 524576336, 555525895, 819906869, 779923210, 55958274, 79382331, 211257768, 792911279, 763907689, 892824534, 456760821, 537412347, 748245964, 46107792, 322370418, 744252304, 861933976, 488735813, 984290573, 663657229, 557607459, 898398049, 600889599, 64274352, 775630290, 499273493, 668500437, 848184087, 804738732, 853776254, 896905363, 478624004, 18965622, 798617554, 564068537, 266004542, 834085637, 184215673, 682506745, 186544621, 273107200, 879518781, 428448859, 195324205, 283497862, 552280520, 282691292, 207677474, 67444819, 813672023, 944553176, 123888963, 115561084, 522281246, 47627273, 265262636, 887351212, 718694068, 562928755, 377791445, 615526158, 881566837, 883449394, 866128741, 241842916, 253610188, 499961532, 887544190, 640941387, 830722333, 34014452, 384505325, 622767427, 112667135, 575630429, 109724422, 764735401, 478646476, 560486654, 280224861, 195506314, 611120042, 917573334, 335697059, 549149081, 460787898, 230282250, 762331589, 848260198, 64092055, 497424040, 680886950, 482796866, 74086840, 463677652, 17546542, 300975439, 249806167, 503320867, 304020390, 970057243, 283607853, 917496060, 79023762, 850066956, 841441023, 812260588, 466979641, 613974471, 775509573, 414797866, 231813319, 565865102, 197216450, 188115658, 355922686, 128125437, 794380141, 798187451, 279802627, 344045138, 891697561, 495243729, 418653745, 241086340, 117883818, 459256789, 800222492, 365228625, 135847530, 135095946, 513715916, 391983246, 725351119, 536702579, 758526135, 15043486, 135527977, 828929677, 869795282, 737277491, 242144131, 176187049, 448963385, 487727992, 951643028, 328989650, 839239708, 419152424, 972331000, 954004962, 352585636, 476239166, 921555849, 659773042, 56554239, 9192883, 263774641, 193528474, 259367580, 425406047, 149743989, 101789249, 670233889, 93735375, 737561743, 842843273, 734686225, 823714554, 950663748, 426566128, 576523390, 931779248, 215651422, 438052737, 98104337, 657415372, 815581452, 902074298, 355326667, 293626210, 187936130, 661841444, 459524145, 192111498, 114617293, 507064466, 570367019, 193172634, 120558913, 86688479, 220924708, 206806437, 860286005, 880007928, 702727151, 47740396, 87974023, 836500825, 842873245, 460035333, 117321889, 316180889, 736190592, 786713075, 41989563, 616809090, 515008899, 7176516, 915668357, 856021462, 316211255, 505146023, 640506796, 921027983, 897198106, 134421884, 685242465, 508541802, 425185079, 714197859, 19898124, 864708383, 191535229, 639560655, 124204087, 217122065, 911096357, 33951947, 971931100, 663059183, 492215474, 788722327, 344382921, 315446910, 371589407, 385495705, 607634000, 535944706, 574363771, 808628969, 172675507, 770535491, 887059518, 99587316, 685283883, 168127266, 92028313, 542385559, 653345726, 775930358, 600709270, 975830980, 324305818, 846149308, 201876788, 576439043, 430156218, 755235975, 39398545, 801894307, 527081347, 705233188, 540768851, 714896379, 815641947, 743681128, 595412195, 744508125, 692254185, 447254485, 79727913, 596667926, 93656557, 490019400, 995729728, 124309737, 129439149, 711700501, 573945483, 548975268, 703303685, 799649300, 841096908, 300763872, 162129951, 930210766, 331666249, 216319733, 186011782, 55495235, 882012019, 110889653, 985400548, 881410855, 941094732, 539138066, 488558426, 579962483, 701098501, 953200881, 776044321, 829950718, 32444137, 365198813, 277327756, 138003004, 870336843, 438898883, 753678704, 552395844, 63635047, 478731763, 904689607, 392226186, 336071956, 831825173, 119880312, 838791264, 788908582, 479447039, 194103058, 564456838, 853959705, 356357124, 961378344, 290552274, 341507724, 97407069, 613977855, 578538977, 370560176, 507525291, 66248123, 158270800, 731781217, 719177093, 383969056, 283105753, 844282899, 107773471, 223257314, 263611363, 354919796, 421831866, 349999526, 647701225, 430994187, 768679904, 701682308, 562381319, 528263760, 144694788, 994746119, 661895965, 943170927, 630890936, 74817014, 429031670, 710444956, 412851070, 746210342, 934338707, 150504306, 203735717, 388155314, 806471853, 727038260, 376212947, 122476429, 918851047, 748152411, 178373337, 799516034, 979080004, 315131434, 667151380, 636746117, 732351233, 991074668, 881395725, 766932907, 449844771, 282940603, 34330961, 90875453, 54154404, 723089583, 824006243, 504895467, 148814113, 928114703, 724072950, 91046151, 959378889, 499369276, 772795631, 804309891, 465662711, 496711633, 561754060, 138646611, 929529706, 265296626, 507326464, 230285791, 369728651, 614699394, 741930237, 60850338, 649552358, 441301774, 438778836, 729471257, 447026963, 391047079, 446195497, 224474744, 112956350, 346824435, 79223530, 994417686, 90405853, 636245765, 718447473, 72155111, 995181864, 194943023, 603768023, 92706236, 139562787, 761950439, 273338043, 442805117, 388224250, 978073759, 260915405, 1150330, 969519647, 587834711, 982032344, 709655936, 373469945, 822632937, 423144946, 114196005, 157227609, 822938953, 930977520, 403981591, 466621364, 232108746, 193169107, 879331989, 427881109, 964057952, 912943986, 916995437, 785232964, 939459181, 143100768, 536018014, 329549949, 414208308, 453871499, 680584179, 981624942, 772584091, 704741027, 930750350, 427074253, 696534486, 543758594, 950865594, 909529984, 869160072, 671424136, 646987807, 258211938, 821975956, 657452834, 269682051, 376561111, 509671683, 43937284, 919180909, 429300961, 127616389, 808285757, 95531693, 898628987, 888169424, 350456711, 865905649, 473394762, 571065675, 43768982, 367289399, 426475060, 477542774, 401908513, 551539507, 411406448, 401164419, 573300669, 676779029, 547477834, 714014851, 626579826, 239296919, 711899755, 783729501, 278051628, 196554810, 952646571, 410763039, 902259417, 966063499, 448059506, 520993443, 273190996, 583128449, 151829422, 175392347, 278435312, 374682178, 748675528, 864361271, 845731020, 141491854, 99670513, 410388469, 477668541, 946388082, 209836200, 801514821, 62797349, 854831341, 394657035, 774210228, 391935984, 638131662, 307875223, 122248966, 349229401, 597939475, 319743739, 500295957, 246901479, 144769340, 729259394, 931692325, 966849428, 118649195, 563829450, 570025447, 971695498, 350261069, 541327739, 230666442, 744339906, 983888000, 871513920, 664527184, 360072474, 256618341, 908001457, 395921693, 675720026, 370493224, 630933583, 251013582, 265591758, 155738582, 120554240, 351779734, 777711143, 835013187, 882394494, 968404671, 800793152, 528079014, 433410733, 309418877, 682329266, 623562789, 11794873, 154588288, 278519510, 442332285, 638584839, 788579703, 500089581, 689775291, 852986816, 188272835, 7444748, 373891802, 468162668, 571467751, 22487922, 62702636, 435756950, 705306656, 215770839, 634938988, 923921597, 105341419, 839813630, 210725461, 318041152, 175932373, 808760337, 859093236, 837378395, 602393114, 280111909, 783204852, 789941918, 689657995, 128222713, 344635717, 581601648, 843103486, 696832762, 529833126, 480232709, 989337953, 474078210, 686377389, 620712297, 837536248, 38826462, 237078222, 604975839, 345680963, 496870300, 447320381, 692442530, 501031849, 749106933, 957011478, 637386911, 925030835, 208387448, 206219116, 900504000, 713440636, 367148859, 689383985, 748110644, 601668857, 545108435, 433700853, 776022032, 363530044, 663946017, 861644837, 548535526, 938146651, 867485664, 813504237, 306425322, 27563118, 119618687, 581757496, 550303245, 293154927, 551718734, 553475710, 816263289, 998043287, 89723174, 142054634, 886307057, 175154920, 940163688, 868542901, 966464590, 427355790, 37139217, 573287718, 603465001, 901525970, 136026281, 85842308, 95713275, 823998235, 587474335, 231382247, 870376689, 456519757, 914813619, 509102866, 941250729, 187233477, 90253357, 651279133, 739628465, 345292776, 303995064, 547385713, 847136497, 808777097, 912624527, 31161331, 393685224, 201898310, 922729686, 118452465, 336700099, 137943491, 766899208, 207445179, 102488969, 254896445, 877492021, 163956071, 664046233, 821239942, 605009080, 92050633, 743705419, 87852401, 230462169, 799449976, 810224450, 216738956, 81569949, 587336066, 214843125, 79502972, 506955209, 154808292, 173975649, 144501656, 120858893, 766239885, 82080031, 320879888, 566064741, 961836904, 955223382, 795001402, 347129308, 962428791, 424412281, 447378767, 43222502, 223420890, 498056679, 800902854, 832526372, 946798260, 175249625, 922638371, 50982696, 326127731, 586574955, 799075528, 638349713, 972044129, 732457148, 549788588, 820146225, 113369075, 630165102, 654650934, 785624087, 977995552, 290053173, 626348976, 205420439, 578568182, 32732077, 450801524, 151691309, 781167452, 705519516, 937153544, 921693271, 301425538, 441576629, 757372332, 308182075, 996558179, 332251252, 470613049, 145550220, 951665426, 443402417, 221441731, 982379622, 747248392, 965106596, 792515236, 22738241, 364671768, 709021039, 6288024, 503844391, 962644611, 327330082, 121015735, 890121682, 298544048, 873430542, 886469686, 590372591, 661007392, 799331666, 736181945, 430751411, 920251106, 215573655, 771499602, 575332204, 342406721, 925681106, 975461922, 835591904, 493593477, 124846369, 848026149, 15224421, 150273292, 660850112, 10619626, 790543495, 764439217, 29733357, 669118625, 718827135, 818729058, 912092634, 502205833, 705216226, 621674033, 197815978, 912511468, 690473067, 910448561, 318213837, 841262230, 272719526, 733349181, 168946382, 166028833, 805525272, 6660806, 385336243, 589954318, 634007723, 16745391, 783170535, 205064246, 656105116, 456097598, 425081831, 822194129, 41205464, 876883704, 350417915, 351403378, 647595807, 996495389, 440631079, 842468185, 643526652, 414007560, 992618612, 70689275, 242363280, 814109393, 876928423, 462733011, 953818579, 735936594, 23933007, 467900277, 790740284, 766698511, 239561627, 563065188, 588765568, 97254627, 573779481, 593737335, 277691241, 430868530, 169064327, 306121080, 999329370, 936318485, 880615083, 195987471, 361332498, 306700125, 8839416, 481412614, 627380952, 783582090, 831190492, 326408846, 516058976, 320737826, 465893384, 239492846, 983782302, 601530484, 810465874, 914703433, 510426621, 223845143, 680982579, 763715090, 778173947, 132729904, 205457644, 607458266, 379357904, 351458500, 232665094, 756131546, 111319169, 562543174, 871372097, 930204625, 933729480, 475917265, 799053232, 792752345, 373074656, 506155356, 223372979, 970411872, 276639018, 71666442, 837864713, 878445004, 464676300, 982920027, 176998461, 164558159, 596224051, 550446356, 761991623, 682012251, 372786724, 764773883, 52040780, 284793824, 476030794, 840444645, 616933077, 213106300, 853317416, 197971826, 863421783, 846394288, 818962658, 352737392, 807121307, 640075734, 952856267, 212989220, 10567413, 496565112, 786907439, 4633003, 450238466, 769097693, 526089894, 676747132, 302226907, 68494203, 617074287, 306696774, 502454456, 300633373, 165918423, 84966902, 923494597, 458766850, 53342834, 762732517, 210280651, 707562667, 797807353, 723287980, 512866827, 334555848, 564443554, 15464318, 681852613, 139450660, 352777685, 287950812, 255789548, 741441076, 303433421, 281631594, 644376998, 79246704, 883137058, 263263849, 972777588, 988707726, 652884506, 311012126, 878328548, 668674283, 116634812, 410227349, 103454778, 222920535, 508062451, 177000261, 240974931, 903747090, 32537131, 507362498, 593618566, 416442963, 346742335, 84689755, 245778487, 194463826, 241517633, 873250375, 309951171, 426959087, 309114012, 473675125, 531260033, 102025471, 255084485, 431441867, 802698136, 778372412, 831631984, 605445006, 931709608, 518888635, 874001016, 807084090, 658225879, 621262557, 995028278, 478394881, 180991546, 466015298, 512297087, 540571566, 805611593, 59349791, 373440361, 391629818, 369756774, 224648449, 561730153, 347520353, 301599833, 600605728, 208436425, 514211953, 1721963, 532489738, 701902743, 101568660, 656760080, 470756673, 587088097, 552413155, 661539164, 223827110, 153551060, 352761675, 712592140, 8591142, 407452843, 389678585, 819849452, 961880136, 123392018, 461278677, 820225354, 974619856, 568848204, 683952071, 76225682, 730871235, 981390351, 113344810, 917243871, 383639911, 614227590, 227419705, 919115234, 449319546, 189461323, 846720852, 957819917, 33082910, 46567976, 712480366, 301566289, 946675746, 863170390, 2071891, 832397697, 533853591, 443036431, 724085269, 711584842, 855384673, 720495291, 843702775, 682252395, 700928268, 593003507, 816381682, 388712857, 981064940, 627124788, 362905997, 526354443, 129795019, 914654801, 660649212, 571387410, 810462112, 887898113, 261678199, 380487432, 625839844, 223928656, 919388390, 124797104, 360285848, 204345211, 509526959, 462446896, 186373488, 577873048, 52912412, 582856884, 379502233, 847139049, 486024438, 989851013, 256030555, 328488385, 141491462, 678487931, 642863336, 348386046, 110015779, 397091914, 818284720, 649893063, 660963309, 819719899, 189213217, 700669015, 182060740, 321993146, 488119235, 706976027, 660365586, 298327038, 862934787, 95846073, 107844375, 330610377, 753258027, 299308144, 136221929, 2754523, 844781898, 61101839, 984802656, 692721244, 557365066, 249738877, 432403166, 787780821, 80736872, 529397115, 742237418, 590181082, 38407739, 857923162, 901325998, 178161860, 732930663, 692469709, 752381267, 775585239, 462459471, 470369049, 530110286, 766034021, 904181852, 252681351, 222386147, 486842699, 290472657, 306226601, 107175057, 657844816, 159383014, 378737918, 715381629, 946973729, 608117492, 982538081, 142274829, 921439749, 987408694, 93071767, 309547694, 299579292, 564505457, 926487994, 510856716, 688710375, 614295969, 729649110, 890946063, 786743010, 344228504, 256852975, 27085322, 332458980, 58130424, 220468700, 366868433, 801303093, 809822101, 928994050, 770474716, 205394047, 434932600, 255064470, 415175237, 41964240, 88742807, 316901058, 50471489, 446609791, 548306296, 262694451, 773794647, 572496973, 490143523, 268284555, 163506536, 608077369, 95113633, 83513245, 126003239, 872116063, 803802487, 168228905, 332294340, 716118478, 50614802, 37189485, 167873406, 774385909, 13427870, 109659308, 87727834, 535742899, 863879836, 766981241, 890707366, 956636318, 513035453, 258825942, 355139153, 911447060, 261723872, 294886390, 770191271, 483226114, 715370050, 627493444, 791355773, 869583124, 667868260, 669594314, 788182058, 286647070, 793294120, 133807296, 337976680, 282620270, 147928768, 561369957, 597110793, 442318347, 767860926, 784127082, 652021406, 676927039, 850659425, 542019572, 78365378, 172099791, 466463423, 503169791, 47373974, 989674750, 416999344, 455216733, 83583797, 188780459, 738923095, 667953553, 854753018, 848300426, 622005872, 39899852, 39392083, 839849078, 460529870, 35590008, 458963519, 33282397, 791753460, 776425974, 484163063, 75338087, 698414313, 2167800, 274931426, 405119819, 94527615, 767083208, 858330034, 44447196, 541354747, 286396045, 18859287, 890457011, 13276475, 720848181, 87512772, 483601023, 759640684, 710388594, 28073295, 692399877, 318395099, 486248906, 20845003, 445439506, 762109750, 683967894, 28088459, 349521105, 881963405, 827778463, 38098139, 735537113, 951147184, 861872763, 152234044, 23814289, 124714006, 173040859, 196550668, 654959721, 668656821, 843944067, 780857412, 71408588, 158903612, 650943721, 243978915, 529344601, 868261825, 842385385, 73974220, 162962297, 608461885, 619506677, 94682526, 843985867, 987572882, 656027728, 4622926, 372881830, 189840913, 921281601, 820605591, 826238057, 651179408, 939965553, 435210739, 946289263, 139768458, 110559041, 955990452, 844643174, 887249655, 356244278, 550795653, 690738370, 126654698, 248030620, 636350352, 483971321, 822180234, 177242881, 160751208, 969940614, 462639534, 371925777, 94994408, 902936006, 676319066, 333131859, 655575027, 486834100, 524343849, 265361426, 235023136, 661503160, 997582328, 46828423, 761303831, 604718006, 731287728, 349048879, 837638082, 693797486, 227426830, 761674088, 242230797, 235667951, 156319712, 746492571, 49875869, 683370293, 28501827, 955991379, 362391237, 410994291, 477182381, 891661408, 165556601, 26378324, 40329180, 668787768, 60531090, 573882913, 75198303, 210368665, 963926794, 650028978, 231528922, 536245432, 957284426, 125276523, 520948279, 755270621, 36390443, 428466646, 507320031, 647672604, 986241712, 90611311, 741959681, 184763670, 806809374, 681435605, 630516624, 303932387, 927915980, 855822817, 893371759, 137322867, 186220958, 730660364, 839617630, 610925530, 632651435, 45380977, 441954296, 250649215, 491330585, 362978200, 624194192, 686522701, 779556797, 232201208, 113869123, 283856286, 936560347, 897134959, 63430347, 813538159, 518570267, 540263847, 435256047, 832911287, 318941932, 85997086, 835668495, 878315295, 316125496, 470766768, 379201300, 534015912, 824821961, 157051240, 474556429, 302568630, 61057019, 124108250, 263135820, 493269611, 824654092, 634297038, 541027601, 821929019, 775764498, 332197978, 157584734, 372775604, 304364330, 14250621, 303841469, 477160182, 603067825, 300674941, 992106081, 722980094, 334406577, 9898737, 322733594, 30894497, 656221568, 302007325, 819340108, 367268827, 505128176, 347208546, 213165887, 802307906, 492776021, 92429354, 765495885, 950439564, 748143395, 909945729, 733653618, 274422619, 740163492, 864066292, 98740011, 378893304, 354055326, 287343018, 666248945, 55285253, 451587543, 814492955, 40439604, 999085235, 633710578, 11379659, 31043141, 979920285, 312307160, 871038046, 489333862, 813336549, 654454220, 425833488, 79615579, 627730314, 6098136, 108700350, 830207596, 332930560, 27189093, 131946086, 305935244, 429631135, 906320219, 111825545, 199141077, 672043718, 446998055, 873633649, 695403143, 110005000, 223959871, 126934738, 753599733, 787771415, 829320976, 8226661, 162381866, 34741494, 606127846, 107471011, 158120141, 338517677, 657585167, 45519426, 656275852, 393099874, 391040890, 960117648, 952623052, 841415847, 626807154, 725558708, 651802552, 472621716, 915698506, 511182834, 793306691, 403010219, 660715336, 620982232, 228679238, 801583387, 334704701, 559933918, 527957108, 68723101, 663323596, 389254103, 902850446, 182452749, 395294682, 796135559, 696646582, 227422986, 17191982, 565351161, 496673406, 420948303, 727069982, 419212282, 870548870, 85497062, 62290432, 530091700, 945302520, 715125691, 907211724, 754515177, 888590862, 609177860, 475638160, 827284515, 85142782, 267096928, 217205397, 732100470, 538837057, 787113122, 85012187, 292357216, 242400641, 16590079, 435475750, 556236334, 962362086, 647310445, 67128296, 247887374, 507466368, 781188595, 402334138, 689483446, 612085519, 550139637, 775248174, 451445228, 936573350, 659260499, 441713366, 923436586, 395788329, 413242240, 835323005, 468228273, 475948015, 750302133, 783333615, 925776779, 38391913, 19122109, 432444282, 293918295, 713994703, 7665308, 517611553, 759165291, 896771090, 909101405, 855340242, 149262914, 836743737, 967421715, 544308213, 311651828, 57205793, 101628923, 502490818, 373152674, 855515750, 59107873, 584075035, 604182482, 935974907, 821059520, 760451243, 317181403, 483371968, 42161686, 9899561, 989937046, 805847759, 860829969, 669431875, 643102178, 705537457, 819008694, 811558789, 273472077, 21147339, 353160324, 761046625, 148521586, 385743334, 474378794, 33358270, 196750875, 271632754, 748838779, 357473738, 288798288, 62077345, 720788420, 392625265, 658769218, 492614712, 276574493, 421387179, 270512910, 606431917, 956193054, 3544345, 492940591, 646147906, 160933451, 631510410, 100328775, 978980048, 995356185, 281372918, 379639697, 847142148, 121789267, 133629154, 414426205, 573894257, 311352525, 412715802, 243808377, 771431718, 321617085, 384750918, 818726296, 533984246, 948681522, 726071241, 460655085, 818362978, 745057586, 701302265, 843536299, 507752249, 778751132, 131831872, 781721882, 711060615, 947189024, 201500004, 115142879, 15183764, 831308196, 294470175, 379404536, 784055238, 219472692, 82477717, 769564369, 468171230, 859269943, 910844370, 802122279, 455896818, 829252524, 289226778, 72529930, 58999462, 329519258, 539669776, 736206502, 21430754, 550809089, 799403345, 577926765, 786157807, 82610743, 937205572, 125917248, 383358030, 99256969, 778699792, 239076655, 965891565, 66012158, 930223508, 604765237, 352013674, 730557177, 891712025, 841000463, 408404669, 280780388, 676421382, 177898, 577820992, 266703263, 601563823, 580023391, 48461777, 655122916, 975121539, 481100040, 445027614, 384361929, 596510606, 659069418, 90805913, 954480488, 572621891, 413384094, 690391238, 308135261, 954379554, 469436977, 348001361, 905609895, 585467011, 850987971, 283746816, 991434855, 901835621, 477989691, 780420924, 676920990, 876266623, 939472899, 880238557, 384635855, 486396305, 428121858, 838032327, 999993801, 538250360, 258327788, 336290294, 765131962, 456971799, 481332656, 94047363, 591950894, 653813196, 301943415, 742013316, 507993043, 481555502, 100169370, 415776492, 866606852, 57559534, 12147089, 866837891, 529201139, 429889709, 468767311, 494517597, 668132475, 625079092, 939474543, 79669854, 298846034, 582485515, 218487594, 871609846, 369603807, 882659453, 656837712, 710518621, 805407706, 670276823, 971798718, 877753978, 431346181, 390208081, 540102032, 434232010, 429266607, 619173605, 382228234, 256473875, 461474799, 271548214, 383415462, 941626347, 158008769, 658691407, 232139136, 475130379, 514406743, 292523572, 649922891, 468866065, 564384083, 20029283, 617738344, 839033640, 738849171, 625134504, 533866771, 434207331, 210288768, 230517417, 852444500, 349137595, 295107382, 585716139, 719046718, 833766644, 650115478, 68622297, 378012693, 476187892, 206674721, 222594886, 637997271, 446265584, 592701832, 745940741, 436326132, 2657591, 202932839, 870375933, 787895028, 846240966, 564073623, 906633861, 302095447, 86864939, 245752729, 91031482, 738000512, 347359881, 187684606, 979344206, 826885443, 686966111, 288213576, 656097046, 459256352, 111800367, 759650023, 246658888, 223177300, 842493638, 240580480, 857966566, 454875770, 792830348, 889166098, 109197560, 286337646, 710882521, 273845650, 448616659, 328002604, 105160543, 450660717, 432485541, 196180510, 634500614, 597877598, 478326977, 154406342, 423403539, 155554454, 743855314, 86608587, 439661356, 110072129, 268386835, 505876859, 526057229, 632852727, 16731310, 412314582, 337359455, 377651239, 897043822, 214392216, 757055095, 444903272, 699968517, 967371625, 186744293, 489924597, 224906090, 477071970, 183160612, 298396552, 862792131, 27766604, 997555386, 420598940, 128162760, 127785210, 855580197, 900502751, 739085035, 158408828, 74475482, 276322119, 302209283, 40675612, 306213509, 249517399, 762609721, 613536898, 534453157, 529222625, 553561075, 911468662, 68879420, 112783712, 456503359, 434171693, 832407042, 983508377, 75352818, 160741098, 775047577, 911641846, 494806343, 451924508, 439605883, 145177988, 448529721, 462328100, 552261273, 670048617, 756621501, 331753247, 401476016, 340328339, 562916502, 740151513, 293024753, 911307873, 653095320, 34226357, 50779625, 901858591, 680063715, 613704136, 247874240, 838899107, 312522997, 501476267, 667228223, 61163110, 578832907, 674001836, 841138984, 335056615, 660319326, 672215924, 610125063, 107779768, 609906391, 244075312, 83910951, 307168728, 110210609, 985439379, 264996131, 962597774, 580699866, 304563977, 488736147, 157165692, 564990488, 813478218, 374564498, 394212368, 5595966, 914196404, 678583999, 468563305, 829021338, 792870924, 79366957, 371736422, 799892098, 161304023, 271920300, 358759317, 353227853, 690609032, 788281599, 252157540, 8170133, 440724771, 463901206, 559458732, 700955819, 989579155, 925203162, 895457196, 56009202, 519398962, 598636114, 134261903, 452597156, 548108713, 400940366, 363920888, 444059970, 804915583, 907562531, 145373637, 750872191, 403622065, 680899934, 654740288, 564119074, 252131324, 744585525, 571172372, 779315911, 773223065, 739700604, 254384639, 543607162, 760514347, 780155177, 678755836, 512638471, 146152782, 926209179, 440143072, 306995091, 738095602, 132979923, 691851484, 289053178, 830720953, 547967908, 792447568, 450432907, 292750369, 581586278, 84388576, 985752876, 842243264, 169506992, 665018730, 818559795, 846288828, 314897442, 912407930, 264950037, 756709804, 382302750, 976617384, 574011161, 575416565, 701550387, 88356975, 669741755, 505771170, 769088813, 99835548, 442384651, 944692521, 498385299, 302237443, 407852798, 263152602, 176912658, 616961602, 790101316, 884971179, 325704765, 945429101, 524119959, 172144613, 77541079, 865963536, 782689695, 326104932, 924848361, 569828649, 786919326, 502166313, 612659549, 350653473, 799459207, 875342859, 339126051, 258758471, 419131758, 803777761, 817968300, 235906552, 457736831, 160032685, 352202714, 115042098, 443193075, 692259884, 821226914, 762340512, 89399504, 93514777, 298795802, 409217827, 981273013, 610823460, 309856150, 677083396, 493348969, 407361445, 899667120, 151704708, 423395162, 58402747, 975319441, 470578618, 242437966, 416092868, 750572159, 857567773, 60342261, 632242799, 574127703, 46094320, 954087240, 122310945, 963601560, 913912383, 31887166, 627620129, 388019782, 410464129, 424625716, 566839, 752713827, 577687129, 949490403, 960233920, 118205901, 585564318, 755447629, 333269825, 431204064, 358812657, 683252906, 74114210, 960628190, 424684697, 732501459, 997500779, 638510411, 729716310, 970953600, 725652491, 209572602, 484246244, 527491051, 851921961, 407380066, 434238553, 766389982, 856994134, 276055898, 349791628, 600579368, 935137416, 458769254, 833061023, 625037734, 431979761, 496537093, 167443178, 657891208, 330017023, 554222816, 966543248, 16182027, 673333776, 568007935, 848106648, 470126230, 555009268, 605719905, 924174891, 838401761, 246546926, 918946971, 36477012, 263642725, 518285711, 29743517, 5761058, 72443020, 264256835, 150628083, 480719131, 740687993, 986552452, 605611129, 378923559, 789494077, 112154483, 571162021, 667065778, 918016919, 191240713, 54016363, 812048358, 392435945, 673029222, 963224526, 962692513, 726972023, 228674309, 111924559, 786964109, 780557242, 730641827, 154189272, 757269192, 696279984, 117722811, 109699557, 983484675, 701141308, 574947231, 957216919, 14906039, 795054753, 655206167, 499604314, 970553208, 194526748, 308821192, 147820457, 64371107, 880739273, 366034532, 617689323, 153320832, 891660958, 113434354, 848406062, 725434064, 141951521, 278495925, 18511010, 986865318, 789051112, 583777339, 486193070, 414130104, 367208290, 535145531, 851541765, 868002569, 157495409, 161491414, 181782102, 16948280, 26881344, 325857358, 218091908, 604464244, 643665551, 538023357, 917235927, 623173125, 504399249, 877091584, 96194906, 539881130, 467723503, 846894355, 649673215, 557874134, 175954706, 77622982, 497497781, 838907284, 380756698, 762567738, 337044353, 722588665, 414011559, 852816409, 430490343, 739987954, 867961087, 114024317, 757620666, 817759612, 778164082, 444782946, 493235735, 676355570, 364445008, 910784392, 187102982, 499046820, 290830342, 976523876, 993169203, 66827037, 321336644, 416665794, 436747193, 425003758, 67784450, 514322589, 596516453, 396337639, 524819702, 319129324, 973825159, 495182414, 797376627, 957617143, 723243054, 891396901, 80683500, 409233647, 59993517, 560851883, 922362266, 896588589, 968475638, 21492935, 382180494, 957290178, 794487270, 797622387, 720001332, 70789178, 688921742, 516349225, 162140531, 443083317, 185975618, 192224078, 624871968, 137717416, 613349347, 628978628, 479019498, 194922760, 59991125, 765950316, 908939086, 72079247, 164240806, 799694990, 955641598, 115577270, 407588710, 810909072, 478301948, 948976973, 367090128, 820335117, 476382945, 599020006, 299532753, 623837095, 234461868, 496474562, 988184684, 704457724, 15048492, 322481883, 192242808, 529840451, 670862481, 58145376, 20630663, 861474540, 832826007, 438479730, 731818354, 212358761, 940845034, 602858735, 535297425, 312253232, 578528740, 548002932, 656672863, 531087555, 198493496, 116024355, 889405764, 298397937, 608337232, 304884618, 700426292, 318854336, 149380746, 437071421, 77635228, 819089092, 454903081, 390572297, 686155076, 767368244, 852461979, 870578800, 969767157, 891043257, 996534529, 314084003, 322337781, 217050714, 288890221, 700797411, 915909908, 2130477, 331971352, 232913680, 510957200, 9446884, 771457896, 678354248, 291041997, 760602721, 589753501, 314790159, 294639766, 490519736, 427490623, 7162083, 833884679, 527657874, 84498197, 299761457, 218830080, 323174713, 116452704, 734781104, 593459700, 963936981, 964070851, 535921104, 303609740, 141643265, 840494457, 182048080, 186874561, 731263045, 19701762, 64517500, 28630566, 692038458, 619577625, 814374925, 980977002, 289924186, 686297681, 582712759, 379471255, 86869382, 851726192, 684613818, 172461685, 240393449, 869852231, 586888382, 542389087, 988383936, 467745883, 420034866, 225081365, 655645438, 956177953, 742133930, 467901910, 781075093, 125113004, 217566399, 774646229, 328562453, 201264612, 761479942, 458568635, 770193091, 188808192, 128288031, 301443496, 8624407, 507185857, 205089167, 689837722, 96811683, 383136060, 2208596, 805233983, 385036056, 377154579, 350176277, 55036565, 508711001, 892640047, 183489514, 86761432, 491084297, 72255342, 365790957, 302258904, 376679705, 360961209, 893832362, 311269326, 196007001, 622105602, 474163028, 875658220, 920747839, 701465536, 59762953, 91983629, 399985450, 529979314, 232123666, 338719340, 363484788, 248830035, 667900051, 996187015, 156448658, 516257328, 746611951, 357594202, 986275372, 455151224, 460230382, 152483471, 444995411, 637514671, 696228199, 178465852, 159693439, 936933813, 646595642, 78333141, 926613792, 361592831, 820505344, 391231198, 40743325, 939984952, 471074008, 457213168, 72706120, 833861378, 345306610, 555887333, 637392368, 787702938, 135134409, 339457364, 907963415, 838944216, 299375960, 247221210, 324503122, 83039088, 106187411, 789717104, 416840676, 620410470, 454481948, 443438865, 417333138, 204780980, 750827791, 36613129, 868626901, 111289563, 446904584, 524352036, 777869900, 960684488, 24809375, 615941560, 240322424, 558412689, 358519840, 322862440, 320406023, 49474183, 563381113, 909660738, 922451335, 913651873, 847636498, 457966868, 429415556, 905682101, 388595610, 972833920, 906923047, 674900028, 147119217, 402665438, 663241763, 628582297, 307086821, 378649829, 476942596, 890920498, 24459067, 281367255, 976462287, 177377283, 443250259, 802191070, 220753653, 432624882, 227339947, 354224015, 803984255, 826514096, 825781336, 178038353, 799012583, 85708579, 789369176, 890836046, 858190375, 776256487, 75051966, 358414810, 241687347, 504338130, 28355131, 889745383, 287705657, 843253941, 203388426, 352813934, 65719235, 343605946, 560907244, 561572392, 916152947, 923819133, 840236389, 443247426, 500922414, 589061052, 344360390, 903774720, 981702947, 302028174, 221072709, 945159857, 916778932, 794799377, 274637843, 591363656, 667031724, 489679202, 57875225, 183613339, 232742320, 853920928, 604473486, 526508843, 516257750, 543851260, 375631134, 175282337, 764264856, 180944939, 95652386, 992544365, 642881961, 678446571, 925209046, 288620028, 477665785, 271899921, 492219643, 406930668, 539050049, 546064626, 558387762, 455280297, 391077148, 118475133, 37868925, 867921640, 24848941, 528601932, 70733673, 750471745, 270826992, 500747738, 667917477, 204117724, 881902573, 295008023, 721316274, 120614825, 771009640, 434008965, 631630132, 907433466, 901836326, 39785306, 537519180, 792921464, 316697336, 498498088, 91088201, 854213815, 830716404, 487351647, 990934338, 87242547, 678854053, 897043762, 229423910, 858889064, 750264519, 157876159, 705825041, 747630120, 573359162, 636898198, 620699300, 359499756, 233210007, 927518869, 496713656, 410498428, 303778791, 27955100, 388755867, 189760936, 601498119, 303128541, 254648578, 882227194, 771537971, 148002868, 480421421, 408364092, 910486088, 614609983, 253247244, 474043862, 711057552, 267001689, 952445186, 512902240, 466489992, 27299593, 756187713, 380470933, 498570196, 858154848, 162386647, 890805075, 934794752, 370869861, 892197168, 915109507, 631079872, 990031992, 882904834, 458483339, 408173349, 719574652, 316288343, 168713031, 5412094, 745115857, 966588599, 238362357, 169588592, 875896017, 52479664, 635889766, 885915489, 370425673, 789699873, 672472601, 211816391, 544833946, 419511977, 384735997, 854827107, 309698543, 706346542, 80292326, 90755831, 10319169, 134437265, 694074941, 53516574, 221067512, 296419643, 720390685, 24485567, 595156859, 165100479, 929541182, 434604173, 881213884, 421962752, 409080232, 391656533, 706072781, 772936710, 982322087, 283115340, 582009353, 81956961, 329692988, 156501935, 769532527, 446463517, 646925810, 758654134, 912689057, 753258391, 175908895, 334890370, 351508435, 447009714, 13770960, 187686552, 376095395, 776352013, 730129881, 70114954, 392499220, 110998582, 400726369, 553694365, 628449282, 614707542, 430459847, 413961639, 501519938, 714136962, 291099846, 852062431, 719825403, 245122363, 436194989, 488824974, 496462417, 15109633, 274907137, 186237676, 176813150, 159529947, 673946283, 997603336, 721487347, 161663067, 724146500, 76060683, 683973119, 322826180, 632521176, 504535790, 444866094, 530167821, 455849187, 637755556, 129324865, 47054015, 370535421, 12746591, 13638390, 205111918, 141495449, 50960384, 57122956, 550804165, 917096102, 142951748, 925121526, 632837946, 129141515, 211074453, 124724295, 746522024, 674577568, 70925517, 641783723, 318549669, 458809132, 727589511, 198254049, 295441118, 528927952, 219644814, 511759801, 766742350, 865460466, 992913727, 138766028, 572296349, 367612736, 990894130, 422276738, 718478425, 263453918, 93636200, 538024922, 61110764, 598388900, 192050150, 229062073, 377121035, 333446470, 833247610, 797329192, 995554135, 792050875, 499462685, 987979330, 240732071, 285829237, 579316096, 986236572, 939501196, 650096685, 940351342, 717571911, 41286021, 314116385, 12331485, 514006354, 465159034, 235168876, 979027020, 877645873, 440488267, 768240363, 357791280, 417844810, 867582683, 742108674, 415925165, 317955409, 26755720, 57034450, 634708270, 902400420, 985714933, 18348321, 26830594, 203974729, 625948245, 54934281, 891418624, 446384069, 169641287, 452409352, 879827686, 844435717, 928021945, 292391337, 28102154, 730351687, 988410627, 373082015, 576136387, 957959174, 569715458, 620211142, 545639185, 349200854, 938494358, 486794194, 290076135, 161432480, 574897121, 465352808, 388157539, 983790080, 26323369, 856308891, 867858892, 240510458, 958739394, 674863143, 7671690, 738773538, 858584009, 386457713, 842786111, 375506567, 515092690, 736536391, 81580195, 724940347, 417928727, 622456980, 212076189, 524277766, 968707126, 658680700, 563073556, 990742218, 12162583, 911807978, 227665795, 56124013, 551945484, 967786918, 956346501, 311279218, 984874015, 879001631, 601505792, 380717930, 526369564, 811244176, 898506487, 26706928, 769652579, 643034132, 35714645, 38345343, 613195334, 916199699, 670183970, 897750067, 736598630, 682626274, 149472980, 80143884, 373899440, 988260721, 25213106, 688511134, 899141405, 83849884, 137669035, 704353890, 531451959, 854905680, 581349790, 969460471, 907195050, 11963096, 633325442, 146760114, 654386756, 621770365, 64276101, 460597598, 728893446, 689322275, 524389133, 889742538, 413398329, 651152870, 971673815, 82578293, 307293737, 779615817, 130024819, 243052297, 414866507, 572882483, 168051257, 332302534, 892228735, 453530910, 192039500, 540490573, 852749050, 410425552, 508527721, 306577244, 905294596, 935243721, 437214338, 598538978, 973882563, 294739195, 484198906, 10172629, 841294995, 743200514, 757087963, 540221624, 138159901, 711529267, 812090229, 684657315, 530510101, 231123411, 435808280, 39419946, 95256084, 573629472, 195933077, 38191754, 645279562, 201693499, 988748727, 215144303, 716989518, 833747655, 383590407, 277011546, 931433593, 380505698, 382444986, 341421648, 487412483, 40653694, 237352830, 716273534, 995404770, 711471796, 275398949, 178638748, 540110910, 69307263, 141985925, 509092184, 764330944, 853210528, 495919321, 586861016, 492525641, 16206625, 172855234, 723959169, 514982674, 128701226, 709859138, 237132633, 436021189, 727339857, 721582551, 237844639, 648554725, 323849764, 490689061, 831724053, 610109521, 255238239, 130059088, 769690387, 251310216, 961656938, 261615207, 322192721, 888625818, 997932865, 312316310, 772413948, 387880123, 485396308, 980051719, 331625907, 128181601, 107352619, 610935871, 858064231, 746210694, 66436192, 222529897, 354207588, 649455418, 880917558, 817246250, 265222665, 66504412, 408773643, 158888952, 743583996, 491199694, 624475523, 520840075, 86851417, 278461093, 828822050, 442204363, 450602445, 113841898, 301017776, 224066004, 989209007, 46901831, 279121242, 504272433, 635535992, 832549703, 181378523, 713557959, 49475314, 847180965, 492840284, 242441182, 661437894, 618616755, 661690908, 239410005, 730028934, 126355763, 568587736, 962704187, 562606085, 792793280, 670148628, 776347691, 152740551, 802225737, 674146019, 265623695, 252040254, 186747872, 353348771, 483021090, 128539814, 962343402, 531818069, 693324692, 488940348, 602207391, 381965980, 241085228, 201544112, 812376238, 459679574, 320645776, 383735253, 767083631, 159463674, 952586737, 699714103, 284750830, 748912571, 626701307, 463856441, 7039006, 356513259, 407960048, 915814265, 370208701, 985518298, 444637887, 128358565, 563238621, 554667773, 100639573, 587600678, 685927314, 450510995, 816472588, 762754853, 971723980, 945065310, 727220732, 667320977, 61720265, 79565187, 562448418, 453754823, 249688150, 24916999, 952171529, 258548810, 362441470, 112318928, 127694078, 490266003, 762799104, 149726317, 997465771, 958362023, 881738511, 943301223, 833717370, 955586595, 122895849, 921638939, 341780685, 73886032, 264377406, 318195432, 590058858, 635179097, 644799840, 699222115, 111750154, 840146507, 390388367, 190379908, 206210612, 98616820, 567736644, 539436558, 829904132, 285230754, 308724200, 802170268, 458680483, 795331245, 766354485, 380587867, 914386305, 946507704, 204562901, 607997113, 229549351, 448944324, 404036654, 275645633, 606545283, 877791627, 265833870, 343086185, 280888749, 503643269, 947485117, 728121228, 170022887, 249151050, 225705992, 317036207, 372568497, 387057936, 906119613, 469941691, 725860320, 858848559, 402656196, 798594730, 559989587, 446454818, 180228322, 718501995, 938333871, 95332816, 432718170, 308489351, 467531319, 172245860, 992380509, 169020904, 947997798, 858936881, 681999482, 603163142, 795713897, 462112315, 443723097, 42289677, 799805711, 163079057, 593871487, 266246420, 351864705, 112441589, 28093587, 141220960, 690661930, 535609473, 285425078, 207458388, 389071730, 747463868, 333586434, 463987467, 962368107, 46794557, 163201914, 507279355, 743012103, 586010715, 991429346, 662977141, 61221023, 660020645, 444278358, 352080968, 986093176, 272993844, 544793163, 685898638, 568594347, 420363899, 471541369, 493860970, 767152239, 500761957, 664863398, 999589198, 619143092, 109642034, 468938643, 868693740, 923718964, 33659714, 933018468, 497126918, 980908872, 313761175, 207054925, 811430777, 768949186, 127361003, 475552492, 586821875, 33317272, 148742728, 608040313, 141161115, 243845045, 281284372, 799262197, 459793043, 984043288, 235296177, 735418198, 517173008, 11987255, 157676567, 902333137, 337180131, 861794491, 100840486, 798795910, 399148511, 892174215, 831532250, 928726986, 56162032, 693824662, 613814035, 572226660, 349885920, 746235094, 489221975, 156348329, 285679388, 356566345, 7169865, 948020626, 203310330, 37331690, 469796294, 607543425, 651720252, 381655643, 188271419, 163669203, 778352574, 888554873, 78558270, 293620169, 974704072, 389992718, 738888710, 523354884, 589425968, 158459138, 826735713, 727297574, 971988104, 642855096, 870892209, 850372741, 642685986, 836742226, 339594484, 415479527, 769144162, 227049420, 263664452, 711890780, 928603748, 481998340, 874259647, 432854295, 550931744, 48028703, 407575154, 584917466, 795484807, 23660339, 74732027, 469403738, 255410334, 121296660, 511155198, 530798444, 527511673, 658488700, 101587449, 78580531, 350769115, 277326811, 407109294, 449271198, 472653150, 316003653, 831151073, 185544030, 244570508, 539590312, 775365953, 788193129, 382550990, 916475751, 277814191, 302691615, 818984610, 613789060, 735768275, 705510487, 235052852, 724472874, 376278136, 341247029, 223798848, 210160373, 387304229, 891994484, 971801428, 920674428, 832356508, 412937224, 516353103, 314980116, 953380384, 259913002, 586272287, 991552519, 942930252, 707159386, 704878311, 360069680, 275698351, 818152508, 313445901, 1731483, 58439589, 57563876, 357203857, 376540990, 288617617, 182345974, 565124294, 353122531, 259851220, 751136334, 487929406, 534636449, 697642498, 169148178, 175751228, 548173856, 644428289, 356108480, 510555331, 55068894, 788489219, 568211644, 99873307, 11258298, 981222533, 2607389, 643201955, 542399313, 191008155, 674367786, 500171270, 75542179, 580051379, 980577285, 64804874, 531438965, 743692188, 457606772, 549484731, 225791042, 77884086, 663176412, 973027663, 314476539, 747435779, 52192800, 718725357, 387735186, 955451522, 189206338, 239421577, 628771467, 215253865, 413332409, 96756779, 292602707, 344379066, 694227216, 273441599, 972423847, 669572954, 633062348, 353296334, 977892393, 251576584, 43582815, 609663386, 105992661, 28313163, 492022798, 251590746, 410096685, 227654993, 753258798, 356615386, 149241496, 646805847, 574788038, 300206607, 881118355, 239183752, 125260791, 76087731, 575712007, 280345631, 908409970, 54040194, 80529929, 677511176, 187702321, 71183, 99989879, 563181561, 902219239, 347096496, 660613925, 231290056, 448062445, 846325116, 853847952, 11589994, 906818303, 664575785, 754674104, 655516230, 972836437, 768431507, 256174708, 296009106, 966888906, 875433538, 763739091, 498797009, 337729710, 526103859, 364926896, 306578673, 435259141, 478996496, 186240860, 800191068, 431214050, 513111040, 81396097, 902033329, 328882958, 581061685, 96479836, 547943488, 678166066, 253287393, 259757050, 369015747, 491272516, 484783194, 476036836, 621462411, 445893617, 585435, 190086172, 344781925, 280736746, 977740112, 105994300, 55839732, 967506828, 100762819, 698200519, 396360844, 769131891, 55779877, 137225412, 564353185, 899315118, 104112460, 620893676, 817615624, 241346165, 255999082, 906633811, 333280511, 745124362, 3578690, 571628463, 494946362, 301755458, 295562936, 677394381, 893904354, 503398491, 808717675, 935243114, 178049672, 481535412, 291936334, 212831339, 678500262, 247553427, 628930623, 231602287, 343673071, 875232009, 159740351, 640627118, 160271288, 514352035, 41517548, 407000720, 388210342, 732850334, 515293208, 343440392, 864031434, 852455435, 320251356, 549997805, 9528187, 703928474, 324962361, 544832116, 117539967, 287491414, 949245398, 226746249, 962994792, 977580662, 77448591, 808048250, 959996525, 81656829, 635095106, 246469957, 487417940, 981504714, 240316371, 950561647, 45455181, 106070819, 124911189, 618592202, 606921542, 239067553, 943972449, 490423427, 375597897, 44377652, 529679973, 204759437, 693228668, 748408798, 895627670, 64215778, 626329304, 47921911, 459245649, 18960141, 107734691, 658377647, 253939815, 919826805, 800016207, 705588600, 863836249, 852536708, 433036173, 490485545, 110860143, 931629073, 525693801, 687846258, 582178061, 854423698, 916673277, 107009956, 522352946, 585003686, 524800596, 810839728, 643832246, 105958675, 144505956, 907641768, 776077127, 610343405, 943929627, 123010338, 229736783, 93086921, 659647017, 246107699, 960062343, 237954638, 559385645, 576902207, 691448547, 252556593, 141336914, 565681418, 971375949, 515288920, 721612641, 666732935, 9865435, 889991844, 834132529, 293496906, 564759150, 250538017, 637534750, 970684501, 85425081, 29494959, 845403426, 236777148, 726869195, 917909604, 365993765, 642896363, 313039432, 994271913, 749190950, 451166691, 999977255, 682337158, 91918970, 279289876, 289224510, 615883773, 890659634, 899914499, 826280674, 213432368, 563656951, 602325424, 62690284, 94172446, 317363077, 387902282, 724234754, 692714219, 123557863, 24798113, 831475847, 734251131, 113059859, 16055991, 230416068, 78418005, 600326923, 631165845, 67315746, 43976479, 545083263, 441556791, 383267114, 700933391, 607025224, 128666881, 401528363, 738709960, 323635635, 231159094, 517351351, 561918240, 942261339, 437635839, 114356858, 513370266, 124889005, 735871397, 323325071, 21527288, 761846369, 828542938, 324526153, 699501242, 308834978, 212486894, 543215456, 430429763, 817106807, 230019313, 65834732, 597421566, 224513890, 802066677, 827122484, 234218964, 363798841, 662348235, 83945133, 251277685, 443979787, 265639667, 56257209, 520878124, 938098210, 618917251, 478280394, 328794500, 398038106, 640452223, 547709341, 432196272, 501813245, 745836459, 929187714, 959778019, 973907583, 269322857, 639648753, 168043730, 557450082, 426092319, 2025401, 407573612, 295910554, 611317248, 812717757, 495849818, 242636539, 694716505, 542351959, 120986134, 743404614, 414309050, 815435250, 416420217, 371113083, 22666966, 378676137, 500552505, 264282432, 550622407, 124320028, 729934514, 131335623, 76995764, 956738217, 148689673, 889367700, 592472462, 322098415, 347033042, 584025686, 860032097, 758951531, 29710279, 222736981, 385101257, 29592314, 795265448, 563182757, 823775332, 145732138, 85234072, 154616551, 684926041, 292475585, 996177557, 252803267, 714426706, 396681902, 89429884, 432744867, 820686440, 885320290, 650712275, 199629721, 932374110, 346807790, 739207855, 913854390, 592749938, 150794235, 62505112, 346342937, 769156730, 132267869, 130747082, 892371452, 694979209, 901899173, 404803510, 469028386, 938793395, 315228492, 574175694, 238977986, 610488704, 774454257, 363592544, 9593425, 809772903, 501606446, 624698745, 162433830, 818647793, 146526563, 174072728, 607713625, 90088088, 445482574, 123568922, 523398215, 756696770, 379701940, 287621835, 100128888, 783895583, 480323204, 262862303, 982178378, 438358501, 426363705, 951029671, 685204739, 127843008, 590883862, 77760632, 733079275, 68279433, 685591849, 881325105, 867695812, 49133427, 829524741, 464401020, 267906282, 371149619, 202199664, 499709632, 292054947, 839808140, 795923414, 890042772, 233003210, 735729832, 679979280, 106332101, 84334337, 483809907, 18286871, 690292888, 793611856, 162859423, 94563371, 881148005, 184849765, 732101949, 955224455, 814057809, 532016595, 539737541, 734576183, 292346932, 492831998, 85743844, 518689100, 545661967, 165461329, 676883436, 845856761, 958876210, 681198111, 239773659, 346380984, 88493015, 911165723, 369360598, 619657154, 843572096, 524314434, 314437692, 149047124, 855764724, 806913608, 773721858, 556052488, 322729338, 261668136, 218686377, 238700706, 65608611, 300702421, 104357110, 933893853, 303762404, 311867459, 867590454, 308805879, 198132296, 751770369, 19890193, 104077846, 328283164, 810664246, 368809244, 526484914, 500738408, 818305300, 11763564, 177946382, 625542215, 619420439, 761861102, 522163486, 983080474, 723539172, 274762348, 565952822, 701890143, 301383828, 877611775, 661229509, 373316712, 722632918, 561570895, 651028117, 997645953, 331984719, 408686159, 939115547, 32196429, 524684168, 773709464, 69164074, 341697533, 91352997, 312064805, 465244715, 212048906, 412955520, 999644238, 95305698, 231256330, 31851688, 441851666, 436927811, 829005708, 429458437, 882471807, 289695835, 550513480, 420652828, 633268304, 689922581, 283322148, 887490461, 55814707, 336565029, 191228115, 968408534, 430309638, 11880927, 115044831, 222222230, 556995443, 213225915, 55317194, 587834095, 235278224, 68612027, 203055129, 236890718, 642813783, 660315668, 341424249, 958793024, 221926265, 682543188, 760676624, 880735480, 9068123, 268190846, 657459425, 957806724, 791601128, 754048915, 559926554, 274770299, 540993026, 437525559, 888404085, 797664218, 483277622, 316075279, 707956560, 650511745, 812049903, 686470757, 237996077, 696094917, 264808781, 484633356, 274467410, 981177456, 901777625, 166568435, 994690129, 188592576, 807628091, 561893865, 345826877, 765846172, 141141432, 722755879, 213282907, 965253316, 164484622, 31121908, 375945818, 150013396, 319543881, 374883181, 213606712, 159508286, 65525768, 561191729, 248026019, 980624237, 812351887, 722653396, 899109910, 518814612, 177686781, 206281470, 391322214, 798017469, 880113995, 958836693, 158566340, 442763846, 280064576, 639732935, 704693675, 933170064, 405464313, 890734761, 224983061, 621044295, 926913137, 222519291, 837669420, 702709291, 941638138, 357276233, 846894458, 437824424, 676245343, 78690711, 801695836, 339546194, 374980387, 810362001, 823221667, 585536609, 345112788, 643467481, 244342930, 942280085, 585726277, 358298096, 86777601, 602912898, 392436685, 144072905, 42119085, 252352570, 979493385, 151774359, 652751125, 839835634, 831311091, 2645566, 861725590, 662025458, 70552343, 65364834, 777723936, 981416567, 659385778, 600566128, 191560119, 62744921, 32064857, 136153643, 146832858, 690235719, 798190130, 365735375, 483744439, 411698505, 336625298, 347807209, 274469032, 385865451, 811501942, 32421921, 467271062, 277060706, 381648008, 909490938, 890847683, 961630183, 194838170, 429601854, 890683082, 67043674, 773585047, 316163765, 535930991, 877037479, 410993682, 560962468, 158112795, 485271746, 537274008, 673153932, 601368937, 512485565, 617771493, 34189503, 692013882, 449429632, 761805199, 391339877, 310859566, 621846964, 675654760, 858300806, 767579156, 253738841, 504156224, 673885335, 870123204, 90848209, 621007959, 110545665, 692597395, 198033163, 342691042, 993077953, 361071795, 798490553, 985931760, 274671368, 57044166, 41170540, 589200652, 961827098, 227893127, 595279079, 515951711, 293149283, 359186988, 610300561, 81487947, 977134775, 432543740, 999227842, 564881242, 972997168, 740007114, 103249109, 906680944, 499493980, 198747606, 646853538, 26315504, 381655025, 274519188, 5211520, 786264907, 693238270, 237077428, 930462951, 39979952, 657445252, 539539623, 665872589, 28343987, 264577804, 781290235, 994879488, 554222389, 672057585, 565796422, 906235101, 181810246, 773733123, 3325487, 733264767, 419457411, 963127269, 551351863, 632679244, 914170368, 775515625, 756334481, 271753357, 586649058, 559262629, 580024021, 259536708, 788310360, 473760294, 688041336, 220402482, 116602651, 464309340, 846122929, 952078550, 598723121, 800808733, 94486104, 914585573, 945348154, 903831230, 508477208, 737576903, 588975182, 491817096, 73080838, 519870835, 692917374, 976326169, 705341794, 725266715, 436945491, 163030160, 756891198, 201676725, 972610092, 573647403, 207637556, 346903486, 70550928, 581367280, 825779730, 711303833, 404146708, 484932437, 793017878, 723794374, 740566242, 94224035, 557233264, 300316515, 882121640, 773653756, 810289594, 511185298, 896775029, 761624373, 730320338, 529871976, 326206323, 314638584, 61062768, 368678132, 1660163, 418882492, 819764121, 718615093, 75518252, 943548344, 837018665, 901154041, 336631562, 145865140, 561781075, 567398787, 925649373, 752960716, 396640661, 536292715, 829492510, 827452429, 37366296, 463321867, 149562162, 309935988, 323544449, 500831833, 531389137, 626771220, 865738021, 318510228, 527872760, 985670432, 82229209, 192754076, 98466497, 545176896, 199357099, 764541501, 498396532, 32721848, 346953206, 430521672, 845557065, 109585520, 758313844, 342001967, 542365952, 840214247, 22926697, 750928134, 191859115, 69101362, 605166763, 184230104, 605816864, 178001700, 359641695, 499869705, 751527282, 630585643, 187402880, 370459588, 398757372, 718664272, 13716335, 222861789, 880375493, 610741243, 664356009, 344336322, 282530107, 193640407, 614583236, 863869719, 368865482, 140611670, 718509738, 184045179, 339697768, 691756790, 748108261, 287555855, 505529079, 316582768, 398803244, 537563020, 157602188, 718630280, 278828653, 32262816, 417077674, 924376208, 263621224, 469139954, 155555839, 160523620, 239808250, 11230343, 187126924, 696856145, 19763358, 708286300, 964163585, 982600592, 716618362, 307654121, 135174998, 203414935, 295153486, 890153612, 545411977, 543242703, 672213247, 342779541, 199405460, 639437865, 241917060, 544718389, 130171113, 534203263, 704591910, 958108285, 715415086, 218633091, 491390385, 452617368, 847551388, 874204158, 898572366, 37521939, 600681552, 194747655, 679406392, 976033529, 68756702, 988492667, 542292970, 283747948, 963206214, 252868300, 585873614, 922271162, 529153453, 44251007, 238125985, 423006604, 307344407, 664990567, 497971417, 982217013, 946739278, 389990279, 35290845, 293574424, 724221481, 316584686, 230347659, 289328368, 594560942, 45413318, 989287466, 520000830, 605368687, 453288604, 514368667, 268157746, 480877493, 274078064, 964779317, 659747510, 334488139, 228734381, 6833711, 436949864, 240424038, 506916397, 870414477, 701577077, 203223053, 84837989, 408090345, 328495248, 813859057, 35468503, 287209167, 727344424, 279555748, 39905486, 834500676, 346842477, 951121530, 521946711, 765507359, 325731550, 48978837, 366020853, 567835886, 41353669, 542212530, 730456922, 43641843, 732300724, 577922200, 2016215, 22206394, 473941805, 112914906, 1500156, 382636860, 505358607, 683961704, 140808212, 534564863, 778256237, 492926658, 282308606, 799865541, 263437720, 634811013, 685288053, 155643573, 903743901, 373677464, 87721942, 488195183, 617111287, 319722666, 28946811, 242509777, 732145062, 734853890, 900114572, 303087138, 166290515, 164179376, 715245754, 591524844, 257509579, 501723212, 796345126, 43296080, 825369811, 551212567, 478244424, 517499851, 352078510, 906410111, 442245965, 967179214, 578013476, 180443808, 411003734, 378008489, 451134269, 490514687, 738313902, 635939735, 879358736, 942517335, 510318590, 809431054, 130088839, 107444242, 489424853, 283185539, 301442838, 621066789, 257800188, 795245694, 304288380, 905906977, 229512397, 350918709, 965197187, 577187876, 135531907, 780197551, 748140291, 45131122, 877738816, 345445678, 414319416, 338129262, 398402970, 980723787, 577470582, 660628251, 259492527, 900853920, 374245746, 404567705, 880354840, 170828066, 81846975, 722079932, 312445113, 334610480, 875278479, 380993195, 599236180, 950009633, 787144740, 253631368, 60200122, 136542058, 239891582, 27024894, 419033640, 125155971, 854451700, 862647330, 153475985, 619603261, 329123030, 401827787, 345004269, 763964854, 402037840, 670445979, 283524899, 782557674, 815799916, 734357471, 887461935, 4029996, 365055472, 966127212, 74036531, 576181437, 27244068, 50493515, 992832410, 214295136, 126375630, 110024087, 720578933, 533415285, 813569116, 464136428, 692644595, 768577091, 540118346, 338509583, 538734078, 332589177, 99909619, 881352410, 826715349, 611004100, 259565454, 610358402, 837755831, 643475600, 746374258, 355200644, 295689733, 241853304, 746612342, 342095371, 897426953, 666832787, 503153922, 782686331, 43620491, 321918415, 64390456, 563685362, 852447361, 332878142, 520432546, 354404823, 175760081, 279203062, 618216320, 264647772, 524020645, 297200807, 578663300, 30171750, 326353878, 885908644, 699411110, 431256548, 567143084, 39677589, 816273796, 44960525, 164980221, 224322751, 283845538, 133780101, 956334493, 850712666, 502884860, 345282523, 383755372, 640157240, 784399744, 872701831, 825031074, 25059237, 787061025, 173303308, 667695703, 311582023, 693398984, 998226028, 287912960, 690610556, 523244961, 638782742, 270473458, 193728579, 331600719, 356953593, 541758263, 43445910, 408203483, 19953372, 757483735, 501173212, 235917627, 521828565, 821627512, 251125499, 990634352, 762521952, 283082538, 929116073, 829346540, 658561753, 999103015, 781248262, 606707192, 662274563, 926205681, 14993377, 364054059, 407607329, 941259695, 320576284, 193590617, 450458327, 699930428, 613715713, 430778382, 115607622, 999714091, 614584581, 313961154, 799937551, 125856737, 806800556, 681689017, 944085617, 705804712, 783383155, 349383223, 114623047, 571089733, 424008262, 939298139, 70456934, 231135079, 886741334, 98919873, 105046706, 788782144, 36668652, 719171190, 80717281, 363354483, 133761704, 584509523, 185509733, 97548942, 747816011, 800243519, 575636425, 102664068, 287992809, 117154424, 899011224, 218809425, 362066274, 234908541, 130186757, 477192310, 933125418, 451436371, 988491258, 169789910, 859338288, 35136311, 670717035, 297393310, 626127436, 448255182, 718335793, 168365057, 252556991, 473853572, 160318278, 22249030, 944954791, 9772695, 24152736, 973816598, 966790464, 172255795, 34890241, 705220272, 275441363, 208295876, 220556043, 326901396, 393106106, 537243592, 473783728, 191713745, 400072310, 141029114, 549889697, 330528106, 80958230, 53310767, 886436313, 693995988, 417955353, 611934985, 820871572, 200118602, 21455368, 67621981, 650399978, 971273130, 668707272, 393967237, 294631696, 785336869, 956163906, 221699043, 178956257, 740495281, 651676001, 588366798, 661177070, 258764990, 502112019, 440555572, 89325817, 75393873, 859522346, 678602239, 711550083, 641499502, 672734609, 449138412, 721374372, 841729396, 917681177, 370928947, 861305709, 839167036, 763194723, 668803189, 102812183, 768109721, 269386003, 452640072, 627110531, 502771751, 390737929, 781504174, 826009109, 933260012, 194385867, 823969989, 437925292, 155034051, 31935717, 20474133, 669859395, 869569020, 878666268, 703201132, 270042290, 174454340, 419287567, 912184192, 495020130, 264462237, 772707420, 688912065, 436807858, 133660469, 637783004, 917357581, 471824916, 10589329, 848178393, 171730368, 505744774, 263230085, 115619307, 80825498, 23993128, 761146733, 793577954, 463447723, 728618513, 46701227, 767465339, 953353841, 329328135, 598187381, 997536431, 900277649, 384743549, 841525005, 214844965, 56962929, 452438614, 248669728, 394012728, 971951555, 279446113, 493759904, 379230124, 303631473, 730679225, 19436253, 325531824, 342953418, 605629138, 984878737, 284422849, 861267449, 971913466, 138173496, 261970776, 24715606, 865951240, 928645899, 389046271, 945667807, 366273926, 773031277, 167296144, 925372672, 97559101, 307909061, 895828493, 421659322, 675003345, 12336192, 895540638, 669794243, 957861687, 584192699, 289215820, 389651042, 360776707, 138609646, 923266423, 254982261, 831751225, 249267323, 971944443, 20995612, 349705909, 391236485, 320351820, 392733961, 853758375, 184136092, 935520543, 812326516, 368868599, 936675232, 764380792, 337386442, 825978492, 91152807, 92016985, 887266270, 389572439, 923085917, 358959754, 305253595, 405906089, 774844143, 102482546, 118979671, 731881019, 343350070, 928878233, 662667166, 579258360, 438058907, 437238880, 233633484, 95659696, 439076410, 912945109, 943313481, 772396794, 223839651, 114268855, 617726726, 188464653, 501015764, 340263320, 663795381, 893522560, 138625760, 754357112, 478420566, 384112406, 337741480, 173424816, 558960934, 246855105, 367221584, 105955612, 13466179, 449620545, 508123114, 49504589, 529160263, 401932068, 395436231, 794644094, 278033626, 57470736, 791182691, 662074638, 840979465, 86268827, 40655355, 603953584, 536118078, 740110499, 459177662, 731492421, 768744409, 904693389, 567389183, 172237956, 902368374, 279322814, 216367444, 461482938, 811094418, 970770165, 872917567, 778433679, 576911927, 295254951, 240628910, 592974682, 739614686, 360447992, 406288096, 577200686, 522308727, 668659899, 131193834, 113830162, 295382025, 162439669, 872539833, 235501774, 625947508, 737390000, 345422471, 219432722, 868942962, 445386744, 909405088, 788650085, 253671179, 801801777, 59851783, 3784552, 445400316, 937537254, 352440604, 926572812, 457018185, 714799807, 829784453, 647890163, 611911855, 973715058, 68919271, 212702946, 16462763, 93746654, 183231115, 16620608, 65995860, 262157533, 860143039, 992154686, 968502284, 714042145, 457477450, 205362123, 730325059, 471508952, 48329051, 791933886, 712117485, 600428805, 522445730, 898724629, 583217475, 235488943, 681499539, 260997765, 934354186, 626655911, 535684655, 314809475, 939884272, 404542784, 467397101, 451198779, 786267863, 819236650, 621712608, 575704798, 940748869, 403005503, 800982931, 750841549, 28417088, 769097550, 100538555, 654650063, 263014585, 417096400, 242840077, 825801015, 664116601, 179561753, 16716216, 325449235, 979666624, 996172778, 636073828, 749907438, 114022005, 963564875, 498393091, 111269225, 557519539, 938849520, 7920641, 952440767, 135404338, 375091487, 708459868, 506637468, 40730702, 757815424, 563518694, 872113839, 483904037, 573092617, 101205497, 418185961, 613211043, 617520538, 115210581, 762928353, 357407834, 158321113, 881460081, 391897090, 645198702, 480877669, 569259349, 393017533, 996423111, 844503190, 513753872, 341575518, 547893327, 322517642, 416876158, 959279621, 302371591, 532720724, 928276082, 976950643, 624960015, 892458950, 887030326, 921326137, 953346674, 233979390, 343289427, 110487425, 864702841, 541291511, 645707813, 61127350, 277753901, 547504144, 904339068, 662100047, 960747451, 357985698, 707527102, 362968987, 879386878, 199723240, 917507739, 245214909, 484050698, 335673494, 669870811, 544315428, 767125727, 86899178, 374099295, 58454930, 631646693, 157283618, 255175567, 566043122, 108554387, 222687844, 906332140, 73175548, 376578445, 620813324, 354141690, 891831583, 932870013, 303758364, 611316270, 437441262, 306957885, 417440880, 81288284, 135038956, 542898752, 30738538, 13694698, 573878308, 696937120, 948223198, 125038427, 307613620, 166087248, 737888506, 519559636, 818247406, 660033628, 126336200, 852360230, 435634933, 218975260, 415040128, 303626257, 362179273, 757627136, 58969429, 558128450, 218750415, 530123361, 840422483, 515999028, 671384141, 87324836, 172842527, 91522266, 171060480, 132003097, 558220720, 649369965, 865406645, 418334057, 731189478, 450603806, 850195576, 507351234, 104029662, 447930092, 801793897, 458332288, 703779484, 692813887, 418275458, 235981793, 857600841, 578866433, 870547910, 803304755, 102157633, 868109742, 512273222, 887291442, 272430953, 163304739, 836775386, 434224338, 896811345, 352278796, 326812324, 537446859, 29332376, 181635429, 129618415, 983981138, 280242032, 665318790, 224417087, 183527941, 384955438, 319353847, 367354918, 302011864, 341797700, 355998997, 881375476, 818282267, 509675899, 481358159, 598073968, 178842231, 243651135, 871643662, 851104164, 143502050, 55411762, 690557120, 302408200, 590185781, 664694132, 796024590, 600419274, 440702710, 722762206, 126454591, 987746023, 54548065, 998215571, 951110051, 659905941, 524243847, 527666864, 267067055, 292429867, 739065970, 952089424, 587976415, 965665570, 84253014, 156217280, 26303453, 509162680, 171525140, 701537646, 52847095, 341768967, 411346937, 829794102, 557893532, 583128942, 822961304, 214405618, 353047461, 249218837, 170419457, 188715915, 167780801, 149381677, 639370974, 239983500, 417505887, 12447862, 346778090, 262884236, 324802000, 872951341, 682450017, 329124789, 376935536, 958021485, 43731192, 169636648, 430481911, 978039957, 146860278, 97772627, 291201232, 451680299, 524419737, 564150975, 845552359, 589463326, 971389491, 297540904, 84423638, 562928651, 257911161, 916356919, 544087609, 915873635, 769532065, 619649988, 739010834, 892277350, 908514113, 211556207, 453881758, 154109269, 57373390, 49395421, 52057335, 408857271, 33428328, 220007366, 623681062, 635017374, 258604533, 879059822, 737025030, 599511752, 442485700, 737941189, 314218973, 520466602, 683086304, 627939306, 299609803, 65677533, 18334204, 277736958, 874573997, 289838834, 92417883, 727322650, 517439442, 756194067, 53087349, 150462011, 533732917, 203622124, 909455898, 542678047, 548322294, 136318589, 201463905, 830012038, 281551317, 513169662, 50770167, 808268364, 591427274, 536130421, 856370541, 589416522, 534855810, 153330195, 130092665, 297015445, 128180513, 15730605, 869525021, 226245130, 747330122, 938124887, 328548427, 535874071, 463618813, 435104562, 390059108, 726392701, 183804462, 886285685, 75423951, 331273600, 539565202, 662122578, 561629914, 662864731, 556729939, 645480210, 70533035, 799059386, 343547278, 912035920, 738623301, 657554073, 476677974, 861595887, 703019713, 388757314, 702109112, 9818587, 983045305, 428796085, 560489489, 592121063, 233696989, 837536311, 658305214, 346194451, 36227583, 678963392, 822089438, 49168397, 420924738, 565756049, 405145070, 655048447, 909945995, 119535965, 981798370, 707856896, 62075031, 681931683, 418862245, 15678160, 401920824, 836213392, 971718709, 395357636, 414634592, 882767014, 81877168, 704673469, 699598308, 640347766, 996123432, 643114871, 640534145, 307012017, 282578217, 315039114, 168897635, 445514603, 814806438, 348229402, 803579282, 550642021, 775717867, 21133127, 419215160, 255918189, 259106990, 116522011, 887046424, 71042361, 115722353, 904292457, 813627079, 184546602, 133013604, 632320055, 271042409, 923346177, 382216125, 509923294, 297008692, 923136551, 822623090, 643362382, 747035701, 305382791, 773712566, 815190723, 436500946, 938663911, 470063620, 89470510, 87084593, 348080453, 928076364, 757776849, 169300454, 249118177, 306592573, 715995860, 736905519, 447112398, 623075636, 918533622, 143003296, 976918504, 431656730, 784899253, 154449403, 481601466, 587192750, 705601554, 236275269, 947608581, 238873386, 538286778, 577175665, 28756170, 991637898, 825356107, 576888305, 208821141, 338998685, 809548955, 137574355, 711452263, 30702784, 421472313, 882253698, 780647965, 946674508, 681562379, 571558493, 752074598, 746911494, 452028517, 972934150, 541334943, 683013877, 557951940, 417133307, 988491811, 196780118, 831601329, 449412970, 471158735, 418548088, 643288608, 282143555, 831633747, 802598914, 979073553, 671513825, 957306149, 473035290, 537765194, 167908999, 787037916, 283471722, 953594768, 835054869, 943322025, 838050806, 2406485, 771526519, 960120881, 668359137, 834725425, 110519363, 96063723, 276590119, 128125373, 150797098, 553638836, 322834143, 348911290, 228488230, 279494395, 536152878, 128058307, 82533454, 392582026, 91917284, 844426282, 774986408, 435187000, 550359458, 571670846, 99874393, 547800816, 727791296, 413883445, 189925937, 387664731, 909885407, 428095237, 56542580, 957045297, 819371061, 741514896, 750998497, 414266370, 253503100, 149775059, 610559110, 136002448, 442588649, 81048485, 511976079, 940808203, 362660216, 417998745, 332898537, 450527208, 709934712, 339764597, 426176940, 604545002, 594025846, 417650116, 458601797, 976408465, 779115108, 616782283, 962880184, 219913109, 761030677, 326566869, 670690635, 782088927, 327026085, 410852345, 960829125, 911409892, 542373301, 815578268, 911861419, 468647406, 330258998, 977087479, 545149251, 643072582, 673168864, 542545882, 635564683, 120487404, 217918500, 817120998, 354251170, 143589047, 296541563, 282246165, 115454733, 971500108, 562342418, 34658018, 411262404, 232413965, 437616028, 167963172, 861521651, 444648016, 595793127, 658343743, 655942100, 253166675, 390492481, 522518791, 564368410, 543929324, 235361763, 619318667, 425658293, 577811669, 397714643, 500714672, 858719148, 646109386, 107904605, 214882264, 185052532, 284610232, 522327162, 200016839, 986883440, 428611582, 791683391, 677085293, 416832888, 348196624, 996622912, 508762033, 737344803, 15201728, 608479465, 292179339, 268746761, 236587788, 276759652, 572033032, 187884421, 775349908, 87583892, 512235704, 516328769, 346345633, 251657773, 134649469, 770059728, 975605791, 343427581, 540167860, 40456799, 112097517, 617138273, 342120407, 212648004, 431679650, 637000534, 807301130, 494592259, 354266534, 313447429, 467367648, 417048654, 280651501, 407223883, 530489675, 878532187, 599636978, 188843852, 373403471, 642207987, 567994323, 508945482, 716692490, 993011637, 417650125, 186129844, 256354841, 412253670, 708407110, 109909913, 801721042, 93212609, 884515279, 251287075, 206588529, 198294390, 561864372, 346438871, 558679939, 515592054, 670958358, 363953087, 540892857, 198117168, 947807403, 685384363, 102832546, 549136210, 101556708, 786789524, 912398949, 802353965, 792090959, 427165683, 730118436, 327533358, 265179845, 916395079, 862126696, 821910594, 966657939, 754947222, 520974061, 17232048, 627861350, 481084863, 41124977, 806517162, 123166859, 747855179, 668437744, 421622922, 124370982, 224660599, 47183256, 781794407, 519150131, 357722361, 334930404, 621336781, 408931842, 901643033, 190069170, 397601831, 804891610, 71354985, 450618439, 918957025, 128972452, 571616460, 171382953, 264871254, 840119371, 352181408, 41123173, 940669149, 271358022, 230950265, 932218383, 320516775, 155277973, 782745518, 382981050, 470951983, 190289182, 170288298, 950817258, 777087686, 578240093, 714356781, 282413643, 312813606, 189398540, 419109112, 220169547, 37573769, 642594213, 283012727, 401104657, 325030725, 100630692, 155820316, 773762558, 601584881, 429743459, 357915017, 93078509, 118199620, 430578446, 877114048, 926692858, 935654713, 367452824, 379120472, 676859450, 741721240, 486194905, 145295067, 70119266, 421784547, 504395518, 945773964, 892531559, 709362401, 325279072, 753828183, 343060910, 683212391, 299298679, 470161007, 72003785, 373519970, 929976551, 248485382, 806713247, 419725274, 308679777, 962970762, 79946211, 820934220, 677791145, 623598006, 469473530, 804816395, 397240939, 37188972, 117900141, 290568182, 906689880, 741482745, 502301385, 692805236, 394581353, 233419520, 820731532, 60232550, 732352297, 560645139, 677824519, 892845531, 182296744, 550202766, 156923733, 826110165, 427036404, 90792915, 736235099, 645338701, 717638327, 288370276, 700265484, 264460173, 248071099, 347098160, 869821909, 400004090, 301262847, 890170321, 531281065, 439277821, 72120782, 943776521, 53079805, 990862069, 599357082, 322717148, 860200814, 437784655, 369097451, 148903106, 452101246, 745369138, 609007062, 242647027, 292602822, 158767331, 228027997, 97049754, 985264492, 473604705, 100682104, 605946730, 521141893, 798278966, 955948544, 887542964, 375308149, 877257540, 968476329, 45618519, 133628945, 684434585, 957035928, 787589955, 471563018, 489923423, 410308890, 238946306, 199998364, 519376450, 820950103, 495952120, 235577141, 932699323, 404120734, 968529923, 439860346, 131800665, 572130382, 552188944, 191955204, 137376507, 119439577, 557889798, 503246616, 123933473, 950270103, 485263319, 718935543, 918526603, 945581831, 912223959, 86926566, 347319450, 789457809, 602382385, 23179334, 813842926, 965191862, 803221204, 972022230, 705001419, 161749474, 338398497, 948018998, 431641605, 335228209, 699807945, 197724031, 498241995, 394800841, 397809634, 319309382, 300594895, 1047861, 387864725, 235308771, 138120051, 912843593, 509848198, 283437999, 760657453, 157257230, 550257129, 427579059, 847393602, 528484250, 382175655, 298770106, 719946450, 350617406, 487022756, 195857599, 374370863, 576580897, 100637847, 706873962, 402231300, 76682213, 587708934, 237177902, 627178756, 981233732, 744622568, 662932682, 956907263, 237120389, 246127099, 671322376, 240515279, 42235728, 134283596, 255862757, 132833394, 6313257, 551148688, 578835034, 147144655, 881299636, 785121097, 482157190, 853460654, 548461998, 15659056, 341379068, 949060558, 551848732, 808548212, 673638316, 852593637, 298241758, 511822822, 470434431, 742057186, 878816575, 796281990, 476870212, 812408042, 908154750, 637151690, 390461352, 23022087, 103948073, 754183035, 812678259, 478396754, 741532442, 56637290, 359335684, 916618748, 895750619, 948626758, 44116375, 608221574, 610561085, 620250711, 618559545, 306363833, 337256280, 661904606, 831691759, 924584333, 341157405, 599309776, 367233001, 28515931, 417318286, 393691451, 778104431, 795261138, 864236161, 622695186, 857856618, 872428269, 512697649, 954737287, 932682365, 757530550, 943062984, 267376905, 940604745, 922069911, 847965741, 196661689, 68058011, 936257980, 901519347, 378121359, 143193303, 590525608, 116014701, 252310251, 830788792, 513280268, 257566390, 409749116, 443168437, 8930226, 31867655, 125558041, 178454318, 133993817, 38988701, 371114911, 871473519, 156043249, 715183293, 868943947, 6867, 94451908, 720287910, 960416496, 352405226, 773783155, 680821666, 493704140, 795513641, 108257891, 41634565, 649824112, 278287591, 804357063, 517001442, 743151280, 120440925, 870713197, 138300583, 335347299, 949293703, 169161624, 760805596, 747470799, 948134773, 107187881, 342634529, 933254733, 317865028, 157873085, 628808480, 653849744, 671168532, 825632040, 855492890, 4485005, 899502936, 60275078, 116061905, 797920582, 784268045, 558143262, 432471416, 182802496, 398616246, 847354102, 804834883, 838892113, 758296319, 555949368, 11615498, 665742155, 673621976, 189062197, 853030344, 913290261, 79472307, 456712971, 737699729, 89031534, 324596492, 506829296, 255684144, 609480784, 103562052, 684405711, 122207171, 370261753, 201307401, 239036125, 40551357, 627362517, 974411511, 579248898, 51164009, 533753823, 109850911, 751203588, 837957958, 722340665, 292561433, 776595133, 396444045, 526429618, 471017690, 919107691, 766358121, 154887088, 922315926, 499095229, 133087342, 981638046, 7582576, 660380249, 561456947, 941144348, 291121939, 557246894, 924560742, 188525820, 141382566, 444456081, 572552314, 324718876, 428351946, 212432507, 50158142, 909403175, 257067968, 862177855, 511088613, 929479489, 651094783, 166063821, 816885888, 133335722, 865950404, 686606461, 29229313, 157484538, 752684937, 315620563, 616696056, 38361168, 433933465, 213176713, 773808049, 777923033, 4807207, 215411775, 858496298, 5820337, 840352844, 573368261, 634338839, 565512387, 335776979, 153064399, 556081495, 140363834, 814941050, 642279248, 621066475, 890981568, 256739686, 509137228, 117410924, 941155976, 655013452, 57670334, 669456707, 512193458, 3433655, 227421881, 328248108, 388312871, 240013401, 900520661, 552979192, 575206525, 582606851, 309815112, 694869869, 548652318, 525012964, 939208139, 600957979, 746212132, 549814217, 564401479, 64844163, 22311890, 111593908, 753894198, 973556181, 534608233, 610580047, 669039950, 701095604, 776704131, 231075543, 352567214, 972104472, 118278382, 530465723, 380616248, 757754670, 732777102, 508023252, 841240799, 260414766, 204954045, 693516739, 778330964, 425857137, 626417049, 317032556, 623755790, 453104474, 610857929, 322716427, 912626614, 231864261, 934264814, 997746136, 741954860, 237950455, 54087418, 153630897, 97374161, 4270363, 741744678, 764347822, 942642327, 213726267, 971691354, 444054179, 257219617, 857399701, 391967524, 409683153, 603268482, 307470914, 541597768, 519443333, 95345909, 506186775, 795390757, 732869443, 985684247, 788427165, 192466463, 637857683, 884211313, 538116402, 933547932, 867492979, 733949271, 704492763, 992502706, 573057716, 695360057, 526857900, 50620776, 427599570, 931999985, 390393373, 362421052, 287978640, 176021455, 664270930, 693119419, 288540374, 745578860, 666473309, 649140862, 902046295, 834337317, 459654487, 814939556, 253296013, 489158343, 49897478, 520861006, 163212591, 19110273, 707003274, 947912980, 61471046, 370178364, 516241234, 107215188, 937569121, 766425829, 484519596, 954888769, 852837293, 942121209, 165219012, 947406766, 998335037, 808706899, 32171555, 653411152, 9534279, 542707804, 477158548, 635116307, 407872059, 789866385, 493459943, 75500019, 553860132, 554216668, 667288695, 968386913, 505078084, 120782675, 54156855, 301208323, 854631589, 634664963, 868160992, 53306550, 996898815, 877686667, 566241625, 35246617, 972105059, 468434942, 343596823, 191617372, 522026394, 922779344, 922836722, 352919429, 805866393, 262227800, 11559781, 556453823, 113647802, 160354768, 294351148, 560201979, 769578017, 33958920, 162301141, 618650735, 683202577, 557264452, 806988914, 151973467, 997591088, 57019290, 631418424, 974334410, 182720232, 716870174, 43207956, 18031153, 342061575, 864969475, 269609077, 695307422, 318646289, 207675891, 539328229, 256636896, 435207439, 588967244, 135297031, 301816683, 115735372, 61824168, 590459961, 988692502, 493336220, 183472925, 642024965, 496388399, 841536065, 702948985, 489560563, 859424209, 915458844, 238141381, 187340213, 216621524, 18778502, 595528810, 328633037, 719538512, 841834501, 514545796, 326606547, 798217689, 371364734, 308456399, 317711436, 823050645, 407122331, 114066852, 884324674, 640674256, 477371956, 931268435, 579221886, 582954958, 931783098, 107913784, 519731814, 734666634, 227247403, 19136196, 754346187, 685224465, 101372889, 145156373, 413231206, 294068422, 860009592, 420358776, 471708308, 53431877, 57757362, 742464628, 659530244, 128476955, 273842420, 858514680, 686803011, 351566121, 866007713, 559025543, 772927603, 611588260, 590599629, 66196581, 718051009, 397773376, 271158392, 546586918, 433431383, 424688196, 853959866, 581972564, 727985091, 535836386, 989215680, 738969554, 638388472, 754632783, 200520483, 629513844, 348473757, 581654747, 294953629, 166090380, 527928963, 973304630, 578362856, 4113778, 259868159, 167179739, 51418752, 718520240, 930319167, 161080661, 422744664, 511317767, 633284704, 287761173, 439078049, 207059530, 529219842, 497566946, 400458707, 707628282, 476755352, 165129897, 521754257, 796988770, 941876977, 225071557, 788697394, 910467084, 858982886, 601418830, 544664762, 549145647, 332430287, 118559961, 488860854, 841371439, 10466130, 267188213, 932245324, 481164758, 354285710, 674217532, 398309645, 522670636, 743580328, 347471436, 276750250, 259545313, 215797909, 410728588, 229561164, 12012520, 675312207, 286960645, 883826510, 707817851, 850317681, 502608624, 301394579, 665484503, 857677928, 497347406, 688583788, 117783838, 501904705, 858934691, 304505549, 926692803, 117352228, 987438938, 124866036, 915267594, 146413303, 256498786, 545257923, 619975724, 611670244, 473215134, 475708715, 143237528, 771401519, 906084296, 935773599, 886548799, 684505863, 875915111, 684341775, 849517043, 381158872, 27462225, 182006738, 217683292, 42316295, 234065779, 984062889, 435454047, 172725540, 521381368, 186960758, 365209573, 117864009, 298131371, 693012811, 556287644, 601033600, 479375853, 912395508, 448120352, 154525204, 756450739, 946947356, 827344596, 98141804, 871933363, 573260930, 193143780, 241660288, 899127678, 3105616, 722228329, 871016142, 72606605, 147356122, 664970690, 815259444, 208548808, 2717315, 313893730, 455389553, 60503008, 479161345, 846330435, 782269576, 108650750, 795734792, 785961588, 643812534, 641548949, 415543022, 729705254, 375356370, 270620817, 276016527, 736070562, 856588919, 546755425, 259328172, 227416177, 334426523, 373440377, 931990977, 538092807, 964455873, 639460966, 503637343, 30971896, 636683099, 844929227, 509950549, 422081599, 83341266, 364792000, 275485263, 395075711, 56340388, 687519494, 143824213, 612773171, 927227123, 311457141, 806900194, 298006225, 250943048, 100196426, 840277709, 290379813, 410317299, 79658427, 521881053, 563858959, 236733317, 123183004, 771925072, 487599082, 36316007, 939416506, 796979445, 28453963, 996736222, 130364445, 886539976, 824967301, 88158266, 56152574, 608234490, 143761610, 646298034, 1185815, 70810839, 42869716, 400457713, 676153838, 904287657, 995577862, 573630953, 931679342, 358525102, 487496467, 665392837, 529805867, 241587693, 281292376, 203828799, 123288587, 950621774, 44026591, 945886667, 423439849, 618027750, 523980976, 101022526, 884295239, 626315930, 442482273, 165329483, 776023219, 553864197, 12683984, 980850337, 606063561, 987546858, 813447371, 805958246, 343335661, 736915549, 345784683, 888383136, 720142500, 414681887, 34889718, 780034502, 997119109, 392870231, 364799863, 693863971, 729994962, 926916832, 529219700, 769241999, 872536558, 245398539, 144691936, 297514252, 3418865, 594704098, 441143702, 854706701, 814068446, 805941422, 507467296, 822043812, 323372953, 883562910, 813655117, 102034651, 955071958, 977966766, 121618410, 1059410, 248325447, 903984048, 484490392, 680486151, 163179690, 470403901, 952845791, 326571687, 56760098, 513039691, 874907527, 680509618, 603557700, 754776413, 357528327, 562521721, 676030641, 13274016, 335925000, 364017492, 461774627, 690090170, 168120482, 657650333, 144738054, 667457939, 141419849, 863381484, 428539235, 100669057, 482522334, 180938293, 270322936, 32646145, 223100313, 718224215, 613648219, 727739784, 165727306, 889649800, 873597321, 756280954, 422426480, 319753465, 45706235, 787084150, 448937054, 959154706, 736710038, 278232038, 236150272, 365697286, 442462724, 467961579, 330418732, 409699755, 979554593, 529964250, 270677510, 117506087, 543310986, 841434978, 994369504, 956399507, 854670826, 796446352, 809847890, 641387084, 130475769, 627708246, 847185507, 223248668, 141915376, 551375414, 995787931, 668223552, 777540150, 449109455, 258205104, 423665650, 893993689, 269187128, 232667678, 470749605, 568157100, 581330195, 959140962, 362295395, 660931525, 480711594, 319994186, 714916371, 215514397, 704522051, 201505923, 708279684, 943407590, 330388638, 754259991, 270420701, 959261432, 806477775, 945051093, 377011121, 98737347, 825307166, 202996861, 938161346, 33992938, 929439673, 26372978, 322429539, 317002934, 665659197, 432429308, 264972219, 609263211, 617557360, 285562413, 959956172, 474666776, 467184491, 25575216, 746466558, 494564511, 828566940, 6427600, 728543642, 606671494, 527262925, 932240371, 458609269, 560682083, 254390152, 40453815, 168271125, 576377741, 224461731, 788019121, 527326870, 633907393, 770419070, 891572154, 627857190, 457038974, 772979291, 84869209, 170863430, 225695213, 9220641, 806628757, 953632043, 232239856, 224373271, 837987444, 710153356, 5522876, 592614503, 41600277, 908580751, 203625618, 389219275, 538472931, 227870690, 972516548, 62990014, 248623875, 626061790, 869835940, 399960215, 582965448, 507525039, 164049911, 48992177, 691561011, 63491177, 49920760, 460361113, 430095238, 398932654, 161072788, 988020790, 84817658, 723897560, 953532036, 582283771, 478032526, 498214436, 355694592, 151566474, 272326424, 448451883, 17184236, 198988086, 15060770, 981826472, 76723068, 147208135, 596305762, 256825301, 532321814, 692836709, 377356131, 284360475, 844543749, 331007824, 498324021, 450490660, 936114027, 632123712, 346907952, 39976569, 771294249, 642601596, 534733253, 568678116, 742764680, 670724131, 305393250, 515900020, 256550799, 596242562, 175638088, 990770298, 553719001, 287092452, 314473821, 791036109, 170934323, 339038883, 777901077, 673442640, 245502191, 463822703, 729533976, 516818087, 46385881, 863665710, 358020993, 404921936, 882733170, 409256296, 464124502, 193128513, 918170909, 246423492, 185617837, 392054316, 531631319, 787475774, 577713038, 164204609, 15595443, 985299211, 611986775, 950837357, 38010367, 223731153, 939280238, 851679819, 906588046, 269550611, 480217415, 632881157, 584987869, 802649767, 641698617, 670545270, 931618674, 395027884, 10676432, 877556687, 103560207, 168551939, 828716884, 7307991, 153735967, 187322990, 598806405, 28909580, 576064034, 938808872, 450160680, 288209850, 112355742, 177940208, 922135720, 151015811, 447109083, 626516202, 700396795, 536147915, 313944846, 254702618, 783530111, 598896162, 243920831, 498819936, 895141925, 570413666, 684485824, 159560969, 900852319, 634985852, 654601311, 415172272, 743998333, 289047248, 37242528, 376432377, 880661106, 766000519, 886060599, 726509857, 53323622, 14517448, 949871585, 936852833, 22180214, 109068575, 71408658, 812561938, 973538123, 105295635, 724146666, 686958653, 222953636, 307142913, 470518268, 324856906, 188332454, 86065415, 378961247, 689379058, 417754821, 197941726, 93257844, 71891154, 820655121, 703155573, 286097424, 691969700, 803889817, 255886500, 251990231, 650163652, 384377763, 549756696, 491073167, 266857311, 962620368, 370152869, 228646534, 617132986, 334363908, 903727099, 596816671, 213938792, 969847905, 590196578, 730327136, 247731556, 90398300, 771188924, 697270628, 472339719, 230370194, 181221099, 964300316, 727139852, 22564523, 384908821, 341843919, 359954172, 780196971, 859790991, 495451529, 715470038, 669425316, 638062228, 170526133, 104156492, 500294334, 856510591, 665612675, 286245215, 741778713, 60773753, 862328491, 710920979, 884637189, 907205825, 291837104, 685166738, 571929132, 27988287, 445985605, 101444297, 147435062, 477743441, 836525753, 434202800, 994518412, 268322783, 557579371, 944789522, 179188141, 773425775, 268992935, 561926570, 362709434, 653128998, 33661168, 615399498, 227542374, 752681438, 324952746, 651736308, 368918032, 76582166, 379211606, 870620150, 276051407, 151986293, 660760934, 125759485, 672350322, 542740323, 18750562, 281189262, 525741455, 297977338, 915709536, 732322729, 146320415, 670225210, 556017803, 772460247, 223540824, 379802976, 699132705, 822647284, 260605902, 245327981, 874158211, 625539859, 422602133, 21140899, 808723657, 470734450, 684015231, 412157494, 560220967, 609790806, 619276464, 761575939, 901323709, 304469867, 713346271, 28593156, 743757992, 782167174, 927876813, 616236967, 954148645, 228408937, 882077811, 318260674, 454014937, 92051113, 906093584, 252902068, 565276210, 609668602, 614175064, 155108889, 568635447, 23325419, 248128685, 288643981, 271580178, 528066188, 679777456, 301303837, 573904736, 371781877, 518601469, 203015384, 236012893, 526584629, 155832783, 895999725, 363689665, 230247578, 45272716, 733822921, 659138414, 707652849, 708553207, 700072975, 49914932, 740884828, 242380418, 808923717, 316201730, 192186026, 675787628, 291324768, 834693704, 561385768, 512041157, 332022435, 101792629, 317907600, 805428113, 337606965, 598431262, 946739349, 325175941, 294344764, 683872423, 58498567, 787560041, 176788539, 430019556, 798610570, 727035227, 683195827, 928910476, 389651643, 643577885, 352403007, 802920679, 886302673, 968051361, 364410109, 119078012, 147688066, 251883393, 292961374, 980153176, 211981469, 585468206, 248140117, 654272998, 451553122, 667932321, 778232640, 564061327, 38096415, 286248560, 646875100, 204243082, 477961855, 286863990, 706035278, 773102655, 502542899, 36542129, 649660525, 24235011, 986209257, 263885624, 187129248, 484731281, 457761908, 270943981, 186358222, 29118665, 230819223, 701504327, 67182572, 513612628, 213125299, 979507155, 704491237, 527519205, 303058622, 51999860, 32463164, 375426599, 163515199, 532198612, 500976051, 582495656, 624118839, 7651755, 785094972, 366479483, 692967525, 356595786, 510811858, 471503917, 919401314, 746581657, 973049293, 233954304, 643778704, 377835051, 348374807, 517188677, 274940619, 939519331, 833642071, 744751787, 882968853, 127674344, 394091028, 299026332, 210524940, 59106170, 790176882, 102578033, 719436440, 317345775, 170941790, 992180820, 442522800, 265586147, 299084939, 288709394, 778747725, 974375352, 608487494, 583576055, 502504648, 408527427, 806724351, 120493128, 354693484, 842317915, 525610549, 942464580, 818405523, 481875467, 424329055, 217445133, 817508518, 636510002, 913419645, 303897185, 906411606, 122749794, 561240492, 511171374, 745987523, 851432788, 108748186, 546664221, 17796107, 899229513, 264642008, 958329466, 136381402, 91878327, 864229880, 12443209, 56888414, 421929141, 517802998, 180565089, 400244839, 669773167, 627378908, 526628024, 103912023, 899637484, 811178883, 32240615, 602255706, 435002494, 84061424, 583610984, 704503031, 683854922, 252379303, 935655177, 895322960, 625876196, 432181697, 214795613, 285090871, 792296741, 422941299, 291967236, 780483925, 468831267, 765697118, 193476427, 757054174, 284270650, 566171757, 511198467, 246968480, 759078707, 458416591, 372249238, 60828014, 195473641, 196737965, 688449963, 869376377, 632843985, 464350647, 101801216, 698882460, 924781779, 118603351, 282838618, 811500315, 791179671, 730662038, 446669240, 372609004, 675577828, 651575402, 285587896, 483311131, 350352143, 886556180, 374376752, 487074510, 331428075, 216051574, 512524879, 719701254, 945812061, 887646790, 417853559, 804345958, 235053677, 505932695, 354550751, 612299101, 148616516, 894076887, 906745607, 361687593, 760664245, 237247775, 693417514, 457743301, 174681112, 158251994, 410099020, 432083498, 663665104, 32744708, 964206538, 705278055, 501878496, 653349534, 857002674, 469835824, 891606086, 13588476, 508310841, 221211766, 144963442, 557570748, 121312438, 831300307, 769837442, 538466264, 15327870, 400904993, 980273988, 47176988, 134446400, 38398497, 418115857, 368925661, 27689971, 676327031, 211515034, 463223330, 132590212, 494021384, 860892663, 4533843, 421056389, 293687321, 978391816, 108148129, 450439807, 942612217, 380287199, 104596431, 607203053, 657645068, 812314377, 698216829, 697899396, 888257430, 82570014, 537999010, 964583912, 533761893, 16030684, 315548451, 936915133, 16034832, 294344814, 41389719, 127316676, 605365575, 165066848, 369815958, 21879022, 321172686, 353112650, 844386222, 76626504, 708092381, 590572399, 210274536, 741941082, 123374589, 622018539, 517602310, 285743942, 339267242, 308979917, 460003546, 619897674, 220048977, 721741337, 791016210, 122409856, 625690262, 686226423, 776994101, 309166704, 63591649, 86632897, 771669967, 547924732, 754994573, 252471052, 80363655, 309702307, 794323535, 954058868, 784060758, 306753783, 568863595, 612785000, 164727715, 777793577, 96022783, 962800079, 387789839, 142509326, 665374744, 215338365, 267994608, 89482917, 174332594, 760819965, 746988728, 555171114, 734176095, 118060865, 455489030, 585348774, 776282984, 554220220, 420235500, 509119091, 469548279, 861291461, 390936376, 342846784, 511626620, 669079158, 452084449, 635169390, 183183416, 926006536, 880199399, 181786375, 129123407, 504590064, 651146110, 224813377, 299973680, 636338550, 38864516, 625215311, 311265278, 208997270, 420857773, 83211822, 189117756, 131055089, 975245081, 707773649, 471460394, 370713518, 128194599, 193440574, 148330515, 884697147, 580507652, 111575059, 390048179, 732561687, 935473347, 639212335, 722534442, 628985432, 763083530, 173569023, 911728806, 981296072, 208798364, 372378467, 716025531, 485970117, 981952163, 766075750, 759671858, 37818966, 285076032, 307122746, 405658800, 686631925, 511708732, 230043270, 457795889, 16633236, 604811541, 435947367, 696733849, 60464351, 827476036, 208566708, 868887297, 37656209, 997436987, 564046290, 933686225, 375138874, 588900442, 602584464, 506382340, 187143321, 905343422, 639532773, 292705543, 505844098, 286985611, 94209493, 549679473, 655555690, 355511429, 856042098, 574243696, 946555299, 564778067, 909351286, 287069837, 664959057, 375928470, 641518946, 168519846, 545130538, 711793246, 269617065, 660845842, 291826704, 859164248, 743372885, 810263693, 189573060, 592779246, 276305077, 621049009, 772171017, 912302494, 249170249, 698618924, 849525028, 505500022, 587868166, 875738726, 388814844, 757780300, 115729899, 258051413, 661542827, 982911811, 526612048, 272961744, 809779053, 193543410, 446771273, 658238831, 5022856, 595395019, 707876281, 551427105, 212484458, 146677555, 852804410, 722215363, 755163052, 459609972, 306271329, 180899763, 452066341, 114121392, 191695983, 624392455, 58192729, 721742923, 44312471, 375430247, 989658779, 253827804, 852437353, 498811936, 383590676, 784290613, 478764749, 629534725, 697646865, 873078981, 813165882, 368850288, 676117651, 726701081, 177560923, 238290035, 483874205, 719218872, 720168967, 183524389, 884802526, 509595391, 552437674, 391242929, 153093999, 653170899, 431270522, 751450978, 413886317, 379546814, 6494254, 150595723, 185861539, 401090440, 352183750, 990098370, 933015534, 95265479, 324984234, 337896450, 632858894, 723955146, 132501450, 357095658, 149898059, 463422883, 364659427, 874240135, 520629373, 87877950, 348164005, 710212566, 728528190, 869961749, 944902323, 145970207, 443128894, 100636898, 48895009, 701601552, 649617688, 277648216, 376143165, 257888168, 812425096, 886385511, 398782860, 965363667, 880703657, 992375952, 662380260, 338702053, 368226050, 527238927, 393366297, 412888630, 821079762, 609340962, 619610198, 533277352, 47287649, 73103216, 943050688, 490678612, 986040260, 326965684, 883544293, 828338642, 460330988, 496899571, 691140830, 802980101, 737262789, 495633833, 276634922, 144522339, 713436034, 723512988, 254299822, 700488487, 432035567, 770908767, 89210491, 418679606, 926105482, 614646578, 107160116, 25899270, 797271634, 381392917, 464881315, 450205886, 88228034, 263641500, 578263030, 930675201, 182249641, 440654154, 666218708, 580777988, 261493409, 665088024, 699266429, 327924868, 956713059, 535173459, 409313106, 958052567, 651882320, 923094275, 764937208, 59322895, 100476362, 193646252, 29981937, 326854630, 424531926, 91503712, 380781939, 382366035, 943520652, 326772015, 894131275, 53069191, 750232245, 358085613, 545599270, 13555288, 465867818, 646420182, 873572043, 756175929, 695289517, 490592739, 682065465, 850566067, 39283432, 580848950, 779248570, 571974858, 768002791, 903017442, 293715546, 33623585, 532562012, 442132210, 24155173, 900589471, 109916352, 229085566, 852173769, 770627228, 305476560, 535344575, 182000159, 430788558, 579386917, 761286807, 628914506, 159389085, 709983421, 103104338, 401800955, 806416054, 530773185, 43205484, 780985107, 921073443, 829422819, 848798902, 509551718, 865029782, 795199550, 342209515, 37439911, 122342267, 474663841, 207451670, 383510726, 368422336, 831103771, 133121869, 231233267, 108856345, 648123180, 363689612, 511469352, 726162675, 153243455, 98867769, 543547074, 845015662, 253249494, 891020797, 837040050, 652367663, 110078813, 389560980, 246415993, 39464872, 372786726, 158240702, 861402303, 599596448, 689015132, 999338091, 943147300, 160619805, 522636369, 265166198, 237442538, 743399783, 287846293, 273057100, 561197930, 934924081, 175194075, 573553865, 816539150, 857677281, 435650472, 364554721, 178091920, 311566340, 286626556, 193543099, 350250725, 169967033, 875106796, 756858491, 932645064, 215717049, 169698424, 879968760, 924428295, 50309135, 609511547, 90357115, 6665890, 466648254, 981194501, 934592498, 28544752, 387882920, 769458714, 853707813, 243462301, 313508763, 925739887, 431773824, 484413096, 897217529, 985200514, 355324013, 965377431, 281551283, 125228097, 205761033, 116227772, 171309397, 189578408, 309791382, 413518160, 298244530, 498981702, 54422332, 275507963, 66368754, 63910052, 683540042, 560154076, 84124801, 854946327, 740524697, 266150371, 588474711, 372231909, 321065249, 976707631, 712680687, 454268157, 115775120, 542731449, 447976006, 276752164, 729469736, 723081131, 935724341, 840240466, 757572094, 909540473, 927309884, 794842835, 734398817, 632679684, 493477070, 142173302, 930279200, 495903450, 369678127, 242312591, 480072314, 238545050, 303477241, 516497779, 452242453, 680792407, 200246449, 134120642, 654812392, 796070273, 129165977, 956398628, 466137529, 979873386, 334106025, 868193240, 72931601, 436441068, 474024374, 70634907, 654788463, 517505971, 983825279, 262222116, 72759927, 658598449, 869014523, 346766532, 93968387, 867332162, 241620026, 582083716, 11824500, 2548748, 665591755, 82047765, 532187058, 521944261, 599679537, 784904456, 909546865, 293501285, 383302307, 29876664, 933064668, 557726514, 165544667, 219776834, 361941710, 503965200, 346441079, 941135528, 567968655, 513971643, 486566606, 92035968, 122886443, 845282859, 590675259, 321933356, 257880611, 720932512, 871069844, 195955357, 834778291, 706664667, 102674470, 913465245, 32663828, 493660055, 301140120, 838576419, 688012187, 271580165, 234728395, 706187855, 681691334, 796508796, 804379394, 408450703, 968344243, 314406950, 10177667, 283473030, 212057650, 8639633, 957904126, 179759751, 526821493, 390954105, 338185810, 287760085, 204969663, 599230647, 630352289, 733971554, 257253883, 555719873, 460756891, 907217574, 942744825, 92530324, 755588625, 560584133, 951322092, 221283689, 782918236, 338904219, 43971979, 379148510, 23932729, 905774773, 103193973, 316348749, 347356501, 981688950, 233205370, 854115728, 439942716, 685632709, 856136747, 454722947, 873398110, 432922345, 755527792, 1604667, 43529247, 329237169, 112163944, 746702959, 181210360, 955041669, 641559458, 674756501, 176158499, 903590119, 933276204, 915984226, 789022310, 25815801, 419250982, 240167607, 422251738, 971111690, 61735962, 383036330, 676403474, 744419495, 247833883, 668464170, 710637673, 540736439, 596967040, 988971662, 205743049, 882342377, 323321367, 512778496, 446737076, 677981298, 125283213, 649169434, 273468520, 880575249, 495088403, 680976578, 319037317, 702848330, 1877484, 630151571, 387444393, 213361715, 397326462, 987582352, 346265845, 851689442, 391764311, 942379602, 281820273, 434242106, 884234707, 870777157, 672300125, 708317115, 586308565, 788961471, 915575629, 9304325, 45840288, 192217678, 953342665, 550698992, 488650479, 348185716, 939051787, 960538123, 244832665, 532249483, 817700951, 788629043, 416226201, 670473270, 489641691, 4340009, 646093479, 810517487, 288718508, 385326465, 549069793, 245523342, 584863371, 89282622, 262864888, 662830190, 151701372, 353953460, 97309566, 681664407, 847281500, 9668122, 827614028, 166804758, 70356034, 567273616, 842634213, 14496600, 783758084, 312164687, 988731596, 902089059, 519859854, 256738467, 952458024, 211497499, 547412969, 51421193, 812066343, 259257723, 760923086, 659252700, 228152351, 333003126, 386366324, 173679268, 676186659, 553597818, 264831199, 954024956, 509205394, 174282132, 34067502, 919136590, 51716129, 988457753, 672225050, 755556489, 144818772, 442745354, 927003327, 442027731, 21347738, 567783957, 177440026, 50045693, 317906617, 971974722, 193505865, 807544008, 883970288, 522053260, 461758572, 207329460, 332165393, 158889543, 148418523, 389932993, 990623670, 314573389, 545492596, 213157615, 844039142, 812658315, 813873182, 530183661, 524587124, 925320430, 161549183, 609626948, 645726075, 483522665, 234601913, 399301140, 133242613, 536844383, 698719522, 928398866, 340499973, 60846627, 506274262, 875201622, 998842552, 324672710, 498755476, 787319184, 3019899, 615449406, 356230354, 393671723, 162964384, 246729264, 648925883, 57471597, 432600294, 282049675, 393771233, 847397244, 888696354, 803568011, 169178119, 941827851, 653027066, 364734943, 578795494, 902404425, 506817997, 373201382, 9493886, 59578214, 31607556, 39399344, 857326206, 914172695, 570987520, 733251544, 970780679, 278145200, 151273718, 216447272, 287433864, 722868806, 598026079, 21569081, 162806620, 22738927, 215352172, 810241629, 18548080, 993682728, 557774753, 281221310, 753156558, 521976233, 222615211, 953923494, 394468180, 693953468, 564669656, 54939232, 944383887, 605671039, 111971984, 164575472, 750562986, 668432794, 701220082, 187971969, 871779474, 635371827, 21481567, 560312288, 978270688, 429166697, 390515497, 443769132, 195572374, 854515819, 197958994, 57949059, 648425364, 458109804, 292883714, 789213437, 381213753, 271962673, 774069584, 648318341, 969191532, 488663890, 195653265, 528213054, 881441850, 208754070, 685159756, 870533872, 672083623, 639071002, 29029460, 509482340, 411349806, 956703890, 173431002, 65797082, 509765105, 497489837, 191669234, 625843206, 560543128, 680950066, 583005099, 710551741, 481188968, 847502501, 650306029, 899637290, 881898261, 930982739, 296489648, 707109208, 286116672, 439370499, 73805808, 874489125, 64902863, 335255585, 136932974, 500838876, 795130652, 693181425, 411075365, 184352197, 647430845, 998394880, 911622317, 678203277, 227725939, 91427659, 342703383, 144403190, 87372565, 684151250, 822169596, 64283422, 853058054, 156085671, 722583309, 525265459, 45377902, 973301220, 163858177, 964070037, 925538467, 615357165, 982986742, 899050529, 241958120, 849577781, 84303483, 154334595, 155607556, 373592250, 632997746, 609928193, 309368816, 471949061, 8337256, 516702191, 847024791, 841612177, 735076459, 183190209, 480912078, 825782703, 79766663, 195266550, 375204275, 645567641, 375311841, 460092851, 993718630, 896781775, 862655204, 87068378, 380597281, 80494330, 37503093, 741713518, 32964702, 62887485, 936286142, 565541868, 494964282, 177148727, 630681699, 707841990, 958741279, 634060759, 375462784, 848255164, 654765402, 847035926, 360046729, 311281406, 966024483, 400888021, 104580475, 762705508, 456179385, 222206266, 979066684, 261043737, 820407993, 754577340, 476084818, 940799413, 613474504, 525906149, 958311504, 749516979, 460920277, 799181143, 381433423, 615172156, 333185767, 540973166, 750338998, 889692834, 853182231, 324705176, 367558966, 318758341, 254623987, 891001352, 899960844, 512777443, 432411337, 984845473, 430657738, 937248889, 60099443, 301542561, 838385476, 561404408, 981287815, 798607707, 465845575, 571873198, 966762785, 17587588, 24879578, 239427375, 132725148, 313330511, 134156747, 511141107, 524811824, 289384382, 90194110, 721586972, 827756985, 358685105, 225656764, 366455703, 473729889, 823457344, 753356503, 213168467, 27775237, 319510713, 536447748, 613014103, 609060280, 531650637, 949737179, 927510100, 918634754, 842113306, 990272582, 848718764, 197342834, 129956273, 725229752, 562534607, 780306772, 463921263, 830261113, 37392652, 623947320, 622575901, 652054369, 853834362, 472321011, 718395489, 291683621, 450370778, 416801621, 206040071, 772165072, 611727871, 135911728, 297272305, 402338369, 211207237, 732398910, 379151654, 372906006, 837972306, 583988473, 15693456, 397084864, 196327845, 833304308, 577368061, 971977476, 777896600, 119020480, 551364586, 872569459, 935564009, 933227176, 281159331, 604284917, 804852469, 214937892, 883800124, 290281961, 82431292, 564788376, 854698687, 445134398, 571467065, 35102003, 856031900, 794851107, 872661668, 836885469, 496532650, 882664294, 245705945, 370750585, 101449371, 406435993, 210788756, 246373976, 160100560, 772831774, 40021641, 827050763, 627634732, 427393539, 18884685, 445407093, 421348805, 743434082, 699994901, 12212258, 4964805, 164371383, 102423336, 844923913, 179803657, 314440587, 741471385, 33086436, 591976494, 289790792, 994501875, 55786356, 630654146, 932343884, 759049297, 935161349, 714309534, 378839396, 736338539, 678948055, 387642322, 192865715, 156726887, 187309725, 219011165, 614936483, 997099525, 922194943, 782029605, 332452036, 559635618, 258061053, 645799814, 468523956, 952993407, 429550235, 773170752, 716032850, 504803244, 794808908, 122192672, 55239077, 33979672, 957698263, 125658974, 490350213, 883120036, 921783738, 554361282, 493772449, 276827849, 214421532, 273074925, 943841200, 819515488, 618284918, 857333516, 668339774, 979607454, 120247833, 433031636, 467329040, 332480100, 989248667, 463096828, 904499119, 202695215, 260178835, 969764409, 600601650, 411417659, 751240352, 66301340, 35507896, 122376602, 2971259, 791858156, 125469167, 910965689, 262644661, 495946582, 11423572, 326946605, 43675372, 13726299, 36384979, 234806093, 545239791, 9758287, 996025118, 750528845, 742470017, 899246857, 535332268, 844855947, 282457359, 466178337, 850338299, 29965412, 517009251, 870868304, 676384081, 490416076, 582455241, 286530082, 978123858, 726213417, 492594981, 663577069, 186646523, 879451082, 503058350, 877778157, 333322951, 591083236, 390985011, 480580313, 531019437, 496361252, 383617974, 856329094, 236153862, 758849060, 297606527, 422807808, 536889433, 543258363, 45981122, 287751176, 827910524, 753093958, 951440715, 423872928, 324326086, 46382196, 511175860, 284924036, 715713498, 138060738, 683618683, 120209092, 799185160, 352286382, 491581606, 110995281, 95257555, 249021915, 651905194, 948943940, 259415536, 319573491, 397415972, 689797202, 482758867, 957988657, 583525242, 965873847, 967841291, 495755127, 470308830, 673614160, 977020283, 92126202, 331088802, 822467096, 253852795, 259601160, 819290605, 81393045, 987777479, 352477491, 147603155, 994239326, 577149586, 570736540, 765618495, 142803344, 676395345, 990940749, 957817664, 444275470, 543448280, 583288766, 776869682, 172048417, 33684937, 463065839, 277255337, 578462864, 871953063, 396591327, 388331050, 738013530, 666464029, 918173098, 333222372, 932268684, 350753173, 975451177, 831494073, 33814005, 648715561, 658749068, 525777258, 935340556, 960866358, 240117660, 64462393, 903495658, 316051744, 381604424, 680134237, 423270772, 755663506, 552662874, 448219049, 38362041, 367803389, 344585633, 452235656, 501912197, 54929375, 280614589, 473178093, 715219132, 125011099, 685127426, 785871550, 969121854, 357135703, 767350223, 309988484, 775481671, 17344241, 447065567, 217961479, 109832334, 261929510, 114946821, 893230799, 705102381, 860810304, 623643765, 511544202, 438556478, 939460734, 459170183, 556961189, 173795631, 277757209, 591750843, 733980092, 537183544, 981979479, 176723104, 140447719, 485064271, 406901458, 265195775, 317350092, 818271751, 631177729, 280270952, 563039623, 195179696, 445102519, 793958749, 990671655, 211939357, 324888384, 509654250, 675249724, 59371390, 729320001, 801299629, 829660388, 439016037, 43053800, 623962327, 718226786, 403350034, 805993814, 83975591, 35453350, 233676386, 346488129, 89440179, 880465558, 66092565, 463954793, 552412961, 469377152, 712009479, 298655050, 7368360, 39340757, 470193420, 785357414, 526288974, 280314194, 621843722, 287585650, 816207984, 453052707, 182642475, 172429197, 805113327, 550082224, 556555607, 446271810, 57415893, 934525989, 242095077, 195257680, 647891638, 706785825, 963200017, 97719848, 616747835, 166248702, 665085415, 852930826, 153266, 561010079, 19501869, 706638389, 527971651, 738990824, 198600031, 34765118, 212961209, 810648069, 736796825, 860674354, 164586928, 802903220, 76305831, 46998881, 487463638, 814152432, 760585366, 644784307, 200071580, 455717683, 502032205, 933283466, 767842029, 814247312, 962148170, 648727380, 570352604, 480413513, 236539654, 91767672, 694411379, 329130448, 447328514, 774058108, 989653963, 949312209, 683169744, 19011065, 516355614, 820262885, 414918628, 256174808, 751093712, 399493834, 954708805, 554549680, 541327068, 309832025, 271344810, 316718181, 55528878, 509526062, 276886743, 497834596, 448732575, 711400270, 701175177, 605323399, 904413282, 573927825, 224571791, 200343353, 270039792, 731127024, 412625930, 247412450, 914171403, 803032343, 377619211, 494880256, 585006369, 980969690, 358276785, 338098685, 834514858, 39249055, 317474706, 829507775, 165118084, 295610377, 491019913, 390093589, 209745027, 976009860, 804315319, 918140211, 202398403, 453677941, 796551111, 947687388, 564063440, 762338136, 13550872, 194560819, 687366353, 70561835, 621949812, 664369771, 788422566, 253057379, 97283771, 614632935, 231191117, 395231942, 636756749, 654956774, 307466750, 90731908, 150961682, 734418577, 243708729, 405078819, 197653501, 848996383, 288673308, 736078391, 758804971, 350686634, 282968959, 831774553, 329707807, 730788825, 817968931, 443108498, 445133830, 532264756, 156700726, 467322129, 548805753, 355901232, 676035621, 610614797, 441549521, 858074643, 576411741, 484206469, 681968232, 290179987, 473000590, 351007880, 717740344, 923394797, 276573582, 147617446, 182180992, 667021101, 743586216, 803829084, 540873020, 974918813, 452962584, 110629160, 305678467, 342984805, 333419205, 302803797, 794487532, 191509980, 464723036, 768066231, 202909072, 619035785, 576343217, 69507956, 298472530, 125199338, 629257959, 843568357, 470194997, 116910627, 806057352, 763133749, 771193770, 249299653, 894578080, 987969364, 370537382, 152943376, 220257621, 49778944, 160648788, 748922097, 478823930, 917708560, 769389626, 565628290, 538458285, 917447011, 186321532, 938344003, 787457527, 869607340, 825758462, 359632438, 800862438, 471720318, 118740483, 363191034, 936686517, 656499687, 428160391, 668532489, 72521117, 881628543, 686071336, 688650084, 5889588, 519796250, 600813040, 421047616, 564098432, 834883241, 267250452, 827727409, 323654108, 314083704, 783643285, 468917000, 470651774, 294255965, 731198908, 183098374, 111387343, 576765269, 597548516, 190611673, 693762174, 836729402, 956831194, 115818114, 35093322, 409262112, 524026430, 917314778, 467135422, 153586496, 113283638, 343806976, 799932987, 493775503, 731030291, 920313943, 772355663, 955681843, 905335239, 229762448, 533476410, 231182178, 187734250, 720434800, 224395092, 475509345, 521251168, 334519177, 693719304, 584030480, 446866506, 957677091, 940859686, 584490603, 592589595, 865567260, 651839909, 1661567, 179072743, 8339373, 773542053, 124546226, 658442394, 198141510, 959991609, 14494727, 946538275, 104674326, 786419157, 690781229, 464620992, 601179408, 462184657, 610610541, 250615850, 732414267, 262614591, 383800351, 352011299, 366859497, 689488181, 725386870, 840905670, 876707422, 411537720, 866812259, 821428424, 380662047, 917021375, 321778392, 297739205, 896361574, 509531340, 436996549, 679466793, 669387100, 267242583, 852449063, 482042340, 879619019, 505242382, 964971659, 312846188, 266537636, 186488704, 778875138, 915506233, 751524759, 197569245, 982064009, 169920278, 881377440, 85977798, 65638280, 26178574, 364836136, 34857186, 924831986, 489316863, 153902010, 854202039, 578808560, 218453581, 902542742, 191480116, 312050792, 166304938, 81224021, 633229386, 893273391, 240832290, 536764868, 665893926, 728138862, 997152838, 979270905, 269683062, 397035726, 637727163, 700571743, 399149215, 636385160, 797682368, 530524180, 204772924, 617220031, 759704941, 114149368, 627696983, 209898245, 326816799, 335620988, 186186393, 59780240, 850447905, 453237716, 943648429, 267252609, 403414524, 519467488, 438459976, 645179587, 167560233, 410676862, 85943689, 823023007, 163626764, 430610764, 774885269, 295188738, 666904361, 695859407, 773355063, 497071275, 867077848, 783601874, 377794489, 470141936, 536652750, 632409923, 83773502, 956534288, 407299964, 203884118, 48948465, 149014580, 794517008, 21163087, 756457210, 72459644, 697950175, 877701696, 388485649, 516706409, 101249444, 211498103, 479720690, 949762021, 89153522, 489443252, 928127761, 225567442, 173988071, 828909582, 673836388, 211538580, 317519357, 87415516, 587860501, 195040302, 698895013, 742088635, 490907155, 352603076, 380370773, 977167625, 880697467, 991585825, 163336069, 469914488, 899103018, 840641230, 43075002, 876956287, 346983667, 658487344, 36709128, 223089360, 867051313, 282662200, 419113128, 58786281, 853759887, 912587431, 441178559, 298027227, 209045316, 263122742, 627450563, 962052814, 884827609, 276647346, 208289962, 74534776, 779949710, 780686930, 411582163, 984490203, 588408162, 208988294, 223942923, 401012459, 707458302, 742575411, 770662779, 289334459, 242682752, 967989556, 358594127, 296343542, 857305266, 95358281, 285744632, 894154886, 745838265, 1970361, 496929497, 455277598, 615596245, 620013222, 521734389, 697646700, 426946694, 410446228, 519886270, 810925144, 514101947, 156869743, 69501584, 730518184, 416952072, 978882693, 632649640, 848784564, 241750639, 661820475, 580453721, 355121498, 448747026, 65775039, 924945395, 835436204, 3491725, 852648735, 85525913, 617710761, 356396402, 904622701, 18011002, 425640983, 977910277, 79971634, 818239413, 374386645, 684597903, 803110731, 163694001, 501959170, 168542750, 194230577, 844776391, 61383752, 211839331, 836668656, 169849791, 403970331, 228522366, 445499524, 128822196, 640295349, 934014912, 352572856, 686391513, 202914342, 884776145, 438438385, 391783868, 506273091, 392665954, 362749675, 753305223, 567787791, 997698451, 391734421, 890477478, 784700946, 95197129, 222016264, 817364878, 257150913, 80359798, 932469538, 181107338, 321544938, 791609250, 395635029, 943306665, 200918026, 291410429, 650147632, 840334606, 630541538, 256573897, 309291546, 784970512, 231194078, 104179155, 127053099, 17758942, 972266325, 601451445, 826180941, 963370433, 248211868, 484265991, 30321538, 34560988, 82973251, 186621859, 239090071, 852277570, 809858128, 625066872, 767400470, 250319079, 790362635, 691256323, 345764652, 730101741, 271374681, 749291477, 212070038, 647898035, 12055089, 173567847, 227262850, 508799897, 766726670, 182573689, 138430086, 351589771, 317476566, 766140711, 614385628, 749564808, 529993636, 485120897, 287076074, 72620258, 56814142, 601755692, 634077997, 894224110, 691285778, 551369241, 743157823, 645547333, 181329566, 25562079, 992601713, 454242800, 714354631, 939885672, 381868227, 647717099, 550549661, 325460651, 255185824, 562861298, 997162718, 710379523, 904822229, 695604648, 820780247, 908221318, 984441981, 591377481, 852155572, 907851364, 332575256, 214794248, 98439711, 293034138, 921610006, 302236508, 575537517, 842056344, 309043492, 829708376, 296051040, 382470763, 523488113, 891109225, 79724949, 98419067, 988840856, 138990357, 867776089, 4418377, 402013182, 65672995, 159038465, 494022921, 209292733, 188233552, 874905909, 108841150, 41756604, 693124275, 478901130, 24096549, 12040459, 357850891, 957310197, 870303081, 709073527, 478162443, 300193172, 221377259, 681899779, 936192556, 925491930, 895098161, 606078714, 43211544, 871847238, 174662958, 722096220, 780753039, 128865310, 938129944, 339361135, 533757584, 771285023, 628083668, 154460724, 612832372, 649398152, 520935637, 378881155, 62535614, 736517329, 342634717, 450063436, 618905211, 941111031, 530523003, 496255393, 18185858, 973428712, 503277086, 801146535, 72127565, 224100828, 38591054, 124994010, 351186741, 906659760, 970542877, 276840107, 255349864, 814847971, 578510801, 964944551, 67211347, 711842002, 57840999, 676950455, 413597191, 399705899, 197498782, 674415952, 122096059, 970553024, 218222841, 280275469, 182312480, 560831872, 875774609, 337346596, 756461002, 635366996, 861848026, 396480673, 279626809, 798568205, 436378474, 448365641, 6222712, 883794251, 947428132, 622329403, 311413744, 894281206, 791771589, 643030740, 441999119, 35788367, 85491639, 324149199, 472939469, 763573226, 396792297, 665809448, 396589376, 284657127, 948403092, 566388466, 343627973, 975047637, 376881613, 543841556, 395483789, 880548794, 487043575, 346363364, 851261543, 836249797, 694784632, 524331392, 703956534, 973888862, 477351696, 899116971, 858183146, 491729618, 93210579, 666941124, 932826004, 156079824, 251862012, 854867509, 574556271, 358660396, 754588001, 154699288, 917658160, 547641800, 779023205, 148239186, 919234978, 501240775, 84966806, 983373119, 168445170, 225843880, 147688750, 987920668, 610172257, 354320443, 561450541, 996591535, 383630812, 470362975, 453746165, 297517051, 207714541, 850469907, 537015391, 358907711, 727468967, 783033110, 426619558, 330571461, 997329145, 351340342, 333290154, 822943880, 976400170, 120268966, 813543143, 304014938, 973496309, 344928277, 553851267, 324048330, 536721952, 740985949, 144617151, 753980158, 953488478, 498857636, 85926542, 752577050, 332422385, 360319474, 881952349, 207968886, 749837034, 811844610, 435789714, 294136510, 544874193, 490284511, 893316458, 361190225, 560189228, 303493537, 888537564, 567172215, 158821871, 574431804, 996135707, 954761620, 213097144, 84437532, 65504513, 976140721, 233763261, 440497110, 375568573, 593316542, 627496575, 64696026, 267569364, 589814280, 425300430, 184015035, 688459827, 240052961, 19895893, 142228959, 589158918, 578894379, 520650961, 287810397, 521223024, 259321356, 535169718, 705385031, 877075007, 338974515, 278580924, 335989132, 542470662, 570916528, 725743717, 823277545, 766933195, 607039498, 938664615, 769695200, 381233933, 919893791, 858153239, 472994582, 977347335, 274161294, 260115942, 9111619, 590553942, 608412311, 563802825, 290942570, 297237075, 514305111, 176226400, 2444970, 736668318, 962456672, 204651825, 290506207, 561707517, 434780709, 587072040, 748773856, 711097629, 967046325, 634138411, 429452599, 437257465, 587541774, 370334895, 506245140, 382592518, 494206885, 703009123, 884474799, 50710041, 421990769, 294896338, 868587920, 986406301, 464946807, 153183674, 761040670, 816736274, 703227623, 151235159, 595678031, 718384303, 894123290, 449909584, 824981450, 849081580, 730858914, 687022723, 932410875, 893983180, 556923651, 347003760, 564924127, 363040652, 568679491, 423573356, 556100722, 333228351, 918343142, 918429603, 948330088, 603483928, 346701349, 931029745, 110864587, 473193459, 677935402, 92358136, 840269749, 844294319, 144818281, 907867130, 867938383, 865281720, 863398841, 710800096, 396994779, 365169327, 149661946, 446634939, 569149812, 54742141, 204457296, 214363745, 877176147, 110846240, 588684015, 367735101, 599398536, 639830329, 958407628, 234313998, 323383060, 139510163, 307740044, 734863194, 91596130, 174163949, 683039153, 203697382, 589013625, 682667812, 688795803, 224130254, 174943160, 902870132, 336788306, 581252012, 580516363, 57179543, 395726495, 752647402, 720510853, 129064749, 646519534, 951922276, 325053967, 498255530, 594273962, 413450855, 872091012, 401679659, 263195017, 107611248, 120409653, 537213586, 260989229, 997909786, 504892413, 279609885, 106638982, 98837220, 860728540, 17419172, 646121510, 368498367, 482271923, 238306420, 286396949, 629464900, 122800140, 204173442, 141954719, 912551589, 828783296, 223087734, 520046625, 983360133, 146845428, 186836839, 76761710, 728801340, 188597767, 224788210, 571190320, 47352786, 860040310, 185397365, 618375498, 136194525, 237439845, 370255467, 593238746, 238069782, 148018580, 629877709, 995352095, 536291197, 123350409, 151254119, 181122008, 829857914, 761476711, 43263565, 390007212, 138714897, 394590407, 67367534, 494042111, 145088653, 665954332, 616898255, 167267363, 275545803, 183753322, 247692872, 65634671, 783455607, 328134824, 160896191, 68051808, 169012943, 723307729, 77131315, 622945255, 721121160, 878731448, 46722817, 919095603, 294021370, 958185951, 600113720, 905503628, 606414164, 657305247, 939673705, 689656892, 614901484, 319412953, 530663148, 297702805, 538991044, 218694334, 294124347, 354057067, 621034934, 600927667, 1568593, 461404011, 679386374, 392235575, 364001022, 803843243, 925782822, 246749544, 929045028, 570257607, 400162669, 593834648, 182120826, 684738598, 375497671, 158279498, 356373091, 248526260, 872646805, 248421090, 61624866, 335978900, 96234742, 138102338, 863165146, 391479795, 897428546, 873914686, 306342670, 939465341, 685841837, 844098707, 395629363, 590865622, 637613471, 108216865, 243437391, 16520581, 681665295, 379454395, 964053918, 682176224, 619058506, 913438261, 300678514, 314866808, 266673337, 311582125, 779543126, 642971105, 606437629, 942461164, 602775690, 246320139, 918484566, 902401275, 340524914, 878347308, 238686110, 989129689, 817795536, 294338325, 406881490, 629733031, 596643090, 575366029, 971685226, 22562178, 918322369, 92034318, 654484876, 229185749, 630390721, 92433953, 593036684, 582508582, 94717596, 645009, 426370509, 882108131, 43135138, 27158714, 252160726, 716882785, 951352087, 525246318, 440770052, 843490743, 663072298, 946494766, 364106435, 991898915, 943821770, 88468249, 476866143, 451102773, 635559779, 640791361, 46064561, 384501962, 19892310, 284114515, 17350415, 209332714, 740729459, 251209187, 444074877, 153907295, 478584309, 313147407, 58611643, 674563261, 267821247, 17861964, 601319762, 779616932, 763004312, 781208583, 150611626, 359321045, 279245565, 715096886, 193976838, 476365440, 58150441, 10215520, 322691950, 598925836, 956839684, 641941987, 243408433, 102319170, 204825586, 969500894, 754785055, 122572330, 379893557, 275171608, 762290151, 232483609, 923448576, 660147469, 288604733, 680682493, 813446233, 966629253, 898056036, 122269825, 26669264, 34995443, 159820450, 619006804, 498115137, 547539955, 60516078, 637449876, 325692227, 373696920, 25242457, 652457918, 88112757, 452888067, 351243108, 967725445, 898076048, 92995140, 854398629, 616229884, 340748769, 576527765, 210302956, 269948132, 932364760, 245395854, 648760539, 991991166, 810664276, 124185655, 728516385, 717169077, 984109970, 10028866, 795043032, 287798720, 395362776, 857047168, 802359570, 812321688, 281808854, 144732233, 519620627, 369552087, 406292282, 386415442, 948448697, 972407968, 140629477, 582429389, 947004759, 659635995, 263192848, 248525871, 157901062, 624315793, 742438437, 770825060, 555539676, 127124924, 968118942, 948217991, 211360538, 175959125, 976632523, 453880142, 379295965, 170863540, 318561318, 101041423, 399120536, 202041081, 350200370, 201709604, 364708224, 40407749, 971052241, 351894675, 185838477, 564606067, 427418489, 789955250, 665341418, 61203497, 71320663, 514294025, 907091914, 237094476, 542425545, 714235532, 466702229, 226159578, 78686947, 551831072, 642152017, 471245713, 363782023, 568273101, 340444022, 829549070, 626677286, 231431347, 71950970, 379564719, 815779794, 288918779, 514947065, 988322680, 613913478, 535198130, 601616742, 974841201, 927284617, 203887292, 14664455, 265615300, 233023589, 978078704, 757273247, 607264881, 37932971, 917384170, 78888919, 966100707, 197910913, 988478304, 518659083, 206473019, 591715738, 285977509, 844646561, 397984876, 629255820, 822996327, 794797871, 712294051, 408901870, 233892658, 750903275, 532706417, 817794897, 833093747, 187651610, 39546882, 150827390, 475804356, 837595450, 635903033, 609291690, 971578190, 382721337, 39192400, 677806388, 906881291, 950979004, 330111704, 616539361, 981221344, 310390437, 601572675, 990833449, 691885358, 687854469, 325683087, 529736203, 247028608, 665625454, 879909814, 485722076, 702938521, 622208435, 817027727, 601864190, 962198109, 808795378, 803846025, 17174691, 388822122, 341277172, 529486928, 906800336, 300583301, 78588128, 548360608, 694569381, 423120988, 321996866, 876406960, 649940901, 67811187, 588579863, 939548160, 110451415, 795134875, 667463250, 952673315, 715923656, 608968238, 912356430, 104693057, 225792951, 264900872, 755005638, 897628730, 308144780, 639968523, 889579150, 878015003, 72858192, 426722152, 32221094, 711686749, 602168856, 815840936, 535922383, 952380228, 754472665, 519852313, 40668606, 3988813, 588562849, 656788640, 862100581, 97342187, 792745171, 602799086, 353119442, 83964319, 554829131, 452230281, 842149230, 28513788, 1027111, 836044358, 472285707, 738337930, 904626210, 604801551, 364646307, 794453225, 668479919, 168931949, 480925460, 387580780, 958263281, 720894663, 919492835, 945139, 165868781, 907309578, 976619480, 628558315, 358404599, 957742684, 961171173, 174838101, 853552611, 47996541, 11027822, 322560670, 372867659, 713108675, 52565500, 601181555, 756322299, 438362171, 98678013, 551088323, 999231794, 865938003, 565705377, 137662727, 70514039, 723637828, 152392079, 598408114, 614492501, 906204466, 274041502, 315629209, 191858913, 219455008, 183178174, 219799464, 54476639, 152812322, 276732118, 594823157, 740031287, 28067123, 749962963, 119930198, 986555800, 946241487, 564118544, 197581676, 569540335, 519248796, 330590045, 632853411, 162075482, 445007912, 697152992, 150272261, 503892651, 35831439, 275147710, 762975724, 667784946, 725057670, 804758712, 293796294, 510465463, 447685253, 116328805, 227397863, 368902084, 530993061, 952340421, 391426848, 428811273, 746882163, 866329993, 701207846, 648055390, 998258163, 975515776, 299153673, 36620071, 154875003, 602337555, 637287032, 698757268, 409856920, 555880810, 511588227, 76478656, 259378495, 344332677, 125154566, 184709881, 166857909, 750229586, 686309540, 34830284, 619655470, 355324305, 407975190, 15176017, 686484743, 726635916, 264196644, 454038211, 591646624, 846401740, 492901652, 436278448, 34037137, 261603330, 975797845, 584925811, 22360997, 248084061, 468270135, 684909633, 121481348, 772766622, 644810419, 761933871, 678983751, 287227945, 960435024, 395836989, 83450152, 360674821, 331757085, 726931281, 676616618, 814292187, 837049975, 700008681, 764849909, 284456935, 293386445, 146145682, 6577886, 433317453, 810327253, 942669812, 61656474, 869155588, 177929250, 283509671, 305080990, 588103479, 132130300, 727863095, 360642457, 861381090, 751283256, 372975045, 708454913, 625253167, 417111173, 924779318, 569114709, 76655987, 685188946, 96792681, 478928837, 815342928, 298484060, 629013878, 370430966, 195022641, 340346588, 853534465, 694745110, 95981512, 12490381, 233730703, 679759286, 923995311, 113910594, 570102045, 893020436, 492098792, 698823353, 45266232, 540946285, 393315541, 373795147, 215694647, 8226879, 16856895, 151877766, 423296581, 357708262, 741610065, 812392467, 917905482, 918435843, 850303294, 773099360, 636219735, 375122209, 414429067, 77821735, 107992436, 377940485, 807850571, 444818381, 897350216, 519620314, 59685342, 379668135, 515179670, 396252876, 821691358, 73621, 578333607, 22116083, 181341686, 897852129, 760663710, 653958696, 919995857, 207988228, 485459362, 61817541, 473156020, 915625559, 445590042, 102760880, 819467553, 24494714, 815322335, 150093442, 232973730, 78310886, 183126022, 496957104, 248969965, 121776478, 320141072, 657067780, 801365338, 649687159, 504815009, 440795931, 422499657, 304153345, 661360298, 675018588, 432839238, 394751816, 675002506, 385164062, 142142710, 43413667, 969129701, 949084561, 190353669, 344791909, 984477153, 680895, 615057773, 752134113, 919784305, 563603148, 497595311, 263319171, 345974753, 428389760, 506234453, 126880186, 496015465, 335544127, 636485681, 35728145, 657864457, 822564794, 54952370, 868586556, 69210610, 753416688, 508929914, 748568134, 410670128, 88482896, 867210056, 576971302, 67959382, 29819815, 147238323, 318796913, 680787189, 200469243, 381423095, 236994678, 338694129, 394854164, 589096871, 644278773, 680404176, 918618199, 742872553, 945304050, 454379744, 313625510, 449484858, 276745255, 801704598, 619517459, 967623301, 912222875, 47730281, 778739362, 537678260, 732055284, 454465949, 234103091, 858942145, 651795944, 445393270, 663338923, 159997102, 482273848, 593575063, 177304748, 288431254, 427183548, 485470886, 174161132, 726175739, 208523217, 73662828, 901140498, 728019145, 242440696, 197855107, 157019334, 197810818, 339849595, 167099792, 125780296, 644724550, 926882324, 831838955, 244910144, 64929197, 965991089, 659886585, 787472999, 337657937, 651935175, 689986755, 557804245, 879768794, 901157339, 171789273, 465052562, 833330498, 254349366, 653032783, 8131452, 618061730, 962151147, 779280162, 6956519, 459777790, 241954647, 82926735, 579234495, 159692186, 270593559, 102259866, 485779424, 52757279, 758864606, 927092995, 454823195, 931926454, 815342672, 334251270, 794573847, 154964939, 970762617, 6373749, 924725779, 68526584, 819460106, 635302050, 430884964, 441998979, 714873763, 736673671, 421546008, 586328013, 87770274, 973479411, 978744268, 184359852, 732502863, 934408976, 539865683, 130372063, 190364528, 748661611, 143770110, 456879785, 197249841, 19644144, 294368922, 465334024, 331665030, 634939210, 774971544, 831754746, 977366079, 916877873, 359303523, 189817323, 207692298, 467205563, 502157850, 367434160, 912791748, 158440570, 106853993, 302751935, 396302601, 233256709, 783452174, 461235222, 790674752, 917423147, 48988425, 530503902, 464597639, 113516575, 536823980, 304677602, 877417860, 867125360, 979831477, 406943288, 276574530, 830678983, 771965662, 297066448, 611163268, 701076476, 217624997, 710716324, 543514384, 954347965, 99125673, 77007937, 59606035, 291919919, 600774327, 490596189, 882564254, 517598081, 173164315, 812155012, 108475074, 39219412, 600832381, 323306998, 664025755, 60818909, 459364605, 235578299, 418732322, 218779485, 912766137, 709481895, 925839356, 467046575, 382013128, 794340454, 209464368, 187936567, 46893765, 230721140, 466571098, 87052908, 579162758, 35563770, 598148975, 982179600, 760752728, 352829748, 787334955, 298941580, 657350530, 856201360, 914997637, 484732940, 333244755, 507069871, 80894987, 585615035, 342133726, 46514080, 914367967, 719891988, 46555133, 252192183, 264065211, 124132878, 894426105, 449835832, 425191369, 881568343, 808185373, 557674333, 566784288, 371343142, 795260770, 17131432, 31798947, 993696398, 503163553, 658778559, 888313035, 836603131, 457461073, 224644204, 639991181, 634578592, 145868700, 331845587, 639257831, 877536386, 864546407, 941206039, 846022047, 69374747, 864607292, 739467908, 170729998, 498428216, 78648995, 366516907, 538292332, 830081716, 130938070, 39118622, 996842781, 742599308, 539097525, 899543715, 4393472, 275989453, 202380867, 688453438, 966096535, 888555813, 264636442, 32207926, 743241421, 157838869, 897003542, 374896766, 556935956, 108196336, 764578200, 517949916, 842874189, 849630579, 883807439, 384920241, 232959669, 441223845, 961390654, 215604516, 216652336, 533238841, 199543955, 883550483, 572363062, 266927627, 251002767, 715596107, 389226279, 965688682, 453957452, 148751958, 306458820, 844296785, 85109282, 624153961, 863507893, 590244098, 402097758, 185467748, 64210060, 677204138, 290734855, 892651434, 824831533, 800754601, 374216254, 539607437, 400092142, 355998434, 236521998, 588790168, 139827678, 148934438, 998221947, 743239173, 874870046, 237383906, 940442672, 373500298, 129196894, 468143555, 183556946, 342084108, 479309594, 199295848, 756668496, 670645273, 80951792, 68353094, 653065325, 269151570, 822272124, 570844250, 117914508, 767804848, 277156420, 415408247, 212241214, 814822281, 235884314, 283706211, 63488544, 655567452, 207132122, 541351115, 329870837, 617832898, 962182379, 697331432, 774648807, 55805595, 908693517, 669746124, 237679953, 70870248, 532388291, 802648064, 153140167, 242349053, 461230580, 286880444, 258710159, 696336057, 695958902, 71058200, 740952069, 841380340, 452998947, 86569578, 23846930, 709711761, 407947001, 682478757, 319865978, 509501191, 200503343, 526155605, 820801366, 350673927, 593974638, 652483434, 109246200, 881259551, 462961059, 900646395, 364935769, 572281855, 367502210, 372367277, 195578351, 296956824, 884604328, 991655191, 332073038, 885521146, 643825561, 961240538, 991804519, 64728013, 369943103, 400222661, 426986451, 90060692, 335249978, 606377229, 599359497, 653970363, 232181933, 473084006, 648470765, 152184480, 50974873, 587267945, 849326925, 543854128, 974116142, 30101453, 811278410, 707139267, 317159842, 530224489, 429853729, 518994905, 759837204, 329037469, 186716116, 887123509, 870276243, 723498100, 594193318, 363176260, 458817666, 660373513, 485756154, 412353727, 728867238, 646895618, 792487029, 485680463, 936035910, 401987470, 220169316, 559059463, 884607256, 851536239, 140631289, 441195472, 838548822, 137020852, 176773633, 644769425, 309477194, 786258444, 424793741, 513515734, 969134961, 992579718, 801463862, 571724194, 201604538, 400019154, 525488262, 871525969, 253303554, 142974982, 950638137, 497206207, 817308207, 119768243, 547100850, 128113341, 754681648, 583461543, 660030266, 570441708, 200404672, 800576744, 67694778, 616616883, 596517250, 308670592, 894667118, 540512917, 319746949, 556955824, 966693884, 487523964, 442447914, 364072746, 436500876, 861460360, 468947728, 440133749, 913674538, 308037590, 660979674, 307743440, 680676395, 276662938, 496889629, 452640025, 808829586, 759324467, 912748894, 2285271, 504706050, 410165496, 938896813, 213065855, 929909811, 529483527, 543012644, 441408065, 622963386, 924532401, 62727850, 920425586, 58875541, 445307620, 104862190, 3811734, 328551855, 423154535, 431746404, 391452837, 520598639, 927052032, 92200961, 180760730, 775036332, 75199862, 801396209, 612202069, 991591334, 323313818, 629546542, 323859225, 540255718, 206588065, 87394027, 243904710, 416469250, 906504116, 96214732, 231063652, 509861162, 678192072, 488305231, 938187853, 663686672, 631286732, 730885371, 433645447, 67175837, 369069164, 396067019, 927981602, 753761393, 110439817, 857044666, 952744762, 56000880, 808456491, 967748634, 143966470, 989129326, 218113342, 154092923, 1927924, 566672225, 594641331, 908397623, 661021834, 721039092, 544401453, 772751325, 533071618, 816754229, 354756498, 641140795, 534176146, 862704667, 390972757, 867048261, 771306571, 798651674, 56001350, 591883062, 50028587, 614366279, 145880012, 331681840, 215867832, 253817781, 510025789, 528386195, 673526502, 237589319, 828474888, 583085256, 818191253, 747739526, 143875206, 440014914, 311500926, 941740716, 165848306, 231709527, 204589949, 919752502, 345143891, 850483320, 327560232, 452154294, 185115584, 492475404, 781710732, 91029846, 811721792, 47268279, 633634015, 690103084, 521949082, 926199339, 429624046, 39707886, 52975433, 370988740, 541448929, 112519783, 421752687, 513178953, 933592579, 722973319, 465921623, 782389937, 65015410, 453872860, 30840913, 731181785, 456734482, 475482436, 303725451, 208332189, 14067217, 854799769, 992116435, 150330019, 461667824, 581851092, 242654210, 380336920, 150266691, 444611782, 180298289, 459088662, 930429836, 452305148, 969813118, 959079872, 429655058, 941142623, 727390595, 746889890, 236216452, 948906967, 340896588, 717124110, 582051862, 182365283, 269740510, 89477598, 957856824, 118207430, 286253456, 359164588, 398536775, 993532742, 270197177, 661355645, 878656218, 763665745, 135022993, 541823186, 606733412, 638912001, 428788453, 757321205, 953512326, 151963820, 37748299, 570846833, 170629132, 441788762, 836843423, 400474110, 661117053, 988959860, 614602319, 766287689, 372544040, 794144274, 369029541, 797185669, 73257822, 817567606, 398611162, 955501559, 836823689, 119897567, 73420241, 127098555, 301115904, 711120651, 278969788, 998173029, 470724456, 425550446, 32957176, 495089597, 558495887, 718046059, 580187477, 818938727, 279520846, 983199678, 471221635, 541860215, 447146352, 682948498, 342548558, 775172353, 216533344, 830556054, 243778826, 95233079, 308679870, 905488735, 837786742, 616486517, 661056418, 693654401, 200307143, 858341718, 621870558, 488644235, 613180058, 375448686, 586807704, 800646985, 193547997, 445556503, 270474255, 731646015, 551289642, 662394165, 767766972, 563216824, 179826463, 49743523, 784491191, 121411284, 422298894, 560666122, 250388963, 318268746, 467884709, 901560269, 985059260, 898723835, 5024908, 366482896, 425626759, 939871342, 333756663, 378763154, 7733482, 998114102, 450253780, 291728172, 626106790, 344316983, 358696826, 622726683, 333557888, 152974616, 797055797, 275254295, 679290395, 399484580, 500526659, 564428024, 246066833, 580981881, 93686698, 166373964, 665486599, 351275001, 83948826, 161877612, 362303111, 879154734, 494753469, 422639262, 278277734, 794859025, 126967074, 223220387, 294151840, 451548592, 947168660, 180971347, 109695771, 883197670, 958618428, 484291614, 864299550, 381813268, 477479743, 334535215, 733981895, 847561761, 233713148, 145989910, 516761326, 522980002, 618175241, 357402987, 798712633, 735511840, 82432488, 894972893, 296008358, 194421899, 153682381, 959803868, 936263878, 620276827, 758444621, 560385766, 514935581, 52348436, 333331410, 106712471, 601563017, 463897864, 967686104, 136693221, 616087238, 468785431, 93239743, 813517252, 937523650, 985382642, 485018980, 435497526, 519653619, 595623185, 422412827, 654609912, 690796901, 419711349, 676119397, 932766318, 447841910, 254045922, 919340435, 970729884, 213067976, 347331865, 481089774, 147166705, 888067453, 389216825, 333317585, 975845298, 69050893, 795319486, 233590430, 250344663, 64086, 262634450, 195682321, 582079633, 980315621, 221382789, 908336425, 316867179, 772315360, 181347624, 550950712, 544516556, 914949843, 701280589, 670485029, 149352712, 299418604, 223356713, 917592662, 896659758, 519001072, 827735060, 309136463, 364716057, 296661076, 73877044, 371464745, 400286495, 169197499, 417460131, 473679587, 229589661, 533671909, 718200763, 504443258, 311837120, 963068053, 179583971, 774932721, 699801930, 808221263, 343159781, 730995453, 42664037, 435349872, 425216992, 331556407, 106185030, 402945942, 993710818, 319535504, 409562005, 693801485, 846468105, 945039983, 459048426, 29383667, 300367661, 731300566, 25887115, 29432342, 48664240, 409841664, 420111337, 525919059, 992330505, 93786777, 236587494, 998492834, 699814898, 264814262, 140028253, 212252293, 600210153, 87893214, 520740614, 391752439, 394668013, 589295104, 313931795, 710495788, 231467355, 562033760, 151729046, 101627161, 495142933, 635129119, 488632472, 825088560, 432149844, 763135769, 561895596, 534508416, 230613195, 141629939, 811466141, 293456349, 165374506, 791447093, 91988613, 247189061, 524315908, 455673417, 515559176, 811247268, 344110220, 33473103, 731838170, 601795959, 398189768, 541295439, 516512907, 257691613, 953618017, 740052881, 559179953, 528814091, 68033084, 461721553, 93787850, 430184074, 633330154, 922233713, 384541746, 431927171, 718005589, 666659918, 777009952, 408153109, 668806254, 785789592, 806219806, 988560529, 861804325, 669647047, 641439766, 941609755, 491008048, 965623857, 766238645, 341865040, 170851864, 527991845, 81692306, 80645007, 107740109, 597752100, 314916254, 591832551, 134754345, 930729471, 198620572, 734620941, 677290640, 579472353, 365391654, 50183476, 702943128, 705875382, 21227151, 760715346, 470512592, 641081723, 989173543, 685004617, 758644629, 58543164, 323750235, 898433204, 467597349, 181965163, 249980167, 649639060, 584462312, 23088106, 439633673, 803059439, 392437848, 590541197, 815596529, 852731045, 136494100, 491676653, 9571267, 249699732, 751889929, 213728670, 107835855, 328926993, 240425459, 323066455, 988491333, 534434272, 657401902, 227989384, 614689376, 246134094, 190636227, 408057521, 888498820, 885534966, 724137543, 682602789, 531889554, 990052354, 102053119, 501512445, 937436170, 434442518, 811433501, 244383419, 587431265, 795075978, 506780083, 609403643, 891991193, 569723580, 237094521, 389532127, 808291425, 690738912, 107036057, 754792074, 390501268, 111978500, 558017325, 169157383, 888756664, 934233894, 894637686, 127875159, 562649846, 328576053, 202447226, 237774598, 834357970, 24427783, 60135388, 695201748, 784910558, 750368585, 89884588, 977141693, 462601980, 607605620, 488465254, 721001184, 458277065, 483200758, 553292725, 820200272, 40747730, 849842906, 341772055, 84861805, 870220338, 661021797, 703463378, 816654685, 611371832, 90823399, 743147293, 999225538, 880813226, 130797481, 634589397, 933036665, 362011495, 431052160, 517474555, 264673849, 945913819, 672696048, 13587342, 725150510, 549270198, 53009388, 621063061, 487588506, 518911018, 562324413, 526362865, 113075964, 868089083, 560667169, 108575746, 719605299, 886156517, 129943889, 867174107, 203147475, 454927741, 501762388, 65807884, 999081454, 122572134, 567685466, 151456574, 857670513, 895943597, 868432777, 228147665, 683877023, 127342527, 509142090, 967931134, 770416119, 545848532, 813161949, 817116060, 331841618, 407920112, 571614619, 458659467, 12739359, 556220806, 475845576, 436273737, 976329071, 638218586, 948956996, 160713921, 709130061, 904435548, 987756127, 481817477, 494718833, 821882670, 3837571, 566789778, 53774802, 171810279, 333757644, 399522037, 631319039, 429891070, 3679123, 145845660, 923105252, 744366927, 893672185, 353405258, 597256664, 820992570, 293900432, 528545445, 963396642, 44280492, 754068529, 237081196, 437975351, 209305618, 598143977, 316782494, 436086269, 33289272, 86608072, 8692183, 270297732, 787672099, 830184161, 983616247, 311397368, 661661717, 783083558, 939206626, 450390405, 183041238, 521198383, 374968799, 348702711, 469871187, 947547004, 841918333, 715885022, 217552439, 518470069, 856689301, 448521765, 435057184, 559939409, 244186000, 28805830, 545251864, 596211380, 374719118, 119697050, 567298537, 386192547, 976884245, 866430625, 550483683, 449734859, 394408469, 563606550, 53349339, 239292978, 299984231, 288437300, 685703829, 211823953, 196840452, 982989431, 424328858, 856570803, 93540594, 591704651, 966102044, 620930157, 681020781, 917321918, 987719800, 924756251, 768807435, 7488765, 30056962, 727525762, 997988507, 880914055, 817775616, 629456833, 659474657, 754791878, 572772893, 682177065, 824667215, 306506500, 291155501, 87720405, 463966374, 836912170, 546417816, 377279455, 142426801, 14788505, 870183719, 544806191, 414335777, 78380605, 1216769, 130897648, 756812705, 1242112, 579087802, 160757337, 71431225, 870703556, 194136987, 587389892, 913043673, 457466723, 119088141, 309814021, 256895885, 900651919, 400850924, 551855243, 776108045, 403500735, 688055372, 721933493, 132434178, 524254059, 625392059, 886219582, 546868192, 423362997, 239128250, 155553962, 814115970, 374835194, 166912258, 182933836, 418489339, 308845236, 892296809, 735516190, 282367077, 530844400, 833152787, 634504338, 589275860, 765416327, 12348662, 113859205, 994032062, 987526153, 856004751, 553983521, 297101542, 496792043, 219116238, 617633838, 544421408, 607645540, 672269599, 563386353, 319070518, 60947114, 246876666, 533384165, 70186784, 838708166, 286558862, 253581973, 645355741, 784276043, 713062613, 76387860, 60052589, 29561586, 74303958, 206543171, 963679633, 166423643, 495758591, 184497773, 923866360, 829773296, 703125393, 779992948, 972926888, 641037064, 878256262, 980270409, 141350692, 689697836, 372225944, 641854114, 993780640, 713081586, 12034407, 828204938, 61053286, 330017341, 893454511, 577576011, 681962229, 111701157, 270348905, 803952746, 867362106, 841175674, 587216550, 798258805, 629336477, 58830688, 589783065, 709054223, 850258410, 693560585, 651914544, 300729224, 887806256, 313709691, 203540796, 19918159, 716796517, 961671569, 98191964, 499769344, 192692775, 713875751, 47654132, 681995174, 753532082, 596188912, 809240073, 862999292, 37965375, 454782546, 838032249, 165445444, 467721222, 957654112, 47607753, 708824105, 344097640, 155906586, 106071132, 767864547, 454911325, 335247471, 818684536, 559503534, 654555375, 75200487, 451361419, 772029845, 932226360, 441049979, 391640989, 388578422, 413537781, 126406241, 718401410, 55943188, 720928563, 425223617, 437216493, 75906322, 446342455, 861319056, 3698678, 705014564, 216099041, 124441664, 894909591, 470693831, 826866836, 754698669, 25955957, 611242729, 356866776, 726013671, 393481307, 795842729, 186417104, 995177788, 989541174, 899685074, 905206971, 825732570, 555839929, 560935252, 117123807, 604930256, 144857862, 767050778, 218913678, 791397625, 285361092, 102331966, 863112520, 163243170, 81352293, 370444353, 217592101, 358504094, 925297647, 447692959, 207040681, 67635594, 887538099, 494694366, 850686941, 906525301, 606813053, 608801299, 291572407, 956280744, 321306063, 484384554, 392262855, 988488670, 79615671, 666910039, 810622158, 384136827, 872547392, 705465857, 172432843, 196214353, 972015542, 820692175, 738586351, 322561988, 8906286, 767332371, 487287818, 90426097, 588149461, 906783961, 377231900, 897564378, 961908962, 63677127, 623161209, 825017029, 133356790, 639572929, 391748896, 573736084, 151048310, 692922031, 831014432, 338093859, 741493877, 658609530, 33833863, 693725753, 355207669, 114583865, 218113322, 689143154, 412555635, 252250396, 83536704, 207229850, 176269026, 743190092, 573162386, 821825453, 140990226, 874649013, 754579153, 571405128, 293076676, 357204648, 794407476, 412549302, 660577362, 147654610, 199843166, 949305251, 968754819, 714469742, 609104384, 919357508, 766844614, 912698521, 279857843, 100292186, 509570762, 111187451, 630948366, 143549196, 238262350, 594640198, 571646092, 160988695, 126356113, 372925317, 692855966, 397719613, 574723802, 600323725, 769040247, 836612850, 548541844, 858447481, 926868912, 288588719, 796830146, 159310357, 590380146, 390496939, 634402578, 398866971, 852312528, 335129881, 442558764, 123714309, 204147144, 132295198, 680988785, 806789289, 619061988, 99026094, 37326014, 878886548, 725070669, 950696969, 576785291, 435353573, 241858584, 353938372, 212891219, 879514422, 255134468, 478698605, 952735289, 895192985, 14762214, 859665368, 434219871, 260295526, 659136675, 213420459, 636687070, 944483744, 203396330, 730690230, 527709474, 39235915, 425646731, 393780939, 23415203, 6973447, 367849318, 785092443, 536998297, 498638586, 144195773, 524352620, 564186384, 700301131, 871175174, 625476734, 784756787, 302506115, 233407302, 858621300, 54331066, 428574619, 126680620, 810976987, 680832517, 46638895, 897216539, 823726294, 238399581, 850567063, 88953133, 819713575, 455604717, 600492876, 747993134, 452082880, 614395621, 782437671, 630165151, 233616050, 495269472, 708409061, 872877349, 174780545, 628506848, 45277487, 482430105, 276344049, 994448426, 253384665, 335856185, 28367338, 536246470, 689858856, 93968938, 659617364, 822371922, 361876926, 889206927, 715643635, 70846829, 458393690, 948547775, 190923005, 250433194, 569420419, 882275415, 354968802, 588398599, 746851920, 590050863, 723850118, 106187542, 272337014, 894073877, 728821790, 865723197, 134487060, 450984575, 336043959, 729517515, 64825575, 716603111, 599042728, 775140963, 833424398, 34693031, 570174214, 598668180, 823055872, 931005411, 813976871, 508586345, 389150283, 555772340, 217646633, 72639730, 419927431, 21499026, 604405545, 478813812, 86104374, 610422853, 544636657, 835335615, 29009863, 781219005, 745385874, 542930226, 968574917, 623646153, 509032127, 222495248, 925199591, 862741329, 344071335, 466582929, 98151476, 471260250, 133630047, 862250926, 803170895, 680641579, 501790333, 414618041, 901898752, 658184312, 871772689, 174549509, 121503449, 402100402, 247133589, 280520739, 618361818, 133516016, 941403741, 339434370, 420997708, 463530293, 49345173, 55896057, 995569, 567942542, 864017613, 439549558, 666825662, 67508107, 878220982, 85707206, 149337358, 493878916, 681445077, 752909244, 717310336, 648796922, 733114248, 633638334, 506341070, 661488912, 143221156, 430597029, 424129038, 590489481, 26754419, 96738592, 4056116, 947524629, 273013447, 513724877, 976240372, 833716388, 285098446, 534490884, 855030766, 122072373, 385775774, 177471285, 597396768, 255738730, 384489784, 916626575, 765783579, 870835985, 334714915, 431710435, 238283316, 905427677, 1965579, 954103036, 841446461, 705212442, 571541059, 124010638, 297159436, 914034835, 952115092, 507664582, 488223964, 737657629, 482962445, 246573204, 585839449, 457151782, 42177245, 380438978, 216249301, 82216724, 158800067, 10546391, 961892343, 764262756, 240100088, 8731106, 96374971, 246730388, 803154607, 464368122, 781713698, 466159943, 976312052, 182791070, 459796293, 308743982, 563372013, 188692242, 743850595, 859374044, 778101116, 325942606, 904972967, 851384433, 707864306, 685147581, 428924450, 758407104, 380988294, 817759023, 936884818, 705430480, 759768958, 203567351, 833438368, 10614480, 275804883, 924895047, 965399103, 892426098, 461519625, 166026547, 961983617, 974784348, 67602891, 343299145, 703270025, 335128840, 960714706, 831656533, 577970507, 664018413, 153941769, 487579281, 106943075, 70349842, 707658190, 831307235, 550904384, 17714840, 296816932, 169500693, 969216809, 134784293, 73017686, 461599976, 992249663, 721567717, 732940741, 822484005, 415469218, 3191344, 177132887, 621917113, 959372776, 704485844, 256097601, 757837645, 424979179, 389696965, 357821892, 596800244, 475583939, 730016804, 896168553, 567647140, 619701967, 989343254, 709488834, 973335339, 560182554, 870657940, 189057896, 695887721, 717832398, 175097065, 258529371, 17656836, 681771661, 685652047, 360069570, 956029506, 265734575, 188486076, 945136148, 272937336, 918267270, 845562594, 240374155, 12607009, 516777507, 805352418, 282919013, 561378557, 966730075, 807468837, 760360433, 359227885, 197655701, 933865906, 111129470, 624430804, 516231656, 176194039, 958413458, 391779980, 951683708, 108189720, 434614919, 877247442, 404086618, 104691462, 725747701, 47961660, 938404752, 731567515, 105609299, 845806235, 570321424, 801022198, 238814748, 538278005, 802037395, 352187649, 723540015, 373142045, 385293965, 431437603, 598331162, 267803640, 670901566, 979615307, 11643796, 193740598, 990850255, 462214597, 380019306, 409416308, 880129334, 717844497, 379304866, 393120484, 587111323, 87007332, 634560186, 921959888, 828278011, 670343884, 326107100, 614533124, 950195187, 981087684, 209700988, 565393412, 770928501, 436449243, 144219000, 152812556, 261585176, 56657218, 780232378, 638415677, 721902505, 60164111, 869231055, 497642633, 476643385, 714190975, 578158430, 888822062, 289762463, 603824840, 889475094, 551470962, 512723925, 388999959, 337236866, 992581619, 76256827, 307158252, 746353130, 42438487, 342970675, 334086204, 812436326, 846825499, 513521450, 75488298, 415464802, 179591464, 89146298, 497393267, 717407302, 651034123, 394379942, 400014498, 806301287, 628145917, 402387805, 435727675, 98213675, 107475937, 42448676, 748268232, 359763733, 589963269, 574465821, 489201151, 292278159, 287739836, 243093165, 269554877, 283467710, 754588872, 65883084, 401722139, 177162053, 803068584, 739984481, 391013903, 562070483, 227974833, 994657880, 34032952, 525473079, 422130386, 939672994, 264103972, 859467775, 319443318, 234544840, 830928215, 165765290, 818369582, 325281998, 416065543, 503466675, 800334498, 124952366, 372672012, 652985328, 37473177, 464292430, 692858557, 660241203, 249988443, 399344836, 786076170, 66136572, 793419757, 85778836, 506393624, 709106727, 300910369, 819436187, 265197754, 763968724, 503877628, 195218729, 880272182, 952993235, 819630200, 408315512, 591064217, 886152143, 829737400, 743042185, 340792625, 304872369, 57721922, 549847821, 704209034, 247233813, 749400612, 979112096, 993797180, 368730245, 596901797, 439697303, 114493267, 236021582, 771724806, 455654596, 568977604, 560266943, 119052811, 579759237, 524242634, 906925032, 743388512, 726448255, 533317588, 408124739, 745827066, 127552668, 507724050, 783446317, 185907055, 254231632, 413518657, 680424972, 797377830, 809859416, 229900311, 584542336, 777607639, 689571418, 667119928, 513798194, 275138178, 496387688, 151331306, 278522943, 70045850, 698731305, 472755760, 877931881, 147342323, 3733964, 951289951, 830697126, 477001881, 114315943, 257776073, 68371065, 547801700, 865403803, 726231833, 541909051, 27605223, 134114714, 483444341, 856418649, 345865895, 611964366, 527317334, 799761393, 81486876, 970470506, 421224818, 504398898, 156108522, 279826164, 827263192, 587467268, 380891471, 633894169, 742224022, 474941911, 948880834, 63436209, 624758989, 596640363, 443630158, 621639049, 987518733, 47302843, 30082597, 479000544, 773226318, 182895934, 783378310, 514032763, 535407956, 719993008, 501734352, 857760309, 298808947, 893574151, 220003540, 855483243, 924546850, 608696844, 692550628, 819260139, 463838082, 443233124, 914204999, 774024427, 620077353, 342851392, 940943436, 521945121, 280233293, 253337221, 468566305, 864916365, 530891568, 108278191, 507647977, 835584299, 33749058, 683106075, 887033279, 393583239, 926195629, 728756215, 598649832, 409668911, 560810417, 821001059, 445796510, 255392333, 150206634, 392324072, 307104048, 253166019, 596581835, 845804470, 857507803, 903550921, 750158591, 391255608, 364300808, 309128331, 562365063, 82167440, 995471108, 453455884, 707841711, 372460152, 753739029, 531242446, 72083958, 461092452, 322582004, 624150003, 71923706, 513465562, 803969832, 539482281, 36884844, 269612393, 872164160, 223776390, 352078223, 157732964, 877474583, 102592029, 736911755, 561122159, 909964766, 403051256, 379505984, 528074104, 107035676, 724104471, 136409385, 334572570, 87571056, 820551653, 804438391, 116006620, 170170444, 211891389, 675033338, 681745490, 869200945, 962339782, 497273532, 384842962, 438715274, 633324598, 737037986, 222138562, 804167189, 412102979, 977467622, 671429953, 323129130, 609094913, 159750637, 942777056, 416085918, 226385905, 390249450, 468490326, 327570846, 676187864, 728760099, 339672381, 454711003, 43340491, 21914911, 352590599, 978117684, 670170980, 445132074, 44893428, 214870894, 332661319, 77426803, 695430147, 881335639, 690593077, 240230895, 486881493, 599215863, 88908157, 350500834, 717654781, 628992336, 816714, 177804771, 600754962, 43450515, 128156091, 228184408, 48536759, 811699442, 341955385, 449671656, 191539994, 298530630, 210232650, 19206482, 86672564, 583275213, 837696645, 662807215, 983618213, 349757206, 426677231, 451838118, 608673581, 817718961, 46967253, 719160544, 516778133, 581188288, 857965825, 715191506, 873309874, 69304927, 180546671, 596676628, 912515143, 384980491, 325501984, 201393788, 749481130, 253437817, 228469699, 43671037, 617039584, 797236815, 379082775, 394909293, 10796961, 177655890, 860979418, 888084240, 514486755, 413935382, 942933253, 369164242, 121810648, 775037433, 650255182, 762852288, 276340966, 777193828, 666482337, 681472748, 277289821, 909960461, 301614198, 903010352, 630073750, 433951997, 176996834, 714724502, 456721770, 279247388, 391679231, 291086531, 326611632, 112361528, 566877247, 44992468, 32115431, 92624015, 14103644, 737871931, 761428241, 745943838, 429538307, 735903458, 380622375, 334999533, 226688768, 158490982, 24968672, 199409004, 452547776, 92611025, 74744291, 965160244, 751416085, 648837823, 185449527, 471527976, 911358165, 768888468, 892823678, 518368285, 456353801, 766491752, 626491713, 866222674, 872605964, 373909861, 813100902, 515038012, 417395969, 583829681, 809275017, 880854955, 315680183, 797075025, 814951684, 229909093, 227587115, 501866373, 828126842, 333615992, 232758064, 422758510, 377109643, 177826285, 437807203, 458979323, 367587043, 685384553, 877821587, 185328388, 610404695, 760673552, 639840793, 367856894, 317509102, 15216847, 929549634, 193763144, 726088614, 621052627, 229353492, 804900923, 354068976, 492813092, 404268959, 812333451, 390335394, 513038160, 676033408, 762825815, 912327133, 230714857, 332447358, 871957364, 237703275, 96877133, 338842898, 464193983, 83170469, 397365546, 593300545, 139234460, 859940172, 218248738, 827456894, 606035560, 457774457, 141795209, 204228774, 457508670, 593177203, 919739553, 464286932, 824474726, 894181094, 822332670, 950436768, 947225400, 726710103, 268612265, 300169967, 145254373, 757602540, 737781202, 741751896, 959300312, 923071057, 368148517, 109428213, 122642803, 956284089, 695430831, 595437067, 695202430, 487977350, 489010734, 328115667, 393297589, 896064376, 225053832, 226056152, 951982000, 812923158, 140677949, 10898936, 661081278, 703357686, 151707551, 686922943, 96852475, 40197542, 750594363, 175955743, 863975447, 192676427, 651817086, 705287025, 258071279, 214531591, 690058017, 517357843, 100456593, 238762650, 873279340, 299387746, 292657090, 303368784, 364254776, 7479235, 358387472, 553339401, 742661462, 541894105, 499481078, 386215807, 335941303, 614436709, 801866518, 701846181, 706148787, 241543165, 248813292, 766131472, 805150160, 279435000, 73404294, 743943505, 826369733, 808214219, 579993630, 456642521, 833023894, 87137531, 902331841, 430364464, 862500368, 642300860, 17896885, 673901154, 404239772, 704417775, 489940920, 639417228, 373810739, 27576929, 184515138, 632114560, 882203147, 264359410, 242432247, 678749831, 773124990, 30324101, 799513467, 615604144, 25340322, 452657132, 850171403, 8886702, 66440790, 42948802, 929772400, 494798428, 817553187, 355408062, 97093784, 942614776, 33457840, 789706790, 166778535, 236994152, 148357667, 689460275, 173537486, 720644881, 289232493, 588135461, 801808108, 506390752, 985664863, 450787897, 147845163, 82039510, 548165157, 522764737, 365288174, 510410755, 822400768, 65429900, 574434173, 489983425, 520599471, 142348656, 798900478, 172800120, 896416492, 558402511, 105471687, 788230490, 662475442, 112912019, 255147290, 254231011, 623127872, 463467727, 733714971, 862612339, 833206096, 354427341, 969175916, 363968551, 610928838, 821878077, 983392393, 304328042, 357730947, 384679254, 305563677, 977919447, 741213960, 433221594, 788907769, 9506325, 113160530, 829482193, 81650173, 682845910, 493015899, 289111531, 358337778, 300793221, 431724486, 56899094, 953053390, 627041312, 682886551, 520183050, 106055839, 541611176, 43992432, 625822351, 908890161, 103900689, 32204358, 542404772, 21930478, 561610453, 479925223, 738648674, 297360760, 517662604, 734069654, 225976241, 670612911, 298139963, 38511969, 286827407, 374972707, 129625346, 250175478, 34882480, 772975696, 971827154, 610510157, 178766494, 772272048, 202675816, 556659102, 573701018, 675201375, 769192785, 554709834, 432646441, 571140022, 280261557, 237541439, 166518836, 721301995, 173696838, 608030941, 298463461, 414274545, 293781483, 582193306, 116833370, 156922581, 216177264, 452737075, 613489835, 761970572, 931476442, 343817187, 292313798, 265613637, 739232924, 735542221, 192748328, 241335959, 811137400, 384020462, 418825734, 499144902, 826383682, 277290965, 412725143, 8206986, 189289612, 88079922, 895264947, 74280659, 420718614, 17334664, 332384296, 887987808, 322292458, 372478722, 135178305, 142638639, 692769139, 178497146, 307487399, 22903902, 755616939, 403188427, 242976716, 723389789, 737384555, 608473836, 692147807, 206140753, 114923624, 525365433, 225093830, 828996751, 935549690, 302848519, 932129890, 693873621, 564732466, 13873925, 194818930, 680090705, 80071375, 316705084, 976705548, 693533608, 928883001, 691069800, 12881211, 267745245, 344176844, 252410112, 613470980, 505088906, 663773175, 855622481, 749432868, 427631105, 711998418, 277192446, 89356103, 232727428, 762222910, 428584839, 216699266, 404999636, 880606834, 596047347, 357481551, 4457662, 76431523, 404179892, 876187378, 621929961, 531521175, 350602751, 182821666, 612798140, 76599354, 703069198, 640008803, 716711440, 965959772, 461964418, 682033729, 962373258, 478808577, 534569301, 427011451, 315243173, 166124313, 604848514, 275275944, 453771168, 177963819, 680453379, 236667930, 879533527, 26884236, 779505585, 118750182, 79601509, 186101500, 753251523, 810739639, 535005648, 126444029, 956444818, 984337175, 541904507, 514952425, 209490157, 732306470, 88467045, 379332127, 390191307, 360064485, 876965853, 708145442, 650677993, 625665698, 443223459, 651414636, 884915149, 722628839, 29393634, 715753505, 207667760, 678410699, 498158929, 406677978, 227448973, 630317563, 635098515, 970473561, 930369012, 514276611, 547027915, 131702930, 56210803, 202167720, 75580822, 362286358, 291186738, 138326176, 604579010, 691905926, 43260515, 719552099, 607892266, 366852136, 490866652, 942175249, 812394723, 181846719, 826898468, 676325226, 407995529, 438593794, 20692199, 390990265, 895368938, 955279672, 179343058, 731312775, 694253868, 798358147, 958143098, 466026544, 347881957, 175743297, 995426237, 279714074, 783290788, 800782332, 761853639, 535124148, 10146695, 779815145, 299080675, 794168510, 489717016, 817867445, 607093356, 949959262, 550609685, 328660122, 100839144, 490459086, 72935343, 993961544, 180913026, 511139481, 895666437, 216270332, 230991977, 195903521, 75326598, 117880107, 835377219, 621112698, 639477517, 487677488, 188485311, 761674238, 375570972, 848003316, 489203233, 639692519, 748160078, 239920591, 56166097, 774887874, 447502099, 316065893, 160125129, 187444127, 128457167, 479042516, 782243344, 305649594, 141832628, 693187936, 956195934, 799077459, 480558610, 333420192, 896804362, 249402010, 684818233, 944832853, 601356510, 982433361, 116264902, 32176941, 38014341, 390339798, 630128929, 176867983, 644372115, 260998414, 407731431, 431583443, 350650648, 366456101, 125948152, 975032536, 939300751, 427201183, 916938570, 658465626, 168122095, 159933546, 339476983, 695773351, 850349373, 561514459, 348714744, 829919169, 456541702, 62192596, 46647458, 572357658, 37244505, 560954105, 789210044, 333363066, 65305990, 320353159, 848995769, 474291579, 254960297, 446879739, 156814939, 407457428, 380919302, 463811121, 542077023, 819460582, 708115458, 795478533, 258888030, 654486908, 330471148, 761553463, 791225149, 280442051, 858016574, 276809832, 728127055, 692140556, 707966365, 880723161, 692102994, 521767088, 393624039, 587685493, 697745682, 878143086, 66922860, 109135169, 546510840, 641120909, 312604023, 350028781, 181748269, 463825880, 622709211, 136503180, 173060142, 366618370, 837775753, 566380593, 588601750, 318019734, 727636676, 785885944, 219857608, 388604727, 359544928, 609748277, 629411059, 17553556, 322369947, 346685159, 579737423, 696819400, 544543556, 66738655, 993905453, 312294625, 454163747, 255405864, 856346408, 394321124, 367860738, 861961132, 61772621, 759497806, 963612926, 230395044, 485582930, 848088534, 794465281, 523204934, 707677293, 694015162, 508212416, 147910974, 21895702, 491017425, 135534552, 334367426, 413083821, 862824539, 436354615, 173477399, 131645544, 865274517, 390404538, 463132165, 232977167, 235147174, 563813172, 822586794, 17425584, 513976683, 750899002, 507162916, 589523777, 239888517, 581181930, 30207806, 145550404, 702090848, 803650858, 489848838, 953739741, 335444227, 394140832, 700547556, 222846978, 120464583, 3628213, 850121614, 597307872, 902923594, 99940814, 724395979, 227934984, 534131035, 23032291, 122919509, 602865548, 532405640, 892335028, 340647337, 462722871, 84304037, 292851822, 332839842, 28367221, 786172683, 534307629, 481323709, 918483765, 75650136, 875004746, 621323899, 340901298, 219054708, 58500175, 134296107, 4661032, 572280772, 905315040, 779781969, 770798044, 141820117, 702125808, 196141580, 871318650, 698200713, 939832072, 303915820, 706266028, 707003179, 299373412, 532007243, 415548780, 687658141, 430982201, 861990175, 661146035, 977103739, 898830743, 446976068, 742094183, 180202580, 62293701, 954024939, 745665235, 734229379, 247976765, 334307900, 761106211, 167248489, 184638632, 435187849, 931836381, 495499411, 654087680, 584747930, 143305893, 409365102, 421717579, 379520525, 665434777, 252549413, 705609861, 145619109, 84178975, 817840627, 941375513, 5837265, 801117856, 51941209, 408335964, 386356618, 296316457, 160437762, 167087212, 52573231, 625889283, 881764754, 554198386, 5342778, 506239227, 805557468, 238385627, 71495799, 691959308, 785715357, 575787013, 779498336, 744499477, 301298770, 417817703, 961763017, 500659578, 113323976, 761815058, 306404399, 405024579, 396661481, 51910176, 576749025, 264555893, 291195419, 991233286, 634179893, 300274025, 464681690, 794949129, 265946897, 540036033, 592682654, 689343882, 666886615, 422758651, 99495966, 387964365, 522735329, 208436063, 236893938, 791958078, 867151914, 231337899, 867505370, 354950777, 301887995, 399497156, 732184378, 988311631, 395766448, 83785120, 719201060, 528475932, 187511401, 567372907, 817807850, 847129397, 797373291, 352102462, 855242584, 304812427, 318744575, 686695903, 32966293, 279304549, 395375176, 365656843, 25220877, 461643339, 811801687, 875312883, 738201847, 39145328, 336312353, 673303641, 692314055, 143146745, 967266662, 683637089, 591313049, 826436766, 997102893, 939188669, 382183978, 220101234, 328559888, 295153904, 592178027, 783800243, 350672317, 979553275, 811240370, 186903951, 763692566, 323215711, 14110749, 271272037, 446399854, 236346461, 707812689, 48421276, 532947962, 345863288, 530566037, 292412651, 859533503, 81621656, 494052085, 563394482, 455593276, 379184295, 732017671, 745085375, 458353293, 611705911, 679275894, 860186392, 612334543, 948512008, 475788928, 681694928, 915976192, 21921067, 442463063, 638690529, 181135201, 770826006, 335870872, 584152909, 626457687, 92771338, 621838993, 159630424, 269239822, 389269775, 445297028, 662297457, 208441288, 164010068, 906017139, 583075029, 639257678, 812397808, 194488599, 738389862, 221059845, 361245900, 699399613, 627502477, 23171102, 557768279, 795937318, 193808018, 902297120, 357734144, 636917886, 190498281, 183214312, 388831794, 232928960, 129827080, 633899624, 475537439, 310807025, 80977827, 305952017, 61467524, 597022219, 197316579, 704659973, 103274682, 653111597, 366073772, 773077543, 454446774, 387941033, 884596018, 31937101, 178679125, 1691840, 437561066, 513553106, 13839245, 89616270, 656975235, 952816663, 44914952, 883989922, 539282010, 283183675, 649265978, 122836940, 555872257, 643101829, 282446418, 320429792, 451939610, 431708289, 335737908, 161908609, 309897865, 733635381, 602246622, 929590960, 209423889, 274543737, 872922717, 691135223, 127779353, 976362929, 72705728, 178295829, 980249977, 142874782, 751856165, 497632725, 971653054, 41209283, 400122633, 257903566, 870859281, 266876320, 705803344, 695403580, 684883294, 278514582, 549105017, 819452340, 573020150, 164515292, 389344207, 839034517, 781445067, 870619878, 397324505, 435193741, 179011307, 454228163, 957405191, 762896651, 976256732, 904764742, 403780246, 936185516, 314480940, 780916996, 622027466, 919008165, 241040311, 380930567, 674876141, 348220486, 712508002, 158752671, 24040314, 492199269, 422912364, 936457743, 820615687, 605744098, 926507057, 832765678, 526881788, 778475810, 807489817, 742584264, 973980571, 479613997, 438096074, 802521735, 739874103, 651618637, 667935919, 626767465, 21474020, 463619823, 816837523, 236650125, 294958171, 156703522, 682356924, 500929461, 898499344, 430175327, 26388056, 900826126, 372392351, 144765170, 531870606, 320960830, 604383231, 51918252, 62325063, 637376141, 250347539, 943077780, 294846285, 543350440, 760855918, 164708706, 718916783, 787812797, 858971870, 160074213, 352706885, 738111223, 875070807, 570690849, 57883185, 373721666, 289558387, 944292006, 441920912, 544851291, 819878113, 666315634, 641487719, 199478810, 905816066, 209003880, 814705883, 543579000, 723053501, 583876561, 207727602, 89188707, 85436528, 255930059, 410975979, 725537265, 71724995, 566862197, 977804219, 153032212, 911900795, 49674648, 294977245, 55475845, 661495799, 430998450, 290807910, 921331352, 981227546, 274721761, 125309019, 222189666, 111872318, 96896366, 483267154, 711308296, 45403989, 684325959, 5624937, 308026742, 275607285, 74758645, 774724739, 444085549, 143426841, 218163073, 236332020, 710451092, 467292385, 635024962, 34783332, 613505528, 53918042, 758802891, 574336063, 355404782, 208140459, 399523264, 140892562, 19046927, 107633885, 90484190, 447967321, 419778993, 426889018, 876624312, 163684526, 695489541, 430738278, 345260862, 592113485, 435728641, 285418824, 620167711, 907974886, 456617292, 971846747, 65410225, 383289235, 965683122, 877074168, 930851445, 248914686, 88169096, 846686327, 283936094, 94764476, 380005007, 19702870, 40568982, 793035478, 673379939, 575316626, 382144006, 588859818, 960133841, 465258115, 981830231, 100010871, 515869200, 699119917, 614916711, 504584423, 383680766, 339514784, 482712320, 859358686, 955660155, 906950440, 403991920, 867224396, 722066739, 997194865, 529297721, 859220778, 399079182, 496611764, 627331794, 490322052, 960572971, 208394774, 20077379, 226391257, 363715285, 814430856, 344545804, 293975556, 469895158, 198054184, 736911802, 321229870, 494896251, 242315034, 438665295, 466175549, 759848208, 626260915, 208418228, 698307258, 212806885, 809956319, 953504500, 368319578, 425565922, 427646111, 733381894, 725889137, 326259386, 210831225, 53463700, 561325548, 20696565, 343642848, 4936327, 702505013, 729371503, 119212423, 809446435, 405052789, 537425940, 462122581, 166198776, 117044696, 860481559, 703813820, 745016589, 29515017, 974378991, 358897646, 974337510, 530542316, 21295459, 494892783, 644146503, 160532144, 461142252, 89849416, 901564879, 115356008, 37038323, 163304887, 866924206, 259085845, 61443806, 581157770, 344455247, 177163797, 750971672, 491911025, 963118869, 940346081, 5736859, 129212223, 505665988, 150734243, 348158039, 315151385, 634859634, 484861150, 755437438, 448008113, 609166069, 922597200, 980002906, 707257803, 142520774, 521754282, 364210921, 937464972, 774241186, 610670450, 811077150, 139231599, 983684944, 323865356, 327017372, 708938250, 753995388, 170411514, 605249908, 247179152, 670454330, 470436518, 138754191, 976243574, 185424057, 858062175, 156601202, 319813679, 661605048, 113697752, 87617179, 511643341, 16544184, 820108326, 562426049, 929278513, 25542687, 732618380, 379925550, 740369148, 78683596, 411624428, 790578922, 907567308, 733023966, 48557879, 832173481, 145056497, 894247057, 359793076, 701690185, 291133204, 290028629, 864763587, 647423110, 66926994, 627354368, 321778895, 220739680, 173086378, 938556207, 358301644, 814114798, 527882374, 314031488, 610600232, 163570097, 72981146, 389126141, 415635785, 371354759, 477963677, 482582824, 269861718, 125756176, 867100963, 670162478, 719061883, 825213062, 439617549, 115796256, 201281074, 1058406, 56360971, 46897567, 858810015, 361035177, 23242058, 746839144, 573221449, 633658355, 22336542, 432810656, 431151113, 600034283, 175440425, 880928047, 930767558, 855487343, 893516561, 298638021, 310221553, 547749947, 505138901, 674848969, 371470744, 461719894, 80017646, 326611921, 90535574, 657732698, 550076942, 259020496, 359632957, 516327048, 903282625, 57822127, 216900403, 151825868, 865526695, 734772188, 42465176, 91514540, 549772562, 518081184, 276639566, 991724060, 857648969, 406441268, 454010947, 615534416, 348777982, 971259171, 542017825, 3346876, 340263581, 797323224, 819685689, 750247136, 99151404, 494374763, 945157850, 720796272, 509672514, 396688157, 917559126, 750605874, 651877607, 755721884, 986261300, 36274550, 721853719, 383480907, 216292984, 337275021, 861848508, 601824599, 225212826, 567417585, 69885990, 630835788, 35526511, 236727099, 751292782, 561217875, 650804818, 587385420, 77001098, 17215137, 198573812, 249800495, 163028195, 228873737, 916815307, 994938458, 686508354, 893707744, 2410559, 273824732, 398024459, 222167458, 986682809, 510734119, 857890662, 609976297, 932892166, 573743061, 592947517, 403279345, 699506935, 153760489, 465596947, 691768355, 657069246, 538512931, 651617941, 336357393, 718184715, 529406469, 359703611, 347296880, 500469492, 865427402, 595095513, 403737246, 101609833, 494833530, 867191839, 151125519, 186232478, 679013513, 268195875, 466678133, 389109961, 512739628, 560190201, 524895621, 426260240, 422633504, 318960207, 916893710, 383318999, 661223331, 231526788, 731291132, 896901072, 440308993, 664691985, 109866830, 648760464, 581844314, 73711016, 919836473, 840602582, 425556939, 535436913, 19776133, 615423592, 9732263, 954811559, 172577915, 447605718, 78309404, 505946041, 475681573, 354807047, 547745749, 561948154, 922510533, 583213953, 865885057, 471507961, 89178450, 287104824, 334131187, 464358178, 937821749, 858689120, 877205086, 45707220, 742727741, 750269414, 827478117, 420024076, 866706916, 711384813, 93945540, 645637672, 967901837, 585435492, 5988584, 136579505, 380975528, 596185830, 31849831, 334257907, 147659062, 611334626, 1119495, 541200866, 390441818, 810368278, 915025200, 521265627, 307067818, 739220269, 237347183, 697815186, 95182534, 640799173, 401039239, 111001919, 108607855, 443963103, 283128001, 307876136, 599768492, 848306174, 86655012, 34770688, 369001078, 938008342, 321772781, 143008050, 318496510, 923355556, 221142597, 515749438, 656668272, 701243385, 562909033, 568625178, 558622482, 990298767, 741647732, 967158955, 556944599, 41571875, 788567365, 452798857, 106958202, 664442351, 356831760, 315229469, 969354021, 536523148, 775734021, 797208962, 182055057, 858322224, 549567613, 144752150, 890310410, 991291703, 986586937, 129462833, 821568762, 556758918, 299695863, 119313526, 185943674, 853747204, 193406549, 792324805, 365303925, 246460854, 583700077, 499702795, 36157149, 102592874, 642868406, 228745462, 51581055, 183593383, 407423573, 799357574, 655823324, 68816972, 460981246, 417222537, 880938506, 343200569, 287383945, 646400065, 967876512, 686161886, 99950628, 958491757, 87939134, 691289776, 790821979, 415025517, 514882372, 489823972, 207351892, 964177228, 263808929, 744175152, 388661886, 200754961, 146078830, 981895018, 627786, 349019794, 873481004, 834417658, 891675519, 788330072, 304453442, 588896328, 481213598, 782796653, 840969618, 868547126, 511512128, 302054851, 738830428, 839309626, 567041149, 704048088, 699661569, 139407552, 716477433, 876023853, 578163496, 766138996, 386886501, 938806280, 775959773, 113179638, 647780631, 769010773, 567384692, 487315497, 546857821, 935669094, 90061054, 306503484, 382880933, 746435510, 520720228, 43734027, 123400259, 999608152, 615864941, 572088284, 543369263, 402736748, 63229749, 435794789, 37016010, 556773157, 806172211, 209485878, 133290947, 968736712, 107387974, 23026970, 671997915, 177921302, 844301916, 438543272, 740310620, 70430618, 594424991, 372617435, 628308581, 829046104, 284719042, 85308086, 611195477, 135706390, 964945613, 331492624, 711029260, 439703106, 158419571, 621768037, 112967912, 941201764, 910224163, 799979110, 264712465, 621925486, 658412818, 350025831, 493035255, 29641406, 500662850, 9688539, 407032682, 747568991, 717079714, 648643874, 344178001, 385935125, 688368899, 528682390, 757153774, 653739635, 841153395, 847002914, 69537426, 186996830, 404313583, 828996267, 610601894, 512271838, 358116400, 79162424, 324584560, 953266037, 963012025, 14319483, 288331150, 518857736, 819506957, 542683823, 314580140, 673232612, 536783642, 37977869, 614164225, 584343149, 989351202, 341116916, 585929445, 958409209, 158660436, 711585261, 628982417, 76153211, 213460286, 570025677, 689075483, 592447890, 654453299, 593653607, 690960250, 744292724, 443110058, 560189834, 251039757, 706957631, 495389950, 945042306, 373509733, 853445354, 559391642, 28337109, 960088727, 759793675, 435310025, 781967060, 522969343, 190493458, 742924036, 182205507, 930964147, 622568621, 240272055, 493755466, 481481535, 374435472, 752034065, 783862780, 578045658, 837740197, 84494022, 900727528, 884669363, 635154315, 944785751, 50138252, 258421298, 429395771, 340815196, 400744647, 928389224, 252657610, 643703740, 707868249, 280664573, 71340999, 957408197, 629263332, 508338638, 583735012, 201288469, 465051747, 752995590, 132898853, 147868304, 980877722, 964311615, 847754285, 41358356, 725300105, 152851827, 757600739, 401628185, 204537351, 568400269, 365038510, 564723724, 977059630, 974164661, 525368876, 63058061, 443176542, 925894875, 764760922, 929685795, 866084381, 294146010, 94805528, 273641320, 697941386, 82048720, 747884648, 898775736, 445163221, 602235075, 345056032, 656316597, 404045824, 354736590, 924073442, 737954886, 427520867, 300774151, 767912130, 626069855, 329247515, 559258543, 419558076, 418770650, 334161783, 413861491, 973129178, 498955744, 779178341, 84731085, 704041878, 454966654, 551399098, 481050073, 622769064, 370802498, 356596449, 143306943, 154098220, 465266608, 404366618, 215760562, 133992015, 825888946, 326215827, 935508998, 744629977, 980016682, 148309907, 75036728, 774564344, 706378435, 570611374, 438172615, 865179652, 963411351, 579575718, 412903455, 771300121, 480641805, 217257579, 931441518, 495703526, 293065831, 720271817, 344062896, 65869689, 383239115, 622002700, 978974025, 22999987, 481744675, 152835372, 901437223, 105941315, 582920059, 102742754, 229944892, 516594313, 948957218, 175018169, 611717518, 580528088, 690156948, 745152789, 671835922, 732889425, 981038113, 994887242, 681877985, 206882377, 321399214, 249698217, 863037449, 642061239, 613488500, 270992250, 965571765, 754979536, 485992938, 389675084, 637951719, 910137845, 211607899, 456529006, 939210726, 48861283, 936611646, 45731383, 526077111, 23594994, 520042438, 166938058, 117597198, 452619156, 292914174, 233583335, 600600008, 499301708, 932818494, 356408041, 589090909, 675307146, 352933747, 306937813, 876647224, 542212820, 264417821, 357235333, 928208381, 736676800, 257476926, 628828383, 31695624, 279354584, 437009857, 801357113, 855828009, 893881827, 838713156, 191363762, 3932454, 354431828, 93782053, 693562206, 531335281, 994155247, 403620043, 908377202, 730856029, 169307128, 575145060, 418827485, 82547761, 222723330, 120452716, 174692187, 815206431, 908216028, 758779484, 410518888, 569208680, 527469534, 896951614, 40095003, 827925175, 664548317, 910481589, 434769340, 29993960, 30469023, 154682991, 975480661, 750371601, 425938341, 144149683, 704734490, 82543786, 517292641, 973557350, 293232757, 553275649, 601006406, 447462299, 659189007, 973560719, 973715145, 326649354, 884937674, 102763431, 619243723, 885921558, 538956693, 75658360, 318169859, 98043976, 589039109, 921828569, 484643029, 612544903, 921410734, 155262814, 605203292, 19769345, 824984084, 907380831, 457075785, 136996877, 451769822, 119593624, 999345903, 827878905, 804487563, 52221175, 223177487, 949418494, 735264723, 573974415, 290911013, 825588004, 52988358, 820731647, 990317095, 12347072, 140398005, 471713846, 199318868, 146318219, 408579391, 621892638, 247944708, 4853195, 267305418, 12975082, 968259145, 160226129, 1052333, 575410619, 551694487, 606981119, 976066276, 279600480, 977675435, 507033482, 135998857, 988566433, 459715914, 238598291, 638557157, 841934133, 974504275, 107640787, 755842933, 927951378, 853897106, 343445283, 462417555, 797098004, 514746192, 121456544, 559294389, 942691656, 612543907, 891365379, 144101802, 493322685, 313571321, 277793067, 946964382, 457680459, 332944546, 947725658, 33773550, 600440030, 536764301, 305781533, 702085956, 399522420, 117628087, 889700233, 826467934, 569666157, 350002698, 387951489, 881659465, 402974030, 267550396, 384640563, 152052500, 483992558, 225430548, 702962726, 936332341, 781106566, 293603523, 228256167, 54004213, 67741921, 285693937, 611305709, 382685526, 13158553, 418972087, 507189719, 498842007, 733894882, 653352018, 207231194, 780757919, 26399311, 470809027, 114608903, 857872771, 922560746, 906431522, 511702105, 649654391, 532673853, 997368017, 400483688, 658189960, 666522550, 166231000, 136986464, 358178890, 506218680, 558106938, 567465474, 709425275, 129778022, 335226047, 881539945, 116355082, 767699814, 598660246, 722477110, 790022012, 637403544, 42734897, 480816372, 948102276, 884040636, 381465128, 440704885, 803549732, 406633837, 945899879, 177999555, 973620677, 653716415, 137335047, 679632345, 763123145, 641184244, 840852294, 703278165, 680963671, 904438762, 71997999, 149102838, 706526757, 624933809, 25540156, 865729809, 398695335, 564627130, 418049243, 230674067, 310344245, 852629606, 35314306, 689926223, 438546487, 238566398, 478915571, 585357122, 61540843, 700066231, 902866870, 921459846, 205103573, 97375105, 34850778, 761359946, 181215583, 554833229, 534201494, 793761666, 191917706, 94377966, 325024621, 693226622, 87474250, 572691700, 447699148, 632002488, 551460945, 221873430, 49448760, 839678278, 701209651, 201446352, 953323557, 331786063, 450130008, 657927543, 500974041, 815932874, 540770972, 555703431, 852093114, 28308611, 439706124, 609689679, 360919963, 432145323, 534071192, 198051340, 810202404, 740535333, 582981037, 560429268, 725196111, 252891406, 631072648, 824319140, 310750109, 837540172, 439213783, 541729498, 218627989, 195715792, 959506559, 595278383, 999535646, 484593810, 820141064, 792491440, 607475234, 770301795, 3951827, 615669721, 487614272, 418095462, 502722666, 636404532, 588468515, 51723704, 187870451, 496861001, 694602126, 101930831, 145287617, 122461328, 170386538, 238875280, 359193939, 181370950, 313519525, 963555136, 526434027, 104431906, 622529798, 161972453, 444916276, 649121605, 528876707, 956400990, 484149859, 850139968, 636813152, 266517296, 838697491, 33160793, 69245162, 765492427, 381352362, 184877653, 478623003, 593329275, 546351311, 101993024, 773094620, 339262488, 402010123, 137984757, 879237974, 210808979, 365900208, 401563334, 399395134, 339185079, 845340858, 151010673, 161374373, 728794907, 65178538, 366447969, 978983002, 179007788, 335362603, 471948349, 207786216, 242410894, 525267596, 46883504, 776098313, 19320352, 441840152, 997060599, 428473085, 273981193, 973694875, 291369373, 632024769, 932145467, 52098422, 743835192, 807956606, 341750119, 712218224, 31157732, 392319553, 770087248, 121315172, 329336923, 66710068, 730658063, 816414614, 43558510, 947739954, 166889785, 530902961, 315462205, 859802548, 109160790, 114654497, 667400351, 358097174, 375837616, 437785291, 568127227, 233309180, 336886629, 311471063, 237581131, 55534174, 644965737, 755219436, 106777547, 545441163, 106066455, 57589705, 596923853, 976575662, 752298306, 548439985, 384640507, 661203957, 868055975, 413552099, 914461451, 304663967, 391478840, 530642840, 713698916, 570034998, 443167968, 899161501, 354273335, 524726374, 323142665, 635348951, 166116613, 491662554, 481725413, 578373724, 989850866, 197884377, 915077719, 994490277, 70408438, 715423751, 797899405, 877627538, 756361961, 171582475, 376669828, 972448197, 460986378, 466062744, 251837831, 868646350, 856043992, 84780143, 717299136, 773009385, 314914909, 189947941, 550116560, 829225634, 396498478, 843363506, 898056207, 640841400, 874557469, 271842356, 793927540, 499909741, 921951752, 889596480, 268555000, 557193151, 31126124, 192474741, 679121453, 845052453, 15866188, 123135980, 474918872, 881327491, 131094053, 895323579, 724232886, 72465383, 819356727, 77209679, 745020683, 84539257, 373002309, 830687563, 570065029, 528871395, 66968916, 480900289, 249289280, 802755739, 744862895, 521449170, 88289900, 170500422, 819726393, 501792564, 777278868, 718552335, 518246608, 441678545, 55399889, 25014282, 226695849, 105965256, 957898172, 132495739, 296600194, 240866408, 928932707, 681846967, 815648061, 955525325, 251984324, 308974948, 536344714, 105195867, 611959797, 479885264, 255571815, 209207239, 455190915, 91887218, 958517615, 819473689, 370029395, 936137949, 198587113, 417833620, 427343279, 267397416, 511185174, 3256848, 539566095, 96723760, 413751530, 332534676, 231334036, 43381742, 614284980, 919600626, 690388092, 876575642, 401669868, 968833666, 71497455, 120032389, 195563631, 192487543, 341879248, 434579507, 534353342, 849673674, 828261042, 944873360, 899526061, 876454145, 932143722, 448425075, 610865076, 575019259, 315038478, 430858773, 874600281, 809222333, 178559951, 662698114, 92358946, 467625489, 478989858, 816546404, 232568091, 826699191, 248267349, 308631242, 716433953, 692174471, 445928818, 410441027, 863719426, 873834165, 932157882, 300828449, 533279293, 262375848, 203324364, 88406779, 764887131, 739485550, 876605463, 369462926, 255267601, 741185260, 94592522, 371619299, 837779368, 656041819, 458224686, 946753511, 100959572, 792835417, 408599840, 394245788, 803580741, 371414296, 344331190, 831806347, 93534705, 11558387, 917777216, 276738248, 196519652, 904235298, 672059105, 493066236, 953205363, 517094998, 116999391, 991581668, 787108046, 521820373, 893828567, 686148096, 350747497, 412045225, 297413876, 551326280, 662246422, 336560580, 34173761, 648809323, 110848626, 255019257, 243666186, 148742961, 552185819, 811463228, 643497966, 480691294, 889045311, 891521849, 199118321, 860663012, 216334098, 632705844, 343818955, 867210958, 787900770, 217033755, 466258072, 881101306, 523987188, 499747335, 17843731, 280728618, 544357740, 345149307, 843989821, 771161044, 257341811, 467575502, 423774243, 193735414, 973269634, 873682200, 788990185, 572349887, 425535717, 247725876, 506162966, 778704867, 977854740, 50133478, 390910450, 361756827, 899644625, 461117570, 881875352, 711264729, 606993774, 335752692, 80326088, 484602562, 111585942, 920573533, 375668641, 462531786, 185368226, 290905859, 870833641, 493744924, 61778292, 60415950, 403053614, 171249283, 592674399, 602958424, 912958890, 866730639, 407176419, 31229789, 615578717, 177375772, 111758032, 61288032, 39521317, 839835848, 36901249, 823630007, 262836081, 994404567, 466729878, 291643491, 568813017, 754269423, 536136211, 682582260, 130832401, 321570488, 757964246, 520875419, 174067943, 373126317, 172057064, 428541462, 444815697, 459969483, 905497133, 513372665, 460312038, 282084831, 674806596, 63368940, 985694402, 823998558, 848587849, 144352889, 505757456, 621798051, 189986842, 920605913, 457097422, 349492915, 622831862, 57827466, 464759305, 436445693, 200423161, 310330025, 338202487, 829925812, 541882444, 343117614, 404870792, 400714360, 67135527, 661751901, 76367564, 63852201, 945388056, 524554117, 134593675, 176936771, 165639838, 57748513, 397685976, 407334144, 293772393, 903015406, 616796393, 621069398, 499571502, 211648727, 364740487, 906168406, 657130135, 31911672, 619614521, 172601379, 511479965, 201978652, 249066661, 907077121, 782723512, 64970463, 713954511, 287734329, 301300060, 701405277, 10514195, 590577274, 526130411, 459412659, 617509235, 27219336, 905152518, 945401924, 915621396, 16135344, 436461696, 685705050, 220716016, 177421626, 57634852, 951969488, 744017854, 130908242, 8489622, 735690833, 213177439, 246902140, 102663302, 47481391, 959211149, 306608888, 208612868, 387839864, 594917522, 845571158, 241466857, 790255902, 182472746, 454577744, 355678114, 922378756, 384289343, 385303267, 767193500, 369219161, 21892660, 785558033, 359902309, 724846109, 897947, 505952366, 817187206, 106520747, 165035906, 10316397, 14937752, 279780559, 174348306, 143789625, 548778834, 188126432, 771390477, 79016131, 92190312, 664565387, 878975135, 307291900, 456360998, 767701307, 244329045, 550945112, 991674934, 997929219, 432321359, 738516081, 495045968, 602897729, 351482925, 936800270, 137077997, 555958000, 628857971, 433668688, 721736414, 878583641, 196787018, 884695369, 83101255, 325712814, 332996562, 844663084, 220080369, 412018760, 40690250, 853220356, 63811897, 792249166, 315039060, 854853777, 585236309, 367687030, 789762494, 835799633, 181904697, 471373841, 305618159, 20444199, 533985115, 370067358, 696327581, 397114315, 720783058, 605714779, 282693377, 519875234, 913743580, 363990445, 527107079, 808877584, 858761337, 837357622, 504037349, 418542, 198763325, 837109129, 172491334, 239258451, 137149769, 681682982, 291274941, 612143181, 535400299, 976152898, 397460677, 432189500, 982663326, 456473301, 15222819, 704646005, 517521005, 262426767, 510727655, 722864543, 168896821, 514841176, 149992768, 517586498, 496350651, 924001720, 47941858, 596734980, 456238075, 120855619, 923332010, 985539637, 486957033, 652766972, 205354940, 401771246, 572672377, 44895920, 414980056, 441740313, 718233839, 960623026, 693148011, 108671946, 170540149, 62751862, 298055750, 21086063, 497313632, 287273762, 372214024, 203779213, 362155320, 805625283, 422923823, 79532286, 800085299, 967603372, 577275288, 986842544, 436348182, 498393894, 499243366, 536436806, 286413499, 158859618, 86711102, 686651162, 778218363, 907329147, 152864226, 269594428, 661131611, 143262638, 953461808, 788528381, 461209346, 312548831, 834458682, 674515219, 126991182, 256106865, 384526115, 649271448, 56959182, 354632393, 386738136, 328544728, 201145023, 869981826, 195262092, 252451441, 142424011, 849675445, 264967351, 878583751, 418039281, 313685024, 516456105, 231024271, 719022448, 604722473, 736296254, 882360326, 385915123, 183629040, 595577045, 111829957, 240001177, 403387730, 910534499, 898778230, 74449797, 840585161, 41708740, 498883600, 470633736, 318266108, 469935313, 499745185, 481239289, 486002615, 527655302, 89915840, 45765469, 958183087, 190344854, 870409716, 808912253, 703141591, 131716911, 700642915, 528239703, 309258170, 708644434, 459315759, 262719346, 551266236, 523941110, 957139197, 533626038, 42737572, 269562511, 991490895, 750703123, 16417315, 754910977, 874789292, 979555588, 542192721, 985853344, 793226327, 434902834, 217968219, 617037696, 326366350, 457669130, 974060431, 37920512, 176237138, 363164964, 807768727, 375440349, 985702091, 587148521, 413950472, 791830169, 298865779, 603365317, 210738589, 699834895, 910737974, 169392146, 248006544, 524784042, 247832062, 330030479, 495015627, 717368318, 789003995, 718311035, 55103596, 337341940, 830897857, 251895614, 531575383, 355160382, 469186422, 44657848, 845191747, 904719705, 920246552, 212202459, 348736098, 50172181, 618971966, 569061842, 125360770, 367885032, 962737414, 275558021, 884626155, 890995344, 824248777, 368120695, 144763350, 992535398, 632036066, 674834443, 738113297, 925123656, 79011059, 390354334, 582524320, 301248944, 582179306, 918146553, 592567507, 954441166, 839779978, 157767316, 626390048, 336121223, 316952568, 870982872, 571028644, 16639722, 389931775, 371758546, 950723053, 120691355, 471014829, 647773699, 122530612, 115302368, 84363231, 586795519, 22942148, 559391494, 657129514, 544354764, 305698273, 540728670, 705354576, 776731640, 298055894, 648065624, 7156673, 363657813, 211812722, 473430592, 506966318, 664756486, 707427469, 90606609, 469636063, 976783302, 453778933, 205288303, 337115046, 723704107, 742894410, 611624500, 700287230, 569761916, 21423906, 644633291, 728901883, 331592669, 130355716, 518527750, 259327037, 441997530, 199377900, 254062372, 65123458, 214726342, 764468161, 757985524, 596529403, 229779685, 170468751, 627184375, 983289181, 12055078, 156971961, 409653572, 69583110, 403940803, 349031622, 105427575, 957882215, 294518721, 98428511, 43203416, 514625424, 405903493, 245495082, 240327045, 917574685, 969540918, 454356848, 390054325, 954250906, 500657114, 230204057, 198667299, 505521993, 585146020, 448894537, 415028423, 749114609, 844332356, 797905983, 239461813, 11402279, 439568077, 16893567, 196275024, 276126309, 546144775, 394741341, 728469186, 706344381, 37878120, 707217817, 328512275, 521617047, 41337564, 302644048, 224804531, 101960255, 31390397, 458980757, 382815881, 369013330, 91286205, 634867505, 757014832, 554176383, 714796325, 958263437, 164240175, 521604767, 340359664, 330876392, 150177032, 172052809, 491388178, 603213406, 80922519, 882814370, 334112365, 683671053, 663813960, 331046650, 180228478, 189387892, 248935889, 352421809, 344574208, 573103458, 517187833, 534901206, 863442807, 839419816, 952680350, 996786835, 321415553, 340016522, 578701032, 324650833, 941077735, 697893351, 819592034, 162057887, 503589236, 65743197, 175617443, 746711610, 289993834, 280282934, 265187708, 138821560, 293729118, 491722716, 486069533, 399872124, 773823819, 349619484, 379093848, 692501001, 40564950, 338848716, 627844594, 372186135, 3672781, 295944485, 812501462, 915018788, 961653972, 105915525, 56293465, 994863582, 359493886, 7958306, 453560474, 293054127, 233589786, 346034563, 898043906, 526277772, 89984504, 613292940, 97907491, 335482007, 326977410, 346212637, 900304633, 28577914, 392759786, 794030177, 541033086, 842289260, 821914244, 23290864, 42548479, 171060812, 604953809, 848517041, 460405061, 373123218, 60291473, 106939938, 903157618, 831533437, 254854446, 696405220, 836870006, 438468719, 368916909, 661070314, 262230319, 908729762, 194454657, 963824784, 20851174, 68583318, 254181970, 490279956, 488456102, 151544368, 103580065, 707898819, 268613484, 355550785, 81965896, 196471480, 512965575, 465791470, 290958576, 113714051, 258275209, 781435443, 644988047, 643800593, 679366131, 297559515, 651802133, 258075699, 627128971, 766411700, 626424987, 593885649, 872970861, 464733248, 432841087, 847333341, 84521906, 938351401, 323756449, 53830402, 12366917, 931280908, 364142654, 70961938, 951255426, 726973405, 341236258, 640185856, 452877563, 930715227, 39321723, 134753751, 763283453, 189411508, 944313621, 842761893, 103221919, 22201455, 813526059, 580096010, 437589261, 275748079, 521251480, 886927127, 717399403, 513547894, 673049403, 636954813, 285493352, 655376512, 325906092, 145465621, 250906380, 239907358, 509214997, 998992140, 860677790, 73226246, 304626684, 946250246, 956255339, 820604010, 821712993, 570274144, 664563477, 528503941, 972574550, 100589605, 72605343, 349317097, 338659297, 143678583, 959627470, 755312463, 527268030, 516617451, 221718919, 351244817, 938966782, 590649529, 98385709, 419912600, 845425686, 928292455, 924445162, 53321547, 883409971, 182716448, 960353532, 153561277, 127661333, 305036831, 599981302, 271829070, 403959933, 55635437, 632156116, 62134884, 171533690, 325960831, 815172778, 852259670, 406308328, 486455784, 418492285, 840757579, 67158880, 162709116, 79971222, 471854533, 891184454, 351216970, 484405497, 337580569, 244639250, 439680360, 57765917, 197700051, 587802893, 650080178, 725093714, 570343504, 496704566, 755682067, 844619810, 537519937, 602199253, 790698001, 972239726, 805556652, 215638907, 578479244, 26594609, 809561349, 609709656, 802321552, 664173379, 582957251, 207372661, 168265125, 224380918, 69914027, 652941779, 264687238, 130747181, 998499260, 911543898, 244831965, 431496360, 7092214, 348965265, 753583579, 777934374, 230914103, 349525716, 413106386, 44923241, 264947438, 842938689, 72324228, 371711917, 840179917, 771435840, 732250556, 443333103, 934620968, 364543509, 901181831, 918226308, 571292690, 634564538, 121450147, 526529990, 279510461, 58221445, 128152059, 737211726, 342685031, 937996350, 139492187, 667763687, 27906364, 999541821, 845276221, 564707160, 930123366, 905153501, 230542180, 182955574, 216558162, 787269227, 334589804, 91325624, 960050565, 278101213, 721572812, 402410358, 265920289, 311427343, 468965280, 676262957, 192018364, 278037764, 279218360, 421112088, 444322572, 887588437, 47622599, 769990713, 471539891, 871178056, 938842988, 212939662, 942763198, 814189018, 124067590, 601257366, 107763940, 212654854, 811184796, 63466737, 344548203, 25805383, 843198355, 505423826, 895739325, 826576332, 828244723, 307085146, 637569738, 941052281, 934927494, 471702131, 430011202, 646233474, 950060824, 318585769, 776398274, 559913211, 102308000, 683158628, 24381062, 964539745, 594596302, 766189362, 762557564, 237148321, 581236907, 570038704, 576899186, 341116222, 105824854, 697987960, 420202911, 744955630, 508098838, 510835454, 798584140, 302039399, 553766385, 189109751, 350234983, 829987710, 714172722, 352130920, 434658856, 730237662, 396137978, 574232074, 628501664, 693419245, 904192223, 543331647, 470420071, 254013415, 246701209, 344506930, 509180888, 201569597, 655436596, 647352684, 288968842, 140770977, 79830042, 862405670, 423766362, 646476700, 760868084, 298415950, 582511049, 700750490, 108480514, 642501705, 953976550, 228764528, 254188681, 341482411, 655245444, 303953559, 154727511, 253144641, 20206837, 26746234, 646171028, 676239400, 24235401, 363142299, 817264918, 621241019, 182250030, 817054084, 602613839, 731362039, 729184217, 868918139, 78875532, 926332814, 635307701, 157370673, 364807478, 455552364, 526634829, 882898953, 956349449, 519058612, 355858041, 904809276, 103078035, 242106947, 819042869, 643562113, 461183861, 227209853, 68300967, 135261903, 147937320, 400228311, 475220051, 110467370, 71861708, 612269323, 49443711, 8735506, 377994372, 242542576, 133444060, 231052026, 737421570, 103881573, 749829680, 98951740, 375916893, 698256243, 600587544, 628426362, 915448184, 726326720, 401051964, 94360108, 225890832, 109047990, 608014765, 117207166, 178135241, 54475829, 531686646, 985311815, 908557234, 620074851, 902064558, 80815800, 25506755, 893427340, 832752031, 152663214, 374854192, 443563468, 822033043, 609030296, 999447676, 319025968, 854658405, 383721313, 332020987, 534498395, 273450635, 382214743, 521254750, 474626025, 891386171, 223019173, 861771876, 235600385, 601292280, 341810572, 319178888, 402880939, 261807710, 58431958, 558346726, 767610898, 574547875, 130043863, 582653792, 665205247, 853710663, 348381595, 512771464, 150080908, 928878994, 647480541, 137224845, 729493060, 139281344, 667693205, 781765245, 356541524, 595011843, 719782189, 445091396, 597253459, 473472232, 840629881, 637067261, 832205085, 665666234, 525968680, 695662523, 96244165, 668314638, 399905868, 341752309, 165246853, 233667271, 896785433, 356834058, 670476263, 628954829, 364355867, 442471873, 940342922, 487614336, 989580412, 147391925, 822296059, 254573356, 463140460, 837749436, 238324279, 705416957, 183624800, 572631646, 590150540, 399554350, 533319209, 621581983, 123928339, 639571934, 654819517, 273557317, 626224372, 849722670, 661734068, 214316416, 8595944, 915331614, 778973427, 352519481, 676746870, 394826781, 785993985, 456776343, 541532592, 611219453, 762186070, 439990074, 198527877, 513700627, 558057297, 174058309, 317504515, 679542987, 752594006, 612819448, 447698856, 908099818, 780654883, 853773583, 763560332, 694198602, 417667310, 368312942, 352303690, 611900658, 7199006, 36338311, 10260470, 390501250, 630445148, 96456684, 572703870, 907662447, 647908159, 201360875, 634967977, 831609404, 496826548, 693220881, 975340069, 269386597, 249493021, 381344743, 142671486, 693189117, 14582518, 184896794, 735968976, 115406696, 658640550, 509789865, 87091545, 225786598, 48727556, 782425090, 296571785, 19137434, 356054503, 929569584, 401246837, 794693127, 812775161, 434951092, 852768322, 802913230, 458728200, 63813234, 859384009, 267355965, 1724452, 111624916, 688525617, 796460793, 503059704, 537745279, 849337118, 416693800, 760724239, 456498765, 481750896, 540485606, 256157722, 111664633, 165685084, 615128021, 715093352, 138762686, 658833074, 620821314, 898941688, 746143974, 389224812, 804486271, 671199795, 269308007, 864296644, 617222375, 714423994, 18295669, 640859617, 841213592, 275804382, 952820676, 313084387, 194564562, 244232751, 985524412, 947346810, 861841640, 173659249, 21665817, 955723594, 128706948, 583643603, 561066490, 578747415, 224011341, 203581239, 244444554, 986936029, 456204785, 261797962, 74934386, 701079639, 217491135, 112368770, 847359156, 827167981, 846286716, 223811899, 328538528, 385331230, 924718919, 843529739, 241819625, 510890878, 314329323, 662753883, 333528620, 37292362, 430417338, 947152480, 95926772, 400100086, 432979656, 614337343, 635554160, 174977697, 416828085, 181662708, 725323982, 656681041, 378907093, 40162246, 587987504, 300883724, 363364086, 902204863, 139308120, 764593899, 883032305, 388442505, 211296410, 223406620, 893133306, 433316908, 687492049, 271137855, 656258115, 134378024, 335808089, 677238164, 767575959, 620472579, 987340936, 450753122, 347758811, 964930473, 71744671, 80761180, 42912685, 880096434, 122670592, 6219885, 242165228, 263297868, 83236405, 25322111, 593084255, 81001316, 988955622, 892918859, 273918875, 748273392, 558388368, 575622337, 774319364, 518325122, 745322381, 995866299, 679428355, 231157485, 777673804, 171817435, 556475880, 890796091, 496877295, 414405741, 713968823, 159215907, 413843876, 450311754, 477710240, 749664079, 863854189, 446013885, 837188645, 76722048, 510314757, 373255373, 49346483, 336568240, 385802958, 873020563, 247301928, 225742239, 184274299, 751742763, 6411149, 882667428, 662141743, 7560219, 984578790, 584542954, 468376706, 28577369, 223125705, 101987409, 424650677, 369154719, 146806670, 493901995, 301299860, 931397446, 296852272, 147908056, 580512309, 708047856, 126612099, 621283680, 626871208, 619836330, 634353218, 984059431, 520320824, 945623534, 969787729, 308981015, 982843342, 808802699, 502199, 510140130, 273697536, 277888441, 322450399, 617787484, 14179824, 148043301, 215348838, 152531254, 339745662, 690070194, 728897270, 855523238, 688863513, 79443829, 962187457, 291201161, 958625757, 593314166, 404415010, 664419743, 672737261, 436389260, 646437802, 626780034, 638545465, 545683824, 287407154, 98653719, 651591125, 815226679, 139550922, 648673467, 612947818, 228967494, 982974610, 239471599, 473285824, 649368663, 169562346, 635048841, 102438907, 263463568, 884543546, 222291194, 98511946, 643095289, 761393428, 928994904, 960381812, 145655929, 108630248, 568790650, 686779661, 707258436, 797061779, 327001108, 975364116, 61659696, 121630990, 446423899, 957876187, 662745895, 47636139, 35072126, 74135173, 491055559, 99945237, 483922914, 216247401, 713800305, 785516618, 888299787, 980152949, 606111756, 788525239, 907699698, 200646393, 18706867, 64615882, 614321608, 348642243, 380871434, 387406184, 972150021, 780666006, 233472560, 216183824, 917413455, 61340305, 278482374, 610699428, 181017487, 723016171, 652886355, 59840243, 148102663, 733231729, 350538247, 314194868, 705388506, 470093976, 184805093, 356259754, 301180042, 56165758, 567022698, 703558275, 610146295, 559256651, 843982700, 785228950, 640426779, 197611881, 422288583, 233256038, 45817185, 458311222, 311052854, 348965917, 390830012, 368541003, 75785418, 612172487, 684759402, 999249762, 916625681, 646489752, 100537975, 903522172, 878880881, 238739210, 622605591, 775039251, 231630340, 41971804, 915730412, 284784212, 348493977, 489527631, 277782597, 250461298, 258783854, 485307021, 5585812, 487453322, 935315439, 605833252, 809633973, 115691658, 145058948, 753760918, 845118147, 344205523, 835565919, 766497827, 797285074, 776087496, 986805032, 359574754, 139631785, 688369891, 954097506, 905362079, 658482426, 169372586, 141283798, 21482100, 141949137, 288918148, 643345878, 773663529, 790736625, 770068341, 142144066, 905483272, 599025477, 708086237, 947869274, 263908909, 626543736, 636205570, 493952265, 602581788, 272887203, 763717465, 117073585, 429896064, 409893924, 575506726, 575231033, 233603766, 701117239, 295197812, 29684639, 765354958, 851729460, 64477742, 592193806, 142814954, 936214626, 675727139, 81069484, 640783976, 970165331, 762478710, 439087514, 768116237, 294821907, 483787006, 403724521, 471290859, 942041026, 988302753, 834712220, 583877450, 367975604, 759636723, 800768412, 195644646, 851662964, 586359210, 426978570, 410259465, 482320312, 148475186, 895090230, 503908830, 462890595, 365923514, 573436953, 627276981, 702101074, 706361765, 503317414, 868099499, 276537090, 320737860, 237231099, 569898735, 473066429, 918377111, 869348135, 500431457, 365923045, 291931126, 921374071, 484743537, 669553109, 883613540, 338441163, 740928702, 316707889, 479827551, 788964582, 420504287, 738888479, 542271992, 102464619, 103643123, 643132213, 684625256, 422147667, 67618219, 426948217, 506568921, 992839323, 831353266, 904838501, 983407009, 288651057, 641519501, 49607394, 724662445, 171464695, 988679748, 380626052, 415576700, 618656666, 158312484, 281252722, 927461756, 853496128, 166200330, 545099534, 898715797, 789079418, 646748503, 937397567, 187407355, 652576465, 186166797, 821802609, 560763871, 705581765, 544590411, 913996667, 416731822, 345982945, 6435894, 828923594, 757300494, 553051151, 109081006, 65321290, 550240984, 969235792, 502449421, 999379270, 783405541, 567297059, 862955684, 153692822, 329609110, 680771873, 402837523, 649681843, 378568059, 444915481, 774925001, 690606944, 899549013, 605106754, 228126473, 520918084, 761474200, 281295142, 238977651, 345740000, 838785318, 9390863, 581127136, 173883917, 267589457, 426535814, 504807951, 790770903, 321043774, 642596780, 192965927, 71809293, 92090197, 171620072, 179029401, 156357006, 124427829, 111124369, 690701323, 956188451, 953022154, 461627209, 47614506, 420070658, 340449721, 378479714, 955645691, 883080039, 783627052, 384035831, 943102000, 945388423, 771797647, 760514528, 889433882, 631783262, 312712615, 3794588, 741899813, 404510765, 592853158, 795339904, 902748271, 467946012, 815005864, 363324086, 916182526, 69249969, 660177264, 567759011, 379192269, 639744008, 266460677, 921189536, 159843396, 929913468, 917123443, 135587622, 520758420, 241139733, 290201601, 562691952, 786420541, 535115170, 458464696, 583003987, 651753141, 385544768, 194861221, 498388293, 691341608, 602596702, 296282138, 147225466, 455413052, 257384378, 747074628, 619640086, 689752074, 567961742, 907321021, 916632343, 953535897, 237329122, 575975417, 580421040, 223512629, 202074837, 414239239, 863938462, 18738999, 319213405, 398504915, 704445890, 850468525, 807885942, 556292843, 225514078, 729834480, 474730045, 582090537, 72847681, 525764741, 499129832, 816591599, 205040547, 687739062, 196622817, 89376304, 109934707, 360015196, 485791820, 842804120, 290150834, 69966942, 957294577, 634648006, 433372026, 165810761, 317678237, 167016715, 446076362, 744350123, 627812555, 163842678, 223987342, 260074693, 43446337, 588016819, 844320098, 667744172, 106882058, 546520197, 926262972, 568655733, 556871674, 985297901, 468339049, 905456676, 5536558, 167693105, 443550609, 107513629, 864163648, 152019936, 837704113, 137337214, 825737936, 962496925, 837794151, 177192052, 542776481, 137227021, 841949371, 153138846, 49007817, 615146243, 491414140, 665853753, 494366324, 526870401, 803782344, 194768165, 439959872, 421539810, 243983149, 467518904, 163725678, 417461693, 37317314, 942941376, 118582454, 210544959, 783790476, 368954044, 997790627, 651294061, 777100064, 192837640, 499911147, 645124149, 102122602, 21722945, 978704872, 935803337, 126443431, 864639936, 18965255, 909556447, 180241728, 457886747, 614586353, 533495084, 221160266, 688109616, 895264850, 782974182, 25467391, 681744634, 519965109, 138541869, 474826388, 327372295, 872798364, 652286570, 731828655, 356026251, 611266737, 250170739, 438109063, 974170519, 13454018, 132874872, 582095761, 74984860, 967005581, 320270353, 186800634, 932788338, 856990462, 67527281, 547394911, 195654858, 189760213, 700930092, 432634116, 533801232, 875365571, 530049968, 322817032, 924726989, 549313617, 547242832, 804352936, 771377965, 650199900, 738494504, 176630152, 338714102, 974652788, 161159989, 549541266, 452943015, 894130216, 9936023, 233309571, 915535297, 664272932, 724476390, 721889616, 354778440, 945085664, 966565811, 856083322, 470215964, 603957, 969146176, 222440421, 84360026, 492127939, 916535871, 895167473, 937459770, 505843527, 345264821, 355898589, 893831416, 162371293, 496792194, 137159357, 504889823, 895125479, 217058643, 783537049, 228634635, 680844624, 100819345, 762810646, 566113283, 373280333, 88192880, 791966655, 47911854, 859580105, 105213835, 506333226, 932654063, 706899507, 238329252, 349244650, 478339597, 875844432, 595127565, 625618548, 691244614, 953060685, 108892513, 179544678, 259218497, 525011488, 180856102, 203321296, 487834705, 480413471, 626214872, 35986362, 615597156, 950094901, 904402822, 669623431, 738096904, 260602411, 94522556, 898852027, 509572787, 397628671, 21231384, 955326442, 214332179, 781489203, 164423662, 839989309, 201581672, 926990810, 490582884, 58083234, 988360116, 381062347, 90692704, 735109653, 816304430, 387730688, 487889307, 549756955, 912474593, 526776048, 150265284, 134919452, 470749982, 71430468, 387908161, 398766778, 776771565, 563381952, 729088286, 651416985, 628718173, 223889163, 868940529, 277494049, 466797422, 225144980, 791804480, 198017294, 256256520, 814496222, 736473830, 893488652, 694452792, 329607373, 383721882, 191647804, 930352391, 398475605, 767969173, 440082632, 682969059, 516256237, 692645342, 322391304, 796575082, 524603713, 298338130, 832717402, 164524292, 326643630, 135897645, 522314652, 601229745, 410084312, 628078815, 597838936, 24284939, 997100984, 875651251, 151570819, 586759243, 544140135, 266320635, 956352257, 145513019, 294316923, 999870239, 633944096, 365467805, 868766323, 938465772, 939234640, 35530138, 439261433, 55322690, 703803320, 975514323, 741215763, 306796445, 41228020, 980596973, 476518707, 994095973, 714734926, 536738015, 692485022, 137463687, 634050232, 169229555, 351567919, 771313304, 702822319, 510928728, 336513948, 373386510, 201315155, 770886921, 567844398, 943369027, 896760662, 930840169, 268448054, 798320803, 45571170, 816062869, 296017572, 909534040, 841114035, 587912014, 580568421, 768202359, 359795374, 990724045, 407825668, 431382148, 246628708, 929314258, 793858438, 130910810, 985040595, 64311536, 176604414, 222056044, 221034764, 399775500, 528232252, 377361392, 68769880, 733031884, 545285601, 240387952, 313251587, 524390605, 232390676, 452742751, 913387023, 203919076, 440825825, 425068045, 904848493, 206433315, 858202097, 470917175, 369778372, 302379694, 406118622, 542907681, 346521596, 858424088, 966589358, 167239515, 781800165, 687200942, 206605719, 903957037, 256868639, 593180040, 937031751, 448999765, 798069822, 836909289, 93568923, 969548236, 351943743, 965270628, 153527347, 144428252, 782437790, 696100977, 735464002, 20351909, 644410745, 887222374, 278881204, 655122640, 866395718, 686446373, 185723105, 289712922, 976321329, 213894446, 20964946, 211271715, 555869063, 345034096, 849725725, 567925538, 26155484, 999551954, 613823712, 149377350, 418000102, 425416635, 834527487, 577547067, 289134688, 576106796, 55426788, 713712160, 593517569, 187675358, 849751952, 713536983, 368043169, 467077528, 276947789, 67167672, 793058084, 916384698, 958356576, 384377063, 812623424, 774912876, 637072148, 795386022, 938970172, 507010343, 270232411, 339133038, 209954775, 300345124, 935908859, 106239148, 549657664, 492652474, 396785100, 619813639, 579817148, 88707122, 654693820, 745845824, 68743898, 130691370, 792063664, 435467889, 381359397, 277076381, 660137392, 549657373, 701623443, 295132417, 346348905, 983702390, 941324091, 225749644, 678093943, 488879029, 474555297, 604097479, 936263822, 36788645, 264977291, 770917348, 380318879, 46949810, 394561802, 843705243, 845921850, 344592191, 93624242, 519922080, 660312793, 857109512, 91387515, 150830339, 389042669, 282878377, 236501999, 13454764, 475114958, 43214674, 673842073, 454121935, 883688508, 516009244, 305787619, 334338138, 116555652, 116702695, 755084284, 370789974, 652456384, 829399722, 879084101, 933140796, 982132102, 38284979, 988009375, 27658176, 791356757, 5263558, 631437980, 840463383, 455452554, 940087408, 723106062, 635774384, 988437556, 137938979, 901672633, 353718253, 874099571, 766753412, 646243365, 813498118, 173135798, 118595155, 272996732, 50628190, 329808528, 476377950, 967747432, 493670062, 233514613, 679189319, 994605113, 819777986, 90272324, 945571716, 64627929, 948533345, 591636662, 692101862, 973001112, 569059724, 746746280, 997040083, 397026364, 831620394, 523057496, 352766390, 534016095, 606555953, 169885930, 959719251, 344155505, 565105148, 321719946, 336679091, 40969322, 751378658, 810199332, 841764437, 652715623, 635840981, 301998524, 548830308, 952544649, 397309240, 537526620, 143894880, 496191750, 618519263, 731437588, 540363178, 231961305, 292321234, 740585653, 829770743, 623329415, 230009298, 271428396, 962120116, 297066769, 234592279, 985985239, 756699937, 202353631, 879756814, 879862036, 646334162, 701133241, 359863159, 553965203, 424166658, 776260634, 103907380, 824511961, 290401229, 236889259, 167823185, 931466503, 899696323, 330926587, 758694143, 97249485, 610219056, 117033420, 414609626, 738674392, 176350999, 516980068, 704284966, 642980064, 902115059, 848224105, 811654897, 854255279, 142816202, 344655558, 923877467, 875939477, 10648893, 54903773, 408328573, 436290824, 440528898, 383631171, 685724102, 106972040, 689335094, 251736370, 762344686, 652982608, 628623455, 290716974, 708935874, 112950619, 481230582, 546605170, 467910439, 965627364, 999782507, 938325273, 563938322, 534693467, 471071026, 819584237, 705015201, 152760538, 15812659, 445279865, 582509492, 325698029, 282956573, 741520496, 50170190, 213448109, 521375305, 908758823, 202725534, 885239524, 625043999, 985775736, 563039303, 962149602, 392349567, 721895618, 641739609, 942314256, 334345388, 537871271, 217536560, 174555468, 28631902, 976789376, 861214922, 985994865, 958865475, 448667242, 469924541, 469594840, 251323716, 790791010, 258078781, 667895355, 127314414, 259251598, 556380256, 286164210, 833078704, 406279424, 36986925, 838891095, 466725294, 53042051, 730555718, 11465443, 96999357, 178011021, 522354026, 349143765, 127284615, 730386777, 971952494, 633816877, 954435093, 768493665, 927587223, 656500937, 7241020, 856104649, 783084820, 440819528, 945696668, 690833672, 379168545, 814716343, 72745960, 658220504, 984019487, 301711625, 644289783, 39882463, 33352060, 781700115, 795183119, 895898479, 449368442, 414138938, 409364467, 431983025, 106262010, 203510531, 898388280, 339477268, 78847288, 615659472, 334597230, 953908469, 76447302, 501357279, 714043853, 93484794, 809110962, 839270882, 36458684, 398059300, 207602330, 998358123, 781928150, 38998195, 84158472, 589064338, 101463895, 897757579, 537444363, 343425109, 617894298, 925496853, 3960823, 114686221, 281035487, 320379234, 542260180, 369716991, 180423738, 927928212, 114936576, 836190942, 99524797, 618554588, 615283133, 977530840, 851672214, 303773567, 130018410, 838658766, 216328615, 800194160, 877550496, 868510863, 656541727, 992797395, 586392041, 990749394, 154558212, 339351736, 893764882, 499128323, 964339827, 651558735, 335732791, 924663073, 530950133, 64125873, 996531221, 78717277, 975737320, 260539710, 296063520, 312847958, 19029903, 861893779, 919580274, 82039890, 911088959, 529656312, 995036113, 421738859, 191698422, 391676066, 950455057, 377652373, 734618252, 365594878, 528981339, 206019602, 485544533, 355982425, 169024413, 588147672, 379998252, 963695212, 483209648, 944288922, 194416622, 402257783, 289142324, 125848830, 148534376, 935347290, 164155187, 682228065, 915315508, 366531080, 846710161, 210761792, 676201863, 277631470, 674665403, 520541812, 922029767, 559522748, 919222263, 802683064, 847163317, 916631212, 111764011, 184435301, 799092261, 637307915, 489987833, 18755012, 169075638, 505028136, 129475745, 606629747, 56819692, 726497125, 580207558, 833766609, 437654632, 852177940, 124605244, 702420159, 315698942, 74943538, 987268809, 167886217, 948972558, 494929611, 693127056, 887427854, 842030263, 975284064, 544431185, 272432686, 248117276, 780141901, 439682803, 175012572, 521242111, 484706794, 23068833, 753687567, 927704500, 949667569, 567223763, 77964624, 539601755, 467392642, 642457515, 379048731, 588340106, 302839979, 420182048, 195620906, 511008752, 359416283, 744373875, 239309944, 633156989, 754366277, 320866769, 378992806, 648756073, 922940184, 72985900, 313210627, 315505558, 854375651, 615862008, 268463202, 389960065, 566106762, 911421335, 468512443, 558439537, 956039706, 148115156, 568947751, 959827605, 104901801, 458849826, 123665109, 317531582, 577021830, 353816084, 541053280, 646234386, 569719507, 598061249, 731720884, 168102408, 450583574, 390692895, 597388400, 445943818, 860244381, 680752901, 477804253, 526707559, 710894081, 797170998, 733641630, 360628662, 507223078, 693259519, 972850222, 82406900, 139573144, 74137831, 49415949, 578466090, 390035913, 617089632, 55159133, 309508007, 151365828, 628887886, 845458084, 121499117, 158637863, 130278875, 426936624, 240903548, 526462135, 265071035, 820178011, 844758517, 956154636, 815879288, 401710706, 14708602, 892462314, 472843291, 768792023, 166490068, 12154466, 785994786, 865424442, 986350350, 181732601, 285521280, 734683514, 88752112, 871235808, 670314408, 889463245, 764432942, 59854688, 992726222, 855137944, 438876556, 842389208, 437808059, 731810435, 919434716, 686145667, 599673971, 786151996, 6541862, 744661577, 855287221, 90942300, 984707823, 572268606, 707008033, 181046496, 434173659, 955952024, 168800132, 201527555, 943263698, 718982003, 657530417, 896474300, 681479792, 854133875, 308540837, 780192930, 377975148, 906734866, 196935128, 652963480, 209455575, 44403314, 507804023, 446587, 641289216, 78892654, 421613540, 785884563, 18654516, 118747611, 855728573, 530793030, 904470956, 999071278, 293781873, 808195605, 985878997, 914001618, 4309865, 338836542, 250887359, 565531604, 171579273, 466290592, 257320956, 842162829, 937396002, 985250997, 865327260, 236371536, 890273472, 659757135, 788095190, 649963692, 95149855, 239381402, 84132450, 817588241, 772532444, 956065592, 108823143, 671013240, 73877869, 634009142, 389988517, 21541094, 493318583, 657068161, 13142066, 100747463, 721304221, 867115314, 270815589, 735934301, 146182917, 698364718, 187226355, 677420005, 647728622, 900766384, 340072913, 187438181, 82413753, 171838786, 315748769, 194200146, 107369241, 197272300, 334379417, 574700165, 615694376, 444878305, 768740317, 610414876, 248219577, 800452944, 690157889, 793960981, 740577457, 160113986, 541729292, 14402687, 276326586, 972483076, 850678576, 251601212, 678605612, 80013968, 323399072, 86730114, 500231768, 372195567, 157607156, 872934418, 370127678, 762899077, 442779051, 799356274, 359928926, 785043290, 260437287, 359867586, 574462821, 788303171, 934973579, 361724655, 633019423, 429119549, 334940238, 683391673, 379502168, 460228897, 571810101, 283033865, 228611241, 714882243, 672031265, 663043021, 529455311, 318000296, 52225462, 474765435, 123853467, 376560790, 861543425, 494679091, 432197526, 653267111, 597347669, 690337309, 814802468, 842591010, 881312449, 321241907, 921980177, 133980808, 475272452, 908911655, 952324310, 385700823, 885282547, 23790990, 961617041, 486614979, 437782579, 296740541, 749092642, 804323261, 785328721, 911607675, 447994800, 900951982, 218796200, 800361675, 128855723, 326442680, 74674164, 373383753, 997379359, 9058533, 853072297, 84658600, 757952224, 199645405, 352915632, 17704256, 455292516, 292894662, 32276147, 168396753, 122648035, 522723171, 435968445, 9226236, 772898560, 82760556, 44651616, 448358581, 432034465, 987003989, 818066214, 399194454, 171534642, 169447206, 152455922, 743308380, 5292754, 624362261, 608977917, 233993459, 798514012, 183931446, 840636913, 671296631, 234185181, 163797262, 571775797, 322842975, 414357646, 273346654, 710702155, 677505155, 104770199, 810175053, 435252410, 757260189, 660890446, 405855025, 215612848, 130804035, 354039392, 491919663, 992946650, 238315287, 445177492, 294336597, 448330275, 917478638, 215542205, 265233571, 915903906, 475472641, 811481767, 932010531, 98984763, 106332084, 423090296, 435039507, 976621171, 911901346, 481032379, 462624199, 113796110, 160753342, 650590598, 960675823, 6411787, 216961838, 410433006, 687775448, 349385575, 164519930, 337383814, 743759279, 943484443, 533656475, 226866926, 363829620, 711963286, 150324150, 42087382, 27245117, 457887659, 878806988, 941004052, 279932756, 834783668, 223889560, 763840148, 91042151, 63509700, 696665307, 122439375, 951202309, 629193136, 140589070, 996795893, 788595265, 882790150, 675389227, 252302932, 749813031, 22915749, 46960558, 72237796, 530292369, 918835648, 761052046, 624256386, 35153583, 492755119, 317496805, 135455553, 167852323, 700298851, 867415546, 207342584, 705662194, 467912314, 173212413, 347549134, 534530874, 558837942, 448607716, 912480192, 340733992, 357791953, 494259727, 559473205, 338094349, 107358661, 974629934, 919443632, 804266725, 156346556, 672166003, 265580733, 180652048, 386861487, 891686208, 56429723, 904492760, 354610874, 938213812, 949277309, 264074359, 693244178, 590395862, 214678323, 548440897, 849957564, 669803657, 547176948, 830433188, 952378642, 622970493, 358356427, 770477968, 432747334, 824596748, 912181074, 837388655, 789063435, 532903891, 102371890, 927295751, 60482577, 631592160, 464511595, 200029933, 254312109, 848858254, 698237291, 464848505, 76068740, 286904382, 436746661, 541897085, 485120396, 113371527, 621394554, 392107974, 451328939, 743092147, 657529384, 128961983, 299830388, 912966760, 505539604, 607521827, 630045541, 327629743, 834154960, 362713894, 2065470, 380464507, 512135230, 287979070, 480845613, 146308471, 529339845, 722074760, 402655684, 862310894, 576670726, 675112440, 675288909, 388908994, 479225923, 323997451, 524766670, 989995966, 999441017, 456075363, 516177806, 705377142, 392767673, 22770706, 83769913, 684482358, 495387226, 15078476, 887980318, 165115459, 838213707, 345994235, 747593239, 425757967, 640269192, 755705651, 715021122, 648390154, 789854523, 944826033, 688322585, 878282599, 636570866, 45722719, 449526205, 34516819, 834721882, 319799321, 690300262, 500296157, 987384438, 412691798, 780802444, 593221585, 767045257, 576741796, 852587514, 232332656, 788208409, 934933764, 36502184, 823495380, 313499166, 103185346, 123138280, 177775032, 421272187, 989002794, 9308404, 320267263, 190162848, 117144197, 621935474, 805712027, 694622323, 626481141, 70024522, 83547321, 866290225, 315263543, 126395120, 411462442, 533927227, 507988400, 775820470, 82824027, 535230537, 131566634, 873580620, 477695195, 397869739, 295535623, 850392276, 655375872, 607604935, 852677539, 200248438, 616806156, 441484117, 371425742, 806560033, 512753022, 532813918, 787085397, 701574571, 876796951, 853058919, 724878618, 554836889, 679472778, 574245067, 295620299, 716069133, 672738051, 356456336, 191835171, 76631856, 878524328, 22920084, 681420374, 645276758, 221799682, 925816760, 981390629, 169779476, 65002328, 999072135, 588221823, 676350404, 13415356, 136439611, 227875470, 572746495, 13807431, 152848548, 959798280, 69312800, 155831752, 881255612, 619480284, 189851758, 867118111, 530173581, 239875309, 716154270, 509380, 976330690, 244035295, 753791149, 508425168, 967223858, 732496523, 905372536, 544841588, 348069787, 561247046, 624031462, 838100323, 49064891, 350140902, 132304771, 120462902, 527136309, 348503231, 115879891, 973665680, 134085892, 325819697, 816881073, 417270013, 339127041, 221944157, 940992621, 853480621, 768358492, 40206571, 720251706, 437720130, 558342871, 860374383, 73004690, 675560865, 588564239, 215928542, 597197460, 553406160, 38889874, 72984888, 739494824, 395120764, 873459077, 501869193, 114933250, 627167586, 954402354, 424753650, 887513133, 700621312, 154517104, 777089164, 242837896, 984145458, 850828394, 781425230, 2524309, 290653080, 591073594, 589896299, 375754878, 472057188, 253133586, 528280219, 913853735, 929929651, 696841304, 761575183, 914975438, 415447800, 922498946, 321642505, 953982106, 506932402, 930125810, 432382822, 243807514, 989963025, 19129206, 763017404, 940278976, 930284595, 907971660, 210549914, 451048519, 621352199, 801766075, 905110222, 516242934, 928379762, 397756606, 465406665, 792727230, 747023479, 161963559, 940361425, 484154541, 273526490, 110292479, 881687783, 52361644, 439616270, 13954285, 624784498, 173536157, 16973547, 281174502, 405082992, 194623010, 24549149, 119143296, 291354286, 965953337, 299577115, 824834062, 76904974, 38531539, 914852802, 852798070, 568796265, 840001388, 411972749, 280181771, 874906610, 117791617, 308714371, 577443246, 648958451, 403939816, 416499200, 356658222, 482218443, 46654045, 644866172, 706627252, 390402873, 866839270, 357464618, 951267878, 807528758, 297273007, 334215358, 720854809, 593067419, 466478216, 22167750, 598103892, 375148194, 771431623, 50676328, 988189651, 326214531, 87576895, 167928413, 736764717, 725416917, 710850358, 337877007, 819907535, 415445930, 770166905, 765955118, 90348052, 985696526, 240049052, 834673579, 77348025, 760602840, 879366664, 986132537, 769389530, 942932118, 255373724, 859960802, 572803642, 470529063, 559268294, 850046462, 964623414, 863712546, 281939247, 596956110, 348606232, 998139151, 607787333, 139883444, 619392108, 901214964, 278316733, 623969392, 553958756, 509628889, 833380153, 770047915, 569481371, 985237440, 319062764, 462020974, 26577431, 735896556, 277013108, 816051788, 476866516, 765285031, 383842578, 660985063, 183806233, 642401503, 362625740, 814445728, 338352299, 615057415, 332147654, 821307092, 138754332, 6211831, 357973369, 27380887, 334266223, 826055335, 852652543, 142451921, 344502567, 50799991, 158145696, 33073619, 958667989, 888412525, 524791989, 514454670, 413102957, 364257336, 288386663, 5226143, 708505134, 206106456, 194660864, 59526265, 664890659, 242729908, 448693312, 283039850, 766378033, 309438050, 944879747, 744476094, 169872210, 496753872, 786934252, 341421347, 615726452, 172103783, 145514079, 172402476, 177516879, 510912828, 19728188, 454509697, 35370906, 784704400, 293837325, 775606530, 558291417, 677655263, 941484439, 825199209, 307265639, 95821733, 74231010, 749790402, 83322808, 340690016, 72820975, 524444090, 143851769, 202462780, 275437695, 19770671, 271382325, 436639833, 632223530, 654846653, 689680648, 31470001, 556548799, 662157803, 388241393, 269780465, 526304778, 693835037, 934991524, 93089277, 376459274, 3504724, 444996373, 850408292, 905567178, 115491281, 48055245, 358446837, 826174789, 962838752, 222372445, 730405872, 531996718, 620049458, 414652266, 561358539, 520507828, 926485043, 402921489, 934039788, 433126730, 45435274, 503611930, 663080317, 101885309, 73676829, 204201926, 811500311, 226897856, 30803880, 969249406, 378834353, 52144934, 615352541, 713948002, 792227650, 701959091, 526306839, 945431950, 970435098, 56402202, 472430006, 815189195, 913018660, 640757797, 806904923, 786791415, 494281919, 386975421, 610654372, 963446217, 495692329, 682335920, 283721223, 298006233, 439068952, 911863029, 386507312, 659819230, 793422132, 21980391, 237284177, 375518581, 423390396, 172568368, 640999449, 646045368, 668879748, 490200553, 748299695, 913669085, 927700778, 373575090, 60619232, 982595185, 759885009, 698143299, 291817647, 221722743, 776276000, 422857918, 51943180, 206375237, 873914179, 495789832, 891822630, 100109489, 714950502, 982647787, 448526622, 362846333, 750665929, 438512646, 414437120, 4186433, 989380936, 766455481, 799384296, 841195247, 141826316, 533345271, 884513853, 492657762, 854868281, 406896974, 828045848, 373392680, 573874844, 295379595, 177993757, 24134980, 613957597, 538263503, 555083301, 883725044, 586016258, 359139238, 947137768, 1624431, 405978825, 921300440, 683422195, 394466469, 739175141, 659925270, 8064677, 707389207, 62904395, 33558157, 117162716, 595898158, 681553365, 860341015, 372742844, 412906662, 738152567, 954765895, 240952428, 615328672, 918228282, 846931169, 926516712, 765601358, 600261914, 886093490, 303663423, 522197863, 253586755, 575272401, 428517871, 542023500, 663672888, 21143186, 456213121, 422077763, 682111804, 210887866, 119981191, 515815989, 573397533, 665588488, 475740190, 581948773, 631060316, 921820337, 343025466, 695399830, 389458006, 251458045, 168740668, 539266043, 91783914, 52120920, 561974401, 495075609, 895966006, 310049408, 198630705, 89718138, 338221794, 473454398, 416035621, 667127870, 610781318, 380965134, 762592546, 733969467, 191916820, 522193360, 371635377, 650994869, 766545651, 797265922, 653292417, 143613629, 258547587, 616522247, 52474416, 263497084, 80642274, 390073006, 501566774, 92185459, 229908283, 579325792, 247795472, 912405297, 565815119, 223290771, 437629891, 81557240, 537685875, 339421402, 364853183, 613092705, 566551213, 598429093, 10610237, 520604278, 708508104, 168435527, 544137444, 242679790, 262808056, 868207804, 102825763, 107750524, 704267213, 90865464, 722172402, 902770227, 691004660, 659303217, 604699122, 18508927, 27104794, 934424933, 719725811, 971081451, 384205136, 199834094, 105138709, 926249836, 605392974, 59109843, 166653325, 763628978, 718025345, 828090177, 594225039, 914473072, 639557810, 979415984, 499402065, 979013175, 708512309, 187485362, 297721314, 673761659, 158508533, 914277702, 22823673, 95168395, 830909098, 975145283, 219883076, 219411298, 63292368, 808207314, 87495218, 607313615, 404474120, 65858237, 107598224, 231343926, 320028839, 166451567, 295142983, 685240602, 807694519, 107342199, 920448670, 63883101, 283203235, 802783279, 91086482, 217851312, 576912851, 321296428, 148180537, 317464832, 110078627, 812895123, 97467963, 200566454, 530889863, 907380784, 951953002, 192133883, 708759249, 509205212, 956819627, 783605179, 136735486, 692963072, 291920736, 193957112, 115086940, 14676149, 451243482, 184974674, 353667148, 980295214, 544185212, 953397293, 201167016, 757623118, 829965793, 944683012, 167175885, 481259046, 818487303, 825698903, 180015174, 300242031, 212389542, 134194309, 890057826, 717405675, 351755059, 674059050, 865469290, 538711449, 954640789, 287751453, 254645155, 761993914, 591389885, 758316156, 300119698, 488886049, 474258135, 141481534, 292733051, 626151004, 890061925, 536416180, 669703550, 770262122, 545719278, 3099978, 187365906, 400676720, 805171739, 404124191, 804257053, 792453138, 108794097, 987785102, 178889039, 501908369, 67838144, 388304515, 773442782, 285474852, 546633777, 679527672, 648192109, 901340045, 368044054, 103018260, 929350204, 103513998, 658779783, 10874266, 611591268, 402371641, 743053714, 923815298, 839708626, 773324277, 757729043, 849579723, 516361010, 837952368, 542389822, 733606775, 150238285, 903736757, 565361145, 869472634, 901072979, 493750702, 267501946, 176665425, 41447582, 586591946, 551827059, 139793259, 282987322, 209089356, 788078952, 568680051, 623259192, 303941606, 457017112, 86324469, 475096112, 44102737, 719327902, 603206567, 957579938, 236943226, 126346901, 624372038, 868209585, 807691535, 252986855, 550384165, 941837037, 711023484, 761552446, 255578404, 760070688, 489637755, 374275857, 846376354, 780988171, 549096507, 836802266, 932160012, 278847733, 254947725, 525828846, 806720335, 48328574, 30149434, 638800963, 216616222, 723606503, 685418500, 325745908, 371768503, 20403796, 763782296, 864971566, 883545995, 685117337, 683080502, 644764543, 95883013, 547065466, 997471172, 874114692, 110226898, 605363509, 596940787, 505314734, 209174961, 66555535, 168494862, 716240047, 763653729, 729771940, 624630646, 612292910, 290853238, 402705842, 825704135, 739642315, 523706090, 744646021, 366723648, 482348110, 518221579, 315682081, 892222343, 139590118, 503705432, 982527596, 31304661, 936536359, 276743046, 715149031, 899281219, 98733512, 799901373, 997265470, 110522286, 665285690, 527610121, 832291909, 543213911, 284540303, 699753716, 232005955, 743947552, 174714063, 605524876, 301754003, 99722943, 461256550, 52052240, 957916242, 129863537, 354779671, 899556058, 616845337, 418231238, 801920649, 844695597, 567471801, 567248199, 563563129, 475603083, 571234976, 353657120, 616836160, 243264452, 819671301, 25261752, 334255863, 268666292, 544649135, 913410763, 320437678, 960579081, 571896877, 526373671, 758636667, 151542346, 344619610, 365236592, 556359503, 880346153, 334254819, 491547094, 824887381, 681402794, 858887219, 668723107, 333743298, 90650345, 311915524, 38788947, 853423051, 217892796, 170157454, 786813386, 765140620, 534312992, 15870458, 548846472, 607483008, 366505848, 370838192, 774477164, 178633350, 603920019, 823281671, 323178854, 404788815, 91011406, 441086084, 939472958, 177349914, 634402063, 223216089, 34994887, 96628953, 959566475, 572328848, 946170157, 492165726, 764772761, 514325117, 889112845, 452679489, 261242176, 186977451, 161304345, 741675312, 699414480, 183151009, 925858436, 623412154, 414867675, 876507215, 29965531, 13350920, 212087970, 226521005, 293363867, 518136473, 565418019, 737797753, 284507674, 310405204, 568697800, 269652301, 220686132, 266840418, 788812794, 766607309, 741012700, 268017819, 761294964, 434765967, 107446168, 639147834, 32895839, 328196989, 458169455, 520771732, 257630506, 266360114, 69943349, 696054449, 309990899, 743068858, 444932565, 299706375, 8818160, 461889882, 270055054, 463400591, 284144360, 648871403, 662512812, 923641158, 242659859, 266545729, 634455050, 834137744, 348950456, 978589918, 485442902, 894066526, 784196185, 524992114, 748029726, 943226863, 110631076, 40753922, 939138600, 60920821, 608712244, 433637861, 573600658, 201065873, 489064200, 157103399, 551295871, 709123539, 218984830, 642509243, 700191162, 590490014, 196157972, 46940099, 899877985, 883410802, 911339056, 992384719, 298195243, 370042629, 58859619, 371749200, 609395252, 832212679, 697743013, 122262538, 329464916, 660470012, 999248822, 493607491, 778821451, 281557511, 795947779, 984052715, 189293116, 595122254, 933791419, 375860734, 558399205, 557537537, 463983756, 68709680, 82003172, 230627296, 890585318, 254580198, 502177667, 224761682, 231937063, 306952771, 166324575, 286376982, 770309579, 447481867, 585281130, 831635755, 447132152, 366825268, 605462131, 822014256, 505821929, 67783040, 898445464, 348330715, 690087392, 987467017, 356838573, 208655397, 719444670, 51193358, 767246027, 245721918, 533037815, 862472150, 878097396, 841228509, 177560391, 765778997, 699263096, 239343437, 691430830, 675770496, 952060903, 325826243, 41790532, 747943865, 984528392, 806260495, 772393729, 473647063, 820187294, 45345688, 781126043, 405883031, 391688249, 407217079, 997387021, 140754398, 527780974, 377151539, 73984505, 204468826, 897795217, 565193851, 750514324, 326709893, 242773730, 788052365, 547157014, 417822165, 206633702, 296671555, 741320339, 844131914, 248902045, 195520846, 87611593, 716760490, 481666902, 663523924, 717847709, 765601605, 636982242, 709550788, 835121717, 829160626, 804462886, 258659301, 931572270, 573483774, 662895117, 452070968, 394413570, 779188531, 579082707, 455159520, 398237513, 291991459, 456064454, 530687584, 223161171, 671757548, 280577672, 681634071, 276357576, 4107938, 611536019, 129182752, 107194904, 264994369, 613174385, 34419566, 931511300, 415443210, 583767410, 449461260, 46536503, 241954011, 384265838, 666828096, 517557797, 401246973, 62796461, 878852059, 857146246, 995891152, 355112100, 783719462, 649443405, 144880037, 400610652, 534395559, 537114420, 60306983, 369789680, 746276874, 456438656, 370527749, 605440513, 579914065, 241786145, 941741973, 133204026, 571370456, 939593489, 734629896, 704232986, 815530792, 582821217, 2923006, 67040395, 668136840, 196368695, 414997333, 694144917, 504630010, 585285466, 47491274, 613323819, 369863462, 90500612, 316562, 726709319, 895087871, 538733786, 135470140, 136480065, 32243015, 278009491, 59282001, 230154666, 960557579, 498186471, 719874815, 227918651, 886016036, 477308048, 553240302, 301728229, 228098149, 769228505, 88903942, 184607277, 222973875, 416668861, 911882146, 317738119, 721927543, 564175583, 703572081, 146536515, 537441282, 649787334, 417137590, 302555504, 786972970, 953308420, 487373652, 934374361, 766615998, 871140678, 204987971, 64360796, 53501836, 473859698, 278249754, 315516130, 22639126, 347762977, 259088039, 192073647, 155078423, 313616360, 73808541, 917296615, 108452826, 82807894, 213019189, 387669294, 799971625, 728768597, 953807922, 230226729, 219952050, 178639079, 756485183, 693070951, 696342161, 89660307, 616928231, 34037700, 332127144, 251621933, 532855069, 365819171, 942564466, 874970016, 466462034, 624484481, 919929060, 252963674, 181745006, 938358846, 313851158, 447420430, 948374861, 732982400, 141557654, 34498827, 831977834, 42663156, 769021208, 380356006, 176277937, 165856046, 297013194, 291375437, 291825157, 380337881, 308484787, 331385266, 200634036, 486208199, 520028191, 909683084, 453127129, 658385710, 762458233, 866009327, 230385601, 765188243, 209638775, 325235896, 277118382, 648945819, 2739468, 546256362, 112024816, 803351930, 972337449, 552446502, 193092258, 175573587, 504418527, 946975572, 665365454, 703367119, 688214138, 676672620, 392989283, 619726012, 185073257, 656646791, 228875952, 993139044, 241291394, 287294006, 726281671, 563979834, 34272680, 137182283, 186023319, 446070672, 246298296, 600032302, 947563687, 577307412, 959042962, 592066578, 929353247, 357795851, 199225223, 124705127, 381363006, 214780308, 469097905, 40085112, 111876456, 49776047, 170097754, 916388142, 708857045, 547144535, 31839722, 941855537, 700317939, 713928541, 635659017, 580267686, 775763552, 465388886, 509728093, 565092730, 964009641, 382452158, 997685687, 817182276, 668713816, 716578308, 52893669, 191667577, 498367766, 548495562, 695193625, 424641640, 543945164, 84391525, 887914622, 181764091, 378021679, 651470414, 876115672, 528323718, 692431399, 232856765, 50175618, 491787178, 263798938, 89676438, 770277253, 644413852, 82271767, 922191673, 312844321, 394706943, 332054739, 83805805, 147413941, 899030212, 957021482, 602795267, 937505844, 766222605, 687346217, 937333978, 805943458, 214507031, 785372603, 530404454, 641865160, 9918885, 800551357, 939704990, 651104261, 555779814, 150235146, 990760852, 93973216, 777484039, 359300782, 566254146, 824316185, 411942376, 254771085, 118415545, 391843727, 126459316, 405998478, 968699553, 751328883, 151121421, 135666288, 817565327, 491253736, 989301962, 170866478, 415583374, 146228678, 382740812, 105711940, 885102413, 475463271, 950313562, 240579166, 372168999, 174515594, 394471793, 76138351, 707570072, 968005288, 884194121, 700360903, 379924204, 504792761, 91112214, 990297192, 322930689, 277822306, 725161923, 946806187, 938824376, 405947074, 185473306, 567115035, 388688621, 532128124, 218242086, 441918354, 350616238, 354783805, 837535170, 714207866, 871164120, 308972664, 487996104, 341544567, 378838695, 892038924, 165012598, 554816007, 457640152, 459186828, 62576222, 523808905, 520457486, 209800287, 977284167, 707973457, 258832289, 372857954, 894778840, 199819407, 786204758, 627932886, 111164633, 327285160, 42396822, 769705851, 156632416, 189341258, 994007887, 937791596, 816552126, 889615106, 256269700, 669917188, 192801864, 72869121, 145832440, 373187067, 543965328, 861706267, 529629858, 959906714, 450652719, 507438907, 883604018, 135835782, 848911812, 706100056, 757689063, 458312552, 865575185, 119967107, 424911175, 881465840, 461550516, 217506958, 414321118, 552542596, 284880143, 611726581, 529394141, 893956474, 228631186, 170658387, 734714883, 49983648, 987103667, 274354800, 889428704, 655441181, 274637546, 893992362, 644362439, 288656500, 93417142, 935757493, 970206301, 41204467, 289292573, 672340872, 142239515, 202489152, 861071310, 311900899, 271620304, 943915748, 412433022, 209449043, 899921969, 7237504, 321861819, 63890562, 603088211, 642484356, 538565731, 549423431, 73564322, 258539900, 892368130, 339487374, 658525198, 530055107, 144779070, 761007700, 825685052, 242794841, 271152919, 943705485, 968053891, 695508599, 54687996, 35573710, 194504218, 538467545, 987989733, 753466165, 644521730, 674478662, 164575323, 807781579, 932838301, 864320942, 300018748, 740469172, 992024, 449089691, 669861008, 357141719, 871695873, 342347909, 268155900, 375996311, 623814553, 706776287, 144291055, 555172517, 152961226, 357016275, 268489032, 567582621, 815212261, 769175042, 614762965, 696598334, 46762906, 535537947, 250448360, 949015924, 643010709, 729294667, 419055153, 759992336, 109801852, 698522110, 278463070, 485518300, 497655793, 218991783, 992843405, 667695911, 884321192, 301616949, 520299370, 839224002, 738943215, 736943820, 177789676, 645400386, 954543825, 272586331, 93285363, 383785526, 232085758, 665141896, 814740001, 926253329, 966151020, 273486895, 471100182, 719213388, 194510353, 27187991, 65567080, 700321486, 321069541, 836586780, 573107401, 618769734, 377294352, 151444283, 619428119, 99686865, 231418211, 634320138, 757374991, 954667757, 599396845, 255832352, 367920580, 902061490, 373249069, 102731538, 156728568, 322451958, 927494730, 113730836, 691188706, 826922204, 146221605, 438210797, 75320164, 893892340, 241277428, 927282184, 649220296, 341333371, 896863818, 136728400, 988894224, 608571044, 196104720, 632102166, 391788395, 231292294, 225902198, 714728331, 986941000, 526410347, 823206315, 811008222, 828224536, 738832444, 324338292, 302137448, 835902066, 352850972, 290555987, 107054642, 142460361, 19239625, 710633314, 333344512, 303453818, 46757830, 282231836, 548547630, 456655151, 568423433, 663404228, 11164711, 661968197, 148335619, 220210274, 34157324, 22574591, 84139124, 239372109, 920334861, 266299327, 359246406, 749826717, 658252140, 817862629, 55932012, 414584925, 109597496, 219709953, 297549625, 510710799, 712297357, 203473212, 196766065, 647851225, 2105558, 499958370, 21388914, 587240359, 6514908, 305075757, 84727715, 577748602, 993586996, 406539039, 940974925, 488805039, 30929282, 606345370, 176789982, 1810813, 234503826, 274624914, 837305363, 144031034, 848859365, 549447162, 847331867, 387636983, 516297469, 277265354, 355777856, 827373033, 496793137, 654451055, 628654917, 134583946, 1009180, 696821261, 787376883, 48997670, 636514636, 826114694, 410994250, 266095672, 943578782, 226515905, 200276911, 991054334, 914411069, 690511944, 377981632, 190814649, 347790737, 788606657, 54055507, 265582640, 980984812, 89971525, 428129177, 821057453, 213573981, 78434974, 745771873, 199069849, 61454511, 617095513, 631778265, 497449084, 825775252, 30551707, 613402775, 19147167, 517276958, 710116720, 806265096, 235832917, 209316426, 873682746, 984688652, 320091974, 78977088, 174335438, 334735847, 633591036, 270853938, 754969330, 665501064, 666196784, 365693828, 873901754, 267376763, 489564983, 295564606, 396997683, 456527146, 432276818, 885216161, 32034062, 10358011, 182871202, 627145896, 310231862, 29927010, 266595747, 943948204, 742848251, 779885562, 280071500, 820912415, 374698756, 322198946, 314493582, 631276657, 889794580, 175247247, 372777435, 675384066, 51683175, 883028801, 661061480, 310780440, 794229167, 6059300, 32109181, 646515342, 148653363, 146619510, 890544923, 360551642, 142991634, 685100611, 679598152, 153949588, 724022756, 486131846, 690202752, 841395958, 155084914, 889229659, 714028600, 442830991, 293524565, 499921026, 44113613, 117981319, 767656995, 791468539, 892587823, 559490592, 891358024, 929103560, 817562198, 557509038, 107222523, 10697385, 444513922, 232405616, 228210236, 631769589, 864919548, 856448640, 892304904, 565155940, 25328558, 271420052, 137635220, 720238286, 994166334, 498825045, 668953265, 497750308, 769971111, 28513857, 703502738, 879759183, 547248344, 448967665, 34413484, 193556863, 921802710, 978700417, 333694827, 162810684, 195522686, 226743345, 958996271, 140720246, 757849811, 813223038, 594311000, 985119359, 479629086, 650526678, 957950947, 404556269, 396588109, 329137906, 484303146, 300127340, 447608461, 979827379, 82242471, 392500901, 245897306, 885946500, 522194443, 950045512, 872284719, 672391166, 929599245, 522626586, 318528956, 235914434, 15602856, 678321689, 668704426, 940366945, 283990741, 487927329, 56260066, 535884606, 843091780, 980089872, 691394855, 695192181, 641065155, 243964503, 795454843, 45104407, 767594096, 139053409, 763493817, 467665752, 247984035, 855752137, 817832728, 843317232, 388667926, 440887881, 221756388, 817319797, 522248494, 276292720, 972206511, 799043414, 446834934, 639371517, 318823023, 831173950, 208899939, 884331316, 330591928, 681303675, 904325379, 895362212, 770095305, 189599618, 549088601, 27286949, 70216526, 785025654, 659920282, 370790374, 497789777, 796198845, 842092988, 325470179, 80591915, 745178386, 260075014, 972762095, 359976624, 657622918, 481913188, 110671308, 489260649, 271236444, 885741695, 40855403, 22588650, 58555159, 46129085, 715376508, 296498906, 697786359, 438571079, 809056570, 267624496, 360704098, 588122085, 211316305, 167624964, 460204932, 52629869, 142386309, 185231101, 822985655, 750508603, 331419058, 323691257, 273848846, 857858163, 814842985, 278780769, 865529830, 994512385, 212867210, 963156278, 438103816, 981176538, 262301392, 110286804, 361798703, 543331006, 5814419, 645722236, 65356941, 370606100, 970598972, 232440648, 371246511, 48796355, 215073958, 473858160, 852276510, 672385203, 826905694, 206421666, 968427211, 449190979, 691021328, 904163188, 993355748, 843431, 777504048, 51006832, 376989625, 872332526, 514273974, 182841305, 127326139, 465165676, 947186674, 668832037, 954830811, 427121605, 582780658, 652219551, 453630484, 77263431, 93053407, 618263414, 62999338, 36786631, 449929453, 439515859, 512745551, 78493530, 790086936, 9181852, 199229455, 95895989, 537289337, 833941802, 902012220, 473753144, 527773742, 177984689, 697953460, 507406496, 636128193, 180693174, 371576596, 158960200, 83935121, 928801385, 393980805, 444580969, 677800564, 473408138, 977987000, 286709798, 157519913, 877897716, 72535404, 822389342, 841347831, 334397754, 455076234, 91796786, 469349359, 730548972, 204442349, 363114766, 251514243, 83403703, 468153080, 22090271, 108854800, 606459773, 386448405, 406232796, 644553493, 674995855, 304284301, 19924910, 44670751, 321231531, 407101818, 886367293, 520897047, 76507921, 961777917, 862351019, 20732676, 118501568, 125272032, 359370946, 764314382, 233913108, 735005473, 266773085, 514383242, 524484147, 469932863, 217627182, 94786928, 717958179, 7645997, 705484163, 752642263, 458792763, 933078451, 144725245, 396473565, 885271751, 191720162, 19343928, 926838414, 761543698, 669508823, 520093830, 334644408, 45361231, 377506156, 191325865, 213699843, 885245180, 949304284, 179045585, 373068152, 131883766, 535647546, 984268926, 907745749, 649194593, 996135586, 347131370, 822598512, 432474722, 544275867, 916686588, 690549346, 475587686, 727022250, 650604682, 694413239, 829822056, 346750045, 515712924, 574896324, 537267966, 680715756, 405318929, 698617894, 598252439, 493844305, 561654898, 275021527, 27366070, 507791952, 236758098, 3621314, 217768284, 207176210, 948872981, 258901097, 463526323, 218694652, 781441061, 426403091, 287182707, 301536120, 355525063, 27109241, 977158103, 25400719, 907361551, 76067652, 680177866, 550334531, 262854993, 816180653, 408624737, 426979222, 652569580, 132904560, 214605207, 853874700, 436510627, 243084551, 744477607, 505620851, 351622269, 450502996, 812183062, 334672222, 80655723, 873234565, 558801979, 943899557, 243330203, 898309110, 355489965, 739662908, 871919508, 793418560, 937084539, 540442825, 279992916, 813521997, 224252725, 846807802, 97667462, 727101840, 577089397, 663247431, 672322792, 513161275, 517707688, 477466931, 885432504, 105604427, 700179534, 374625763, 710102641, 637143754, 509078501, 507944610, 699582225, 699426986, 427305354, 691579931, 48162701, 552689395, 140127099, 44469840, 859798071, 965833579, 121401988, 5991380, 394995396, 917786436, 262941698, 360722204, 637670716, 848746330, 254083261, 21865752, 262965667, 848162371, 585772463, 237714907, 625027033, 283282366, 645520067, 640659520, 703882511, 953747691, 698912972, 137181406, 222768065, 724696773, 787865788, 315457753, 897181930, 528851639, 944869670, 471336794, 382043419, 930672674, 857664033, 937985233, 680594136, 820153225, 576190483, 725726516, 541189371, 475111193, 128562652, 654005454, 235001028, 479637964, 444383674, 64986812, 194111693, 740423174, 495517674, 830908079, 575129298, 738774174, 412933269, 317392224, 438269026, 587174094, 106163303, 128440002, 561848600, 475693373, 172198143, 556363162, 664104810, 620134984, 91832540, 775858650, 703611648, 513534040, 750328963, 309736303, 121654908, 681511435, 775759252, 155713708, 920729521, 579891965, 545932017, 817840992, 396074513, 721796561, 268744848, 280420239, 565858607, 593826463, 133787231, 665835605, 917773989, 225503447, 939386741, 300009043, 904069960, 297113700, 218452811, 343821595, 617710070, 729368220, 312199970, 860548261, 708484334, 717226601, 493305976, 166107943, 368437257, 42178241, 67245808, 638217600, 112353513, 773654885, 106552006, 13095082, 639443142, 276348987, 249953947, 941783032, 937454552, 280120582, 128915091, 930807774, 275278864, 593884710, 450834527, 971226773, 360600843, 722323950, 864433795, 132864464, 438283852, 432422424, 476451163, 366884532, 465083434, 522118465, 992093678, 225337596, 638350671, 68254211, 653415523, 465370598, 104610268, 127931498, 567565243, 358697068, 982546783, 173633308, 661158808, 783403941, 179242631, 765607866, 927425122, 717367097, 403778684, 645096804, 666489106, 344706728, 567536589, 356209768, 197910700, 307857311, 629047232, 664152486, 449681745, 171944152, 778635493, 737809033, 225945196, 464711909, 539635085, 216482431, 310132981, 288972354, 12587729, 300731585, 881277843, 778510306, 629492641, 20488953, 389279630, 760033934, 521339848, 44827398, 98753250, 528682012, 850303299, 606456873, 310985608, 327922283, 518189374, 781504789, 430596209, 580743964, 201537036, 66240561, 216892199, 949208236, 648450625, 991759958, 682851397, 123761300, 138024329, 838263710, 632121450, 287827450, 854239173, 298773510, 197844173, 497303272, 787275997, 615470884, 29301378, 410470242, 827556303, 130183083, 359980258, 290088370, 512512521, 782053533, 646934382, 441796175, 564424358, 428067532, 404330383, 25763628, 543842907, 884890235, 111891494, 429327224, 267445390, 36165148, 461391906, 965120189, 899329871, 516273115, 868231051, 574653262, 656590044, 203414902, 260638163, 718784274, 771953351, 231805749, 414980166, 227127313, 242780055, 129572417, 885866866, 624347391, 411868679, 680458086, 18891738, 824125642, 61780152, 736771478, 327436650, 20460561, 940312595, 435433626, 232361716, 660279273, 902337553, 598029870, 130092027, 464146546, 132189384, 498250962, 143335477, 677095538, 122322693, 501410823, 488966432, 24701331, 796700479, 553655794, 473131675, 824885152, 129559393, 389514606, 978177070, 779894562, 526767090, 912150692, 3564975, 984395235, 832137502, 333536587, 554861526, 770954443, 812263181, 964072670, 549158847, 437014408, 959811851, 193898864, 66553921, 111310648, 37635031, 422495178, 1267976, 220953753, 160029588, 495071848, 414490539, 675176154, 41190988, 75063079, 78527425, 648464003, 836184266, 768558621, 523055089, 825384408, 251457278, 802658332, 76906832, 865834398, 790851014, 54380599, 177251801, 338716811, 409784561, 87490564, 534898305, 50379126, 905660617, 664541158, 186779861, 585783842, 417495359, 82335083, 971069357, 300068823, 687055942, 911755793, 685823383, 364902119, 837754448, 869182194, 851869403, 804481844, 869894905, 584412981, 363301412, 637290687, 472532773, 537880535, 6817605, 160158418, 599863883, 779689370, 376232112, 288438496, 489855425, 879051559, 205090660, 555580683, 977599423, 747502208, 899951826, 773658028, 830861814, 594185721, 246223684, 391635301, 558886030, 913862062, 421083356, 233072043, 805963007, 670606738, 166234910, 513524929, 780688767, 752499408, 226316407, 99803298, 266455194, 854913536, 746846472, 243380361, 116551013, 693913815, 291322765, 859981652, 110179745, 992426500, 396046095, 981922854, 308817468, 992119952, 191772453, 32611569, 868084580, 342047629, 417890622, 921092308, 198124377, 565704037, 633585242, 353232539, 899506237, 745583993, 645823243, 171758967, 29624318, 568145488, 637400737, 751989216, 840298263, 376776470, 885069999, 366311867, 422598308, 5508279, 211151472, 3518008, 375172589, 690162992, 696851746, 981712991, 648819021, 97525159, 47648011, 374575199, 416457230, 885323554, 4265748, 644711714, 609739289, 851800408, 433693436, 928301476, 389663048, 275255271, 227599668, 851081069, 148041745, 797997258, 985213944, 938164680, 434565586, 462423608, 323528714, 164498759, 394002472, 569990550, 558331102, 359729116, 204568678, 462026841, 93962144, 987984146, 484895011, 935201284, 736471142, 477932691, 636329402, 181796073, 498554067, 634204437, 828692161, 393130875, 100009453, 916121991, 62749540, 252334891, 165087365, 798250177, 95011610, 658626243, 480755453, 738577744, 310444056, 521452330, 592999686, 468394899, 736617310, 610498979, 612943267, 366993631, 862546570, 17951016, 790064185, 754155467, 538091725, 777945721, 624870066, 978852293, 631489850, 320335666, 31593561, 727988577, 781027069, 276152127, 784693293, 602695456, 371022678, 295574370, 522071061, 32099198, 401588837, 911140297, 804810930, 994083289, 248050966, 30866704, 898676818, 817504258, 101981787, 618114849, 413211769, 14178467, 140698057, 807317690, 362373326, 863182341, 345550551, 183565922, 895030413, 255278404, 907217031, 879651355, 634642215, 730393096, 988512818, 801079146, 866436747, 16410848, 155561041, 906662133, 309456312, 865028793, 54194983, 802799120, 210518327, 681119809, 756785139, 710266603, 568879867, 150468423, 848233027, 428747535, 922466530, 441886678, 937348972, 245879329, 607707990, 675334155, 589685544, 699331710, 283334007, 689999253, 424679942, 798165657, 344077470, 619465735, 919405968, 820989852, 169861542, 803635471, 147757805, 983541579, 8665958, 33141145, 314091164, 588296497, 921807097, 656340970, 260161982, 411911436, 601051316, 291186147, 266856594, 679916642, 840567625, 106597021, 160707411, 218554335, 477638376, 907675004, 733688303, 106647334, 970888183, 565480668, 392843648, 845040851, 52536636, 724120587, 282677805, 580986069, 848447821, 68397422, 636733694, 872307209, 486915544, 590234256, 368703101, 401349815, 255246433, 211682417, 802092425, 348533398, 492493936, 701779679, 287459525, 933081624, 530172487, 285879503, 204202546, 639042648, 300458454, 577932612, 333296101, 480684236, 427158922, 445715628, 90596498, 482036401, 26853555, 599944143, 304660591, 791805288, 610141770, 2547543, 662523453, 789766113, 595224518, 304058592, 749911800, 424158990, 369866764, 733250448, 24702422, 228296884, 285416973, 911850828, 244954781, 393765844, 780705610, 917450016, 591970886, 894107606, 382347866, 960652367, 175938699, 374122613, 963126214, 241663344, 475667724, 564346512, 795757165, 219622959, 354806504, 651037207, 656879999, 730318477, 731064679, 100668833, 80158702, 605477678, 112843526, 433935817, 355102069, 23263918, 408001344, 888106525, 919717069, 27867329, 699518132, 785029461, 435225195, 181117717, 7362147, 971544316, 476257355, 598911138, 859992855, 657525327, 406862911, 842770655, 605174041, 696295692, 722490813, 271291613, 452612378, 984588179, 552463781, 973930300, 347192714, 831174772, 338792926, 926658718, 136194008, 728135000, 248734077, 672525638, 157286212, 625949182, 840977279, 307852187, 184122026, 950064121, 267362244, 97703492, 779545718, 36077308, 521201538, 442395250, 160034086, 741340074, 830887934, 55289289, 463428633, 137442517, 484598268, 794082709, 181530995, 44614660, 353446952, 842067724, 92510571, 379321664, 489611123, 455887095, 872369624, 349536139, 550367488, 992450878, 764167381, 610260568, 930077428, 508594603, 882218283, 492385860, 137427308, 517565575, 226354785, 209070201, 397279403, 669934080, 83885990, 447218686, 978445284, 969824244, 143826859, 186457288, 232227875, 897993770, 186715696, 551513149, 685878572, 881984069, 291052371, 128662663, 756592875, 321649771, 262680980, 978966275, 425089033, 414721970, 38046003, 684787109, 447601355, 431686332, 427402691, 701190430, 679550538, 871779218, 745151729, 316367146, 12531654, 858149787, 380864967, 846967279, 460041162, 367161340, 194197318, 680148912, 255627152, 942937079, 991512153, 94722244, 537911494, 238737107, 76864945, 738382956, 919923301, 533173053, 4562390, 375390578, 845822725, 794771959, 397430348, 190088380, 26483312, 855103808, 816574997, 271651484, 214193781, 448561830, 659166558, 912169577, 881222711, 112461577, 91136697, 438034297, 578970167, 764383845, 989818514, 973486424, 550345525, 550113745, 95399766, 695006934, 8510998, 868442774, 844969229, 884799375, 398282147, 991558745, 432475077, 470532843, 265601940, 144927195, 696078058, 65266810, 112409476, 627709496, 25032535, 6122589, 3921096, 249662531, 546789039, 988658932, 173026746, 280687406, 787749787, 130206834, 798576721, 275821054, 865584157, 768099738, 131977952, 602909966, 595377425, 156660081, 982620523, 737421935, 974503484, 280302445, 876511646, 962560136, 690767146, 863115721, 249920229, 517885676, 807839609, 750229365, 805919304, 313801336, 371638316, 521694327, 207603667, 570180618, 786418210, 595243772, 330794721, 729982463, 755933912, 981409088, 357772989, 350470949, 317442162, 830670910, 969529044, 7380030, 832502845, 94699140, 929466928, 868162317, 487819111, 46112180, 220128340, 122159192, 14318914, 6900982, 714550145, 149877474, 436135112, 265287095, 216471097, 955305170, 479222186, 757401480, 569675057, 80479001, 869083095, 820498507, 390712218, 11340220, 807919310, 623082294, 968710133, 186506982, 400904779, 430212029, 475835303, 168705278, 897090587, 723083681, 160532094, 127762133, 109544493, 255061856, 992546939, 895374679, 45974608, 74844752, 106114422, 333079892, 582701308, 765538334, 977958442, 180473105, 244136098, 283861898, 40077381, 663488676, 257745356, 207675270, 794166075, 720128904, 811270022, 465963923, 384129335, 125526, 25087659, 621721147, 507559251, 800837299, 509044030, 855123315, 100838233, 864309947, 458299965, 823887656, 258691522, 530189461, 366246791, 726376303, 171991274, 802244650, 176159774, 906633701, 767938229, 912292637, 267282985, 794871267, 637157155, 758738202, 281012774, 110322484, 550560891, 153920061, 8929141, 304062873, 872086238, 2112991, 583879213, 887342839, 732177190, 42117337, 470851905, 719499773, 435997675, 679551338, 269136386, 774202279, 910301330, 656870988, 761107532, 142771154, 605022981, 727431809, 108021054, 769369443, 675141554, 361859825, 498122992, 916044195, 9985553, 434464950, 167576817, 317869762, 6666739, 484628538, 577467327, 67538332, 681807261, 518777609, 147247863, 318369613, 320666343, 41379596, 679304677, 121730718, 519320746, 446828420, 108389082, 226340833, 109146948, 10539797, 105261456, 807190738, 716405530, 90679838, 669208798, 381218255, 277638353, 113426630, 986200394, 6817061, 116957816, 798116365, 804951497, 82771417, 274248083, 637434665, 963837805, 104767126, 521688110, 207992644, 184528020, 880168610, 292105828, 462565159, 893413666, 987048684, 178939572, 311034654, 97950597, 92861577, 484809271, 466973628, 948079944, 825169323, 39595498, 25341561, 731225167, 7971826, 310244912, 843119184, 532264576, 868886913, 918568347, 68056849, 991053848, 538705966, 852456588, 260187044, 886564684, 298118217, 586591904, 226793674, 726223908, 395194684, 698734875, 520277038, 502845127, 22418028, 793644271, 229779211, 895969769, 45483793, 378784833, 789820707, 103841540, 882804781, 942817218, 950192936, 456592742, 168788250, 479880167, 445723838, 373708910, 699624610, 246325559, 684521209, 416713076, 872382716, 54672381, 143126141, 399130387, 721587971, 315905847, 639243274, 177090086, 358713472, 616177263, 207315429, 864630240, 67969160, 356657341, 546501647, 596294075, 623470249, 691424601, 138951796, 94475401, 975419886, 589735793, 701141964, 511715302, 825082194, 838321142, 613499778, 64557369, 336953194, 285398204, 317967785, 813178178, 661058942, 967558284, 606771084, 202786099, 456017525, 458510105, 892954292, 444818182, 389929750, 681389384, 752652221, 412708620, 927787735, 839359664, 996298805, 23533991, 512272015, 846429310, 630354788, 188954657, 374308777, 466894362, 322712851, 405420025, 334180702, 205039746, 164297336, 28721972, 218397376, 432018907, 347050705, 402698807, 682595137, 83305626, 556219542, 871214774, 163781368, 756570891, 916391537, 93283723, 46657910, 535064380, 65487798, 746355436, 191347526, 49369001, 446625102, 894756215, 111298355, 393259629, 39440153, 990928537, 851367258, 190555683, 922390639, 73568143, 310609857, 114044093, 814846277, 908516237, 948253455, 690058249, 211350443, 886976115, 940402753, 632771915, 252763431, 938245954, 367749372, 541623946, 409823032, 805367493, 514776135, 146175008, 624074422, 18567765, 917289009, 767760044, 538072587, 540026174, 750812894, 801080822, 549480431, 380432461, 412554448, 304582547, 62734604, 92862684, 837492344, 726683225, 272564832, 382406393, 848185153, 572428803, 149169980, 469076169, 907623008, 480880274, 968582281, 302497686, 362370729, 746838057, 287409648, 821251455, 938009060, 685390883, 330586700, 467124027, 494883743, 298146703, 265322675, 77049368, 502829687, 850167841, 259102150, 219454343, 72362565, 100658302, 744835584, 777769085, 328965558, 483580194, 21782712, 991356904, 239916041, 286759892, 961628695, 859420851, 817566180, 348081232, 288010000, 473808032, 772185457, 147462916, 522218708, 552302591, 875556430, 16824647, 821237091, 370991751, 639034459, 730665681, 584446410, 762859713, 759553647, 932765415, 350676275, 923022506, 458590179, 930973310, 741908379, 805648506, 426151361, 648174641, 515245923, 870648210, 26014080, 22498323, 608237031, 715344704, 254154867, 990016734, 391786278, 911360120, 90057114, 406380826, 179322924, 340070608, 103799613, 344726786, 370231239, 999486787, 851548538, 745347546, 695869214, 343068002, 577680145, 814980907, 274394061, 949530439, 221331984, 416954415, 501814843, 510525179, 242979819, 445383725, 215990227, 244430260, 384057063, 853082964, 17075160, 624981478, 488308309, 331833185, 137755164, 614376589, 770083754, 270718486, 451901455, 356291725, 610118134, 951107589, 87161119, 215298392, 368249306, 699826115, 80591074, 955242361, 632405964, 81865111, 734929277, 248018992, 578553820, 529186248, 617826644, 416563489, 121275918, 691691292, 282433447, 545272379, 811980387, 695545590, 191117363, 874661470, 40520756, 597300062, 914262840, 281521481, 513067583, 581990545, 381324079, 829634584, 112764833, 825887609, 782477501, 290965687, 230889734, 331549596, 821209610, 283514843, 976101737, 428784429, 288525239, 70041764, 230483226, 715512694, 719266065, 433080245, 298914345, 979632530, 139359018, 916375018, 986089826, 875506586, 317201325, 506102794, 358868316, 365580246, 896582478, 388184632, 263404785, 449511860, 282019773, 273969306, 320589558, 985701953, 936083299, 352574638, 482070630, 704976399, 638196146, 680017796, 537595290, 851755038, 656526520, 719215800, 419305835, 794106824, 999149969, 381533413, 339074639, 540846975, 239099488, 516339330, 881089881, 598046359, 393879010, 103036887, 135100054, 943573534, 384133219, 58572467, 507154747, 926918980, 624731297, 185468209, 582961308, 313380625, 944133358, 658021196, 863183442, 394253977, 462699717, 658560363, 159825016, 875515535, 127931283, 219294797, 779864582, 3143573, 845201338, 688010561, 440434604, 259893240, 113733001, 493949437, 931514638, 397343789, 398212362, 762989606, 353684960, 938511580, 863942140, 475082174, 723332268, 201464684, 900469989, 661762434, 659493793, 465953627, 589012154, 703220231, 66918752, 595439808, 907917908, 251515820, 239077580, 50814325, 963483022, 637680574, 152030544, 84623408, 499128468, 218922767, 711608339, 750525579, 306004955, 506471078, 308623673, 499375812, 604285430, 489243229, 495800932, 323057068, 618793614, 508419196, 703386049, 319430692, 319397708, 334670922, 314091517, 323321799, 457891080, 399548305, 240643983, 246158518, 139844742, 116166715, 716627755, 465525683, 497559202, 639922729, 518826480, 167692468, 660632745, 672592268, 53419655, 559482296, 434756145, 258170944, 756893145, 346402160, 996060750, 165775561, 386748977, 973240318, 614511342, 933957513, 162390279, 400942219, 520676223, 602848380, 455209322, 779442876, 24581696, 363701794, 622359036, 227868951, 658722164, 764017474, 414844405, 759556594, 445765779, 758803775, 507622564, 392259538, 226148895, 71014294, 385489486, 554277260, 178276729, 331121920, 718169792, 614033655, 763182756, 20496231, 721865060, 657631915, 338501902, 902149547, 504943649, 184647095, 9466010, 235526459, 665390991, 456832851, 85584027, 923654948, 817849657, 307265985, 769529360, 184419903, 239590506, 312076411, 385496213, 498292871, 413106995, 133732393, 366130088, 535164586, 465516436, 846092680, 773081423, 671764117, 418830949, 973275101, 137019646, 721511685, 422332747, 336984377, 597595102, 670524687, 915445180, 327530345, 685057355, 633969394, 371510260, 785188981, 235209887, 374249082, 594578015, 281632663, 636018206, 483044735, 221339043, 764990149, 647028937, 95438409, 177139767, 538130318, 234693248, 194266169, 453824399, 846219910, 391788536, 572422334, 459537362, 970863412, 152862275, 87672942, 117881465, 890855859, 873276704, 954584393, 597197928, 577451915, 863422104, 975559009, 843736499, 482758053, 858353149, 440979850, 527548516, 7826895, 624895622, 976799342, 869730151, 507234719, 927339116, 426208875, 881378440, 235770328, 80425348, 679320946, 109657840, 895566718, 875288411, 971110722, 361876227, 834416433, 89108973, 186989605, 780681382, 28621790, 124599180, 530022656, 660954560, 487444251, 376993519, 839801821, 290926339, 890219393, 358560703, 22641218, 472319322, 685887258, 558877830, 133777475, 481475132, 311972232, 485020560, 178393141, 107457876, 621746267, 805522720, 340844592, 443931778, 159235621, 602179541, 701279528, 793743989, 641680638, 641559301, 861991780, 618681923, 784357772, 320252054, 661270908, 427411707, 801415456, 826073677, 666443923, 25474699, 497629230, 314798937, 393638601, 747146839, 866590461, 518628521, 29148794, 778409637, 951026854, 31537657, 670137666, 844856087, 565615882, 723321808, 289457756, 109362603, 928032692, 409911704, 675120887, 857893694, 567644159, 512802566, 821526248, 909462110, 833680249, 653367183, 503657139, 893985069, 4795495, 730201374, 840300262, 589686895, 114656060, 9462272, 852911067, 516609337, 560491148, 331179145, 503791916, 984373564, 25631242, 811421057, 33022969, 228416760, 561257853, 770905197, 919269343, 880087157, 612343519, 799294814, 962468763, 386240357, 809536758, 913675190, 82915917, 772245514, 16613786, 39426731, 421928418, 892205469, 694184486, 199989344, 664711522, 492114218, 533266135, 976641254, 198450951, 509064592, 297765089, 779679828, 151323874, 338229337, 316044756, 347233701, 338775949, 525449709, 471128349, 165970209, 895524550, 316377467, 334513182, 592217911, 724347031, 451562485, 226286713, 304933131, 770025968, 120011857, 884388151, 297731104, 793624727, 404633967, 171585120, 295016152, 901171333, 447566468, 657389730, 272421694, 446604613, 888715163, 686982250, 236018582, 768747890, 754427934, 177448958, 203487903, 381527447, 145005095, 710406550, 900922915, 248418143, 979451262, 319422696, 132281935, 266833980, 892861045, 700439483, 683282529, 683810560, 815131118, 814047867, 538445447, 965017260, 756568745, 173630784, 982503169, 732917863, 251754395, 604756650, 936585541, 152472594, 619613700, 411232815, 60237169, 618229305, 194067977, 564512889, 322372681, 809116037, 626301659, 141804528, 313405648, 43562580, 702640798, 176139020, 473185006, 399789158, 77315250, 587944530, 991596040, 795858786, 283209680, 99585728, 968785498, 291099573, 306245221, 664136147, 217532797, 308460345, 358178322, 390542347, 971198694, 356983440, 449170942, 834321855, 410460067, 927961374, 910278484, 798925182, 987278862, 821649892, 724276171, 535818592, 271234917, 35431884, 258436645, 731521076, 215858930, 923072510, 148865698, 849881965, 909155961, 417786593, 642327422, 372852122, 725590391, 806004744, 743136952, 689261696, 926163496, 155461968, 886750653, 443617717, 872082461, 894984342, 466195481, 332445695, 281455236, 464272629, 40492141, 254366111, 957720292, 862076940, 590082758, 644299236, 272389128, 645164442, 165660634, 732490782, 854447608, 45120507, 184135140, 573342439, 889830559, 444064213, 189535693, 511752800, 162371925, 712976184, 37685342, 577835978, 936048614, 53585335, 752972765, 871524330, 771082834, 173953188, 571950551, 556884443, 382842806, 869149543, 51479837, 722772515, 241929905, 228012093, 26893718, 393568960, 704773367, 758251356, 946726336, 125230878, 790933824, 102982183, 678496528, 404488267, 114945532, 826140429, 377199163, 974278452, 547379621, 972163886, 529955641, 954900849, 640317383, 362581886, 976366702, 161406748, 709506831, 465186497, 72669564, 736570024, 848972609, 363908436, 220219936, 281328683, 150853825, 377477296, 593296856, 447289642, 44544499, 771127935, 58346288, 809207841, 952114413, 753297865, 752338228, 164724545, 294253395, 549354656, 222654357, 703494745, 369928385, 578550761, 779652257, 35567207, 929292764, 227463502, 952363846, 760652858, 841021761, 631684552, 786711797, 61230976, 76927106, 781024827, 305280240, 37119608, 678398547, 939440863, 29465386, 743218133, 981456835, 53823537, 459564701, 138379351, 497335354, 287614205, 182364340, 553363278, 813281662, 234590247, 771239140, 174139613, 791649023, 284781874, 145135864, 938543124, 753636917, 762033127, 493409404, 732207810, 628323700, 200936350, 579308100, 922737923, 541739267, 230098819, 728928382, 526501501, 226273674, 758771938, 451862268, 817328493, 32982710, 166301073, 416005185, 944382472, 432404955, 896698236, 448825163, 502960284, 564773546, 447307636, 715887450, 746444735, 981502044, 623974732, 42329437, 219771746, 426980951, 675269512, 485136719, 286766630, 737911851, 814363575, 267823624, 192841247, 596497932, 625150027, 606162299, 112947565, 705234078, 647280173, 455057594, 9489015, 27671366, 479513853, 770577772, 653429357, 193003474, 99253163, 356469971, 412542737, 247630833, 754310131, 670604724, 959997948, 245627607, 322682553, 459646831, 466238872, 361733348, 882773310, 955007054, 98017299, 1446804, 178476978, 900725798, 32878459, 826369594, 323368735, 354058316, 97285847, 688470607, 420217062, 615850629, 662740165, 315966771, 292244686, 3568966, 360992955, 887547740, 132402962, 261888854, 412349890, 215089089, 847004371, 90154240, 225359824, 294210164, 918068772, 143271942, 881014340, 686903309, 189395866, 1630732, 132785032, 937700037, 19104664, 644779560, 487930571, 820559099, 626371921, 945291513, 103021506, 55273960, 346419653, 748756733, 487890500, 772043456, 842818597, 589266779, 368413026, 721901535, 282216918, 114098724, 971709920, 566502117, 930892992, 802897581, 8086322, 843593745, 224960156, 854371102, 145094560, 443410503, 483238131, 537816407, 885952108, 209583387, 352584793, 400307582, 524089952, 672788038, 949723864, 406323646, 748711546, 724135094, 739054895, 48961690, 220654535, 120723925, 369162099, 604977528, 908726354, 552647259, 833058237, 170043566, 618281091, 562481210, 713092882, 420036979, 47696057, 238681659, 850715074, 820156087, 775050615, 59466250, 487941365, 573575010, 97013490, 804905313, 162035649, 384616643, 706386277, 740343000, 909801648, 366636493, 971824042, 939819254, 383858576, 41933223, 434345068, 35627830, 420878974, 505750522, 501271782, 888957476, 657924066, 862522064, 696696344, 456620569, 188151819, 317553232, 117856457, 736669610, 228657294, 129342759, 449437992, 879658454, 836032277, 430951765, 751036166, 536510807, 418207197, 273694955, 375545295, 89230756, 576499536, 494876059, 896832147, 714785581, 766133995, 93417732, 448005768, 983281562, 787550188, 435571479, 853769629, 117779713, 613491359, 721937405, 278753632, 478479048, 538600092, 482864297, 788529883, 863776105, 183386108, 469516689, 515260155, 892774231, 375766772, 7432613, 308953139, 990173408, 285746126, 845513951, 934881187, 394801139, 778931010, 52555128, 897126789, 972607432, 346807412, 814093872, 3558959, 902621567, 398534178, 710562957, 564246839, 473353810, 326266446, 468323041, 718649795, 478233183, 555958733, 615529465, 844923228, 874085037, 859042190, 272812189, 278624398, 128157542, 466521155, 652204146, 156849759, 695347439, 890738231, 848184647, 884608657, 750689479, 142734872, 477794563, 655998080, 267348423, 141382030, 592972697, 318586976, 841725525, 613163927, 478373561, 768061498, 306537301, 745818906, 704238036, 35170304, 718045662, 308130588, 938057060, 145550739, 495190083, 578734693, 94747393, 434933079, 970767467, 156779183, 695221976, 779106618, 139683918, 89026022, 150863892, 323281695, 492511262, 222450917, 323783018, 863030212, 885710595, 228560193, 649546435, 238229650, 537983697, 817758459, 67354672, 674289070, 821977494, 427290375, 183740893, 592307069, 838465998, 892493693, 880218082, 709003999, 93735787, 522675061, 43171774, 477289244, 671471914, 153499788, 717484738, 80835228, 720514738, 976244638, 36752814, 127449427, 395222237, 731867422, 7919279, 255763534, 663625576, 784807324, 955379794, 357648329, 884138681, 784551508, 410187927, 695905223, 986350322, 63426320, 717713543, 524937174, 632613350, 758613589, 304099351, 660445119, 456208575, 330776984, 849025897, 530710178, 389701476, 600307398, 495857306, 679022227, 159667985, 73780096, 980362098, 358984535, 438350712, 704893508, 830397114, 116527401, 918397664, 577499186, 622486359, 873239695, 361657356, 518549088, 155846305, 219632345, 337517133, 282226753, 461247509, 6885132, 66562338, 147374436, 771725304, 103264168, 826314837, 949276319, 362876600, 510359086, 221406573, 733798471, 20821273, 752895239, 556182958, 119657439, 33275080, 583706551, 75392656, 394346826, 557546873, 883958898, 884527777, 404699669, 58744526, 573587343, 687272352, 453445347, 966238055, 577904557, 623386407, 201172114, 990867534, 542023739, 394798048, 35833862, 794987393, 681610326, 842479075, 358042337, 952783949, 957996555, 63477643, 104233239, 298913779, 795075497, 199499454, 146509436, 45455927, 14970160, 434980017, 251088739, 343745115, 601973298, 585644347, 982791583, 361280185, 623648418, 234110168, 793632526, 908884775, 31476606, 898655721, 525722884, 495410566, 150318000, 295598687, 776262356, 573442592, 860813942, 844170921, 749549701, 17432005, 299109124, 267856965, 307443312, 911618743, 548324334, 610519302, 577548758, 267186903, 144161536, 579753165, 386925029, 267803827, 741514941, 298228311, 972985765, 856176704, 368722411, 477632208, 471607062, 568970998, 388955953, 413988014, 546197977, 592987192, 867890942, 242343593, 767703209, 709444538, 359818743, 115778781, 687923124, 508384625, 520963768, 465740029, 482498138, 990014489, 259317605, 470419324, 454627814, 888367793, 965631525, 6428179, 274099801, 609378277, 983267586, 504846854, 661193813, 837377644, 128602693, 230772084, 972144732, 824238062, 608199167, 585174727, 694222814, 897316075, 604333568, 144365992, 128034914, 222475852, 957234885, 751456466, 271886818, 104081651, 110112429, 23377827, 732891202, 29497639, 582686190, 657974581, 965115852, 888020801, 785217580, 778975843, 920772200, 408451966, 445260546, 681129971, 856484669, 430871902, 439688975, 927674433, 17398105, 431771155, 494288815, 622291860, 975424374, 185654443, 860668006, 709994083, 247716947, 374263597, 346313944, 576986609, 989521489, 100166572, 896398883, 712201483, 62775698, 774157909, 815193205, 275173169, 571071146, 202197836, 248231645, 321758305, 656425367, 857443748, 491557182, 342818951, 393049423, 758289196, 583495191, 24092835, 648946144, 527933736, 74171861, 722164275, 536301948, 604333152, 374841734, 930353067, 229688770, 971695875, 473689652, 62733344, 97397920, 586892330, 672630018, 877688726, 345881835, 541630586, 292842999, 697044731, 613924903, 384657229, 730518630, 466013490, 265497920, 539266071, 835402055, 99048699, 217511961, 388579550, 593844230, 974862361, 37520031, 163334738, 478083432, 866472869, 978788826, 753962123, 369095809, 775642533, 201208402, 547241294, 607966772, 31038265, 181482892, 338906553, 99253681, 850672701, 172974830, 885599313, 240004600, 383562200, 380705618, 958229177, 238834068, 781430420, 681515890, 574105558, 587935108, 976641016, 369589366, 611509680, 597060700, 983749622, 659505561, 596854469, 872037008, 752144508, 645240488, 228743906, 472197764, 664685114, 75182261, 715221353, 517795478, 733980605, 94711816, 22825312, 991757408, 113618975, 510970151, 201436640, 760070997, 356136135, 119087909, 728046808, 8760978, 228560174, 917253060, 776807068, 305953917, 897798222, 998443461, 499539419, 65569746, 913638635, 67291603, 845978333, 277188269, 485698765, 60387605, 984974923, 42377636, 786640071, 968823523, 692397460, 711023021, 673523842, 199786670, 747322880, 448533363, 946295854, 956369708, 896503864, 757462287, 507537609, 981345845, 796017216, 542626788, 926630528, 54596548, 135242165, 20901380, 863890381, 744157011, 159624689, 175598331, 300441711, 971408203, 110534112, 431243276, 645331541, 602848200, 896299561, 323476907, 56165970, 683223539, 380233270, 69506734, 30022816, 528594184, 825855452, 732244375, 449082769, 451618894, 51107680, 360380744, 506102321, 366555209, 748608940, 625838480, 865914210, 464007151, 931216776, 916603640, 362085585, 307766384, 300468559, 493788504, 320256175, 152275220, 938507240, 246384803, 401493070, 236117137, 808940098, 488267573, 810647845, 376791520, 338857320, 371481789, 460184354, 753814967, 300569339, 742816438, 860706434, 154667207, 1090452, 824890575, 971382428, 850798002, 266044698, 482378205, 779590001, 884672021, 722558055, 817511014, 945552405, 618859187, 278225671, 651940041, 370281153, 925772006, 949014744, 425187004, 320283046, 854213357, 123620996, 727876434, 566204377, 508125238, 930377710, 704481227, 656295127, 597103905, 631067827, 652396527, 306172439, 284894943, 327010131, 900238280, 37934175, 899813308, 812187043, 382275485, 450940583, 192397563, 54791348, 162282907, 352168858, 646052568, 524502310, 993599455, 618245735, 36579571, 638600680, 681109464, 944676067, 399322942, 435204567, 743556310, 438427297, 989904106, 427171542, 934294425, 421002062, 223805420, 55724708, 990045779, 688928730, 908067807, 969719168, 244268511, 517980968, 477347474, 6272999, 101163619, 969826239, 563161774, 468762770, 172908578, 469599895, 631079711, 801339653, 679605593, 341542662, 763042229, 19752450, 838222544, 505602421, 30223585, 164908585, 1835264, 16584340, 694260371, 632256408, 878800483, 528478033, 741651287, 483911650, 252092509, 955537198, 75728316, 860741091, 410025604, 561590590, 448522299, 229641433, 831818938, 854664773, 402900878, 719043613, 284005897, 439504827, 321241490, 869278804, 414435269, 225997420, 851958233, 688094097, 66392819, 687681629, 937236613, 84364391, 465939120, 880533970, 685206057, 244187284, 502752732, 89572177, 168806495, 396351124, 547783015, 372637225, 867703057, 794369428, 357447313, 321191211, 593520631, 970593744, 16466697, 909305570, 701385914, 467227165, 121537293, 930552900, 845448039, 397714171, 42624577, 489458841, 27432022, 857110251, 718389774, 14893785, 724222793, 648176111, 24898899, 377079347, 319769874, 711896613, 474592654, 544613262, 402933611, 876853234, 729090766, 13390978, 545113847, 698105783, 266755191, 945357708, 976441454, 523167697, 244803572, 714548945, 761096543, 878905752, 33652876, 986913493, 466853737, 229106853, 683084926, 718499998, 778692866, 117243099, 684506618, 153345563, 593715110, 219802998, 574399415, 852474880, 137347507, 395356511, 872994541, 234537369, 405255220, 370516685, 894385132, 314919993, 139388997, 202051083, 566494257, 362806145, 275944027, 903718088, 223269743, 593676842, 409875240, 266890064, 954743263, 131177212, 375795383, 393217301, 14334261, 253943, 243410402, 70021669, 653019962, 947791479, 844210296, 942376539, 987460123, 320567859, 842670250, 420040256, 749870788, 500885212, 656368390, 296742091, 998011681, 300254046, 203041286, 422548960, 362156105, 374696068, 700126777, 396105639, 107543727, 996496400, 860697512, 160618180, 621195983, 861934674, 614584769, 992739385, 132413480, 74060255, 167353934, 509855069, 635941754, 193689556, 205744475, 283443181, 918285068, 284061219, 872741583, 474673680, 386680598, 176323625, 165735674, 49167066, 921019467, 909820097, 662276521, 270305041, 572270073, 358003960, 23570494, 307048078, 762520383, 656181628, 122613652, 139706913, 971960147, 861024235, 205593721, 190814322, 585910722, 975820212, 60013359, 743242843, 407624848, 341703805, 928114757, 993202082, 939337128, 216625635, 692635927, 905257665, 685056171, 663311367, 69015624, 290830943, 243640749, 613027607, 851316576, 617159940, 751574082, 165854906, 643034729, 126241001, 124179082, 421910688, 913661130, 915426342, 201177239, 830239507, 454180787, 340032463, 772265035, 337435614, 492022039, 963474952, 785296692, 917809070, 230285437, 752452154, 157433557, 641576930, 392520831, 178675770, 615832996, 972109245, 290496655, 592574604, 711566818, 453976527, 394743426, 312749889, 953072649, 439916787, 655457104, 469798958, 652507290, 986138993, 830941086, 868674135, 283592490, 308204879, 626628617, 647956234, 350070017, 311268507, 549419795, 950231647, 100702003, 234048018, 296992616, 859543006, 412086642, 652380563, 68527126, 146743684, 258949800, 283051874, 298084961, 807548752, 183360858, 430380193, 533312294, 422521633, 486521225, 632664384, 468647859, 961892799, 802884232, 198632121, 174597893, 206891862, 661817911, 938341879, 511905235, 136777228, 518930368, 492023877, 21092494, 505777299, 334282892, 754965224, 774109097, 142527948, 452478340, 611275307, 76267052, 294424583, 635868027, 189473034, 203464234, 208260502, 914337295, 5449502, 583069984, 573807798, 726172174, 392404392, 855734542, 7869854, 755519607, 775580068, 510748028, 647446358, 456481592, 843669909, 176830206, 295859048, 462956720, 534470402, 750033435, 206367618, 222587521, 487476397, 415884702, 507757020, 664879180, 372851707, 485874958, 3132555, 886652207, 673694439, 530102341, 385505060, 322196234, 592969233, 61785386, 384096189, 664357339, 348919328, 618720769, 629365131, 832050663, 626659191, 349256044, 140534488, 543667314, 508629321, 555038296, 170753012, 267021147, 455077219, 496550364, 792327848, 255846653, 481392200, 984491996, 492218647, 910735103, 968718123, 558737048, 570631527, 50994189, 545894813, 403129445, 756367192, 492253301, 177483970, 408874400, 602030164, 984811021, 368810601, 561018121, 132167344, 817302017, 465556088, 829557570, 932290042, 244267177, 346727037, 380062167, 239325289, 303103116, 521223271, 284444581, 513565801, 287512098, 472119429, 367487723, 771996688, 479891691, 73211156, 152568680, 39787939, 763036262, 853492225, 675895321, 87881748, 202653840, 212707842, 956819998, 486974493, 384874939, 749284902, 463418928, 494021680, 672741344, 67580418, 445660891, 251464638, 452393416, 77876388, 881359362, 384439481, 348070830, 514867739, 910812855, 660199634, 298611134, 497918205, 438296056, 674247040, 752838624, 471629878, 81702702, 292354901, 502792181, 344784832, 387195789, 850122428, 89206526, 949842912, 891268554, 540118076, 989612297, 103971152, 512095042, 767556296, 644371148, 754101087, 437677831, 717969450, 187851377, 294833269, 139660003, 48728479, 999840279, 63548856, 915623868, 298153315, 974993823, 453010404, 500520620, 599312869, 458952404, 498508364, 472966103, 518128159, 646419195, 785731024, 77202214, 760710272, 400868146, 88657733, 685427853, 257432335, 916960739, 359749806, 611097095, 723516200, 259673093, 920575067, 643303185, 182591561, 640971636, 427628730, 407385389, 953361452, 244104799, 847241347, 291816677, 652541607, 765683099, 443134757, 695859808, 142338581, 470603016, 313594505, 977848442, 471309141, 290428986, 535053736, 791525051, 293151538, 396057400, 529145106, 666514822, 449865677, 893149142, 76144955, 614155641, 267575372, 716691416, 269183911, 751447630, 284041007, 652882141, 314515696, 376473650, 344700136, 151249058, 751954196, 333100634, 411992149, 604969978, 934509525, 829854323, 191186467, 454693521, 621730992, 235739107, 879499552, 630455782, 132313123, 673888783, 615156957, 585011106, 251385303, 72040097, 363686528, 381970279, 254590075, 616888953, 708579000, 733065862, 799933954, 692170412, 985910718, 907052423, 672446141, 716448470, 9869559, 487965908, 812209174, 704298711, 414554429, 473960516, 910938228, 898188637, 278631992, 483775364, 282478176, 222183301, 25297205, 904014607, 204635941, 252588634, 618166752, 780671141, 971922329, 949713118, 76320039, 410294617, 375130302, 557238195, 713405573, 575433396, 388398939, 876707550, 677676365, 15554012, 763371288, 785108460, 915875788, 799029392, 562226274, 579388245, 967283742, 849591072, 901410152, 5953949, 67953386, 194549034, 21398098, 622841474, 195733792, 608245585, 491573872, 3460793, 638416968, 492503384, 871601369, 898206710, 503659820, 996756683, 926938907, 118536847, 307411702, 671366589, 811465578, 74475747, 159890309, 396577112, 57130728, 972361100, 63940840, 822622594, 109919645, 23410699, 419883261, 548053789, 958277403, 629143331, 905016839, 425418708, 782029291, 836574119, 772547494, 716989422, 857606219, 738930594, 308460088, 649878024, 430001391, 701273509, 283577497, 695627865, 550675343, 81652581, 941764865, 961527467, 359765343, 191756171, 289633135, 73509928, 887642154, 537446908, 317299400, 296745540, 612052634, 239488767, 909721054, 234392788, 482634572, 487762863, 600957408, 47036947, 521467446, 313984964, 257297609, 665439591, 153886627, 850507068, 335389923, 841709430, 159072311, 695116265, 132488113, 729560082, 843079370, 375828700, 993581180, 491373926, 463177512, 522804816, 787863279, 667741911, 671414075, 9991723, 894955753, 603781876, 952050326, 719587075, 326995628, 715935676, 990857063, 467330452, 381183594, 740449363, 865301390, 773733751, 526728632, 853289632, 594028613, 754009822, 326121524, 565378752, 22461772, 194193672, 440626417, 476382425, 111431510, 616707695, 468775019, 475700003, 147275721, 628489654, 144745858, 794381849, 143437926, 317551810, 220158888, 20023789, 236314163, 989294734, 837990755, 843403758, 151452208, 113948040, 193410917, 35548436, 710920011, 790466414, 578326703, 115621592, 501656187, 315639071, 899861924, 780672483, 709471069, 891094977, 582907908, 960301654, 750379587, 750329387, 827004414, 522715315, 490667359, 860362697, 85722053, 790424065, 863684771, 494378558, 570643667, 993854808, 384299481, 392225670, 831512811, 945943746, 461812251, 529539555, 749339896, 542726492, 3182055, 901330116, 274019928, 238078133, 574982164, 301536026, 888615546, 499460388, 360809908, 483986403, 524724137, 377709658, 866702841, 500472399, 672149531, 139120967, 310363096, 425955060, 348320867, 190041205, 97689705, 729143696, 317597030, 469235905, 546304699, 718747985, 20499054, 423650821, 698388599, 578095732, 520423204, 705887409, 139585969, 371880116, 431173003, 311886281, 968501915, 447743037, 40101232, 313689773, 589503381, 78397679, 940582346, 602317970, 182120381, 556763333, 830400453, 556678000, 241180470, 238729133, 394041900, 33446825, 896078686, 526048645, 409837013, 111837481, 34832563, 102240508, 656675663, 978968185, 773644268, 212329182, 960204282, 725916795, 6844440, 558054729, 719029253, 111115427, 528074764, 75244612, 428022979, 426964245, 306099774, 841018848, 289684018, 40129108, 19747878, 28347264, 954521052, 489135164, 446922364, 741745648, 875832517, 865961047, 190668414, 357209661, 961396472, 530242029, 402951340, 704991658, 476319894, 762270144, 840045085, 300398659, 648056908, 824189564, 87937299, 785897064, 50959684, 907013334, 539473830, 178560650, 491613226, 477443776, 292485623, 973278698, 155706116, 281234147, 284057220, 707128971, 781970489, 480208045, 344185875, 238162548, 528648849, 892613203, 606119495, 638751813, 914694249, 225201731, 713370199, 254646276, 628773034, 836439714, 290404801, 915227671, 721053196, 272607306, 389523861, 531120227, 280543797, 500162281, 405071377, 627554379, 833566521, 814816409, 259209838, 15463240, 144449887, 86521977, 24819118, 760203840, 668488541, 163871356, 334991005, 769400509, 350149317, 643903598, 103786149, 540204047, 335058078, 695012700, 920224117, 225969531, 749496306, 134737063, 414686551, 499384652, 568997584, 981094729, 877394002, 721047904, 252708713, 280958055, 414685103, 968542238, 333111225, 774578323, 616286163, 606784208, 164429160, 459009649, 882455703, 391473068, 183512354, 405185368, 911939230, 29013854, 430533409, 276853689, 886148431, 196970250, 767105826, 985009631, 547341828, 940016528, 362082858, 346964655, 432907865, 63521823, 395523453, 295454982, 737560176, 120859052, 501874116, 601461934, 358334820, 918091002, 928021145, 222617777, 309508300, 904863823, 689698635, 416245087, 882866072, 429214330, 301889189, 136921610, 764310925, 905112537, 21141538, 487202134, 227325915, 375426791, 234999850, 959277900, 82471308, 757984131, 763004833, 13663005, 998663310, 283936066, 487602651, 780235805, 640196003, 23111675, 107036684, 78275669, 870982991, 627691773, 364847970, 4482802, 101245831, 586662208, 379215959, 723720729, 877123119, 273086523, 839251202, 776886235, 644799129, 800785765, 575075159, 789678676, 894097913, 472883628, 227131420, 831968333, 446326901, 618054882, 416138324, 603226193, 823923357, 819464591, 758716338, 333669576, 60090455, 770064393, 586461332, 174823544, 391386703, 443927621, 185484745, 348410923, 111434050, 463972955, 181787976, 661643698, 542296249, 103951102, 367644272, 15423011, 215434293, 973970425, 793514728, 978790306, 875013010, 135722184, 505461421, 540848702, 886809095, 549744798, 5322212, 964859955, 500163673, 192134440, 297851696, 233569867, 819195885, 269113164, 323749292, 594657342, 767350855, 539272885, 27469050, 605113655, 61177120, 803921492, 393192907, 677571824, 253666927, 753332747, 460203105, 347330548, 585356511, 750413947, 671800938, 491139257, 595882591, 750885218, 660030658, 272819085, 656166214, 432087430, 464585977, 357793435, 10784281, 703183910, 203835400, 264966305, 283107011, 256472618, 804887378, 615854988, 408713312, 839948505, 335710948, 493344652, 578778221, 13389406, 23118014, 500788223, 180559633, 934452548, 844557572, 289428260, 981803764, 48683000, 23756059, 329713461, 972364698, 979797294, 412749844, 439160488, 449082380, 728537107, 521218475, 417629958, 40685151, 539736873, 381703290, 972148592, 466162669, 273903358, 882831115, 822941818, 613616531, 389159506, 374623590, 661572291, 937629984, 129359022, 374964021, 23742733, 395202341, 889831891, 706398744, 724258172, 917421255, 798016574, 363220946, 383217636, 545539839, 246783507, 59785412, 181783871, 453530806, 679472694, 453200008, 442760707, 425145850, 273517367, 43731953, 161920275, 924206779, 223788943, 421117142, 511325125, 883938109, 558137568, 173738177, 880033802, 232425800, 852989106, 428779397, 984363186, 611668086, 372361140, 270319705, 859326168, 749131269, 388132211, 658581205, 622628683, 629800783, 903404769, 573233870, 868895894, 669545198, 903639363, 792014145, 742890725, 186998221, 448636381, 67599799, 667321631, 480558801, 863035816, 429888338, 723621433, 62583085, 776264398, 412399914, 481815635, 956344370, 614300472, 686812631, 244675457, 329832285, 28848103, 2697511, 510411732, 614676878, 485659320, 372851197, 568752910, 333836008, 607777797, 470896496, 802293286, 557915729, 930345878, 321232213, 296449394, 67911068, 246181752, 42411462, 262877732, 134945560, 462489657, 439824502, 674209842, 983973778, 531096174, 804493070, 249574385, 278414950, 783307514, 381884998, 64837249, 841102165, 422399511, 775574194, 112094155, 203499190, 872780125, 494846308, 334655173, 137179058, 498602896, 752801950, 512663249, 821985164, 234110700, 721829057, 622433146, 95105957, 755537437, 419916077, 553233387, 442430650, 99406790, 4627040, 550710361, 135347745, 325234493, 631747959, 183383192, 866430442, 800386396, 201181025, 458897049, 553652852, 502530447, 412158448, 563084317, 356660941, 160683814, 890587031, 707807103, 424769895, 10455852, 633215192, 319325081, 361665019, 825266428, 896140693, 322339646, 928509258, 158839937, 415794452, 144434166, 727726258, 766101843, 59874021, 705644100, 708860815, 55193581, 612020180, 813921614, 447402477, 840111068, 8435236, 135725863, 903346899, 590654988, 91045802, 266210650, 909919644, 699800007, 769651359, 602710946, 558792696, 71671666, 957695728, 866701099, 447394867, 483336, 195761235, 435105560, 540147693, 788964356, 91109948, 36875258, 169761456, 443270184, 609623679, 220050899, 185946429, 501443802, 615701831, 636867551, 32643289, 93705400, 929186296, 28032229, 821433066, 227229689, 826864543, 670430686, 517425554, 737466506, 527370218, 503957102, 208726442, 887045003, 329996220, 210698842, 461655647, 967317415, 958075907, 308955279, 432590028, 523316196, 322638126, 282814621, 156038067, 486019341, 429137252, 980207372, 326786466, 397178056, 880829785, 26523394, 120677657, 129647657, 32830634, 817485684, 887437757, 980189051, 438479269, 832906596, 798423720, 500712799, 895875356, 923019807, 278276477, 769909500, 312002037, 465025970, 419952408, 13692192, 646526157, 435136877, 216962664, 864598415, 68646405, 900055470, 652293355, 602678642, 823218134, 395625850, 469554345, 146901696, 117750671, 462022225, 549344634, 830019744, 305855888, 90900185, 636024393, 313561485, 842200746, 2879340, 701561655, 744968231, 831358278, 827454463, 439567426, 19397510, 629875032, 917938469, 521842365, 152750838, 836817682, 226635833, 881132469, 960975306, 514066895, 231120891, 954917556, 380605781, 260908764, 218490278, 600785190, 622445009, 646351565, 679514908, 164810572, 766419095, 696535552, 167281927, 788663709, 651804001, 185100394, 3738519, 89966964, 275029260, 432223930, 898355817, 976593874, 273287012, 852005970, 137865349, 824122073, 720855479, 360609288, 186586180, 762314393, 130673517, 996920400, 230527787, 566059957, 339424855, 706619899, 176843973, 157684059, 374759536, 802611275, 603051562, 13778683, 533816399, 683004118, 247266233, 184940034, 903724584, 485187961, 874504080, 87990282, 747018900, 370268122, 690164203, 451729099, 447812476, 771830200, 926367103, 37385803, 430343206, 28242169, 457964487, 364871157, 855353117, 399940797, 154357357, 336179495, 216295293, 319437115, 863759272, 407491591, 465859831, 475203322, 559261707, 337910605, 895264137, 59954524, 254131850, 280201598, 144980457, 532369901, 350415189, 860438782, 1954678, 34323965, 240298892, 404441857, 60190787, 670955762, 811279885, 43792209, 49089169, 817206426, 446286862, 716190483, 168741772, 94598070, 526388976, 172319375, 271413000, 199310825, 188945369, 880401288, 737680213, 979679965, 19391133, 75173092, 854816147, 470012780, 172864703, 973220799, 153420212, 566755961, 505233305, 782210771, 95782702, 917897101, 130881277, 628110684, 758403751, 351144684, 447552044, 413649586, 326598576, 832896137, 69463496, 911695849, 476449402, 830811978, 764806830, 141003442, 809169736, 777397059, 782826170, 984777853, 17578294, 765047854, 121613960, 839848438, 503945392, 41504949, 219819189, 476232242, 670795687, 678679635, 81140062, 612946389, 641882244, 413011688, 220171227, 771224989, 83300200, 481501492, 808395990, 74941182, 964472655, 37243715, 41678873, 298193070, 433512888, 655846685, 960522658, 657856250, 198710843, 485595375, 355586750, 575361906, 695458738, 356765224, 792475192, 325582206, 259811838, 117291444, 275375360, 310204636, 589661442, 966285854, 323334208, 129498971, 24550623, 759226110, 834147855, 917061774, 113510266, 527201183, 625138559, 428037626, 910365879, 526393685, 824402330, 552599085, 189931802, 415408109, 914676730, 837478711, 920598959, 373991286, 154607935, 785244720, 750680878, 545966531, 167952613, 157640710, 568939201, 650596468, 823646521, 580687576, 709153103, 975419200, 874675972, 523564734, 101175410, 534283755, 572737346, 806838446, 178350757, 169228671, 155348015, 47779969, 338575448, 530070372, 891973254, 278615417, 400030371, 269450489, 670394984, 20163084, 242078248, 207144502, 147319471, 941370069, 454363049, 190542134, 979618731, 212589466, 491141458, 445880942, 812125384, 551615027, 38733742, 148564997, 615465136, 881131607, 834719791, 311348816, 344927814, 797332174, 697269099, 195152230, 152922706, 361732648, 21761433, 251596344, 973631064, 384046530, 548611002, 63974156, 729465166, 204767910, 263712917, 682757653, 231127666, 720055353, 79571776, 455251113, 978194383, 697340135, 598860348, 897341527, 545388661, 584347624, 854569435, 443622226, 296552712, 806485375, 827162607, 912411972, 190629017, 466361239, 78082596, 878574115, 927236430, 133022926, 665059116, 442395640, 188667982, 246938116, 137008176, 435682134, 515911203, 603109111, 985901192, 205508082, 137609386, 579053645, 707007682, 460427423, 668067486, 54163938, 50869429, 597776765, 60279092, 613562214, 539491146, 426967456, 694383723, 104153965, 194859455, 321633536, 216716175, 723946489, 598034580, 653682552, 598484205, 470902840, 384482997, 690065459, 747345797, 431946397, 210638055, 639460920, 912442193, 862410032, 650109461, 284290518, 180011320, 81229705, 179074915, 129200230, 547019930, 652302919, 462120958, 334859530, 971246399, 365742247, 607740651, 876928927, 814028476, 253226085, 40454651, 975513980, 185146874, 666068442, 142127351, 15002703, 561514579, 238143367, 518118500, 549815169, 469050297, 134214131, 863821446, 161245893, 944778762, 147370071, 792252966, 397382467, 612650960, 110865333, 717247991, 274514084, 590073189, 926272742, 172823588, 988461737, 813825342, 252048279, 245486075, 930037080, 302898101, 323483718, 972812584, 570336174, 343227136, 195608904, 949529883, 189557698, 676946461, 747397225, 775960207, 343359766, 860577047, 196814966, 969699354, 38223709, 140317069, 742942656, 376607434, 707703648, 678027587, 160504353, 809929655, 559985965, 484352969, 212604463, 747274005, 19001009, 706117935, 798150671, 340881849, 149224590, 145523532, 614999168, 690076151, 36324933, 559836883, 386192873, 17924141, 213111444, 683586308, 414821306, 432758248, 729187856, 674692699, 207215021, 332145964, 989745496, 463643349, 906524133, 619926365, 573759681, 619153955, 945424020, 19268914, 854484929, 379722424, 438027624, 689759237, 436699079, 626597785, 948159753, 729413360, 84841897, 228903267, 4133565, 655483858, 352811911, 597892042, 433583703, 40651490, 476887210, 974642385, 509216974, 351039073, 918908423, 788268877, 703230369, 906844999, 631776301, 633810890, 661342638, 820767066, 529287513, 818074907, 365673414, 841090989, 351715650, 155398794, 829882473, 80331817, 217346642, 503264759, 560884696, 229730866, 10223564, 587589820, 603284955, 629031787, 785599008, 696600649, 917809089, 761547658, 549910992, 613013252, 201525026, 85319940, 296646687, 107111939, 113561621, 977383909, 621614010, 569938732, 134796306, 979832788, 85856770, 973570168, 405276680, 392218709, 785047805, 44033491, 637822642, 817782261, 435332195, 853572799, 526248065, 568684108, 919531796, 892378758, 322793153, 877237671, 986202142, 151624699, 841425445, 986819494, 296265185, 267600309, 766249218, 332771742, 533283752, 9722176, 396354337, 652810554, 280238106, 601048287, 985961721, 313848867, 860326133, 761100835, 193938756, 613751030, 226460810, 392711505, 481647206, 680434029, 969293975, 839113834, 100858700, 800070943, 842148501, 332932027, 210404362, 754774592, 637864880, 850856694, 380922560, 985398955, 409191254, 848143357, 910207277, 734272550, 803892106, 164601855, 137470120, 677844444, 654012878, 676618932, 813072637, 412072715, 203090446, 348403033, 582462763, 999012316, 849482599, 841724757, 510725878, 853940988, 866956852, 371445093, 765502680, 379970159, 147437980, 553490036, 274126882, 508859393, 336796355, 234497767, 897827973, 130947578, 594809601, 119721158, 170122591, 454176250, 515153759, 184640936, 105341481, 231081665, 129225783, 398708924, 853244274, 926615748, 356651613, 108944941, 527343359, 132999871, 500657300, 211617119, 856062327, 729381297, 510407627, 442295699, 8675058, 536795506, 617476335, 673437673, 30049431, 404736023, 428491447, 842589131, 611244416, 428703767, 838086560, 322715089, 746078343, 295572477, 539027837, 459912958, 72843174, 633098559, 704025570, 519320691, 584508041, 345348266, 873171314, 896388508, 675848335, 834912657, 339280611, 327538346, 687346553, 316010124, 350898917, 527431262, 990111763, 881195875, 490539261, 933985776, 526809806, 984229806, 204342482, 68857086, 211059657, 276149523, 543822042, 416708215, 364218789, 954581082, 766990654, 570557635, 760985962, 321995161, 627887515, 707170569, 521286925, 584598932, 155154133, 297154708, 418193500, 950000698, 859919910, 610641606, 392872719, 103444879, 623616448, 717575348, 331477884, 489714627, 685648293, 385994040, 137399537, 126671339, 261723963, 818530024, 779642501, 825128127, 31144579, 444478493, 363058123, 60819043, 368384729, 536452070, 498886001, 438687071, 211903, 371477587, 337970666, 658144928, 496123934, 389304499, 755468521, 320098713, 768123154, 349708627, 746789236, 251058579, 656772896, 839107938, 412973672, 890957355, 490447456, 935783640, 124201870, 259695746, 701246591, 552181236, 634216722, 598014781, 207061367, 83069179, 686901012, 67672091, 800074573, 875146055, 259826791, 165073664, 868379633, 529358890, 679270160, 188798933, 542571733, 36169340, 647202077, 357311372, 741324390, 773711234, 734120589, 359739536, 199558445, 898733786, 963329359, 224943710, 432656541, 709497749, 646206861, 148347593, 319996792, 227574945, 409639385, 82663481, 868285688, 825780133, 68068914, 340799413, 368150374, 509219481, 111774790, 842451439, 407915560, 133342361, 82583545, 115727180, 686788017, 301175859, 959141481, 432463736, 818462041, 586632746, 111048861, 678692376, 127627852, 689773187, 417812429, 300874165, 449822362, 754086121, 235404102, 81894269, 310840252, 140116853, 228299430, 40333765, 713712701, 475693548, 303431524, 317710476, 18781675, 995347691, 633224101, 426412928, 873245745, 243345685, 473387800, 598809347, 984691522, 234616149, 281758137, 910644181, 973643461, 558971107, 902771476, 616848690, 704929320, 194630440, 605797346, 105473450, 758077281, 483399994, 606769612, 342641359, 554560343, 348923306, 299664482, 877932472, 448466448, 208040108, 714222397, 533808890, 908480468, 438996166, 897985437, 321728638, 877584589, 312306003, 807022094, 542686328, 682426633, 50735194, 281023888, 761573964, 733666230, 463285107, 199608860, 394674195, 775636150, 684377584, 243190456, 744257172, 336654063, 239175974, 652122030, 649311908, 194001710, 93726195, 781819876, 208686309, 802274666, 106867070, 174384668, 668437304, 800206152, 851986182, 753791828, 959655269, 588001567, 307429068, 331590306, 722703913, 624966984, 686941729, 516030376, 363386712, 628178598, 378041649, 965284634, 813411706, 879921791, 966206670, 129369061, 742428919, 195847790, 411448780, 84784016, 478859655, 955998997, 886141861, 446017975, 353666488, 740346564, 482173112, 234519227, 38699520, 557917158, 651333224, 258266141, 377224132, 339347195, 763878862, 167182733, 45021313, 821750626, 712570389, 993419900, 439810939, 690229381, 89033680, 400331498, 137573431, 856156226, 503931033, 984465390, 616258383, 917380757, 897425733, 165781677, 41690127, 162396962, 681298979, 517085387, 346621719, 351453104, 585103608, 771156186, 395419047, 895945477, 968111087, 944998645, 314406054, 873709484, 154514168, 504628537, 488204045, 913597941, 637411493, 947667884, 323462959, 575271371, 334602760, 809555510, 361072263, 321274962, 564235008, 431596384, 91515943, 491334386, 571418178, 765499270, 139340910, 640666477, 278215935, 591040321, 416363964, 1995671, 99621793, 217336801, 229643079, 432748804, 817910972, 396862213, 924275159, 161976755, 770171368, 103529195, 689021614, 646812387, 307321584, 108679891, 11938124, 595787772, 477255846, 445194238, 772117424, 24597004, 567921438, 866161270, 85235883, 530705321, 374109656, 130175222, 464411471, 773436867, 726810722, 361380010, 792138420, 681969726, 101264309, 512929436, 637715450, 378983584, 924554568, 691789138, 930563259, 703997098, 472549408, 601302106, 647957411, 723206215, 380374461, 670386060, 119162650, 497675890, 487775467, 72480854, 202659396, 23887702, 398671296, 1999348, 123724170, 539504275, 72623298, 370768857, 628374982, 98723401, 772254270, 430624860, 538102714, 744766533, 101536943, 649747299, 950396748, 460022909, 69051743, 862249036, 833692894, 996627841, 359402900, 722461967, 812326177, 878303012, 417936410, 794945149, 654906853, 734828852, 991668909, 435832160, 393494750, 487910545, 645356345, 68529419, 503773330, 653420197, 55702251, 412754847, 982247187, 310363374, 153719268, 890799621, 54740803, 505103831, 457987221, 198050999, 957075752, 517473602, 609021220, 214470420, 928957225, 897037513, 940251066, 266171200, 967352167, 512825184, 641080210, 240316843, 119296738, 790836781, 271036494, 564718891, 240437801, 575822398, 499811850, 509844866, 340505393, 534010926, 327855072, 295577155, 156430156, 172285052, 964290789, 932663298, 867468297, 560057761, 600387848, 264083757, 401557592, 650182034, 512165575, 615447217, 659945066, 202167338, 542126120, 575916613, 604954907, 65204498, 638320590, 660610621, 537024156, 278700619, 182141314, 672161746, 722332663, 234905441, 733729961, 226627851, 392211316, 826082044, 327388795, 325163474, 731029515, 169072352, 3172244, 247377838, 824245176, 387825910, 595238978, 790473147, 466865847, 545422842, 915330772, 589927680, 71658543, 755122818, 280711874, 913579545, 158650600, 523282547, 137107586, 379862163, 771768427, 218376966, 547554940, 551505063, 628056154, 473144889, 912762135, 401379801, 715654592, 373993357, 148109083, 47200765, 425266941, 343117081, 838860071, 81880322, 28088407, 108444053, 292884367, 149450009, 611792622, 208775646, 785278516, 693591357, 611499531, 687190552, 327767275, 570410671, 52252580, 205149673, 15018995, 840516650, 338665571, 130395614, 435633263, 435587094, 710630034, 522351464, 913013626, 692776223, 873420688, 299132709, 923157215, 584912703, 26848188, 892653319, 182182022, 596681579, 847331875, 213034433, 220180150, 604166339, 438339371, 203933461, 725980986, 937742527, 672348436, 810364920, 380591683, 422543528, 450778799, 827547811, 275750903, 727209490, 225890121, 353395362, 906236537, 544192282, 696108261, 665827574, 7301038, 570561256, 987375753, 160397528, 695495709, 465862639, 15439736, 823257273, 344722792, 925039584, 20722330, 662145562, 208660231, 199316546, 857698943, 413738336, 11038803, 614339716, 620578386, 679203395, 892744094, 252120140, 546716576, 4577532, 622311829, 543759485, 263979304, 146886217, 913799756, 728225874, 386254436, 111693179, 280458958, 177869291, 837826057, 269514170, 921806680, 518093334, 718566756, 8413874, 748121564, 374924383, 488681989, 10245092, 705370493, 767396408, 261771006, 568898079, 759539047, 750754236, 458631132, 507281165, 350241408, 277087737, 894618950, 882232726, 450061830, 67517527, 839931063, 338626055, 369123753, 216768300, 100706657, 531979234, 591345384, 546463694, 522666827, 940269364, 828067530, 850495276, 56453709, 209182802, 372642360, 78088705, 724446084, 840479550, 355267370, 725886765, 757077244, 346736049, 986046571, 159128071, 499491915, 660170486, 959903583, 190748713, 809688682, 760623359, 937588985, 942986555, 36224006, 970554050, 897654757, 462400513, 761879351, 950739425, 562063407, 378416442, 553303038, 955384062, 619717313, 109736187, 90021555, 861964768, 772593880, 653488509, 731447034, 597394129, 231725564, 287067082, 857042326, 315203483, 92013894, 510764951, 695054835, 211030045, 297021365, 36358761, 866276942, 908690910, 8798654, 487947918, 510757672, 257450556, 20202156, 649227974, 979676386, 97163593, 287939509, 337180854, 697234603, 591135625, 240735784, 829411460, 294855475, 455933480, 709697827, 853999051, 380890053, 94599176, 895600941, 313903029, 227305725, 724744100, 43509288, 148447743, 558770044, 561969914, 485053970, 407866969, 645782330, 998338943, 501670404, 294190977, 101742766, 148581185, 594174162, 493788945, 635685882, 387437303, 224258258, 47223965, 244137039, 882532960, 884454174, 988560804, 626684755, 831373287, 146800882, 470572376, 177542112, 453795671, 868034510, 583084552, 992279220, 373552449, 289064098, 693189422, 165758058, 541893857, 812654237, 51069031, 753211094, 936951506, 570651564, 87824144, 15458327, 571500240, 160187504, 19678878, 120773681, 476424281, 901437080, 49568804, 143026671, 138445954, 683436926, 341347512, 111201467, 240939579, 350808442, 453104822, 496837500, 456498333, 830835400, 357143412, 348461076, 980153102, 828352233, 519696001, 563095536, 286160147, 887388667, 561645666, 802118464, 479889253, 468516391, 895499711, 170481210, 637037904, 970734266, 170699225, 245063595, 637446114, 825423110, 249977800, 672589628, 902304263, 723020912, 363535271, 28912153, 199513873, 988208864, 921565255, 545318416, 533099232, 927965170, 837252656, 528435610, 52801022, 313459005, 467499133, 805299227, 725855900, 595880296, 429980643, 316180527, 775236894, 373072925, 605266432, 562615710, 1416075, 390650440, 290897570, 27195528, 37065283, 265406664, 839186793, 858287923, 546461799, 719087557, 307517611, 399372335, 336769959, 697100102, 729052564, 201293977, 725297197, 356047179, 273940330, 886657635, 391360028, 991844953, 469011440, 654864209, 326646237, 190122407, 111922175, 593060360, 11139886, 856289972, 893285144, 962022504, 479007048, 631351989, 433316134, 759392787, 402973091, 734536845, 392681583, 54402165, 194501220, 311268186, 641311472, 776587549, 80610194, 11297611, 451175179, 574189162, 376127950, 409346648, 984474260, 914091079, 251251991, 888061288, 417722974, 814886511, 266029804, 656964879, 519758541, 490415133, 14776453, 464749327, 274356045, 189803876, 297678971, 36037836, 578721963, 759000892, 357788348, 833781899, 408287809, 465859548, 381748924, 709980593, 888752079, 887862109, 633202799, 703160239, 925337750, 770267105, 714475025, 287027439, 530228279, 993751438, 611423230, 555095556, 227042284, 256786683, 119254400, 951014317, 272825562, 973786030, 650038602, 620266003, 628142830, 929992934, 913611873, 777981674, 408961295, 644274305, 557758644, 352212577, 322883244, 2094305, 737200672, 102198406, 413944751, 449835909, 177129363, 550111, 904674402, 662608864, 692591866, 189503717, 674987886, 695721620, 826318861, 514892264, 607979473, 870284867, 283279530, 145296367, 41535485, 218373303, 889096937, 415184833, 849710779, 603773042, 378172653, 223353508, 564135467, 960785806, 695566719, 397936028, 647804665, 922627934, 130783376, 369624937, 802093398, 607283897, 978469359, 27939508, 17726866, 306358838, 545751475, 384646133, 291106855, 403057297, 936206708, 271587521, 616723043, 976197719, 124682885, 20821272, 213725125, 360815155, 12984006, 572081175, 448808927, 501466811, 748852483, 472797420, 631273504, 831413042, 282321371, 887473428, 419190716, 562976031, 818124656, 648350385, 176572040, 912418298, 749581949, 32733729, 291166717, 309946628, 727339308, 297286259, 495510142, 431280958, 701857693, 951933254, 67544028, 733091638, 171823910, 274034655, 199475264, 21293100, 726538391, 215683958, 909784147, 136766448, 815952041, 550720313, 388101750, 588666598, 872737174, 883641509, 82289877, 543174009, 406716078, 980028570, 842266421, 58665878, 738891336, 823041609, 199754237, 151820478, 642334, 864965487, 525663296, 917924767, 498402365, 560331469, 831688528, 56236599, 180452946, 770874473, 413376481, 970425158, 558435562, 196620306, 417963034, 323134218, 762907871, 231956615, 837976966, 984721345, 310169007, 465606382, 68584293, 530559590, 99283309, 197039309, 672340749, 531526210, 694862380, 412332628, 573770795, 866031544, 71106679, 36227310, 377736023, 49795231, 224041198, 495037778, 149076857, 834876656, 142487953, 585435496, 930555374, 339223721, 767780099, 625524057, 539127371, 935472604, 374983606, 165639254, 348003946, 1682744, 781090636, 669081603, 626087694, 2733792, 559196987, 333631315, 55056022, 587238946, 403322675, 274138348, 48973959, 970162532, 428921366, 189877745, 711323306, 340298758, 890873323, 600731327, 414128589, 54237704, 118821324, 311795711, 741243180, 27999789, 234081642, 147523790, 862326330, 181300107, 291790734, 418058841, 935535260, 327051146, 50643613, 955703377, 25682916, 921451000, 463171633, 146790728, 967676318, 787254636, 22186060, 331899278, 504935318, 145584853, 845344218, 587599845, 922933241, 490707457, 826762708, 692344618, 514267314, 239415669, 959761625, 790534688, 183495244, 186682708, 940050120, 687365969, 836778252, 434889101, 672407543, 670227136, 81896022, 20238283, 375398933, 640815614, 367511019, 657558587, 97671402, 898007057, 986347383, 333264084, 165127348, 19918232, 63751216, 95082539, 884697399, 369848290, 91299984, 767648004, 23436239, 574228714, 746176362, 190792858, 799804684, 360511345, 880492978, 855466159, 590884351, 551377072, 987037538, 760216494, 330180927, 92754080, 158202802, 443233085, 876276412, 89231852, 374471341, 972946666, 534672107, 833075250, 249609254, 877128107, 446940825, 755477847, 448422812, 315759237, 13441835, 913263792, 257432346, 723582487, 27280292, 364374608, 886937566, 413437928, 493451020, 4321643, 187386166, 458746529, 924086384, 876644219, 686011598, 991153516, 832740712, 147297302, 827773094, 570872726, 656044579, 614039695, 741942136, 824613952, 629446770, 349099469, 782516680, 388015093, 713164859, 83115104, 10023073, 357221175, 891328064, 242191899, 267215672, 711223046, 855252943, 294107093, 854566994, 706306199, 781274072, 59005082, 867405564, 845361755, 91098375, 890349499, 877696163, 94865898, 239257842, 885932341, 31512324, 503363405, 715574862, 698583510, 249922657, 893766168, 863809123, 961532743, 41539712, 938275516, 134980143, 725149781, 462132644, 435727808, 904632846, 503989081, 445742253, 800553085, 968687183, 481848516, 786212076, 316990316, 852413351, 966119527, 802035818, 691352068, 559188038, 467672215, 966725646, 103309023, 199082064, 1943787, 689642334, 354850002, 342794596, 636643208, 684872997, 624271041, 439058095, 324078780, 115199251, 2992591, 252240895, 161344473, 815594308, 233859206, 647218957, 534389599, 985753194, 317448183, 262259057, 625411508, 136712464, 770244572, 190948738, 828792670, 531323973, 85640435, 101932110, 186821045, 157356351, 861511089, 40202281, 703685030, 445242304, 242827541, 949206745, 698851485, 805148988, 421529317, 692398587, 589132016, 7293050, 971216856, 694430837, 211231214, 757949205, 40213979, 321177826, 559992900, 32581327, 933898668, 889535851, 15236563, 335463256, 980995218, 363888389, 504399333, 452588599, 899476252, 468273948, 227113690, 416428840, 958148369, 233641603, 227802873, 223985809, 742661549, 425060689, 219472166, 422696977, 520053825, 369257086, 920969144, 910986455, 829160950, 640829716, 478614608, 118267052, 961381387, 648939749, 143010982, 910186688, 602278662, 632903375, 39792071, 598530118, 371035370, 506343945, 935859039, 496299794, 540598545, 768591246, 872103357, 554156821, 114351396, 213247302, 123063911, 753603304, 468046159, 996234403, 792695779, 375622539, 402149559, 416139607, 397626933, 295248598, 761559364, 523319326, 213378200, 677550064, 372866506, 629461305, 595778975, 276525452, 40738986, 153300253, 218634001, 434286256, 227755774, 24307844, 199568942, 92774891, 551098, 321175865, 660440645, 43143996, 34589181, 519670209, 536452993, 117017075, 159090321, 928933017, 417604752, 84037364, 547336819, 536623980, 812439267, 846791930, 234636575, 371284385, 76030958, 702204702, 914566311, 648316068, 212741710, 887005567, 620051754, 714578128, 204767842, 724132078, 910707507, 395899965, 771258454, 138497137, 651745835, 810091578, 210294924, 944228553, 18810899, 742833053, 164736102, 539471892, 334886475, 889501007, 489563079, 278675907, 580422251, 228915324, 400229888, 825003850, 355651582, 562311291, 992144674, 611450487, 936142297, 809058383, 474658270, 125619605, 305820845, 397564345, 52938144, 39043934, 436420008, 743067832, 420835988, 463437850, 47237821, 926761391, 942906804, 37122037, 108933757, 45972715, 361804789, 615629045, 19071187, 387864270, 980410305, 66390948, 778480481, 590297494, 643926966, 402767687, 915992961, 99482091, 68917739, 295997733, 399393334, 323728730, 332882564, 37963112, 826564075, 882102927, 451778022, 184208726, 25816765, 783000162, 260517300, 345797874, 370197267, 330689958, 860612214, 806993201, 627713438, 68583227, 248616976, 232186504, 540673706, 4784893, 475211296, 165087482, 331304402, 732057186, 88263445, 929798260, 317611539, 642390000, 910243703, 821169378, 893235431, 523560544, 618672740, 458510941, 396103049, 189060325, 952097948, 740301852, 656530939, 149223917, 83257050, 901358400, 878678945, 458446086, 267075523, 244812507, 894601168, 856540645, 388811884, 422551855, 619254501, 502155396, 384327450, 773713258, 343200661, 142915670, 204268998, 624613504, 698897140, 589601115, 214008284, 507762827, 1604194, 108226210, 737964381, 941559547, 767673890, 154675528, 528991668, 38101824, 840544908, 390638203, 773522108, 263081698, 537747520, 29068346, 800404714, 981960705, 536103693, 303807550, 758200023, 446462674, 745914704, 130499918, 793642784, 852236865, 979116599, 1042173, 624990758, 577560739, 856934499, 876697839, 937836949, 591922306, 280022578, 158247142, 949007534, 919736718, 641092750, 803727694, 563396667, 350913738, 947589381, 561728489, 138931333, 292198335, 676961178, 240385775, 89909073, 289390602, 338161141, 598150924, 569871851, 774224719, 525888013, 883914387, 54871050, 845945544, 327507923, 736009308, 518424558, 892563061, 53742558, 740438646, 767746320, 259663386, 740738982, 750496453, 565725970, 923498679, 975192790, 531123649, 194511916, 371127252, 100115981, 220337145, 654141928, 659722111, 902305546, 406287649, 387955351, 186684332, 738762278, 307932376, 100527290, 505878191, 468654453, 454356348, 270159138, 108520149, 465743849, 672878317, 907567439, 1942659, 976942342, 24480076, 287907851, 966692673, 738273603, 151751185, 538914720, 649286221, 923254076, 626295701, 592937118, 796747973, 332217235, 34203454, 852240269, 41261869, 761325525, 680773881, 106505004, 774339351, 468961631, 407639950, 624225234, 557939831, 598115444, 445538811, 337842817, 834836041, 573101968, 550997603, 865923729, 988393286, 328955656, 700719369, 529532213, 234868590, 805650406, 117210614, 797161163, 883120282, 329095529, 371600455, 801021020, 914944690, 467508936, 483324139, 808972668, 94609499, 450160798, 275288836, 375684640, 78086665, 953341740, 108117292, 513829132, 618580029, 742024992, 509459504, 983101205, 780891316, 173116202, 446489274, 377647676, 819478237, 822636211, 204173042, 907986873, 856715467, 138057486, 706155563, 105582416, 484652464, 178098756, 737382114, 57533768, 565778670, 40631348, 573191607, 70183169, 67761212, 290331226, 239968579, 222437945, 301046556, 37282350, 417365229, 982100598, 697491762, 672331421, 22327956, 309524598, 562613497, 962631333, 605833259, 670058615, 745301737, 671090242, 485243679, 524562775, 467453977, 571670397, 625710655, 304260717, 733289806, 470442516, 829810873, 78685437, 20833642, 844422598, 937833216, 412770649, 544209888, 478858675, 470470680, 543246987, 752202203, 628930275, 311865230, 827745484, 933231175, 753651445, 432195872, 856388032, 467173938, 485394987, 579660697, 353233650, 137673728, 579613430, 275157216, 8858807, 803599285, 877066453, 668383501, 339441263, 789824033, 296742271, 318505077, 965279051, 940316701, 161636060, 401398617, 802711339, 152569979, 656571685, 330391352, 637702015, 698653496, 527513263, 88981166, 49883217, 904975739, 61526730, 866708478, 555994509, 930973729, 745718556, 621707643, 631552040, 588928750, 329593778, 355924482, 872387841, 625493622, 957490753, 59055741, 748792118, 568501428, 18231262, 478534408, 840721885, 478528983, 724790785, 100662416, 746447634, 443691228, 524563504, 782613693, 83155022, 103677456, 104897255, 90790813, 494886476, 83411569, 684018755, 304258627, 871858603, 748318381, 409467063, 270461779, 509150069, 309489940, 358808979, 907037228, 535129595, 757136671, 481710537, 106857185, 88035911, 140022532, 672558124, 762154893, 796777309, 978323660, 894686589, 607857062, 687108971, 845810038, 519476074, 895900425, 947698400, 876542483, 353685904, 246980826, 252759804, 452637388, 95119712, 256415473, 568800502, 870007019, 787533081, 894162728, 162847778, 104222107, 5239243, 559586114, 857759079, 455482179, 911900730, 349892620, 591109076, 236615612, 314835664, 186385368, 957833150, 6223684, 847144244, 255231641, 223649578, 900134958, 45065774, 329153060, 199924467, 360163679, 13118980, 536260534, 759026219, 483239132, 954124616, 557532121, 743136234, 564563052, 239640408, 301445981, 655177626, 880070988, 141909332, 624490158, 848909201, 890324412, 104079521, 47569930, 472755531, 406385168, 901797416, 825065896, 457857337, 58722550, 686086124, 761767849, 961916328, 975984286, 797987808, 865667357, 262002236, 711420438, 969490657, 32052966, 640886686, 288132838, 964427287, 551480800, 554302483, 477208113, 4115396, 639976898, 870351962, 136484728, 72537482, 954909778, 593570183, 246443724, 391778991, 188974872, 648593032, 33801184, 845578813, 77178209, 328068171, 44190603, 529091954, 735243254, 172858699, 387549621, 222170903, 344008626, 471045165, 806333193, 118135719, 578688624, 984391632, 222344332, 628987806, 245045784, 639315584, 73624396, 616453349, 180930119, 862964309, 149162184, 696193987, 485512032, 806058161, 651135003, 826742419, 228164197, 95384875, 794878797, 659696323, 797190375, 43817130, 615298977, 417401797, 382463090, 840644414, 606779971, 359521383, 888969427, 815320078, 486680913, 928810555, 86975384, 239927197, 153877767, 138417615, 260117703, 355747243, 271105881, 974680130, 742240050, 374386720, 208299762, 232123331, 327676717, 342928368, 658792728, 332816606, 884259907, 289916484, 219353279, 654513788, 694413452, 658749235, 698861615, 314346789, 871411332, 757717079, 729931833, 4792939, 587098582, 605065398, 775197910, 135906509, 60433757, 397212961, 163868357, 325914460, 252429539, 387702911, 518247922, 356596202, 238094728, 458202321, 772096974, 221879136, 414176129, 925222236, 250761564, 520813613, 940430626, 322505485, 852650571, 661471667, 773844505, 278808680, 266644257, 76296661, 631237884, 591544247, 584539403, 700278321, 760392072, 252177764, 141397789, 208669499, 435266421, 512189755, 874998500, 161451211, 7097959, 396925241, 274725840, 977766646, 670190637, 374026840, 60414724, 22747600, 836224026, 333047602, 335473319, 993628219, 826925738, 952474987, 45771171, 35879095, 280510139, 688787380, 761252043, 26440720, 199665673, 286733215, 23973351, 443352152, 899626337, 553691876, 474071783, 22311156, 37851248, 708460541, 563429260, 450011464, 338128508, 858623514, 293245884, 388579228, 628900561, 191573884, 783784198, 700832250, 318329505, 256142324, 954484270, 955654208, 414293981, 523743962, 993352704, 372667523, 839528543, 175659585, 479631987, 359047710, 548936912, 354619052, 248010895, 511222741, 271935408, 24085422, 27435277, 961795785, 335856255, 53661728, 644042281, 872263181, 838992643, 993485679, 995205684, 775209046, 208243694, 409198639, 200077280, 369866808, 143325878, 635726482, 362263813, 178749003, 494573003, 678155088, 498717956, 297862095, 145270200, 97930526, 624097768, 683527612, 789269883, 553016431, 41557175, 497142620, 958677374, 758152984, 411045706, 791284352, 912656483, 894840447, 76640326, 807758383, 561268995, 718687889, 16441829, 229165748, 952137162, 470717017, 885208747, 907653743, 929495455, 414273261, 118501093, 770561664, 58280920, 160801570, 663271673, 757088282, 744641894, 777318296, 444931666, 9417288, 849524568, 386660453, 91621737, 726603621, 448796317, 437042702, 543230123, 209263946, 76812566, 297109928, 439661896, 907238624, 950244086, 475724855, 904520640, 720324803, 718090837, 75107562, 177755585, 230137580, 392827659, 817195182, 284324165, 847904640, 517545111, 324343591, 287576109, 11499181, 659983771, 328022528, 622153440, 540491512, 492827575, 396574943, 974153933, 47124996, 915839924, 826460602, 868316640, 941663871, 987895056, 502221233, 16327855, 486331179, 82141720, 746474738, 114610168, 550564894, 380513970, 744902720, 340505726, 912998074, 672470757, 29763093, 282256253, 690746659, 5475517, 778737224, 938583342, 610013863, 473263301, 565866857, 875437001, 890191126, 886584672, 114449935, 263560558, 241690576, 54136113, 198073818, 396564093, 126032581, 93781893, 283579935, 458147252, 330774449, 958604493, 837622818, 828455295, 879360316, 233713208, 281395527, 642646424, 641196401, 10282061, 916750232, 696321100, 363323064, 801618277, 686288508, 506538239, 861271145, 734502589, 19826372, 178546072, 567642473, 89211433, 864778467, 48237475, 772276026, 932732927, 553826596, 868436621, 930082200, 317968579, 139063357, 257158986, 11531991, 918482810, 580153234, 31893426, 752131122, 767673941, 292419962, 444502179, 86528930, 218808013, 852926385, 864441054, 56999870, 209713647, 16964718, 873839236, 798327405, 860854669, 714557612, 675713259, 614904315, 641506210, 158104335, 463956250, 50000759, 923569756, 982146307, 870716995, 90623719, 615678611, 907632994, 515214508, 387521866, 864675345, 274852144, 459128474, 307570740, 832009749, 548991322, 178059216, 535301309, 715691677, 7001595, 897800309, 335382416, 499092098, 252554797, 376732482, 911704383, 93243265, 799358476, 219078616, 722172342, 571257903, 918304992, 589915714, 927208817, 412399384, 272706890, 584952840, 678614054, 736779663, 43991686, 16850437, 693514730, 342721536, 89064752, 22996571, 201119538, 843750432, 584982649, 255808971, 783113987, 914550646, 783253974, 527788360, 1175157, 125976589, 177294373, 583157735, 937406907, 912329722, 205117287, 152942703, 868937353, 12312701, 180116823, 183038126, 161688158, 982709902, 753441244, 279653759, 581984382, 609251671, 643973187, 74812143, 618948562, 329340528, 644408206, 284486532, 643088021, 685340831, 613260733, 238803448, 390629210, 477246927, 314631468, 484522358, 176869763, 471726124, 616518615, 49671088, 562964377, 854366776, 74104779, 603915632, 849994841, 199775987, 446064875, 913375323, 816970829, 994524776, 33181833, 219698713, 822805723, 176000036, 159945632, 341104588, 859432898, 989014498, 182062389, 278750273, 688132377, 387122639, 287079961, 899161877, 174827386, 804047990, 314667286, 51007466, 913360949, 22116663, 754642953, 169809325, 535307994, 850657923, 767440636, 861399850, 318965148, 71993365, 5577463, 992761894, 693146589, 614390785, 306968895, 619303707, 353981550, 594177583, 975356487, 570153116, 4746818, 981451698, 835481635, 697498929, 466113547, 746145401, 84832381, 176353235, 230538872, 109104261, 589502499, 433427713, 118645757, 351386217, 769099884, 866839364, 234259657, 768037661, 135144462, 482266612, 158729290, 28589546, 978342107, 534676091, 108743029, 163417352, 378126625, 626632, 988229716, 896340482, 761718960, 803124974, 740662870, 267320485, 632741843, 233059468, 253359330, 730709911, 29891023, 689484272, 732722693, 594995529, 708092108, 738674529, 424990963, 722653374, 117100423, 678700792, 451213798, 733501019, 399066562, 573193900, 199431873, 477828389, 384150527, 205421013, 173493625, 258768944, 71883192, 62041544, 858591076, 421368162, 601972739, 196437267, 734692989, 650934025, 469845212, 481697106, 474610647, 636689907, 693622338, 346947495, 706683936, 765675611, 410439717, 26987929, 712847473, 259898874, 318898068, 509070887, 186610756, 742950475, 236252999, 175013378, 621461599, 702709543, 868805463, 490609141, 78196249, 884515727, 357750503, 622724559, 705068542, 692813903, 332564227, 659282953, 118550240, 300551516, 24694617, 632965635, 153461951, 445320912, 117784276, 633627830, 358247129, 4106907, 196414013, 815518369, 64043674, 375120999, 275727304, 534916366, 875940224, 558210819, 11447865, 23765014, 845927634, 125804914, 922961485, 495735635, 858289034, 737333890, 75357382, 989087569, 567135645, 752971907, 160189502, 671487871, 41060148, 348609717, 288228056, 883699788, 729996451, 166744306, 54438313, 871159843, 188407169, 839903093, 339025808, 397360477, 138510581, 812210888, 460902098, 835029594, 729531266, 742591004, 935978435, 512583295, 123275241, 680778882, 300225948, 265242443, 317952789, 577006954, 23049121, 104906433, 666591052, 471690739, 368183712, 167058771, 785414027, 909464135, 347342394, 246054011, 97910637, 176113537, 210999240, 792844466, 295032906, 19337355, 269589873, 916923720, 761072124, 981650632, 727400536, 275679701, 148865843, 692987449, 459375946, 502866219, 448463847, 433382234, 921861884, 848224196, 801844940, 799410651, 94483694, 880383339, 608675183, 300778538, 217567688, 237564338, 783198986, 986197964, 481105696, 876893692, 715888144, 117351355, 76437238, 101770230, 233705337, 623737301, 960817426, 975408481, 859463800, 151319006, 479996291, 923014779, 757769453, 958202811, 90801987, 972335969, 436641091, 492613433, 244555055, 329477934, 264980378, 526765819, 808839122, 382651674, 236115455, 783853393, 797263840, 313335452, 520158614, 832855497, 943008345, 332652169, 277519074, 422967085, 815707168, 515528155, 535396524, 42490491, 344269524, 848594873, 460986947, 701712440, 593841025, 226908365, 709264334, 424398110, 227895029, 447859940, 472704873, 427231652, 642487389, 173218637, 165740294, 528710519, 300576236, 797563678, 352034750, 283111386, 54800829, 435521220, 968235480, 60206518, 279521888, 461896615, 655081807, 433059254, 266315393, 578634588, 25863984, 784307242, 226598340, 819869551, 356177718, 573990920, 569863176, 917450289, 916426613, 296813294, 481944220, 220785575, 529630661, 742646945, 841862282, 913467868, 503416997, 936252815, 194728864, 864378732, 870621643, 455074263, 376999145, 988848511, 748457800, 849282634, 419189555, 482980065, 983806406, 761889108, 617915794, 294798916, 301369462, 430064550, 887208218, 131774460, 953355059, 997156258, 821515322, 548383891, 105999193, 288751755, 698785901, 759657083, 787180615, 565119108, 784029245, 108349158, 346168985, 321877566, 580537858, 911662668, 516278215, 993323455, 666349712, 156206057, 160373356, 27675306, 740580334, 272324629, 109194116, 290334944, 652979061, 38235029, 444352054, 425128002, 196281509, 344688437, 541053390, 582574293, 627771249, 38498456, 653588729, 662925524, 465272002, 180324443, 190151478, 994967185, 532903788, 176170757, 964349220, 315688047, 153066044, 887407187, 56245483, 249378465, 531093669, 16125315, 535215590, 772379870, 660756778, 412820161, 689237785, 854667828, 900747708, 376475488, 229370515, 103910175, 669691607, 656567998, 504170526, 725251334, 674079917, 222025149, 985528867, 699212243, 717455868, 964326758, 777468463, 720347762, 206555442, 708842432, 257860672, 106836526, 684143170, 361824278, 212931955, 901053483, 523696942, 91284935, 687795296, 218384703, 732600307, 744181257, 801790407, 40197276, 244303431, 454986079, 248859038, 451803647, 238053653, 172001576, 587802882, 13630417, 958141635, 196061799, 598460023, 751450329, 384537807, 967493674, 515596758, 48906676, 582089974, 303400517, 793862043, 835825729, 750711822, 925828052, 148610750, 725719171, 366822870, 196823152, 700851709, 881290485, 743833522, 4559747, 663693345, 481830141, 348625558, 337263790, 648824098, 103287254, 325651489, 337806058, 451425375, 733578809, 611777402, 706436254, 126387209, 454241045, 477690344, 736548663, 321508267, 54232950, 641065711, 504146847, 147331322, 721787858, 581274362, 977219200, 973757095, 336991224, 736113732, 443099783, 594263753, 732273508, 215752388, 640488543, 170226111, 744551402, 771798898, 795132907, 967955804, 374926011, 925382144, 677880992, 707069929, 742102393, 232760194, 468873794, 700100362, 340304984, 30963577, 132591643, 76571739, 60720961, 601528430, 998010554, 336748644, 848035066, 988334412, 779294657, 509144980, 12296911, 110743260, 425434375, 37689793, 521365632, 570827690, 522402822, 319342248, 33840888, 28794383, 208865277, 306404957, 577902325, 627362682, 197225307, 967354744, 327607583, 995046593, 219483249, 643181786, 518721286, 147802717, 613850530, 957715949, 788765523, 575081800, 592378607, 41613163, 316577788, 258189609, 362913811, 24752798, 438089723, 989836432, 462317716, 805356780, 390983350, 208695236, 258437296, 103172720, 991593938, 478915231, 849883436, 979307735, 64493260, 256382887, 325220636, 329603609, 977602793, 539386960, 588397808, 545049934, 430359429, 58917947, 403648582, 214226332, 461952564, 215740397, 745581239, 780163530, 402580515, 504932198, 699847774, 641865438, 816189933, 463913562, 46008541, 199178663, 789991008, 33831389, 352554169, 899826256, 406827683, 840894144, 801896398, 139900480, 484511984, 751636039, 216223443, 195701572, 653969196, 162279668, 468739000, 810422975, 474177765, 649269433, 573406381, 600123884, 883236989, 641216952, 995143609, 592337387, 385232717, 474279209, 825896400, 146484804, 829984340, 366055302, 493204668, 202858194, 666615971, 899885178, 817495825, 761427604, 753317321, 471880699, 199297827, 613890536, 114893285, 251366547, 100877825, 217148078, 211259596, 103927955, 555322207, 533890708, 836806576, 727916749, 925734695, 205717666, 602661755, 393600854, 329465452, 565568162, 601509331, 926321089, 591431897, 217003180, 123786448, 642756968, 961133618, 933705616, 238897363, 716913670, 630052439, 819891451, 806250400, 971983085, 636033283, 914690358, 135562565, 516486958, 804993063, 839384265, 755684753, 219048965, 483107545, 303718549, 525920632, 39776635, 978567190, 505603463, 733968071, 227726523, 229209265, 679019984, 998744384, 230069189, 622280382, 133767596, 127541207, 603621825, 600485516, 633531349, 828048210, 927720292, 966831846, 876764616, 720907578, 604651646, 877480912, 392491057, 775072223, 505329548, 861955106, 81750820, 994460119, 900014485, 337737751, 219763150, 509179721, 957891636, 24189536, 902776195, 520624257, 172850005, 416970501, 632408171, 70922956, 935733322, 151196410, 409808424, 58803908, 86964680, 374811518, 806158453, 620689049, 322138318, 949418368, 238372051, 541769710, 48314539, 382198807, 880752086, 202521821, 699352338, 903125324, 992197010, 946415578, 401229444, 859655411, 674337845, 873956531, 261064823, 807466392, 211012148, 319647258, 429836866, 430602146, 575048328, 390949136, 464809699, 217244005, 143977053, 569465140, 337165442, 373593551, 969672493, 623127572, 203721884, 901783750, 423066739, 675202857, 639226719, 799147926, 832551467, 578090091, 800578961, 440722441, 61086112, 510435053, 813061883, 236491506, 697621099, 77792055, 656005724, 769268854, 182065319, 78283950, 427682322, 381874639, 848069242, 197834153, 288518385, 534001268, 134757925, 495776606, 524849321, 340851317, 364554418, 233856778, 47383536, 905791080, 976981972, 125208802, 660869367, 425741511, 328161723, 576471354, 754404038, 45704892, 267830026, 882256895, 917850391, 196157104, 173144447, 551304429, 696351313, 457364479, 291235790, 787680919, 736005593, 49285343, 447630282, 108703947, 895040448, 826323619, 269161214, 33078744, 640976080, 438272942, 93821615, 141720521, 899718355, 649976297, 499281992, 177234568, 978819950, 113921785, 525605503, 116364221, 459490632, 406850286, 66787286, 978843940, 729261363, 977788895, 163813450, 19845682, 846651157, 97388202, 172436373, 21707882, 92347935, 656934455, 607736510, 625200830, 371370901, 783598537, 231946254, 537813080, 41262898, 655328366, 75242288, 917554931, 539904272, 895076766, 449069191, 912162711, 580323870, 771479283, 275631001, 282863956, 481895988, 406635865, 154461988, 578414718, 93677704, 201051804, 517893897, 297226924, 153855445, 621003604, 650413633, 282505548, 627908721, 484325355, 62774336, 755822291, 861600201, 724096550, 759447738, 232371658, 218977564, 375010668, 625965690, 719477078, 630604434, 394544818, 834256218, 723657850, 19133611, 136215140, 767532185, 939399491, 202267257, 699157695, 111058312, 506643241, 182163930, 15622900, 462453645, 714697945, 208853275, 918280307, 435864912, 405563206, 822919097, 921804869, 172563582, 679208276, 375344648, 588176313, 337444794, 359893838, 950382905, 954783046, 767050311, 217196475, 691936775, 563293960, 154229928, 783988367, 619466254, 342420375, 487729093, 993860655, 151119668, 675691771, 207764395, 271202460, 932935469, 299103407, 679580523, 149080288, 902151168, 374505235, 716973016, 111816188, 237199583, 320103933, 716643108, 644925942, 105301831, 246927093, 777707029, 572691100, 445903283, 572966412, 144789296, 356953418, 703978866, 925105115, 68675314, 988391794, 576006078, 329381043, 738230746, 915831267, 858890807, 269576224, 870079760, 955816271, 500507103, 676331603, 516725018, 262646925, 759407604, 527883194, 231867289, 502171709, 921596511, 318005073, 886621595, 312499574, 63184007, 633792175, 603872362, 434754409, 116789233, 318049834, 110744446, 943273943, 434092413, 752379629, 799860138, 325845182, 531648630, 221840062, 106169373, 509501522, 606395633, 855552865, 850614506, 412675511, 691068032, 208918921, 418268447, 857823299, 230878607, 137210435, 735130367, 848655596, 946931943, 329551662, 330331718, 490482599, 349580520, 296289627, 28293470, 437307928, 716687383, 159324409, 855579064, 646701697, 2446361, 223609807, 977932576, 244338211, 24858804, 601402636, 11736119, 787975927, 663669728, 904477826, 756313469, 887501624, 998245234, 218716169, 878226893, 715356045, 340727873, 190843558, 194111916, 918593393, 732277812, 308474835, 915856129, 126128827, 394433645, 800711313, 284051351, 198156234, 719961820, 558310795, 399909379, 211975590, 546665530, 787316710, 33839515, 859819784, 240731047, 982535680, 700171188, 517165396, 995687249, 495434226, 415639736, 562641978, 698900196, 596398545, 122805089, 306026948, 649293550, 358378147, 546846963, 802395315, 805940159, 810407110, 45678207, 666460755, 18801930, 307148243, 230447442, 205170490, 448859471, 250619995, 177735844, 995928581, 712170954, 254543520, 864769114, 347250571, 209381482, 913046514, 307778017, 861040405, 41925641, 64587327, 360846805, 746213632, 211704111, 529995132, 250209244, 97557442, 385892871, 653978197, 182027083, 87323387, 545481560, 932028922, 432696011, 528519625, 402135902, 749717939, 805389087, 33809638, 304221620, 771348604, 957470627, 903182711, 663728329, 465925204, 794074954, 221592460, 87267331, 951767644, 899901797, 231980831, 962832292, 37024624, 364288336, 463176474, 454431365, 788890279, 100963160, 234629650, 94187924, 99573398, 833652843, 963911527, 846006632, 727510478, 694097083, 818014615, 281522949, 859301403, 936380981, 140595204, 310152817, 960600689, 974744358, 134955503, 491157933, 189310132, 739751083, 199000782, 577206506, 412777518, 165238566, 374671392, 5404806, 606277785, 995783923, 430618267, 342753656, 860566820, 725396666, 890572714, 739913982, 101603574, 985421988, 265143077, 513863735, 38519119, 121839461, 659193735, 611010198, 601970924, 863491753, 227049742, 436828925, 141231691, 445560728, 749681781, 251807630, 244351636, 699566475, 103376687, 893175329, 820507668, 600954304, 393509854, 441335310, 356371445, 658240897, 982567685, 33347138, 529878438, 738525721, 418609585, 649829296, 508662328, 623104120, 601378163, 458448379, 505721601, 458898861, 444557395, 54448773, 324333692, 417727922, 221704711, 966583607, 342943936, 925635097, 456229777, 731586014, 956601068, 368910027, 742101747, 287140096, 720352219, 806123194, 33214573, 627708762, 765590266, 417469625, 654659517, 80444722, 310168819, 283472239, 431157000, 994700526, 424233374, 916586806, 119083644, 878962963, 363097918, 631087514, 578281721, 474583963, 700611138, 570218502, 947890758, 439017890, 867853218, 994545562, 357360249, 125667357, 370568649, 814525865, 897616150, 552704708, 895132013, 937376033, 767131643, 601976012, 246172451, 388030620, 379769850, 478567208, 706878980, 678612405, 22824816, 49168082, 421079956, 778417650, 276151131, 598985619, 780824848, 109516812, 256132277, 697285997, 71775236, 703366180, 871803636, 126356176, 724903520, 572902525, 455631452, 431539226, 944921053, 702106624, 871508530, 674387542, 117735537, 367937701, 538294435, 784719843, 95078354, 934070308, 446528680, 176783020, 310947952, 951920948, 470083580, 895777955, 785379837, 922818833, 50125441, 395529631, 235908509, 78970540, 757675428, 812136035, 613913184, 992345608, 969942257, 139593465, 998827633, 142051992, 408347328, 434576374, 941360108, 867704791, 44514963, 673092196, 783618681, 903295492, 491040837, 134993168, 638446808, 673863934, 609791977, 556216911, 412905691, 933762644, 954329214, 500014459, 747939355, 210141915, 893481623, 430693652, 773764199, 597584234, 159689303, 90603809, 25552473, 711044253, 724464655, 360642601, 266115432, 285392525, 382699610, 295853384, 481198254, 57718534, 857701627, 68207094, 81471805, 429137721, 26729441, 331014075, 915647574, 685700667, 162353624, 352523189, 254218707, 207190661, 928729627, 859922385, 267550339, 402174955, 738449825, 464281485, 422097800, 950254656, 116016411, 268834473, 492896999, 522073737, 781622818, 833177672, 557613596, 869375883, 893552811, 133012714, 682487547, 679290831, 693297576, 145359676, 718156425, 326115832, 565765892, 716128352, 444949840, 596360092, 312367736, 303595431, 951827391, 112117754, 747490134, 705993265, 184187238, 856830932, 417712834, 905441744, 59154231, 86266221, 477730235, 758477893, 794086885, 9275768, 789290005, 397566916, 657322632, 379773427, 952145604, 896071274, 785778966, 486342883, 466206062, 956554037, 325084209, 350109889, 337981625, 779712770, 598591778, 434285273, 305990117, 946910804, 955120653, 321984641, 742345993, 474568621, 812950947, 405226223, 558366266, 956233325, 717387302, 282435213, 391990840, 468924299, 434567010, 963087716, 835113910, 73434340, 967873746, 324255939, 933287613, 973374103, 265618461, 864644253, 461043860, 12317123, 225589385, 924570490, 702597938, 662641272, 984304159, 721466420, 382782200, 935358092, 576933391, 567103046, 174646569, 484792560, 55271381, 939544536, 879291312, 52267913, 998135787, 387445080, 980826304, 483785309, 997548019, 94499742, 885513208, 744556193, 473063832, 487646939, 201228014, 657680049, 505964265, 710663838, 319097863, 150233021, 478412154, 805931190, 48258819, 551560240, 212621186, 10309778, 245202016, 671556868, 832019722, 481043169, 9926134, 948320681, 557467209, 202340205, 469614796, 777853125, 751258166, 106572147, 806969388, 986288223, 18400253, 490927211, 586358942, 854817676, 517821188, 675114326, 3545591, 270819541, 426862274, 233059635, 532424142, 967308563, 862883781, 107468479, 749856192, 220172560, 38004576, 20079790, 32052584, 434472477, 795007218, 367419058, 630305154, 804438648, 993992124, 719443630, 117805384, 969690878, 204037209, 412245129, 13335291, 632824265, 571057077, 145463798, 615401968, 302728640, 890214411, 767759628, 888315103, 810257598, 913597284, 537873883, 626760643, 85334238, 881477739, 558173088, 261790262, 735604298, 705068351, 450680812, 630031932, 658467519, 53055467, 599459338, 292361404, 796174920, 328013787, 262619415, 944614734, 608649327, 351266611, 535183845, 477394045, 851046481, 390712654, 336104920, 86506767, 245666427, 259287704, 140224198, 271815312, 486911725, 472999413, 711450505, 594450474, 903584442, 785973294, 842260510, 88075012, 774666323, 689650444, 775886615, 894957828, 473471273, 657000775, 143765212, 765995388, 112494575, 84934592, 655657069, 249524564, 631078596, 791737715, 570647530, 910824506, 243195281, 354592274, 738871568, 336192069, 41511533, 443707990, 446212074, 172751618, 547533709, 663570759, 231767466, 354930158, 398918419, 167436662, 143854977, 147689563, 938465764, 2141944, 156833993, 981214897, 256817481, 466838607, 734591179, 191740704, 398512527, 383454542, 487641579, 491765377, 391520479, 199731977, 7904583, 789647329, 483142279, 803623674, 69362682, 603814534, 475278689, 82409695, 797436957, 472479721, 359497005, 631843050, 870740280, 14977892, 161285848, 502344055, 905480435, 386967807, 882245594, 603508694, 309584903, 193608434, 549389, 146509832, 151957591, 532106608, 334787306, 548437385, 530969919, 876891035, 625805202, 357952163, 940442287, 621808600, 529873177, 80454530, 984004593, 374487658, 18401524, 345902051, 730820829, 562280823, 930145379, 531838871, 716095126, 139364054, 271137566, 485586987, 646651244, 859434483, 7321046, 527061315, 941499634, 44226127, 386433217, 447494199, 533936544, 816211594, 490826019, 152764240, 59102950, 399186509, 826172572, 924208156, 770309955, 346476679, 450263409, 736885870, 387641739, 618806371, 952949030, 76515549, 783371824, 539190738, 93520496, 610891056, 601753186, 480010471, 930457478, 725012509, 340040527, 492813434, 310689091, 841909023, 733250758, 270464284, 47649047, 805884266, 391116274, 252833558, 567811713, 433660874, 402152444, 393763319, 612059551, 239247613, 309747647, 731059591, 160051055, 808519438, 366751450, 943031258, 693353913, 93516529, 397825388, 832340442, 480626389, 693224653, 629601708, 504527445, 305526380, 319170207, 718179590, 692788944, 896302035, 570762620, 369074462, 702582223, 567981835, 217686944, 362753964, 976950014, 158282446, 721345830, 671728065, 596914502, 231316911, 413509312, 657283946, 297746870, 297117676, 110831191, 427507611, 867157038, 557608717, 161393431, 103553642, 686090572, 540501845, 159152102, 794565502, 256736129, 71951617, 408762605, 75773853, 489388268, 122088665, 53362091, 695701942, 933598447, 481929016, 479812144, 683649568, 941728039, 73246881, 509579706, 902869154, 333789811, 282110242, 68645161, 80016240, 981159566, 661884631, 386760512, 628992642, 745678743, 271264634, 282528714, 959168875, 411816585, 278538896, 165105309, 156310340, 911146077, 835702543, 178155708, 873515162, 330841430, 311190343, 992305213, 828609438, 321969032, 285686323, 275914044, 755994722, 490178776, 651415176, 752683677, 407058020, 784216847, 460936518, 765648511, 847909019, 58802140, 213851988, 122147687, 703503259, 659296388, 407828544, 636291435, 99202264, 502177173, 348045573, 118837791, 401785787, 253562698, 270294629, 445036000, 120017891, 301203593, 42292275, 743660810, 678926129, 745364989, 551770787, 642344407, 137896600, 241084194, 574078682, 771147028, 245361893, 598571765, 410377730, 185005291, 485445844, 623635266, 399989848, 809683189, 391704003, 882090461, 655162610, 685175369, 253411887, 897699616, 443277452, 367637260, 75410721, 822067932, 377317239, 839252455, 129397490, 457091362, 694712970, 374850947, 879847573, 644380604, 711766247, 579552753, 757733041, 73672174, 190632101, 135815374, 199010005, 226260125, 125323918, 950261431, 750774187, 282446815, 869606609, 714001078, 905530782, 820406752, 913373069, 714937243, 549685191, 507241118, 991324431, 87759167, 277305386, 586904331, 70747648, 568337072, 985781504, 222011631, 434696635, 843161480, 29340152, 163490810, 593190831, 156331822, 644954613, 952189828, 237088421, 54148739, 852392196, 951489521, 970488108, 904196111, 17123549, 703657844, 870583346, 816431445, 973912129, 193393190, 885675624, 162353711, 6330230, 514941105, 28611593, 468662067, 52784252, 920049608, 957823357, 834517461, 233626994, 717066690, 875038261, 700066579, 946555793, 443081114, 677106421, 720653417, 584035256, 872632096, 884481976, 377267098, 678619876, 276278890, 731183382, 592891368, 518651344, 157305825, 223606459, 40034272, 536301543, 303787434, 898672665, 448123244, 518778417, 369047663, 861865423, 772008051, 938908066, 87128664, 18710570, 664705869, 953299331, 756087730, 131423446, 949535314, 481435329, 2937883, 926205432, 24873556, 657319513, 380668149, 693704253, 463417044, 227733299, 203656422, 412948856, 570383048, 175829013, 597107939, 999720730, 643494790, 121253327, 99420842, 594892939, 440349270, 535098875, 605304253, 524684254, 469189717, 557838805, 446794112, 752384500, 14995492, 610978769, 799363692, 226279953, 690752635, 666071815, 294691454, 384080106, 72089041, 480942040, 65375711, 364019370, 701972324, 692958618, 557871188, 435283186, 72933907, 190843887, 47180310, 79098193, 5291061, 116581784, 525065177, 612180760, 221874215, 760835915, 951106130, 779943332, 434658855, 813601879, 220022781, 29977433, 974103375, 620616379, 291157054, 992512061, 524492097, 69801687, 671978067, 277846855, 758944636, 856878262, 747176142, 195744446, 891115620, 36184750, 920534878, 472672632, 187690384, 150960175, 373931469, 837244584, 401482968, 967811698, 360190175, 539313304, 372561953, 715444492, 523882816, 32925822, 629678171, 594721141, 980291236, 896726270, 270821215, 454995482, 56045993, 42964824, 122314470, 443437390, 862319897, 553710746, 219202237, 745358609, 748540098, 813255077, 715690201, 487068842, 493307756, 720065965, 447466656, 764778601, 804140531, 708702907, 961283988, 508995696, 343126227, 996055530, 611828694, 409944706, 929558610, 306780598, 148859593, 544950106, 156024556, 504027054, 270678514, 510492742, 761974487, 886573626, 521132112, 795778869, 607712479, 34843299, 300937440, 425842954, 895981540, 26170345, 576454449, 245680176, 641175439, 83342413, 237046185, 728712527, 965781970, 439623652, 272986137, 31990924, 59982710, 599415512, 989171478, 737774117, 108023749, 86691575, 376060351, 301098182, 877642664, 842792080, 660356726, 770166722, 439196075, 990857499, 486662337, 562801925, 801737667, 888469835, 879578305, 172725841, 498084102, 482130044, 801900198, 212839669, 294128464, 518471289, 719903012, 334580491, 343811891, 811372629, 842797260, 615764588, 869486736, 551319662, 31688492, 269242737, 990723766, 877127641, 19789341, 220907188, 394253697, 222922350, 759658362, 630635057, 708770995, 688841013, 284852866, 43794635, 769121162, 772757734, 1521182, 633148981, 993700291, 434560258, 910709580, 886097061, 95703680, 167340826, 861511274, 342609547, 825074422, 638356184, 504948765, 325806698, 860655257, 246827418, 71457463, 81672595, 440291305, 923127341, 240372819, 717147309, 789355260, 914291164, 644203760, 440250857, 216284978, 525147746, 472991425, 125509497, 791850965, 796887149, 153200397, 721701055, 99074213, 465722586, 276102406, 37715875, 228010876, 254924595, 743280567, 361766681, 674132793, 331340677, 364773883, 87064511, 621799210, 56669251, 591849140, 386990363, 265667983, 651656785, 300298601, 929568852, 236950562, 614811986, 706829363, 297859592, 543444534, 284143317, 548062366, 766266394, 622288117, 768090026, 79669532, 21562950, 914481872, 570736020, 584448671, 155175504, 129215297, 656958671, 736749746, 756436198, 907086906, 183521790, 771415567, 556746206, 439558792, 119830829, 974758219, 467651174, 289366509, 534987299, 887297249, 485955861, 891334711, 21846240, 400918358, 92902288, 229374314, 60174580, 20359127, 55200491, 574623625, 246630786, 714281692, 241300107, 103882130, 42821839, 699255217, 699502405, 947383072, 16139504, 362271564, 735426286, 944543293, 231402985, 969882764, 488765548, 379822556, 957405603, 869332430, 438652494, 62240664, 709840342, 541210901, 986680676, 579098867, 78741147, 513871338, 991708511, 395502492, 390033023, 442196646, 467108804, 827139292, 267234356, 710816254, 535341206, 689856655, 161510501, 722100916, 222594928, 376575523, 824647138, 34786009, 218035162, 324563849, 917985133, 123140270, 401031954, 924681659, 801861863, 737499662, 988315564, 888257982, 271992752, 592572543, 321641411, 922669019, 834948900, 589771447, 87092850, 875207623, 522307358, 746131012, 179260455, 207409941, 711395040, 459971351, 993670161, 306974067, 243817123, 72046196, 375323283, 447590155, 959819751, 3797644, 689542458, 506805346, 639036655, 665530910, 791615532, 975647220, 967339648, 841156217, 273395283, 860619420, 647167879, 544496846, 359045841, 326737625, 204302434, 844723793, 303391485, 453723952, 646928346, 14796465, 326976973, 136407743, 813894099, 498728276, 941887206, 732022205, 416505597, 953957852, 358500298, 548934941, 804603808, 987772952, 188101806, 398958775, 167953947, 785405379, 401607973, 541294567, 955906333, 883045907, 89369548, 352313571, 801427558, 28675525, 213891337, 504793296, 113452797, 230842673, 743283614, 795597972, 956264006, 392502934, 203554572, 302869862, 848285298, 449348562, 777243001, 613673492, 26279331, 507710279, 102354984, 84680172, 434920919, 281754688, 421225059, 719728402, 663099488, 318958004, 48001614, 858036187, 136463015, 356692794, 795945758, 960314955, 297810209, 798822447, 684438556, 170984262, 605286957, 762912356, 942144110, 883764994, 234830872, 392572243, 114723979, 9825158, 456260550, 211719926, 746932365, 16011430, 909796064, 99240656, 717734509, 504433111, 937537350, 910567750, 652949994, 35107895, 614036709, 710114323, 963968830, 921802600, 337455468, 317115091, 138571445, 880633362, 332755305, 305205170, 656105809, 970955082, 118491027, 55325117, 823907745, 948394270, 467987255, 978591523, 488583135, 566837329, 188274513, 91035204, 708391277, 584782346, 112523007, 465045468, 796258301, 285473046, 108676950, 563183865, 43716869, 489342646, 164777601, 222890779, 557857518, 362713625, 303334580, 209783332, 59850555, 553640467, 317406794, 906343958, 726157386, 953545759, 725073925, 630334821, 991909825, 801812679, 95758285, 897578163, 499600771, 26015217, 152843890, 469891779, 965906557, 587589217, 719162688, 767349432, 444922408, 460108802, 736320907, 91326268, 533630913, 759890386, 532643315, 165432720, 95918616, 911085805, 831121857, 971339825, 553795528, 821419266, 837947352, 781487476, 857316822, 631184816, 515055805, 214303180, 470481593, 927838783, 259047525, 560114577, 870864173, 666379994, 306944452, 865019772, 30601728, 186425580, 703473358, 920189829, 335695794, 399242801, 577867559, 546003323, 402486500, 580066715, 626865208, 337826767, 119750471, 860315616, 606064963, 877518931, 63246205, 552461707, 620241410, 550885527, 433385572, 541732676, 983903595, 688303046, 55234638, 390489773, 516540126, 645753762, 393229056, 476137274, 823578460, 273331425, 651395264, 839784132, 101724208, 278641041, 948001607, 671216039, 609354011, 978009708, 700185441, 812907203, 369821140, 633639492, 946769577, 754476448, 812749149, 568035712, 438724286, 794758864, 587301637, 975377060, 421786701, 419659076, 24739420, 23655917, 467520864, 655283484, 801003811, 90417860, 199237944, 211835718, 198601391, 67724420, 464312891, 750407363, 986000309, 900816505, 490080793, 128378891, 777489548, 188663414, 377229270, 327724838, 157686441, 851350389, 76407393, 986308228, 355047429, 504418631, 21815577, 731723478, 68703864, 523348798, 126773319, 429403891, 693970387, 790787099, 228462453, 88743532, 264386651, 492707318, 149711911, 3796539, 602260943, 500457765, 653135627, 407021994, 884012335, 192051176, 288514117, 501204559, 532172264, 540743224, 22246933, 10781531, 572464564, 403328374, 335366763, 423635882, 532840306, 320484546, 669570043, 149035193, 683866168, 878385057, 50059176, 374680006, 758564188, 744035311, 571432764, 450918694, 948585720, 677196126, 598816074, 264588905, 696060753, 211739055, 673193609, 943516934, 849647427, 797614313, 121621207, 211671330, 863624966, 192620241, 60359768, 138104991, 154491954, 256044758, 820786859, 554324389, 713830218, 695975900, 298571581, 347291302, 513275510, 130620151, 326904264, 236972746, 994806400, 640789335, 181055944, 644140736, 954391397, 457972384, 989299722, 878070843, 536596941, 28084744, 467742682, 217512446, 447653555, 161379095, 978100048, 3921623, 507179562, 812439567, 708045033, 606220503, 285072843, 959608803, 780153849, 488640945, 65877042, 104355349, 284970671, 792541299, 812720515, 407226950, 151192522, 427060005, 262002878, 506777050, 208387646, 47096413, 59020022, 873384922, 275482273, 458695480, 588574696, 591992149, 516254703, 743766789, 907933541, 383922609, 123774052, 157361774, 361940926, 133332059, 402910183, 628038916, 130271474, 808687986, 624241682, 790552664, 256943795, 212585564, 229732040, 230479527, 595442726, 91593003, 868995993, 392053722, 689585704, 34246593, 851238635, 373357393, 271442782, 451766866, 846150751, 443839563, 423694306, 408375918, 39472223, 686530001, 402903330, 66936463, 334291847, 765015161, 595261508, 819037061, 211715109, 349295066, 482596304, 122210447, 59014616, 110916204, 770441374, 78811955, 992046866, 360958674, 420240279, 455144667, 840732051, 193487950, 640326867, 995498804, 24302988, 531416828, 321619782, 882205664, 305153613, 65377558, 508103272, 929040203, 95061629, 964033350, 532009627, 179465422, 202848478, 160331737, 857843566, 394793139, 159385904, 503906408, 495722268, 132840530, 159533803, 775598107, 97310262, 689544146, 755959078, 11875115, 45861339, 355431098, 554873993, 555926730, 637455756, 584801036, 917983625, 765838997, 916750144, 20328315, 233371525, 573195536, 825347077, 204509639, 281435706, 180564683, 150781818, 683142950, 139126363, 874999918, 739514581, 898053047, 793256551, 61916704, 943733373, 605077900, 70010124, 279553450, 756358322, 898845610, 824675564, 87307510, 886113896, 877219654, 278479335, 312015704, 252953139, 101056358, 87592212, 484377778, 919125230, 530332626, 83389722, 35660014, 355182181, 175973606, 588804930, 34015455, 946447642, 277606432, 660411037, 632866678, 83689902, 594156861, 585362557, 891369936, 752210135, 319473216, 527607934, 343964504, 9448891, 39571255, 412005096, 260572594, 553442632, 603088728, 388555074, 274550851, 385410709, 679709845, 562030827, 971389251, 320438387, 574393622, 814192953, 852554459, 102502191, 705110736, 94755547, 480565643, 923840443, 678132840, 437093781, 960062720, 377822123, 482764670, 414806603, 884158957, 892656699, 480560123, 445526956, 492654139, 696105629, 345706449, 734865729, 104141738, 604686695, 38736258, 665775379, 434615684, 510076459, 490543949, 746374721, 143843308, 784230143, 392472423, 493911294, 579101083, 838293704, 606841257, 720603087, 366726769, 974957338, 24410007, 552413388, 749561201, 628207246, 566914501, 697988636, 743626254, 323558012, 659516524, 732146047, 267835662, 309304919, 736460803, 70735393, 835938574, 582484767, 110763422, 791277502, 952756060, 345420535, 775424274, 295354834, 445890438, 207243497, 894592295, 237263859, 10492927, 851621263, 255459119, 197798251, 902666505, 502243711, 320439701, 864851236, 623127419, 476264055, 425984583, 368004001, 445694705, 596070499, 618638555, 990516848, 931782426, 498527607, 405600032, 1151131, 858841760, 891706366, 303805880, 951721625, 306331661, 705477536, 558567821, 965319875, 483719540, 34956968, 822881659, 207455675, 447441023, 545766993, 36356081, 416455212, 653060490, 67906909, 571945438, 605869258, 606016663, 591202047, 617694528, 654354516, 16216617, 399655753, 257556101, 895299177, 873426846, 207571358, 405987609, 343056122, 398983752, 726990156, 468269717, 315744497, 863824163, 198047293, 913740619, 75380832, 217842425, 501260924, 726206463, 255206611, 571392720, 513525377, 811634732, 367418683, 312557137, 550745217, 473951547, 231007237, 217464995, 386328426, 631027987, 287289561, 288717503, 181378639, 324061344, 475198625, 749138335, 105290315, 930568215, 441013881, 728804504, 130913456, 406237514, 755305163, 949228841, 684366558, 127104731, 617327478, 324172543, 311080274, 267617986, 975060213, 796002443, 451304456, 852008236, 218992782, 358658108, 372945009, 676764009, 961854828, 951166529, 427247144, 770594287, 676616132, 182741851, 923341027, 31395991, 821351005, 37407233, 980334526, 319806314, 35535666, 657538873, 226273987, 50022851, 318889819, 123331953, 637665596, 335825363, 89815601, 816658693, 903680590, 197584150, 987017041, 225464928, 175746815, 710280296, 32619209, 896850490, 17056936, 798119896, 960214732, 154597819, 271730380, 10444742, 397415556, 44102443, 198585465, 878141206, 420703292, 829257302, 442914311, 102820836, 521623138, 681146988, 12919006, 723403139, 480512759, 824139186, 64240489, 174761079, 75451643, 760759950, 742349857, 586626270, 441137984, 461638704, 143403278, 755526335, 776157513, 777393630, 330375340, 288113944, 754852740, 583544588, 265492182, 630393369, 542841600, 106276733, 255871560, 110210626, 480606590, 198312331, 212911412, 628857639, 828460463, 29255345, 205671928, 424448764, 944946206, 514764895, 802506430, 856201400, 50506787, 903568461, 185447234, 138705431, 18435588, 280117939, 131700925, 96748848, 124367007, 528331242, 439159838, 943502919, 698872631, 686465470, 534132010, 368508341, 818228684, 801188404, 558241535, 944660607, 500299769, 101202419, 621288023, 948248937, 183386288, 435145601, 652365670, 577948346, 452909887, 447813990, 341232756, 266919445, 938330489, 486187074, 145029355, 239985187, 719690568, 870873472, 976236731, 454913746, 688054407, 761804294, 124791442, 431589143, 141060986, 293531343, 33904383, 552054926, 393587330, 899928053, 169186322, 629558651, 815706846, 111309700, 913253231, 466241745, 443186794, 474989480, 134853748, 430222242, 166328651, 181182399, 68478150, 541212304, 468845521, 735159972, 526728175, 360385646, 600775326, 53563748, 202058511, 250114111, 691898669, 694023024, 148210928, 896463642, 384805131, 752429500, 128581511, 581613137, 843385040, 340309457, 954902600, 896101128, 59357655, 841731313, 772972509, 697074319, 341292534, 50028066, 540760405, 612179701, 658853655, 123146683, 151825203, 294433096, 687482344, 332710623, 994571171, 327741434, 938268060, 239617768, 852243804, 832707364, 469487364, 963798544, 786779856, 646998168, 59735304, 513288824, 56370746, 629306813, 935310368, 868739166, 31445160, 347527650, 429567504, 624260513, 399245432, 331489083, 753222515, 991305339, 240921207, 519816336, 326982448, 629063984, 729121927, 448202940, 639740177, 540200778, 249910113, 844598327, 88379307, 885112199, 455771144, 854034468, 64770041, 904811317, 393544099, 450784666, 26624688, 849775592, 428303722, 367363829, 124529968, 757106641, 469403169, 605874202, 427203604, 825518061, 142247132, 798433036, 296131179, 249731398, 812922340, 92042241, 229225655, 793099829, 56963915, 370303216, 641446197, 417091584, 456012704, 279423083, 530736167, 813034379, 825193291, 670989221, 883080271, 329034148, 275652331, 767110037, 497398031, 189338610, 299270266, 853356399, 207150975, 28559930, 974528185, 521564665, 144094028, 583233324, 209320740, 240940503, 116896968, 518389043, 213432051, 46003217, 229759731, 606609889, 59542867, 550996024, 165433039, 908398934, 360697550, 103535620, 661831325, 5493708, 90901253, 724194600, 715687616, 779416548, 862084635, 890252951, 432823896, 637728509, 847844277, 986837318, 58023721, 224673693, 545945887, 460659762, 574582954, 617268290, 461792407, 127021687, 368222023, 311514655, 492795660, 289766883, 21542433, 219224407, 665420660, 798783491, 731766572, 906998051, 109369113, 12198040, 999651049, 813349411, 456526521, 528837763, 566808306, 90888863, 875732736, 584381398, 515554866, 614267876, 607884750, 288632594, 139625743, 995235831, 479068777, 197595882, 605884302, 953636449, 17180596, 746452100, 522582483, 5625022, 597027810, 371253501, 754901298, 809727259, 553177652, 871918464, 197380754, 410041781, 584872492, 775079732, 604369313, 840522191, 186456895, 177589864, 183617707, 261749392, 907511611, 468862990, 973926180, 893451975, 782430199, 565182789, 354567177, 472561266, 819488128, 275369710, 583277583, 307541545, 924630197, 132330953, 373621508, 890965249, 306818472, 691909319, 457367293, 170557809, 8167254, 692938934, 317106152, 121909352, 690058774, 546966269, 757421473, 567424819, 373901780, 293106029, 169965861, 608178820, 729192105, 902424626, 578725504, 378311739, 393840972, 906457257, 178740056, 64096581, 17825860, 911676133, 577740677, 957327461, 548223878, 253244403, 552932477, 489696426, 588643977, 822380692, 543307757, 555224802, 827508175, 558728552, 476725945, 956162131, 499426969, 428451398, 420947141, 815706841, 560340615, 338903261, 164125603, 431688620, 628077769, 891958695, 575348362, 169317483, 93249596, 367529249, 464929178, 237816176, 937624467, 386983676, 724568752, 666224267, 835399050, 98831732, 378688050, 43603683, 250298706, 671448306, 73897892, 758539755, 218226582, 462239321, 949290693, 139933699, 234073587, 92932686, 17423716, 750257078, 911348627, 880446548, 682699018, 919277454, 383271670, 182091357, 537512370, 346428237, 625100286, 977327704, 184697480, 516433597, 671339433, 295774660, 664196885, 860832824, 491830118, 519637621, 401846665, 3236756, 406273946, 394759696, 543910663, 456560834, 599187833, 904562767, 682896997, 435241417, 827253216, 611153962, 811491417, 524184089, 354631220, 106748306, 417141353, 827536042, 522536304, 530172712, 297832406, 626377097, 773892821, 36126589, 15447846, 574486364, 605591929, 812992360, 621943731, 843061434, 420180936, 998543464, 238770104, 551763032, 374184564, 791386479, 576133611, 59029442, 174479047, 81944300, 951982225, 199980223, 64150406, 523599541, 550416746, 251190725, 412890008, 192685459, 564217807, 519225350, 338059055, 754517414, 885914561, 121427557, 614153812, 273748761, 256830262, 373243648, 281347054, 312053786, 512772780, 731766044, 137117063, 639853415, 397102703, 507959958, 539324649, 30267054, 670243141, 923821324, 90190890, 556871775, 254556759, 232411400, 164778370, 773001683, 485961588, 437518957, 446882230, 806968891, 337731260, 588122466, 891084133, 59354650, 528212765, 363967953, 409729156, 749397779, 865963510, 994984418, 396626242, 919166206, 246318167, 981502167, 931653579, 751222506, 218809752, 405073734, 4532018, 837321068, 369851791, 632660799, 534077321, 290181683, 574765444, 280833688, 386638568, 414616570, 878940481, 837256906, 534176386, 683405088, 527205742, 554029276, 973707470, 926218418, 805198159, 548127578, 618153533, 831352019, 569120112, 893432312, 335326621, 695024589, 88153108, 734209087, 501640460, 592626872, 699714920, 908804399, 902786113, 938264490, 322856039, 514423870, 775779818, 568324492, 692511065, 500593288, 92137828, 515316879, 872900556, 808501909, 348588594, 415108625, 705813204, 823261325, 257029720, 649238306, 4602758, 509999656, 54240148, 884623622, 625222997, 8337524, 473177317, 2578318, 637885136, 185652842, 964636127, 111364282, 710750461, 392924468, 40910775, 13792703, 176323409, 908466799, 480838251, 95219705, 654297641, 803522552, 729395241, 176866359, 767085379, 770002686, 348436329, 185637164, 690712390, 850946692, 393538175, 966793735, 496134268, 996162233, 74722555, 621913407, 320133931, 750958228, 670083305, 450786159, 922563272, 782243246, 333390531, 990355559, 445696418, 234032850, 602391289, 526994517, 853564719, 197346267, 419934551, 373130434, 163854394, 550898012, 99742522, 379445770, 616386087, 470461908, 921394814, 78749611, 603705366, 417582434, 526581272, 216903314, 544652969, 231751123, 572002521, 151397469, 784370380, 259566020, 239966543, 457475397, 705323938, 672514807, 600833839, 378692192, 918952712, 667350735, 235127546, 263466721, 130397397, 505492700, 588993627, 781406736, 107058048, 323158833, 516193246, 642089833, 604332447, 517766458, 181050754, 296603336, 254050811, 553633571, 876331708, 835274488, 434590066, 954078834, 405915282, 120253641, 316755740, 713717507, 873310568, 152653407, 395349273, 265356765, 726512626, 175280010, 567963832, 325435798, 331594733, 181187208, 472690791, 692624915, 69738262, 315532393, 202587714, 788874016, 956992800, 507760974, 25820766, 98197528, 823529458, 696071325, 388326621, 552287160, 599590437, 122349948, 118126315, 904735249, 785089331, 623016822, 627347253, 401980614, 340692347, 974875669, 292142575, 613829532, 281474443, 210106126, 848339354, 885851818, 713035921, 523923911, 963542425, 344335649, 54455486, 839120867, 7188941, 80199908, 875869442, 120972490, 905881964, 198306766, 579767306, 742115620, 545388659, 334121761, 241996633, 165534126, 834067857, 5024936, 330117234, 354792567, 895817652, 196544891, 619200438, 147844901, 24697273, 457801553, 26246128, 656629366, 539389941, 338983328, 506201392, 691003756, 709097430, 724203261, 669402775, 407411547, 477410687, 852890293, 332207915, 794526295, 445521419, 378926239, 482916799, 229081349, 992375007, 502785043, 592883243, 57209750, 339143016, 326608004, 307982654, 213631050, 213402523, 5623078, 742865777, 565231613, 405943731, 531162433, 285350922, 756472962, 573086062, 772114013, 285290267, 818489830, 107780660, 439525179, 937617767, 786211358, 975106247, 172803122, 863301995, 194094436, 395667505, 535524551, 413892242, 441226860, 957928802, 472413969, 790856383, 485817004, 734002030, 149224737, 875569194, 580093363, 428917023, 98456830, 175938310, 974784950, 724664398, 152209863, 747173946, 724869296, 433130953, 372802301, 714755599, 369893012, 349646375, 871988466, 715989430, 2761554, 516214803, 227508797, 849199808, 969253999, 392878238, 129796416, 481506151, 598350112, 385984052, 669008412, 649664858, 796550837, 646895086, 358366917, 696648839, 923621792, 904465128, 375443944, 169579469, 41375509, 861563210, 979421962, 532402283, 670399601, 645886233, 555631027, 569896618, 464300709, 513724022, 654680596, 27734668, 640351837, 953303049, 410321601, 459795181, 727984121, 711630338, 216442289, 949876633, 729689207, 496295377, 978229373, 322377990, 909064786, 762532444, 287593860, 614643102, 406513405, 293938318, 682278645, 137728775, 837809616, 914524367, 835826674, 191869166, 258371544, 945366142, 131919275, 132237842, 616400645, 258622239, 866827154, 76580799, 11360703, 35015356, 212822992, 469934136, 693103669, 752680498, 160551299, 647537409, 588312765, 585999042, 787658715, 901235003, 599631655, 372200085, 908774390, 770255120, 49419869, 132035766, 487483805, 264591346, 616187794, 707842749, 914070902, 799191025, 488289472, 417980383, 651889616, 767125200, 537858738, 931874306, 119333394, 630188315, 486368131, 865882528, 485502973, 202803533, 99704330, 388685950, 225156442, 816392546, 442821322, 722411188, 690571925, 289698428, 312796466, 899616526, 519873375, 20577215, 109250865, 180742426, 344381294, 767026131, 283231776, 317535021, 980372185, 80680194, 916497216, 951941598, 432590720, 253377124, 199653406, 960824076, 849569972, 699710349, 861242777, 735839002, 674497328, 514887148, 706014636, 243639681, 643651163, 896751718, 376385969, 932497019, 250415717, 796740227, 365970539, 818929660, 652924464, 211936696, 938888693, 68332353, 629836974, 240713505, 402180023, 863496199, 471406187, 628293952, 247473359, 489075424, 95672813, 357950963, 854350552, 977179892, 426772707, 489727457, 47283181, 369315446, 685982172, 402878474, 272863472, 545594062, 880614195, 523809060, 468266279, 57867943, 786549214, 162375475, 881505964, 507869870, 100226782, 153114660, 279043645, 331455386, 570304411, 294271874, 720480009, 207804944, 628818087, 359892484, 13944981, 871016518, 294925852, 632012029, 548924408, 429680012, 824763990, 885061290, 443657567, 821036866, 109807506, 430063558, 784709803, 184497110, 192759027, 886538686, 307067594, 163300600, 217590498, 295658353, 97475007, 889865059, 447045308, 251879665, 617938816, 805200461, 317820121, 172823105, 519739460, 27434088, 345004965, 830388216, 670276003, 97987488, 261577559, 411266475, 547517810, 139585712, 213313004, 132940405, 33959132, 593786318, 65870342, 618636285, 142902294, 181640054, 236017938, 868157672, 934800176, 349976041, 491353864, 617140299, 623391795, 833082701, 200414255, 249437788, 670587269, 467799265, 595183747, 530518759, 271775030, 973987231, 967410812, 331055451, 85691420, 871217806, 784238111, 217087106, 142955950, 214823588, 520486398, 194468120, 225433779, 266245913, 622450599, 391363196, 528004129, 162375480, 225004114, 661554063, 717138571, 731109116, 132625988, 443981911, 314354022, 522476229, 76519209, 715693282, 764792761, 244025024, 441493591, 342150848, 54304721, 10268496, 476612482, 741288871, 185392925, 523939369, 964606549, 35840038, 664403022, 971457920, 532275255, 445141744, 896365524, 789560903, 855499264, 692508211, 543396423, 247647635, 528492444, 743339750, 606369318, 28509056, 92507673, 325075628, 363523162, 985554070, 713657471, 530950947, 812123156, 709712306, 201110324, 397321626, 289652927, 215276557, 923866494, 954196863, 789695565, 91945646, 626932655, 159507413, 109111288, 585107543, 12040255, 876164274, 955137308, 459349142, 224496129, 602371928, 193963733, 852339217, 942526969, 483778590, 123547926, 512738731, 291837641, 912108270, 761260155, 962748446, 946231493, 362757695, 940910130, 267037921, 210782441, 230101958, 549374739, 827565563, 536178844, 821938264, 599286108, 687432946, 418953749, 345137577, 430949472, 475455354, 692414286, 232043948, 495686070, 906520417, 803772211, 676238551, 421491919, 526254866, 105764492, 876482329, 252657447, 690247805, 275902140, 70444434, 793098729, 664029323, 932457224, 837165873, 780880334, 419477052, 457032795, 339801262, 335746320, 776990202, 528886154, 859367142, 652604200, 558979173, 426549489, 980598207, 586988010, 214207579, 346903227, 881849263, 144988567, 153071702, 219451686, 809254444, 608151000, 463478210, 740132416, 954949389, 340143813, 704314012, 777172007, 681768667, 146052793, 23509382, 532119563, 341768134, 708277884, 211235982, 521032054, 213141855, 906757652, 588238790, 572009227, 631089535, 276838513, 741044447, 975498976, 903143980, 997949600, 454771284, 203298263, 820672370, 925803360, 195370734, 838468454, 71095031, 444686469, 854868748, 263472406, 719168662, 31476295, 619903857, 638544124, 865634194, 342820932, 255376898, 315523318, 253810913, 439045348, 342737765, 720393936, 976077747, 11861469, 240298120, 879514682, 272654885, 41916195, 360663064, 399891073, 687403157, 52655495, 248392258, 963547933, 831221387, 654880823, 241083606, 158926478, 435546692, 170031571, 42942965, 837695612, 849987587, 662207433, 559779547, 314434373, 423394846, 126499316, 950613938, 955764874, 709228301, 969479765, 956683751, 104041662, 17311774, 502842508, 723116528, 566769714, 909358116, 672394798, 807670024, 134101290, 337269907, 8764977, 861404457, 989504901, 767947781, 19060231, 740212491, 223008453, 251150175, 875465325, 563277497, 382552251, 721248125, 882503941, 581047391, 125341635, 480601904, 860945503, 199629045, 2445709, 247340841, 120299749, 81726234, 947724680, 488155179, 980372235, 270316949, 144537329, 690384732, 349591941, 195901272, 177403790, 595383380, 284022828, 412683562, 446614261, 870700094, 467902928, 417800125, 857103984, 635027404, 140703851, 966362444, 509881815, 645077640, 435304314, 150271151, 801691965, 397760862, 156902047, 896735981, 723379951, 605556446, 44926290, 987262253, 964883964, 925952956, 82067207, 782687305, 171013134, 742361547, 26916932, 172056916, 717090264, 565682898, 384712997, 798845192, 280285208, 749480450, 922662983, 181012998, 872699387, 462837624, 481599323, 322207803, 389059804, 372809674, 953216622, 235375651, 117246626, 96092370, 118304807, 237287308, 116357753, 779355834, 185058774, 511515187, 119023206, 500009423, 276336680, 917418177, 882394329, 789182161, 417859658, 838818161, 555340108, 824513730, 336000570, 654243900, 202735182, 425493447, 62698932, 437750624, 399368615, 803491949, 614303367, 461326634, 190820960, 962192539, 126493065, 854076827, 822229125, 872625498, 449287672, 727952117, 474230040, 342610036, 526238466, 959391806, 726753821, 479648914, 787969345, 679938775, 705363071, 374329836, 859969315, 923641, 341935016, 597514285, 729814341, 547578860, 997851781, 404229552, 564677574, 332468453, 979631688, 648609452, 360427232, 299541485, 278533542, 232162187, 963199445, 488051781, 704121568, 347086797, 700992548, 416983902, 952627528, 262627546, 788310447, 820890892, 49903382, 911454602, 281959941, 986336377, 604129133, 779296528, 458739406, 319277357, 178858325, 355815948, 546423376, 466519399, 553628406, 24176718, 233067608, 752532201, 15644275, 344849896, 318344296, 517434938, 22354766, 330339578, 218909267, 227468396, 192427778, 485662259, 635167609, 922950780, 939143935, 345027358, 223763297, 903968814, 42574525, 308849320, 23565625, 23049472, 796591277, 457297239, 132331425, 700928210, 270073860, 277576843, 239834397, 940788352, 83651201, 843698450, 759448659, 75990126, 324930651, 661569875, 239056670, 362840640, 705615949, 124854377, 165458626, 144942732, 131161420, 192121504, 776834208, 20116917, 743072950, 61017796, 244829218, 247210515, 866002525, 12874149, 647831564, 979829723, 846508741, 320604057, 35906079, 696200617, 797030698, 240328425, 230373178, 665427560, 727911082, 171662079, 369134044, 481525086, 657839092, 981004623, 818727414, 615913584, 174998952, 583369564, 197080266, 135956558, 438639830, 779708803, 881543088, 546514786, 847800039, 10368116, 35801875, 726235065, 904512120, 3726843, 11185078, 731287073, 485887032, 68384342, 438536276, 784290645, 385980416, 810160018, 48191486, 962432837, 111661143, 492480662, 133001808, 296488752, 595552214, 209941904, 117989364, 736533878, 734583917, 340429774, 584705056, 106441671, 987372648, 702023432, 472972360, 212151481, 184886735, 638771765, 674641491, 703904152, 214957196, 326944018, 395502189, 338261859, 802543769, 105017473, 248919482, 374175306, 829465788, 699698774, 525659904, 432804329, 692088999, 606722318, 525776565, 629212706, 988579806, 10918824, 136192365, 698953232, 875307137, 385915609, 590303023, 21119674, 979528606, 514393580, 979960462, 311755769, 425686900, 798086039, 508698026, 795115399, 121425841, 880322784, 373133753, 917956028, 812377385, 684393382, 350595103, 764702415, 871676689, 347861690, 159849951, 416968025, 484268832, 242808233, 271938857, 760271398, 557208991, 587407559, 339937039, 432430834, 65829453, 254812704, 57232736, 906926533, 590768986, 854615174, 994464414, 904099276, 3887339, 874014452, 920967869, 16783209, 347881069, 344430099, 275520101, 479097490, 281503360, 364382864, 280283997, 909127956, 676197607, 90078546, 139833427, 739159518, 886434255, 440925887, 985844197, 718675310, 683695028, 108432598, 688106972, 308515134, 349757525, 963471592, 901788528, 81817728, 897373937, 291296587, 509684038, 163928007, 785463577, 818805259, 26255347, 173998120, 114292621, 427131819, 118791366, 635323583, 372891633, 34846749, 131009733, 460603578, 255688490, 472481758, 656573822, 291038548, 713745397, 185934679, 700239366, 509620109, 838893172, 153209851, 133891471, 149186827, 571460932, 864845581, 222115293, 10808367, 591557743, 867198303, 750857767, 663616665, 335875519, 13151796, 204606167, 693164308, 954068659, 599825463, 101048752, 886384998, 403142636, 595163986, 977368280, 819899090, 382309548, 771199875, 317175819, 464980899, 680629384, 928240674, 306585372, 26911062, 788682250, 253822316, 670722050, 896328866, 805750944, 825748866, 388039354, 668112168, 281537567, 475977413, 277074498, 901267601, 354342625, 490782690, 335687206, 881397835, 973028076, 67941591, 934935395, 254977886, 560957438, 127212991, 43533261, 917135361, 50615678, 908836888, 262016023, 294639532, 982480372, 846045900, 633711742, 849358853, 831602147, 683542894, 807192521, 973731119, 234301119, 388012241, 697304626, 939156789, 673732021, 739404503, 977359758, 117696058, 933598179, 301416194, 938166280, 64615896, 603226361, 881531792, 625249490, 597069725, 334605535, 475546538, 91076994, 152602587, 434920574, 986417308, 205997160, 882538833, 904166323, 741623894, 289196829, 330399017, 816325142, 538546215, 226163500, 501994842, 764703924, 765895514, 766269480, 369967944, 259681486, 4080783, 872492900, 412610698, 56744913, 49809638, 670092149, 674594403, 372127468, 244480505, 278398879, 942704125, 156265510, 142593027, 288500759, 249747737, 568528484, 349499455, 77617002, 572759255, 886500040, 203757949, 389411, 70031951, 97840481, 998282423, 598203765, 998917564, 320040596, 440810676, 259391869, 763647638, 763019007, 55476636, 400594114, 590174322, 272688639, 515198545, 585149855, 203851119, 3794309, 735915268, 372720454, 691250309, 78909735, 356994765, 27783701, 927865675, 747603597, 981780489, 429434735, 23189274, 555869608, 746135090, 780296853, 688468215, 181083173, 605306912, 245056942, 890305751, 582686571, 621809327, 317990501, 389998816, 616472905, 260290585, 342773224, 511385122, 617229787, 788851853, 36483706, 782990791, 246604943, 929951373, 336738744, 186183331, 488471064, 129240758, 600591985, 952540640, 323338010, 194810959, 413377403, 342308559, 929047418, 627606965, 62150818, 731000663, 396665541, 857706920, 919424272, 799817122, 54646692, 773914864, 609140816, 711415282, 162162475, 241595550, 342721278, 700772384, 215296622, 765702607, 952534555, 909137902, 555924686, 485762830, 325404603, 812861931, 739915172, 179855502, 408089634, 264440160, 421817967, 39220063, 883549144, 105737139, 320115125, 571748252, 872002998, 143437917, 935860655, 7987356, 71466615, 165219462, 59822091, 943882534, 761161364, 268079465, 631666153, 98658794, 397859642, 269864201, 444790905, 292748133, 958582770, 21180084, 969010806, 482177578, 14545913, 411480884, 798512626, 686783801, 832326625, 728834225, 972759358, 182611190, 953365160, 164379651, 684994171, 64762306, 74875093, 342153352, 630438687, 162328805, 757087073, 354611607, 489075819, 682809466, 305286149, 596285536, 61326957, 293027632, 596651815, 947294533, 356078206, 680154435, 623532737, 762470029, 251873842, 371202890, 687429311, 223491489, 995620848, 597682913, 353963854, 826666768, 337273528, 946395447, 832927799, 611716120, 485955018, 590520942, 894933887, 626314889, 107197198, 982675527, 642028690, 843472635, 779525729, 790057946, 15541342, 294867857, 744923455, 289165393, 24228805, 776422466, 956171435, 461984750, 284876668, 374458663, 75466896, 796149407, 637113628, 388393382, 91601423, 99791158, 784852854, 484360610, 740435208, 481290533, 143295214, 544298832, 837961200, 926947700, 988336878, 5594250, 894942247, 219975346, 15692861, 832389087, 559839536, 70410436, 946464952, 145540485, 36692335, 902759121, 908283695, 124945922, 80765279, 341295000, 785511160, 307101006, 511954457, 231167958, 996376865, 227148030, 154449115, 905351267, 491945067, 548888398, 508164497, 426675728, 39809278, 221953963, 243117578, 821428571, 647306037, 971801476, 339027155, 979687520, 806428809, 351865235, 345779077, 82306700, 44789764, 98770155, 394220600, 771805411, 504910043, 198399841, 377418968, 346128723, 24126763, 193981871, 134996732, 883175758, 852736656, 77464355, 793919717, 233836373, 299279394, 81975700, 602950636, 769270519, 71769852, 140234415, 122970123, 135520209, 693837605, 671501701, 162547038, 508054991, 822003495, 981845257, 62193772, 277719338, 337955121, 136938181, 633119711, 612214871, 134593311, 762110987, 14020211, 376447533, 777375950, 477943852, 881825916, 822941991, 171879161, 320251461, 609823953, 731623555, 294090126, 575216799, 250701966, 863091600, 597451902, 72943974, 815770024, 908301756, 561811660, 605923948, 498741425, 84219393, 505038743, 636822679, 249531467, 497563538, 306227746, 912237320, 750395173, 43409910, 336822343, 751604482, 265427814, 134437898, 90315735, 763071382, 388944971, 546255169, 728662460, 303269992, 870900855, 294878815, 892751626, 836433028, 991728399, 760181134, 222339665, 816584249, 86948350, 838169829, 693632823, 306231010, 926404969, 465372159, 578885656, 940866498, 989847972, 59177811, 622174722, 284232470, 406048732, 583296646, 27498724, 305694037, 20299956, 690408192, 43772832, 872696386, 827901436, 915345129, 285600320, 535153090, 965312970, 808958749, 159223913, 836080124, 688545791, 519683983, 713159792, 286293696, 785857936, 142715010, 298714340, 128255969, 606168910, 806759653, 704798670, 984453529, 437568354, 271999451, 854756175, 145849286, 924301292, 499553758, 736945151, 953144257, 841696625, 967184839, 415655679, 221837355, 821277722, 648540177, 946006564, 899785853, 501560805, 433104870, 345954902, 907161459, 912202318, 114488077, 945101210, 570246375, 177603713, 538537426, 645946655, 348740772, 573207144, 85024840, 630088990, 519186282, 377641330, 50506699, 916760774, 714296077, 382210965, 97267951, 850310003, 273814072, 127571186, 605808115, 642624949, 444216071, 384137058, 524835096, 529431281, 606917679, 914666295, 673045402, 727684950, 811276531, 927216464, 905050883, 908863052, 636824339, 477281895, 561802481, 232288076, 354136350, 313458930, 27366405, 51743277, 70168874, 362729730, 833343404, 225160894, 491804093, 635580717, 470906327, 776318228, 624660869, 17549263, 121866884, 378741611, 527111610, 337601097, 683433280, 393237344, 188424573, 871424405, 971714964, 601837397, 458703733, 942200387, 571041325, 939473345, 82455756, 134348400, 516633551, 373093018, 637727955, 218472766, 312953676, 216790016, 540302537, 698505546, 492596515, 413615913, 775469517, 78844821, 764662331, 548737313, 618461113, 861719519, 88517857, 25689847, 69541244, 261694736, 963431208, 505627162, 917678032, 25090003, 919447034, 150421681, 675163763, 524105114, 266591629, 822330245, 213917461, 503540969, 507888733, 747168479, 306272965, 212154788, 986505252, 113720094, 245248246, 271850740, 364747737, 859460328, 76391370, 750350928, 524201929, 760033134, 524225229, 951422519, 74681719, 384337767, 855726809, 993234648, 496022941, 141836354, 661983865, 241734272, 182615217, 429553803, 145028716, 612282033, 411350951, 812663939, 185026205, 187297446, 429847897, 400684482, 668249714, 701930481, 68715836, 134352137, 482530834, 514198374, 400272148, 547697842, 753603109, 151304765, 89610592, 333034951, 616208927, 829784258, 583002796, 502669966, 968079576, 720927468, 759778498, 179060971, 375983284, 890506524, 923580273, 698388276, 584622404, 350560329, 773603465, 549583398, 127531738, 551419740, 703184440, 390822989, 89246273, 195726528, 345414948, 821674555, 767784291, 450715317, 738273554, 789103822, 358295480, 335674854, 635395185, 483496978, 987332907, 737204477, 499626192, 997467718, 403223837, 243519158, 208034261, 789451757, 839614163, 242939257, 808680322, 830922465, 293517255, 164616606, 272122296, 75236905, 661220217, 176567830, 980010963, 159791228, 212998829, 931592664, 955307539, 258904336, 924302416, 370376507, 395018286, 112249039, 399964156, 287463073, 958749888, 392376697, 475849736, 125756802, 443662069, 838095140, 247129997, 602401326, 829723870, 683632933, 327222270, 818164402, 162102577, 625972185, 570906044, 192059920, 84418535, 914698616, 215253032, 402030922, 21588927, 274024006, 51222153, 531401699, 297945783, 731816774, 435824195, 576371916, 74304443, 88117985, 887061802, 232078550, 124651538, 803653663, 487860248, 270331864, 637333062, 426844140, 145063756, 485375850, 322638292, 631363074, 857677132, 173712225, 204321347, 197433663, 625119729, 819196000, 804965804, 862461505, 901100998, 568008839, 100828115, 442110859, 720455311, 366562416, 976219283, 653177636, 743741951, 1849361, 788364361, 744179628, 344192351, 517009086, 976207633, 460953285, 104860654, 280206414, 967833945, 326856998, 49824640, 803835707, 840627853, 715113404, 50523349, 192865174, 150722996, 246419192, 311613186, 610970783, 206508347, 477111167, 354650023, 9480865, 662204097, 505582851, 189924322, 720279580, 119835756, 136939315, 597341395, 556251351, 341066385, 763736481, 44922188, 174868947, 670025393, 824407228, 973465606, 212019201, 636241597, 974180532, 810586517, 820629105, 65915858, 661205843, 525721327, 906937152, 592345693, 493789271, 619937966, 153852684, 670711940, 233844720, 556723154, 162080383, 44388277, 642614307, 546157083, 396092567, 979517246, 511962454, 660660237, 767789240, 905330159, 131932931, 149171447, 424255902, 275233673, 680164133, 776504573, 683725889, 561967859, 48813492, 328326866, 716768290, 35631744, 704579812, 478207308, 151661324, 799547941, 251567590, 834582546, 178324734, 490897579, 474591706, 353813792, 972735823, 529859376, 524899041, 202092256, 867148210, 668012517, 25393372, 536105304, 660587872, 878700944, 868304213, 599547665, 288599644, 410092866, 268139206, 805296075, 494784412, 979483793, 693276076, 3895546, 391957131, 224834966, 310336172, 790710253, 849232929, 658313449, 170771815, 698583917, 687097887, 634244394, 900195156, 391039352, 502105176, 659802409, 649056432, 896091376, 363367255, 496180042, 528460735, 693641170, 461058185, 858524043, 10567356, 41870395, 115986251, 511256039, 216035388, 394393214, 769841776, 7458909, 823119587, 947217211, 940339000, 132022182, 475489600, 411788773, 374550474, 260216000, 577425772, 877667696, 351367797, 785319485, 497823469, 623812479, 749673612, 958143454, 77034827, 443977869, 584413468, 120760475, 716169776, 887332826, 18541430, 43221573, 661053774, 544455703, 663122182, 510017152, 570228911, 313142518, 791520065, 269147422, 882004807, 638428159, 314208964, 805353049, 630394971, 575312348, 528640999, 383683348, 216861490, 331208102, 171902635, 783860509, 868888158, 711043522, 337584911, 967763508, 386782162, 393625490, 860517856, 939793122, 493319478, 600990311, 720295170, 88649298, 102727777, 972238949, 10802639, 149985939, 995969047, 650428181, 768514899, 3689616, 573737947, 203602507, 622291661, 931286939, 412024798, 17432533, 508598027, 353540032, 149296186, 243727657, 44644125, 626360355, 4858210, 386612508, 586909961, 251321314, 350431503, 910706553, 503285068, 504177659, 848345362, 853071872, 190934306, 386354581, 546053049, 617336993, 101884862, 112753661, 408908689, 674170694, 585370311, 843543461, 636923456, 884642839, 135469277, 94514620, 306316538, 806598159, 563332529, 520402356, 733144094, 49738436, 632381134, 314211249, 392725553, 671717322, 551043007, 480705635, 679513168, 979151421, 481948991, 399445157, 483779857, 167108722, 313573448, 443572157, 612289900, 810772752, 201678691, 997091158, 507689594, 433427171, 144686080, 757641722, 675693039, 247216765, 478255627, 756001916, 493525993, 220858511, 769376704, 393884131, 14143216, 46821999, 906876828, 833014109, 834989591, 553498566, 937493147, 597868100, 770561380, 232605235, 315732038, 660821563, 852230908, 85554710, 73404601, 216282752, 821414681, 780008475, 30145503, 31485079, 44855219, 18763977, 840181395, 198829919, 148448402, 389913805, 789666776, 650205680, 677942376, 139720241, 662291893, 436398364, 112714720, 869701755, 595160554, 435720808, 580217335, 155540364, 416916801, 883754932, 633995704, 160924721, 644548818, 62365481, 966429941, 786912200, 53815463, 14659602, 979270893, 975334178, 47058317, 818671954, 56124984, 49171302, 367505228, 464210911, 654888105, 23261283, 226148028, 990662739, 520422469, 819618457, 180301666, 701902241, 582327208, 139591813, 886569931, 405939634, 261333260, 755952511, 210237075, 354841367, 98200116, 355285070, 146111878, 814226772, 312905590, 298200415, 435479253, 916918427, 603874473, 329161558, 212492270, 897147420, 592873674, 136058392, 405547565, 494067980, 100469719, 510457057, 705918878, 277448179, 214279452, 92426137, 400265179, 264933650, 628321026, 123389566, 517097856, 328948639, 611781273, 429024820, 824354138, 482393830, 470026310, 394281308, 102667525, 622978008, 671315571, 788110765, 508544349, 573317959, 382329083, 562010429, 894758142, 699010417, 646640322, 941705980, 469619113, 428692917, 309714554, 441811184, 419941274, 333651414, 986876915, 821572372, 89221933, 266983422, 283232677, 694497269, 449578604, 42714537, 98088051, 356882680, 677097438, 532922114, 194309347, 352383242, 631296505, 251571836, 378259657, 729909797, 640474377, 46456271, 90915313, 64687353, 252101746, 6974642, 395667468, 904694369, 415186542, 193203444, 400423393, 218321903, 13964681, 818629488, 555127406, 22730349, 962124748, 65681244, 139969497, 866173168, 431028072, 647557611, 864249644, 194041039, 113682920, 619599085, 869076971, 436774138, 189973221, 185133230, 891476829, 171155270, 107424865, 72063719, 372929778, 902405191, 748112377, 803848843, 931876359, 648343726, 361544746, 372545632, 298522228, 307624886, 40295053, 208098536, 227240589, 669282131, 980769852, 552961468, 445937351, 340064974, 210032844, 214907535, 237622708, 572549061, 955005291, 251443953, 70933859, 445706597, 931177099, 446669906, 57869651, 104705179, 887340594, 839130917, 364840759, 228489387, 197562772, 465674382, 508729749, 80888508, 400783210, 969616440, 200291604, 115425473, 34600624, 18479891 ], 22480 ], "output": 8927232146945 }, { "input": [ [ 828599843, 865671620, 268152502, 420919927, 514726024, 418454583, 372824897, 602275432, 677909634, 150379409, 960426655, 629390732, 377310314, 108147602, 465047922, 59640863, 929318145, 885366351, 761969700, 102260335, 121673169, 951764536, 236897324, 988865849, 383384309, 245218983, 127356706, 109666872, 457126943, 589857666, 20910064, 155989875, 824326489, 652341632, 527404452, 256643279, 284460421, 64288254, 526381895, 115717557, 957162589, 600342048, 836746037, 110586979, 864555396, 857131569, 223598223, 16661330, 948842456, 448657622, 290450381, 776178128, 615911386, 128141637, 790328491, 257573702, 906553538, 429776581, 100578009, 328017372, 71508951, 542138746, 726049588, 253228755, 990985058, 109702597, 757778877, 556244947, 701984303, 883553155, 971483889, 977166660, 759975042, 211112124, 929057002, 336701891, 246220039, 776767120, 299871777, 837196549, 677390160, 777684836, 361138502, 290611639, 704210252, 905697793, 996599940, 392605262, 97553999, 642660217, 696536179, 188558926, 970806554, 139067505, 16315689, 281795969, 301335945, 602051962, 978337149, 312212634, 102895990, 403255804, 495903492, 472383193, 595788779, 508786163, 416928687, 337450524, 856501937, 910943966, 813093579, 191621355, 686061374, 324738410, 531907061, 15008160, 773132506, 310052408, 908085986, 144327302, 765965005, 894696364, 301997192, 273333438, 335892348, 718706150, 534719944, 183596457, 810612493, 771391784, 129848457, 737512513, 193228197, 305279900, 200239454, 381562327, 319658359, 380073081, 335844865, 206496566, 599747899, 410434128, 909921711, 444944075, 968088830, 327885918, 850220199, 228962121, 62492720, 941420281, 716322175, 811333785, 489923926, 35710008, 328283785, 300045303, 417999057, 454087945, 853024075, 637786554, 781083967, 799688121, 369008905, 417803881, 330172795, 226872448, 267130712, 308038343, 168033583, 196712700, 547569255, 368820034, 864056814, 493522266, 543464833, 766176959, 969097245, 918475590, 93946487, 38463160, 369542775, 559798530, 147244057, 481680393, 590302713, 226254956, 95114057, 996323802, 949271070, 562888497, 623445766, 705280412, 607106265, 707763294, 596809267, 748234891, 989017998, 629692181, 141585338, 103339066, 425899085, 105082242, 119241579, 33260787, 420400272, 360390508, 865396521, 574893916, 465561837, 584904942, 670280494, 152874289, 281148087, 946544973, 262805587, 909931874, 36085956, 825583274, 690660476, 555347893, 115700574, 923515382, 565700029, 569832786, 997700145, 675065807, 55404292, 301029063, 191610827, 814432647, 55272387, 784597627, 274902320, 635219356, 838890460, 792906811, 331353839, 98657817, 586002090, 925002395, 501610251, 375523817, 421776119, 299445620, 386764591, 402930607, 215056367, 919803562, 210661097, 602623004, 941446837, 198064855, 251568239, 796455362, 136368966, 794862894, 267520691, 739773863, 259536209, 616339351, 111515185, 265106116, 37041246, 15122462, 386886084, 290625744, 656393587, 562461646, 625872249, 775338380, 316156584, 531478290, 909089114, 360156094, 438104229, 949173694, 242317454, 194557384, 34076296, 681899192, 670598948, 726237687, 433978878, 957493285, 148694420, 510223827, 126800955, 869516645, 836749617, 74295208, 16263968, 898271310, 122702809, 684586156, 918915407, 450640462, 889841893, 57504387, 566819542, 661640920, 256388679, 737047318, 987787018, 991862097, 497888030, 193436109, 995013271, 162443180, 921373146, 244682835, 889917991, 688835662, 556930947, 881839756, 751650881, 710344361, 909193805, 878654134, 552726569, 919818340, 667829403, 293801507, 841248583, 275489657, 301549908, 366586261, 11650130, 767730231, 341805477, 537705783, 349864937, 140125139, 840952215, 237759524, 921862147, 881478215, 533589790, 218833447, 763702017, 875191297, 341604358, 202417055, 650560418, 154291448, 554963512, 629272881, 785855995, 694770130, 199329275, 733553, 172599155, 917845535, 623175157, 999023688, 706411369, 235505901, 364063639, 539108524, 204457505, 934280177, 894381251, 843609054, 874367657, 717956457, 26727528, 230356052, 314313265, 147142727, 541483731, 871386366, 665602306, 502304661, 5591878, 710649547, 859179868, 304851997, 988925613, 283674835, 32654031, 213017970, 612846833, 572289873, 524911064, 202708031, 876712938, 574930717, 979341839, 926566289, 731527455, 796204708, 881790366, 373397129, 313692985, 534023966, 933776855, 353898979, 167863768, 596841408, 342040425, 722258830, 808592485, 405918143, 170958343, 346031281, 420320106, 855439070, 730708088, 267686748, 602448481, 198555542, 799312872, 829644989, 666209589, 990109843, 146104399, 370372375, 233225776, 293787451, 423594726, 145694368, 460324665, 955747620, 542777827, 443307037, 928755487, 689348729, 546250923, 448519286, 61046483, 206534991, 5898710, 134145158, 467510247, 61250681, 856622311, 979803469, 434131713, 405530107, 494654140, 604554150, 643292708, 97349468, 449650273, 340013386, 331746238, 654787198, 10561272, 671891057, 802595926, 269806135, 666994296, 476320796, 796370357, 989778052, 354031665, 409989241, 549821965, 449074695, 415907754, 76026284, 2476615, 892444923, 441030595, 621681621, 393874374, 348365553, 762609990, 804038133, 36978160, 981764232, 737864451, 154153270, 911328675, 761584980, 431556615, 480897640, 658327585, 896622912, 846084791, 704617205, 679105805, 733695907, 950074501, 978668672, 374675745, 9573904, 909490396, 926482471, 649473071, 472837541, 105979626, 389453299, 80522230, 527654699, 556480792, 567866205, 492569724, 724453155, 18868994, 255364099, 918233109, 500357995, 908976846, 232954924, 373787894, 56625377, 113222780, 238586132, 647504015, 320779713, 332162373, 641331439, 13360330, 437077888, 812873848, 704242261, 160171892, 582245243, 850169684, 202635151, 344043776, 311427960, 482242799, 580203044, 859968347, 690563036, 560572771, 46100693, 612049812, 667225002, 709195846, 206795529, 407653295, 385257906, 62983731, 195996089, 851897986, 216003661, 517827331, 902039468, 339161088, 936919784, 374103134, 42316993, 977288006, 569557000, 446723478, 279286785, 850403689, 149057924, 674805862, 452976335, 449967061, 769026287, 989327005, 610841629, 631097825, 20146236, 623392357, 838706652, 853149796, 896293128, 841552834, 300193242, 947040853, 238715157, 25716009, 593200364, 626256719, 114313833, 8157610, 221430122, 264759850, 727256530, 151186642, 974220847, 383076961, 790719585, 286232404, 617952912, 547835225, 954418266, 130350811, 373868945, 272905953, 975060920, 127958406, 383543866, 979863035, 878791318, 157072308, 559527588, 178852009, 346259909, 510494361, 351324342, 624822096, 17257412, 939964381, 866945676, 915652628, 998452168, 147701610, 249833444, 226160084, 373334707, 248736213, 534258305, 644353794, 893345475, 455427348, 449321473, 989589167, 486586003, 228390139, 7994781, 543917621, 815068895, 427323257, 863870463, 284344207, 85237340, 700711775, 157656914, 25888262, 884690815, 530455949, 375736007, 286943451, 793701583, 197659832, 378953669, 713506742, 333456532, 344381730, 465460368, 110051314, 670360714, 531933806, 228111030, 933876919, 191146337, 243438361, 873646752, 513342437, 987625448, 237317360, 962792975, 559543382, 933302130, 309402462, 286144166, 64772983, 559865593, 581854015, 27980997, 893103485, 179337397, 884943830, 492075055, 982349932, 438717489, 84656543, 492855970, 66469930, 555658770, 390141782, 899199035, 254665653, 183984161, 168593166, 957276286, 123216728, 418402712, 526981671, 795683302, 190801522, 792697014, 516168150, 884995354, 431136068, 980466932, 118078935, 781538805, 110380103, 860058686, 724913680, 530065178, 244353045, 835711450, 742747577, 879887087, 217002103, 182160454, 991493230, 623248306, 674119923, 91170455, 60901489, 397443937, 776739209, 417439753, 134060639, 916961899, 381114647, 507761310, 633743602, 554664051, 265141450, 420377659, 406190514, 645701601, 727855316, 570280689, 332057390, 883758955, 50185190, 921767569, 193307417, 807437219, 392061890, 113879768, 382236260, 370864678, 746804470, 425376043, 438845052, 310546952, 475344898, 367828409, 379153501, 987265670, 213172065, 692860657, 906203483, 686470339, 307155723, 66625585, 36120588, 40929623, 431191306, 559615655, 601632368, 50707065, 388989588, 991895280, 464970487, 373223820, 320989883, 453119565, 840018162, 929326097, 168276803, 177134185, 383277525, 504171035, 517524358, 459228851, 246334743, 662746477, 786002114, 308322543, 270431012, 601794488, 725616985, 546261895, 136331474, 396112372, 25622768, 518946829, 196881250, 9844691, 725426937, 222448808, 686120091, 586922000, 677996783, 342293181, 987833693, 535217483, 901324871, 116257886, 972803884, 713565552, 738062324, 641273843, 66115332, 584012826, 750655032, 658335924, 977813571, 483885840, 567085488, 606962957, 539115870, 130370547, 679129403, 773517462, 830992244, 982475782, 946469585, 391895938, 687225033, 447647742, 426100275, 826655815, 752406016, 477405821, 68376566, 777020030, 71798660, 513268818, 804802238, 947080731, 36908828, 129582071, 670669802, 562826196, 318131699, 415630848, 324644461, 293428187, 221891218, 58765904, 719848918, 9656095, 476263328, 705675492, 947106102, 117155625, 105967135, 683081333, 553363105, 177085197, 941541349, 851230898, 363661686, 681177502, 611971602, 532856740, 107698880, 136290820, 897324700, 146868217, 599750793, 788935846, 839273980, 690082526, 8182824, 774459615, 134065251, 541847482, 918251013, 117945369, 967056027, 451556502, 519839911, 530853614, 417354031, 390250481, 927313287, 720802263, 299413493, 619989481, 764698074, 837990304, 236247521, 270103056, 156749830, 270299552, 571934060, 20399003, 959540543, 511506166, 815304869, 301811973, 854175948, 458685384, 118448667, 21178372, 737371873, 891350939, 330125483, 430860700, 208941057, 125301386, 251458341, 825039974, 294067121, 60842182, 224788700, 448434916, 344846765, 24538665, 142851513, 915037908, 692086761, 296344656, 552813336, 917175236, 494285516, 482438746, 420025938, 853488547, 942895941, 701919609, 120657446, 941731431, 194913958, 384960150, 764502047, 216392982, 996659452, 766785176, 170376347, 884928816, 592829894, 568181757, 813963953, 444206394, 261540623, 148904644, 212341976, 874126606, 338892163, 614990943, 841915658, 658045624, 156097863, 366240307, 983218710, 330644035, 697037476, 242620373, 208520762, 609588225, 435625451, 487132830, 114382436, 706388776, 479576434, 439587706, 211493173, 790304623, 30258532, 32810769, 386535327, 551705706, 63883873, 315240887, 474512061, 353515099, 452259197, 277067691, 6956908, 703730676, 62015359, 307223974, 633236384, 931984108, 587180310, 802289579, 840190927, 750700078, 321097108, 277742569, 260997694, 139809613, 97823293, 994914884, 701874958, 417934753, 127671839, 234892208, 666914277, 880966958, 225845201, 98758433, 865773942, 251301220, 688498978, 492278235, 954902898, 327761186, 892837655, 603232766, 92293244, 895456082, 454075959, 363187846, 125157164, 733608536, 903796954, 480503953, 347445099, 103199321, 520128982, 343973760, 596775697, 147002642, 619585277, 935157157, 385832804, 677315912, 963468869, 532139366, 666481700, 795910605, 416273074, 738206283, 538420429, 157861806, 195990990, 219421677, 990982554, 109440797, 488348200, 643025920, 819799425, 44675765, 220509510, 492673054, 726918021, 651238200, 130784228, 224813057, 211378499, 190553094, 190150611, 724733209, 523201408, 997134120, 983685124, 229563496, 562321810, 377079271, 445733167, 643724885, 10465012, 159914907, 794349901, 582032053, 525330952, 260585126, 396640032, 415206197, 765458661, 176318444, 142039475, 667397957, 161369488, 899122238, 742145130, 916154777, 590687231, 365973803, 179681683, 809647706, 733054411, 609692951, 477625452, 376481476, 731550523, 127129705, 334856802, 398971417, 254802082, 248374034, 22343825, 541192518, 972224230, 647271858, 664966012, 418843378, 870225286, 957986659, 525378166, 614987463, 671236498, 667047373, 394096015, 538892174, 892767029, 520460313, 368768872, 974547743, 140525832, 669399826, 295252610, 116912205, 349445283, 692849682, 980869842, 988010151, 970841408, 271386955, 145421338, 894639252, 909102471, 463498195, 657095334, 331463287, 472769863, 205556805, 664941478, 494238695, 28657180, 518273474, 988081879, 561847401, 964485874, 914370198, 10777013, 119833225, 319121113, 615513056, 654777939, 564823530, 347593334, 882152818, 963377285, 583601495, 833949899, 352367355, 152761312, 865744890, 206971132, 493698019, 422222528, 580710801, 123126722, 4887469, 329145889, 75559868, 175184094, 915817924, 433337655, 21191195, 526437589, 902954629, 26306854, 341664899, 34289680, 646165855, 631342251, 884592499, 486114852, 393815143, 93792320, 387046222, 533453183, 24074552, 902460001, 8453701, 992983189, 69209857, 477764135, 829518987, 326396249, 609122139, 978837311, 232944989, 384781270, 171203738, 400960817, 839446220, 309135789, 183969898, 805936306, 392264410, 631719057, 764522943, 347618867, 860551815, 817987013, 892115815, 44715370, 510501493, 71533052, 360601651, 703156398, 15626307, 504917488, 521798398, 758204168, 167452575, 184042120, 183843829, 333497285, 129513461, 172065751, 406546545, 222508032, 443481544, 411934226, 130322860, 90965162, 545008280, 160846951, 808451819, 837069456, 621157439, 829776694, 305305287, 943303045, 899676498, 198728808, 641414337, 105721680, 916535471, 612982843, 993880027, 479597670, 157232696, 323572976, 579510467, 849081135, 857065686, 719086358, 767483007, 114968380, 386256958, 766616349, 275433250, 228664542, 811739185, 235815878, 963824573, 832843503, 274798965, 464195233, 183929798, 681143470, 783686482, 92099060, 595126950, 167315119, 674729160, 400158672, 685249571, 201081086, 958256912, 74934210, 794185868, 578039929, 481911896, 540867926, 976408393, 93655494, 794524200, 942798996, 707281343, 511056337, 518815816, 147488901, 508496525, 153305405, 501478974, 886482641, 377057141, 204362382, 695372607, 939225243, 893263650, 782142211, 671864800, 498716534, 675320077, 623019104, 481415536, 270684658, 515507146, 121099386, 890208415, 112631203, 47997684, 44589217, 277389572, 556980487, 646148705, 500973966, 912465197, 726160323, 185462722, 133974749, 556197332, 186077815, 87692374, 855183587, 31074487, 29532228, 504838926, 47266139, 699806342, 196845099, 113103170, 183072003, 180024155, 74882115, 516584232, 445207471, 725038328, 541854813, 783320779, 59014857, 353293403, 206458202, 312240889, 963982764, 206556283, 49784610, 750220838, 655613976, 805202066, 329638578, 12364054, 534322404, 963406532, 68546814, 249090113, 720559823, 205682228, 490806510, 944697730, 420644240, 409204114, 313673459, 100724202, 298425760, 672602865, 852954733, 346012924, 221975484, 343625993, 214811613, 748539504, 830916606, 569394837, 673339280, 921136065, 425635857, 94209976, 457432550, 582536060, 858932493, 620950125, 317283332, 147266417, 699441387, 559528209, 641343518, 592585038, 900517203, 83453925, 542552316, 662976150, 859558690, 764276700, 623591110, 994041576, 751341426, 245055900, 899299338, 272026990, 349930419, 916855426, 896141195, 667659200, 448076586, 654910441, 959915507, 697939987, 256096504, 577111197, 559729298, 874627888, 24705605, 827339424, 885832142, 241936822, 616061101, 164128885, 670006890, 666861376, 814638741, 216250988, 701684460, 545509996, 624316031, 231286008, 150858817, 411757941, 892129845, 322630908, 623909365, 610433674, 197809475, 667852791, 106032478, 208850686, 118774831, 786722511, 188002367, 240895022, 970519072, 971290473, 897051934, 526637798, 211098438, 620395998, 210149576, 55376700, 891924421, 684531201, 318057812, 398781431, 679581192, 728579433, 124168772, 413442808, 956311571, 399632833, 822274567, 888473001, 11830154, 360958068, 296234920, 96706494, 474983636, 264768077, 714995166, 744455425, 286541864, 666985848, 918946862, 251743884, 487567304, 665971394, 455470141, 639828898, 579468591, 31108776, 598037666, 697493893, 619939334, 353926506, 270951947, 392122380, 506221041, 14313319, 888222231, 319416695, 297927226, 254792061, 975171242, 258277910, 660193920, 890485643, 424043593, 410117396, 116547400, 111021866, 893321768, 877628910, 670752243, 612968338, 773249306, 114572208, 760032178, 470532915, 419374336, 256183139, 327641332, 181774813, 676697529, 659781816, 758527663, 149989837, 505096148, 917655044, 66174877, 772466978, 34006047, 861808291, 544682119, 172581747, 205273762, 235444455, 145873240, 856902019, 47605219, 389994892, 633766723, 868596334, 542111473, 768725174, 124973664, 440713259, 838541029, 558207364, 371177727, 314270252, 18948060, 581015676, 619670615, 663998897, 977264034, 865563482, 458529084, 344198155, 14460002, 344877934, 208738449, 582333023, 568194469, 118580501, 449551192, 731978301, 516825334, 595938529, 538261508, 489713486, 418748153, 884019981, 884775827, 202886291, 16088188, 560472651, 272321345, 455443602, 704038467, 920535247, 954236907, 813247177, 321966218, 526696445, 248194993, 6887961, 984476062, 291219961, 332830191, 654262014, 321198670, 124535495, 914362835, 199476542, 855633153, 497064732, 12141945, 892524304, 797964243, 184136456, 931556783, 174259524, 762484949, 718179034, 659625084, 150729666, 701886672, 923420696, 123198724, 422206309, 309725222, 67401911, 775753364, 92560601, 634414555, 617766040, 877944968, 626493940, 649237243, 55502152, 450740277, 655271024, 597416390, 749528620, 899677436, 298156327, 123563664, 61006198, 877904388, 878040395, 432870307, 789010304, 189901823, 70031145, 946424171, 384899732, 136909426, 495468333, 276534874, 100540812, 229024679, 549527173, 232931204, 58090991, 375842765, 979378746, 379195751, 822492038, 530954881, 972487767, 944856775, 461425718, 434378953, 197001723, 488511431, 562189816, 785040193, 832582261, 824619020, 714270360, 205500751, 446179418, 425707299, 870547414, 647346388, 453795083, 341287282, 721730501, 554388611, 113263761, 829820482, 530111591, 69409240, 611444739, 865514380, 274175535, 177093595, 357937347, 203689030, 10792650, 323540700, 733807561, 57183637, 768837683, 887793353, 794151645, 307631760, 336736941, 472694515, 886791219, 323493916, 331411129, 179853549, 791388504, 636148676, 694385275, 896923414, 480463167, 661289820, 258668153, 89378953, 406534000, 845936045, 213582106, 216660798, 621139897, 825245832, 660191060, 244656214, 525614606, 908256154, 226769940, 98535768, 40168876, 813401498, 453736441, 479568471, 474225439, 41620551, 437759124, 807911321, 491360790, 972693237, 9290339, 298013032, 308411815, 520124354, 22416487, 961320008, 88206133, 203176295, 845115627, 144816734, 351817546, 692009684, 214983566, 674999112, 555902924, 319372216, 312294143, 200959150, 907756386, 633910232, 765391808, 150830089, 498965131, 83713675, 240904873, 251133442, 167988487, 990331842, 729246141, 676020016, 93519979, 392792541, 186114353, 634454245, 637182296, 583487971, 20422680, 37219485, 430978703, 772753745, 329623818, 633999, 130094068, 670708839, 391845763, 190942373, 141031081, 637956850, 542855766, 195179208, 409548678, 952400957, 30017341, 353243676, 856633620, 102253239, 627546021, 176131360, 47045388, 332689923, 150791427, 620237496, 648201892, 769040720, 478665391, 544705363, 49705428, 749719764, 546334967, 762022154, 770215415, 403365641, 903898674, 646289768, 574828421, 55529566, 610922917, 365554566, 55337366, 551860606, 251252796, 152497089, 144586603, 32524594, 905112396, 930568502, 735520328, 603720530, 669906652, 86049247, 359416806, 407828259, 960062109, 523721933, 831396395, 592866608, 522688094, 297762597, 756750371, 409778086, 210281842, 375108485, 513082670, 554677890, 889847625, 887270575, 247901151, 176208604, 677898559, 680690160, 90078420, 526639234, 834082554, 952176369, 591893142, 843877360, 920612909, 738601605, 837909872, 552393398, 503954565, 450483350, 43661875, 389810619, 236138255, 153327087, 971407707, 766701434, 441642617, 850330522, 1329196, 242395100, 517478935, 158811223, 455719915, 439911488, 839142248, 986661072, 530824300, 930588619, 279095320, 233572743, 123561872, 215508421, 850927988, 631247936, 978365601, 191948010, 749761238, 16151105, 253458665, 995829819, 228013963, 374068079, 621257487, 24034333, 88042425, 598261590, 131297776, 74714893, 260736675, 178089821, 217216710, 435585715, 895078035, 471233864, 86613304, 34635592, 119654678, 23075526, 717800058, 573396664, 590722121, 199575898, 734924399, 34279446, 645856786, 633651071, 711177473, 930601604, 124020450, 389345326, 653569980, 919405048, 494398676, 237435650, 769842894, 585140182, 649220108, 53977725, 930129941, 861601824, 743809219, 414251299, 47901808, 733962893, 372725937, 599326923, 337243707, 393720339, 301478401, 857819516, 635851296, 385279386, 876739293, 286397693, 110952489, 949090474, 391630064, 582676719, 33535607, 144137576, 859270387, 300559369, 758119311, 569557719, 962094742, 892444861, 461619798, 13785597, 926037376, 826579432, 96928559, 809608720, 318055038, 920190250, 888639077, 175516096, 464676861, 859495327, 167045726, 531546498, 615856356, 478500800, 585325952, 794955347, 375088694, 11966994, 599630819, 895826675, 418932536, 647968132, 443662572, 884622262, 512249299, 746607037, 281399861, 982340670, 784702082, 768143446, 702170026, 407580537, 83157213, 979998300, 4544254, 876541553, 662602670, 990604724, 796233533, 403467069, 269635231, 233740574, 708132534, 149312587, 918404682, 321126466, 956863973, 186041991, 535311669, 789064057, 379329984, 356121878, 667636333, 505804845, 935522206, 357051262, 850552885, 156235057, 445610215, 530716216, 683229944, 361154378, 472186183, 152836374, 132527592, 744895063, 291010586, 567475680, 791768434, 534726818, 332018260, 644559782, 140358862, 33303691, 720330817, 445779673, 833378749, 268798261, 208811927, 63875971, 248817787, 128021918, 785949986, 48102604, 553617739, 507583162, 579643860, 746225781, 710506025, 85503793, 379045570, 573021995, 976057934, 286789472, 707404257, 357250711, 115968199, 408512528, 744770802, 265149248, 126053997, 791103252, 280519864, 635077158, 794631690, 505019464, 664638116, 435106264, 372229526, 496109794, 151499426, 228147022, 779636274, 469298914, 970158643, 384012849, 867820658, 290633126, 991788705, 746618545, 923519992, 118584993, 563269321, 856547045, 263717000, 471266894, 21309208, 465115394, 677316300, 227852207, 579762567, 864083653, 670276272, 8851256, 781283540, 556937697, 597316262, 884254423, 762171444, 895745749, 151006341, 477541931, 396680522, 69486261, 148848869, 674554545, 53894403, 715760015, 850627734, 78296097, 35712642, 25982862, 133293045, 288406070, 762073964, 50246512, 489426550, 180413512, 596209961, 279069663, 564126187, 511105100, 279259524, 5313562, 529472512, 350118335, 667336813, 600494695, 54830156, 788612770, 980375689, 498382852, 28322898, 389955388, 510257239, 27352408, 663252063, 366467965, 341624313, 967546213, 864460561, 246132495, 328926686, 745069155, 469046760, 962578412, 666354420, 229031996, 972890600, 716665472, 499058085, 48617639, 564470899, 431544237, 473560879, 664925124, 160379287, 464235672, 872428944, 400775455, 672540284, 352041510, 892548930, 375519513, 787025229, 434142280, 903924060, 354800194, 938964671, 759276102, 160921058, 752071733, 281278956, 298989426, 376484461, 966499980, 413907794, 132871708, 631387564, 839365701, 608813545, 451293451, 844425328, 925838624, 170921889, 303020892, 272890672, 944838649, 554103801, 825368422, 503837370, 966796005, 341392108, 882204148, 846221227, 631007429, 965521104, 404457970, 716231140, 389413161, 974446896, 719389238, 891269361, 808425688, 68230074, 425995554, 794060399, 986850317, 818971876, 410333767, 33926887, 921302066, 555693744, 974591642, 304680173, 918153818, 346767786, 859224877, 864170117, 455158065, 970444144, 821583899, 646205971, 59005778, 263190207, 228518063, 39009606, 965115027, 551980517, 891312746, 201637120, 520593933, 624387914, 178151952, 176726026, 846976910, 392261611, 379548881, 772157287, 808534868, 284880534, 293159683, 492026306, 600198368, 283621675, 310389315, 337440166, 521552136, 275109514, 656906283, 679648223, 954539565, 254985941, 808237851, 450299417, 636383103, 462432898, 107573507, 58605097, 409259640, 579920286, 398138501, 558907399, 997621071, 153589176, 372997049, 697305903, 548405412, 329409198, 499474971, 533066543, 237718373, 289024752, 335818784, 115328835, 365515272, 63981305, 482693625, 100111341, 405363927, 659697112, 687282008, 626512666, 683348256, 143127100, 273319192, 64762770, 304679914, 578385691, 732370780, 407330506, 274510495, 907243911, 251386653, 118105330, 200024618, 67941825, 862042746, 129627466, 372921685, 240687511, 430438035, 951337651, 621630165, 740751577, 749634418, 852764616, 545351731, 782542728, 105892144, 91443620, 897279606, 449632563, 264522069, 684300694, 963474227, 828942576, 991210009, 395790047, 548871983, 408543394, 457757454, 849494178, 275301306, 60530239, 789430945, 303917175, 952499504, 105160481, 649122659, 894325863, 180882624, 713260, 755977921, 166580903, 806501402, 414371850, 718235359, 14396178, 36198780, 731807630, 266188146, 994687345, 641354827, 696953915, 200289005, 341595959, 15486330, 575006127, 538415540, 162453616, 976643243, 538497763, 651041245, 310575940, 44071897, 57457524, 52921372, 291949337, 626752062, 287165322, 237699810, 359062316, 8676107, 75957489, 938191479, 809442031, 595844171, 532449407, 116904287, 436185482, 448131104, 311878172, 411970093, 943377453, 302250094, 899556482, 692669942, 624205549, 609800512, 741901369, 401922255, 579153721, 398119355, 209792996, 939158866, 417991096, 422620671, 572861158, 602140576, 687674093, 599953998, 917468809, 333045712, 866527801, 225017864, 743431472, 410613342, 346042922, 485693974, 973005865, 179794800, 37228565, 457884108, 567967090, 831901304, 55896213, 814456889, 974802119, 889541202, 614963709, 680757344, 319681131, 417713296, 19486949, 47053440, 988331006, 431311984, 940208966, 476828209, 738094997, 825004377, 673568711, 562841057, 540475966, 941837764, 51784682, 73640367, 826274606, 749767833, 162106101, 681520728, 862403250, 491621947, 664916077, 74608940, 999079907, 430519656, 854436111, 46719282, 549686897, 881111844, 341885645, 69368215, 773016521, 283654653, 94991418, 234579217, 269289898, 889781212, 454163500, 37054273, 978658282, 465917628, 917786328, 114987754, 804710892, 781046373, 94240424, 408790821, 467217517, 696787959, 477027891, 466830691, 217539827, 537992930, 15358246, 793666147, 591886225, 975678961, 656053336, 301848230, 763290702, 791988185, 367281689, 360907917, 83044709, 407746726, 792805103, 771462635, 29170669, 207201975, 157902680, 84751532, 26657176, 904509213, 818139313, 24750122, 705275307, 70950919, 194738881, 841091298, 700411972, 258195675, 115096740, 477202740, 225672290, 412817390, 884690486, 743968342, 563667153, 115920059, 805498005, 928806486, 620989830, 118731892, 125924656, 269776711, 12279843, 304403099, 606236043, 32855264, 431766742, 387508514, 389641780, 39558882, 731041158, 421826604, 287728762, 626158323, 962285331, 91729401, 683294230, 16276986, 171621921, 976847964, 952982657, 99170642, 991016194, 604668335, 681762769, 180338074, 263693669, 117202798, 320314177, 482456090, 758333754, 411105111, 522077020, 161121291, 857906119, 956055918, 116507159, 995321953, 550959464, 194780582, 670426461, 170800436, 316692661, 896396485, 16108411, 622029270, 267568160, 962206702, 840343897, 67243895, 325077007, 318391374, 520710524, 614045706, 484416215, 50157901, 592434391, 790554160, 668828408, 994834279, 736401966, 641539825, 619336042, 481935181, 829677566, 913666450, 767904265, 36821601, 198794631, 890789682, 748356115, 857213432, 891077620, 320782852, 876364159, 220726031, 992715057, 223700361, 48801266, 200481653, 704137677, 413251424, 574845152, 543137256, 973547901, 909434953, 986703172, 68543486, 419075791, 207443964, 806456342, 617073802, 711842201, 349451743, 893343578, 331292393, 566423571, 515236515, 206277282, 883829885, 862538439, 73691848, 790325036, 466901417, 126639824, 442547817, 976045526, 275308241, 907426384, 988413174, 307097052, 747041002, 492281361, 630095938, 881607776, 114837838, 829391406, 471517573, 468308955, 71378044, 188113879, 405266585, 256837121, 49523722, 955411002, 763990373, 563786506, 742356878, 560354296, 621322822, 471181415, 837699620, 866782178, 546361829, 370605708, 575689300, 948152169, 845975946, 485722222, 351499658, 112886479, 42739305, 495286028, 844096111, 279222156, 164915774, 381002447, 70930305, 701413185, 220705107, 692949773, 479840993, 332440683, 332882558, 855627834, 343492934, 164201123, 893472056, 283507468, 139658979, 355128365, 510444605, 226876971, 624460096, 336872819, 645090880, 766842209, 379129364, 658812998, 801794265, 433721853, 164671453, 844639843, 417514158, 173138379, 216114775, 215311252, 240827572, 304066432, 477063832, 333500264, 81785430, 411177026, 216906089, 662577668, 24232087, 952269807, 164848498, 581681641, 607083720, 695367490, 294282883, 835508815, 778162000, 424770273, 833287464, 322680566, 669253612, 952736400, 781686366, 539994987, 759771284, 265258402, 684856419, 322720725, 801954467, 430103031, 225112728, 159343134, 988984692, 686049106, 6679870, 565696315, 403368955, 604174612, 851861514, 651306252, 12388737, 303401870, 344646688, 677054709, 593390274, 289898133, 927896920, 724530779, 616711626, 138925499, 164391113, 401847286, 731203780, 292067550, 190534855, 550547519, 154741820, 242039188, 417520617, 369890125, 718860561, 320572437, 471164526, 20787989, 651287911, 257086303, 678594762, 265141383, 380946260, 955294083, 379274180, 607020694, 33611506, 302862976, 697735829, 724588518, 952431660, 481656501, 151328613, 85691433, 47776924, 586418636, 133146195, 303543635, 981040667, 59009440, 491027921, 494807285, 415467286, 588368759, 364928164, 562043312, 339091196, 920776619, 283828029, 973107702, 408545666, 873753681, 875863536, 488774291, 847566383, 915550686, 402921007, 983118473, 97008856, 811960603, 993349593, 695291839, 670246201, 610863015, 762738176, 582237662, 988131565, 314930467, 895943239, 343804228, 727138526, 473778750, 804045262, 150051415, 780655512, 540358879, 903217188, 761671052, 689756961, 362399601, 439442357, 252162184, 32556273, 639168988, 72669918, 38442532, 160057157, 275341488, 394027129, 203768619, 363100704, 131186105, 335443374, 128541348, 870959729, 899885225, 378873829, 183457500, 773845842, 660659145, 812592655, 622798334, 739670514, 51353227, 58986260, 264526989, 784158058, 224843367, 2071777, 61164570, 884674617, 836805235, 22734745, 530205616, 877149424, 530810742, 607629431, 196082119, 595667879, 778019083, 486090496, 910410852, 408679576, 259647731, 164041113, 851590622, 105361715, 13155524, 804113410, 18419233, 369962965, 746821462, 194510186, 340630247, 975133680, 220124543, 614778492, 46265831, 522056437, 290657171, 868576933, 237106803, 684661369, 315564784, 228141615, 260561340, 736971789, 924821822, 429769529, 495112260, 651867738, 11383728, 476396563, 633486075, 330207345, 700904910, 217747339, 878989262, 352141828, 744066259, 767049717, 348279841, 616608148, 131932606, 783060056, 303871614, 770269218, 504026739, 266218322, 308357091, 830984817, 716895404, 166043359, 609075807, 147776795, 672865279, 373677702, 599837547, 91319456, 135024941, 403526015, 458103106, 241308400, 405489190, 650047662, 824140920, 826651090, 470129927, 254331556, 936393483, 964506738, 924411241, 587093093, 961827241, 385793173, 271968298, 705662612, 918656828, 781651139, 903450325, 910568055, 141015273, 732325093, 525624736, 708633570, 934915426, 907222913, 859703483, 888947908, 341388553, 624190321, 272144047, 46261983, 994918162, 281938434, 61251102, 150987122, 119579376, 36524156, 299930893, 620873890, 397686344, 572325349, 652807260, 133365494, 893404676, 352810144, 543210378, 121576337, 996740034, 39311882, 449270742, 755145071, 135118722, 784608413, 467364704, 420633505, 906051427, 480278441, 705263930, 6635256, 314712065, 980764172, 963934221, 304828442, 762414268, 669398556, 246304407, 203906787, 771239491, 591679945, 251219038, 920689649, 715520048, 855425142, 230310053, 903515573, 140056230, 723564635, 444827381, 421396081, 266463626, 645960683, 362045342, 640083405, 25148071, 663790312, 393564566, 41800522, 585201363, 856089419, 191922809, 568878360, 368720830, 516969508, 665783556, 321711703, 950223890, 191469837, 367690386, 840307075, 343502225, 547247713, 877356563, 431998014, 485248364, 782188255, 688981607, 69647033, 219821315, 645760963, 758588912, 362815294, 743868341, 242763721, 725064651, 193989275, 114161129, 808331630, 609560311, 746612508, 59682118, 786912304, 582136397, 433692764, 306059974, 269568524, 362829698, 702165152, 719727160, 341310774, 745658100, 162835673, 788745138, 194578855, 662517799, 294307993, 824412973, 891816963, 99551202, 371414304, 161188831, 999744912, 78381123, 168611666, 610237658, 222925691, 940178055, 923265295, 842879093, 5215815, 611651207, 825471563, 891271286, 446112175, 772681861, 902339384, 109961852, 97123323, 767938670, 179593925, 165093319, 288519026, 427341772, 940055168, 841436901, 507317113, 506840447, 54738927, 632303616, 911426517, 280974950, 750506956, 671496040, 147362280, 394774492, 955628430, 274413366, 828663038, 957128370, 975665974, 333027078, 136699831, 52487986, 642401547, 941462937, 302088210, 155936182, 590063482, 753055757, 810617967, 219311478, 420526867, 255328261, 235528697, 54476606, 173933640, 687207048, 560334408, 741676428, 82162136, 712504832, 81002833, 234651022, 417494276, 417898077, 713312869, 830728417, 110387772, 789309513, 355631006, 676005119, 58212356, 356213953, 170331785, 229291138, 861231356, 841630905, 870432377, 197943388, 544006979, 207107136, 999382211, 15817297, 970371154, 657776906, 767437063, 592836217, 798807312, 982873518, 400736523, 890575650, 563696512, 949629867, 196206457, 453440633, 197735785, 651099055, 759454437, 624650118, 728930379, 518948324, 707520243, 137668048, 556199142, 401143703, 104983403, 706494074, 418289547, 849890240, 457736985, 407366808, 907335991, 910428797, 808604257, 27384322, 780498611, 752525444, 814659663, 597336929, 206876907, 531101791, 447739120, 786487057, 302462309, 466977488, 94155565, 13665355, 901170816, 458626086, 5799708, 672944870, 872054532, 763823655, 668349209, 958968867, 552653892, 659199227, 234161175, 507069778, 426988298, 321521521, 529183206, 631371309, 387464242, 791751768, 533137762, 965323539, 537489394, 937758227, 632471461, 706337115, 14453791, 364059528, 402627136, 987496317, 96079003, 166541187, 136719197, 791002350, 173352140, 822802487, 618891306, 458594236, 600043704, 302128543, 904141402, 565701289, 766864823, 305223248, 598615334, 24788579, 634202344, 302398613, 468350634, 139499448, 463914920, 417392656, 706618680, 686428486, 765930296, 64107522, 955834173, 262931784, 970138950, 439981087, 383993042, 899893288, 320471194, 24231579, 690743662, 271139670, 917330924, 88313250, 627366280, 647840060, 253894950, 818009426, 227993903, 106471957, 386667047, 972167779, 406830203, 253126137, 958114435, 87433990, 640725709, 863462384, 158218870, 517593382, 621264016, 615673970, 917809640, 390583625, 604150956, 776414010, 742349538, 938411694, 674883188, 674356201, 805924912, 572203337, 480529362, 351390294, 664612169, 740426278, 324534272, 978749155, 114681879, 853541373, 21209453, 957636788, 14276385, 784802880, 319299900, 66215045, 527028750, 466986056, 892676669, 504097395, 460362196, 500519460, 43681569, 384737396, 630582092, 796376728, 668731309, 337454403, 330920022, 320600812, 304456603, 365236504, 465488822, 562843965, 349227467, 75911892, 996351351, 547315606, 454564616, 461033754, 316821796, 230309141, 707515912, 46399621, 435457131, 601820760, 478272426, 637614513, 29321609, 157334433, 285537177, 907113141, 133292022, 518841823, 258840079, 482038521, 539474628, 70551943, 10021931, 330434721, 610377927, 719830068, 855360948, 719447591, 487676946, 482922172, 735457352, 689659556, 957019739, 211401492, 405496965, 730373992, 502497737, 429787625, 624802610, 144954774, 867637938, 609588383, 830467274, 506465539, 994931101, 762228827, 864219684, 997560745, 51482220, 371646156, 947858019, 827575929, 689201855, 540043822, 34249228, 707271961, 52819820, 854729228, 949889717, 462482634, 450409837, 236313573, 80409895, 986596879, 711290674, 35045704, 424749221, 359207787, 556492276, 347242463, 411626864, 116212355, 907561717, 1431440, 780224527, 372931595, 402228528, 345089254, 911637108, 143255087, 387086586, 941891089, 238704193, 991381153, 768481701, 613101710, 240671921, 23146999, 751053352, 834710359, 817363145, 145870828, 424573086, 882092624, 897985955, 440058976, 350537541, 851417004, 591083088, 890870508, 669645484, 656962639, 289963238, 50896250, 524424570, 871936469, 16349729, 231693539, 135844306, 861238116, 575170734, 842692208, 54612018, 504880033, 900557519, 635932361, 190485926, 113493802, 599590496, 631960592, 634727160, 914311968, 775067037, 182294379, 410136430, 884499271, 588581771, 217778385, 55873993, 808775803, 549778311, 168442360, 351498999, 175469708, 46933260, 292709087, 490125879, 917819962, 439590902, 822251911, 523718715, 690391620, 639957077, 633528692, 105841464, 295544905, 349696, 559371722, 443793861, 409298470, 350699964, 389196214, 712024289, 680420114, 913531492, 735468942, 145377416, 73742316, 88787712, 255987076, 403943786, 385325650, 532444316, 523003171, 784277521, 320910560, 872614996, 985102950, 798250011, 724925120, 681734379, 53170341, 252717752, 676234466, 267913577, 884656981, 635161547, 454461866, 342913954, 863585232, 850486588, 822286488, 147036597, 332009383, 628060386, 390584951, 879246856, 961886757, 566341134, 441686870, 169385677, 436992704, 184769228, 435427341, 269080510, 803091106, 942907850, 745279852, 587290715, 512202483, 36742933, 424434380, 19438765, 337623824, 539691614, 690306009, 285540472, 891259861, 609050463, 731011994, 650156597, 675716992, 182679372, 645586240, 962350310, 591975849, 241322906, 27131419, 878518811, 515969603, 881325542, 948286698, 435914447, 542115669, 440230117, 17422426, 430389728, 358032038, 737298263, 394721487, 424866960, 622966861, 514292874, 101496398, 55143196, 401510643, 787474179, 96997753, 788752200, 411474430, 964965763, 324495441, 803112019, 151845129, 602449576, 25611157, 503217555, 474059504, 7309414, 970072231, 192323389, 278467518, 261062325, 626754317, 472352613, 309736078, 455702815, 236704373, 984163607, 171041462, 880148828, 302804327, 792114717, 706825524, 170338652, 265757507, 977757737, 556141497, 369747076, 505946546, 234711819, 520195872, 5822476, 924026229, 851120262, 705591670, 551201455, 945657967, 153519107, 464182779, 513814510, 793713755, 356737449, 869775056, 625544496, 169591926, 578849649, 59466194, 182123804, 8479595, 467941853, 484636900, 542254843, 155815183, 359938756, 615454503, 717869350, 847453721, 13861566, 790857, 764966412, 762964885, 305866317, 138064019, 494104449, 514736951, 764868773, 937785201, 198414787, 417538044, 967644620, 977940062, 374385626, 328300457, 452923868, 765676214, 475535901, 882926654, 391616471, 937698641, 392963416, 882407124, 397111500, 711425304, 6142641, 243916765, 476273485, 401569590, 810578724, 288852170, 374038753, 651477006, 993818334, 350027864, 919776667, 4513095, 358889700, 529256997, 820595100, 747610661, 314237403, 237568745, 246200784, 230428602, 57967230, 130801643, 193426241, 690632609, 353031554, 546614871, 216480432, 70449585, 766387109, 722955401, 514823187, 158460627, 453391193, 66253915, 521772803, 467399503, 301829934, 666719648, 775603547, 93383667, 507007147, 242835874, 68131441, 575986665, 783593664, 760268660, 539230261, 100570353, 976140505, 301463107, 324258589, 189316304, 240368671, 12314404, 558081946, 47652859, 747422930, 225317812, 246586982, 828975671, 122288734, 872739991, 21950477, 271930483, 300012103, 279651517, 598297957, 623394303, 438486782, 352382951, 885131623, 826065691, 121494523, 501142067, 242932446, 451075565, 334144435, 92175576, 120649969, 714656189, 577795890, 518948250, 776663786, 631606451, 569419530, 915376476, 784679654, 224948834, 256992107, 429418437, 181109535, 900888915, 782245916, 810509290, 726374840, 283423119, 696154586, 378592351, 721062446, 952646407, 898515366, 560036836, 659229621, 931636717, 406666164, 855049788, 458462542, 844804866, 263615269, 475632671, 137394349, 536555889, 300309876, 88545535, 50662416, 770621697, 982386322, 698415565, 339983731, 692168116, 421325678, 368516474, 930043692, 277117008, 374363766, 759645846, 661898533, 788830384, 459890938, 823746302, 197328245, 553863773, 255154490, 539707002, 555031746, 938975556, 244241012, 335870325, 442462465, 398023920, 650121463, 670524663, 996896972, 885450353, 702758389, 863893474, 152626179, 538347227, 985507570, 487573664, 971416833, 14796999, 32332875, 843845480, 844081227, 52021748, 391068362, 873999479, 354673395, 478765700, 713927395, 565705429, 93953169, 435879951, 696367723, 520186185, 829198375, 144629106, 895917295, 923243097, 564783092, 233348507, 116319957, 627170868, 332154917, 25248570, 77363481, 837587730, 56337999, 176365943, 727611426, 741677735, 917035705, 95760614, 508547946, 32046251, 447731026, 485537751, 190722631, 997903709, 635996146, 564472008, 482821607, 898579281, 323712781, 103083810, 824255884, 925001944, 854655415, 740830349, 720995753, 187171016, 614184537, 928557937, 597147377, 5793968, 385625349, 626291922, 721742604, 734725027, 317242605, 326267357, 993222185, 462652566, 783747295, 926399507, 57036384, 831330338, 712918858, 673524509, 642444923, 530294037, 811898893, 579361410, 343836405, 119621368, 328308336, 623989406, 440028917, 631293485, 138788591, 638088866, 176195371, 238886775, 511892703, 943685205, 675779942, 828003739, 46345872, 182097984, 983828200, 581947395, 701127653, 252745954, 718290441, 800246400, 586200696, 845587469, 616274726, 488298192, 861792982, 594926390, 255775302, 386296953, 994874469, 730809632, 709489553, 785697162, 973830499, 570636023, 950807148, 827123775, 920056603, 43090916, 106177493, 801746069, 675951176, 250027614, 137767301, 127356929, 389846905, 995628081, 989257085, 625488331, 65415516, 781776255, 362528406, 352015357, 904344420, 956444571, 608700610, 319993227, 411947313, 502946629, 122630325, 408950697, 625555324, 728351331, 278118562, 787813576, 976735764, 334334273, 225206141, 943125251, 4699199, 359920161, 866121197, 108267662, 58972992, 982818068, 308336239, 888969077, 847425498, 122104611, 338828472, 667558217, 234440459, 387563106, 761697717, 366073269, 166770301, 21456818, 291343772, 982962823, 96114085, 976432626, 285621830, 624920493, 359108938, 869563324, 691312011, 132118060, 799584770, 435252101, 595833736, 648216757, 720530284, 337387799, 863552072, 506094129, 861650482, 494096841, 515508154, 991050983, 522671161, 883135704, 129176212, 254098981, 91029982, 900876893, 430235197, 550355489, 340672878, 358277170, 221516844, 220064613, 637330913, 40758957, 69243845, 954082945, 885427339, 55256695, 824698156, 624067251, 171911931, 684495945, 753743689, 555665266, 121672550, 348864740, 238896599, 969372870, 940681782, 717139498, 733695390, 932357798, 311564310, 41770255, 729611250, 450109190, 82529114, 312232006, 797628956, 586571364, 841114000, 586529624, 412029742, 861960136, 982071890, 385848311, 847032446, 829969277, 588761923, 835587720, 872042331, 1077140, 775879516, 71301237, 880061731, 537839027, 285751880, 688002130, 308495118, 785164109, 633364582, 805327119, 914708118, 690024687, 514883939, 285828482, 157579725, 744651606, 529787554, 806277914, 794848115, 544545935, 986215590, 908480174, 599251696, 806232754, 171158572, 964208503, 16840279, 715789171, 562462930, 377354702, 281401794, 4397430, 810656126, 179963207, 968482368, 858515210, 553525273, 490316549, 846820037, 410107789, 36841573, 417086386, 109162617, 889933760, 607971903, 948794331, 863005936, 511178321, 327507196, 442275703, 570121358, 459690327, 47194941, 181180867, 244181565, 734025803, 429743983, 239885765, 25763073, 59842683, 165813850, 15780968, 504250309, 77855484, 437807550, 558426307, 973995623, 304286302, 403848552, 294808708, 332391595, 46711825, 20468401, 454878395, 643346402, 97396612, 791249318, 559494998, 392114804, 743027606, 177739122, 220364710, 442867942, 804158637, 404740164, 922594561, 320942249, 867610581, 683865215, 227691612, 968670095, 607531597, 63664041, 317131687, 965681699, 771853299, 243969267, 159242482, 54196208, 104526277, 603593930, 884120641, 449492358, 148707740, 332738763, 582689558, 986260190, 191990626, 156948278, 643640942, 331509537, 516449055, 105151041, 99670689, 891180142, 900016844, 112792128, 230551776, 938428237, 691336380, 288038411, 127624669, 200476633, 867198871, 482280265, 572747752, 187812581, 481549914, 661435826, 297814818, 354476810, 171424489, 273812043, 49767938, 85421445, 193859484, 490602190, 115754599, 549819846, 328513196, 219328682, 345897031, 80875019, 988431373, 349358270, 634628471, 708216871, 184052792, 691974015, 580509023, 816248539, 851485121, 164545996, 695335716, 227624128, 653256633, 947756877, 542312054, 685179482, 616265948, 597430641, 81357536, 254245769, 644493817, 479825983, 322199999, 301556086, 820383584, 137624291, 891632965, 246856118, 640371563, 611023787, 431815004, 260576095, 187617233, 373570564, 210447258, 155745832, 255631546, 104909985, 549384747, 150175037, 989626546, 292721229, 756879739, 740826592, 364799860, 851298646, 344813122, 27379986, 359811653, 453302036, 220154195, 595900848, 797657876, 944335047, 736818987, 999929537, 613744933, 137535671, 208049776, 536888140, 398718376, 31721379, 577162438, 89859138, 259071762, 657169480, 678426690, 935715, 499432148, 366005902, 537280279, 730284837, 800066682, 888596977, 37257803, 972488117, 881391637, 981400354, 497312278, 878164656, 40281976, 532310690, 818868708, 973029253, 102666829, 757355635, 54262293, 59339894, 886125531, 499807610, 929026418, 546789241, 876731651, 684290535, 999307663, 918687033, 913088520, 164823656, 163425664, 83153423, 280834357, 50368959, 528147027, 45785402, 363980891, 82700457, 192934738, 267584176, 162739516, 23265870, 192733101, 687118561, 478429393, 696803840, 177217618, 184491208, 168690619, 715604507, 525835190, 274997150, 885413686, 744027061, 209697429, 649555629, 421042299, 851500931, 73838271, 17506412, 332978321, 712225817, 923947608, 457233028, 56752074, 26933422, 152197779, 377863981, 706226518, 461989342, 17937053, 532230603, 104662121, 45719605, 238733069, 640410838, 748964102, 782895903, 317331983, 231713341, 587297749, 903931312, 422456902, 586054174, 911839423, 745116295, 216977220, 696390028, 658654321, 416785130, 749613256, 455491420, 638686719, 320340094, 737280638, 176562600, 478037697, 761804417, 480697913, 872421398, 626204026, 88126643, 743317872, 599602160, 316605967, 312578409, 488117017, 417694807, 539465601, 557977961, 660489469, 766369445, 922825664, 230609683, 106236315, 732961390, 814352260, 894337105, 465711680, 638221975, 285337323, 476346332, 43150863, 680980638, 713908368, 320746958, 920316486, 17305431, 613252044, 783937321, 374775344, 849262584, 848135493, 914661694, 470495997, 309656989, 952032040, 270778730, 720152728, 767630195, 407673278, 448061854, 360160616, 783936593, 481944469, 222750120, 215899142, 456395351, 163016879, 276741130, 374191385, 37527458, 712156815, 201270025, 534492624, 223801835, 328810020, 869906665, 892743807, 11402464, 849496784, 907532827, 610488124, 65320928, 405167057, 566277427, 478843133, 405409045, 77917407, 714918132, 865703981, 619724063, 845598027, 633804295, 856183232, 498347906, 60997222, 126936191, 781288270, 597796676, 552086796, 48781431, 609194663, 768034617, 394810845, 512259321, 66605680, 443847694, 217408576, 867693571, 313558014, 536697738, 113324907, 302434795, 396301303, 238580878, 606276922, 652043504, 28511236, 489963005, 659679103, 212316433, 700623122, 744833116, 937523761, 744710131, 696625503, 303097611, 906705352, 954757700, 65096330, 637414235, 549109000, 227172242, 667242926, 877352699, 45695567, 607942419, 565696190, 715093746, 121364623, 398361749, 358349436, 389537047, 503537671, 882661463, 700416382, 334976758, 610464376, 188732113, 463017594, 565236480, 946696269, 705119696, 913505668, 448910537, 317208769, 608273636, 355405974, 961421199, 596829613, 809332307, 955109676, 349078812, 862758076, 873767895, 283586853, 270317138, 431245698, 957945012, 164977825, 280414334, 370322803, 114745561, 522205850, 589329677, 115914632, 399656774, 733302677, 570736323, 186259475, 430160095, 717930141, 133259694, 863434156, 473764600, 882224347, 668950909, 844967027, 184371623, 194116780, 410312682, 739200901, 659818425, 813012796, 278320519, 863798766, 171794024, 622657669, 292866468, 108979348, 855083418, 55101958, 653534991, 795611540, 364724922, 564460187, 894956571, 103203448, 185415100, 677144135, 749812726, 133395399, 730056497, 779009877, 212557604, 712683965, 648791408, 670212948, 183946067, 903045165, 394801933, 250222961, 852531752, 334164052, 708212624, 710892150, 289763913, 87448618, 177750594, 453891729, 519817604, 933986662, 799152655, 141584606, 298131787, 795706046, 56298573, 236036114, 366303547, 432151086, 348760376, 960486558, 944737835, 321686651, 386357461, 442260998, 547915449, 453165930, 696753060, 672900656, 70890856, 73654733, 578177671, 484979490, 785777853, 164548321, 613506738, 40254777, 99399938, 754106992, 736146481, 914975573, 680820321, 983298163, 24477543, 699163605, 812954051, 897306078, 742918632, 560802981, 371838828, 6832482, 450449939, 711889560, 454906962, 357202971, 997470423, 909873559, 286761100, 580077677, 201031123, 231196183, 192835912, 533177940, 17698879, 780574936, 575140174, 68450878, 813906297, 324611304, 870645700, 845605162, 915835098, 243203955, 636043260, 953925039, 69901516, 361886627, 926660922, 220986080, 680559274, 346252674, 343241707, 299832030, 856221186, 733424545, 682375661, 160618214, 527054304, 133575843, 893953282, 360865465, 248986440, 536082224, 734631218, 533944131, 936124961, 771580134, 437757008, 623522633, 834408437, 220819431, 805498219, 648330911, 522331625, 424963350, 243411895, 684489299, 874248463, 799442467, 301736143, 92528877, 864381993, 87782118, 356042358, 513796302, 443706825, 739731819, 732147161, 164472208, 916633925, 51595936, 143051697, 921808706, 504519129, 392827718, 703441437, 624035456, 72305228, 491697035, 764188138, 448182012, 421533317, 567684692, 367452643, 313643855, 88864886, 324783865, 32716877, 788095468, 69777159, 226617678, 679532177, 397843577, 609450662, 149497464, 697993450, 52361156, 369054477, 820789569, 226066764, 866920311, 220238078, 368942075, 712767874, 575616304, 962868938, 719776465, 220689795, 924922752, 483623766, 381922400, 280873124, 272663035, 640819228, 615428086, 475679704, 823397864, 552585913, 341067892, 561146559, 5764890, 310999770, 187457698, 623106053, 249904571, 135911536, 857397112, 664825834, 631940748, 40366801, 696907283, 529519779, 76980068, 356341232, 385625595, 303082381, 348812101, 831126145, 827997833, 96607480, 832744047, 415770949, 549659486, 411522024, 859919231, 820655521, 769101965, 44585549, 793688192, 533891148, 954176295, 214822681, 604507557, 198564889, 349423317, 324240674, 240667778, 249033933, 805319249, 488810209, 91708044, 388826409, 333646969, 747403000, 171884721, 663678903, 704112873, 859132026, 388466309, 780849265, 109849773, 959303722, 480451662, 326336938, 532268077, 154871578, 115551264, 657231099, 507623280, 870106161, 367406017, 717452200, 280585609, 584695841, 853755782, 712980877, 87242245, 406898611, 301680714, 331305085, 862139013, 425635080, 360016971, 47630670, 19967537, 85968792, 450913006, 750844730, 282116872, 248957167, 431154755, 999468664, 269804058, 702554777, 733391025, 789454127, 431572185, 386024828, 578004261, 196833306, 693861850, 984491783, 869950278, 895040331, 717986619, 675418395, 911793836, 919868568, 400257115, 663785658, 531843277, 701416534, 123693391, 809910800, 669953198, 301631508, 125796028, 191054477, 74610648, 922123278, 576394683, 454711828, 924476548, 553082558, 607203316, 226249759, 230694505, 955954503, 454074574, 208937360, 450257409, 656254645, 295957327, 559734884, 354833937, 218253320, 29220634, 899071166, 575057149, 998186180, 877896853, 498844753, 307994726, 169973825, 711605808, 937405367, 223799704, 43378601, 851816495, 791872710, 327293886, 68287657, 998807821, 553307419, 361933396, 821383595, 68571747, 694227846, 443976053, 212943316, 343896711, 485487599, 842655038, 452508303, 708655088, 646874819, 667669602, 199101168, 858287232, 254434917, 105144904, 855358592, 419235847, 720394732, 624458610, 160153045, 966499372, 729740233, 90995226, 810078720, 722456059, 727621938, 257796955, 33911741, 456293126, 435202604, 593670690, 915393707, 370131662, 609481923, 977539253, 227714313, 693348975, 695983710, 204859255, 58989258, 819383723, 478266382, 580473275, 99493923, 664024552, 466676321, 759290086, 457173603, 637726081, 835924660, 804645417, 161075380, 462444255, 7582308, 449908368, 968689473, 688419865, 195368392, 306465798, 983867849, 859852710, 483092141, 611695073, 471954682, 286970292, 255452146, 353241057, 409751689, 696965761, 721453921, 760915524, 242825422, 784172013, 120252093, 908400365, 691854491, 624532869, 989712265, 211653350, 557967112, 750668328, 79050937, 898662283, 994696902, 997236182, 807199495, 587507132, 276026514, 792271944, 567790212, 539447429, 366917735, 28502284, 10549360, 246289652, 348010279, 81259315, 748658727, 414766742, 82394785, 616942233, 216882656, 962272543, 717583924, 461009759, 583874983, 36997842, 632228170, 613578461, 898438060, 438416488, 88484246, 105288319, 606646343, 8097640, 305759695, 728874573, 291463407, 919725433, 25939916, 428064797, 202440698, 921039088, 330720146, 863253581, 280918538, 953631517, 974606369, 321953123, 88717232, 77366669, 674635633, 912205305, 843024086, 376386224, 162691402, 584020918, 822472977, 363529360, 84196960, 792551661, 443179686, 197477502, 215198490, 944616992, 814115071, 852952973, 469511846, 195135920, 590211651, 529766176, 885374518, 203224129, 916483862, 118995747, 112191206, 77646253, 474110887, 422454489, 203804137, 745103142, 625025139, 832687087, 554855161, 72054073, 921463586, 589840487, 193500629, 697771797, 896041163, 435094471, 973687896, 858296329, 466602078, 877879932, 867477388, 723526117, 242759432, 340256879, 843680337, 349765125, 353084663, 476581400, 308073242, 701715476, 976923159, 654495343, 947669501, 783359798, 593961290, 127918212, 852393256, 880387217, 990381010, 622361454, 67089461, 390231598, 598148372, 727642725, 338562314, 476396273, 976694899, 73240871, 297376207, 431061405, 696276225, 995887344, 945573952, 578822120, 893935478, 280065979, 310167489, 6778595, 798489328, 568120597, 636014006, 659882608, 974381413, 369827486, 803746658, 877328887, 780331109, 317768025, 460601169, 138942135, 720901534, 775567683, 92071869, 642237659, 706772178, 919841674, 445684832, 727408084, 18730395, 355290859, 500715412, 429885391, 483408011, 377706713, 781390345, 394655247, 77914580, 374913832, 217217567, 75571032, 555699025, 413848763, 130368387, 778539156, 797887316, 582789454, 347538034, 31338125, 64346687, 431497663, 465438247, 455787050, 668237171, 537821844, 951852592, 215241014, 703065561, 389378244, 14196301, 877581832, 812225598, 974487062, 591817796, 357960500, 499314417, 836724946, 511884930, 478915525, 210460501, 99344118, 814407575, 637976737, 968096599, 995339996, 452232042, 618743637, 494154491, 276137068, 400473040, 523799498, 838097572, 779491612, 165821958, 47938239, 66942925, 765268599, 591683517, 748832620, 447735957, 937818833, 171801647, 707591069, 442282226, 190254356, 836208693, 474048037, 92597924, 836924627, 438971034, 884202289, 239656614, 905940272, 5262321, 608211097, 207399306, 672305101, 738257057, 200410235, 644257584, 666201193, 66117389, 374063703, 321250518, 932161852, 169467874, 241229165, 945396871, 974085257, 969200548, 438385203, 634927067, 271736926, 367313869, 857133553, 474293079, 32407754, 607945757, 833410088, 702847641, 762660133, 194535993, 414258876, 481853920, 705225652, 370959087, 354584373, 577873897, 824348169, 786527127, 141346572, 752819738, 811434807, 599611568, 750764349, 326665778, 180767651, 238504611, 593955723, 236825540, 803078184, 610752581, 138185040, 49282684, 269382947, 280467708, 181224802, 306750131, 407927712, 350096868, 946918055, 105962518, 83197184, 136395804, 939279606, 376590958, 556270744, 586985563, 888653774, 59804576, 253962715, 366252042, 572563969, 492039144, 10717845, 282586145, 680374037, 79765891, 237993114, 428268843, 640461917, 115956220, 446239416, 179115161, 873935818, 678180151, 743320549, 518770015, 696116846, 378823638, 314120304, 154543048, 529048022, 534348141, 461249347, 496656514, 323930245, 815546093, 813853770, 805116319, 446799672, 528900927, 756019125, 925889843, 414944063, 938554378, 894601074, 850802341, 271034078, 543418565, 691031379, 309920407, 273372497, 858769791, 933050180, 620289498, 676907652, 164328481, 983644966, 985663460, 863428535, 683079192, 388051593, 156025445, 15049547, 221171542, 398862171, 175559375, 830688125, 6143337, 895391983, 137607104, 573950894, 880776866, 760864245, 127645518, 758563570, 661429707, 979165353, 145843008, 901028513, 41698376, 613416567, 83657137, 636250653, 163307703, 559105224, 582294135, 418632856, 250292839, 979671451, 371132547, 848769831, 929639673, 21743537, 932209691, 986338858, 813002495, 26448098, 521462051, 473085959, 743039960, 991121031, 803221667, 572348317, 538005366, 193316827, 768793364, 558084810, 47635349, 468759688, 831598888, 407252244, 220017263, 293852962, 391235735, 110948026, 750399572, 915446433, 413242180, 191407130, 69165813, 93663506, 308797217, 9838689, 691692674, 806945803, 94688310, 211859557, 206216719, 727886675, 992756783, 96308540, 78407719, 975362671, 645408051, 199449987, 909017069, 719221107, 890790264, 156358146, 374698681, 308879682, 98908103, 852894373, 458917560, 854976533, 166775056, 774891335, 287225965, 943726302, 802090163, 783415384, 833650091, 241948300, 244405239, 254276491, 625561612, 171753114, 695677323, 307430554, 694502174, 498863907, 32800680, 128233097, 550719570, 945114851, 298301410, 336353289, 364341725, 426019222, 57436179, 822712749, 495452213, 283412581, 369763929, 901088177, 923976887, 132094136, 38406200, 95463995, 744945163, 867800246, 612885406, 812275875, 728073867, 397985789, 453190782, 268367315, 716300508, 36580744, 620590581, 946010568, 947237432, 958196918, 751532225, 549314471, 206475229, 242778136, 83641891, 48272744, 659066466, 495596780, 752324317, 247793081, 797761450, 446236261, 397307114, 89566534, 161554936, 780405698, 866975173, 477740601, 205147205, 948188564, 27946893, 252853492, 895202738, 751165885, 577537969, 987710566, 765625304, 269802968, 737079884, 933062597, 574349473, 699905460, 919035865, 717643562, 179573075, 915594862, 396534770, 977988138, 112547910, 296948561, 2668961, 245765922, 581292193, 160043887, 216305935, 625419688, 848209740, 649680512, 308840302, 612672280, 925381164, 284128409, 381665421, 20755600, 722262996, 267101634, 809885303, 312327752, 616182499, 539050147, 999591019, 119907175, 764287073, 878650541, 653954106, 807778509, 683053452, 790095725, 864719365, 210876443, 576728027, 537625493, 781884569, 623910084, 323674747, 698781495, 658896386, 748424360, 485446168, 930995716, 263463904, 992234268, 253968134, 599449905, 801422772, 744993129, 760278206, 607711566, 266891611, 732641883, 892317384, 919065328, 508152523, 927469523, 52040365, 565574992, 164626358, 153630636, 368890363, 107047032, 351118040, 70364209, 596687899, 30816606, 737917341, 674042270, 699708926, 633163809, 806326816, 24067565, 878493182, 336459284, 800295385, 678590777, 598557205, 68390014, 187547582, 834389963, 223586800, 902590507, 246638025, 183635334, 602554882, 178742214, 856302919, 973927761, 597522767, 914214171, 398324888, 848821845, 804126004, 248847825, 668752568, 417227418, 234554455, 375964051, 791320973, 842730355, 972167772, 747272510, 284028160, 606405833, 73146381, 912271393, 373861617, 683306303, 188045881, 533872199, 745605069, 994510678, 723151431, 886152710, 796730190, 375566262, 741223603, 886392006, 504629969, 837145921, 710774963, 547066962, 341506694, 493967267, 926522503, 595900126, 905524360, 455203032, 52023086, 767985952, 131248580, 152730720, 794416379, 279201929, 504351989, 705247397, 54558092, 606019571, 465649276, 555546924, 207449657, 817604094, 950893684, 130980837, 844979278, 180672739, 366052368, 61996013, 188627822, 991353682, 647281422, 366229979, 626211460, 445329516, 744761064, 53041294, 795181764, 615929071, 564108885, 237306242, 903195884, 309970869, 611247981, 765233718, 435368108, 814930868, 735577543, 365464861, 16954988, 93373600, 827949853, 333171320, 151793314, 739638536, 202420319, 303034784, 18402913, 131302523, 82118273, 641362084, 871458535, 238939114, 539607897, 418917176, 558774648, 511794432, 286272525, 780538055, 762785354, 305102677, 254757210, 968550159, 82930546, 754361264, 996547291, 116667922, 893375020, 665735123, 837161642, 824842047, 221166381, 470238222, 973334134, 925699061, 235270945, 308171557, 87955967, 989121237, 82361425, 993234612, 414854485, 426235352, 180336275, 683214658, 620689612, 610154547, 399471249, 930023533, 664756686, 279265076, 600320562, 516493010, 614829669, 24114991, 286177366, 169845226, 535046162, 67508707, 372545487, 994873040, 44577490, 500540721, 354768346, 161153235, 393535720, 307400382, 476538452, 305304986, 181297083, 550064794, 985276513, 564007274, 491316825, 205319983, 219874978, 567978835, 427693025, 880165526, 962703544, 475285843, 259858481, 38249293, 300191796, 108826471, 832592837, 250846883, 397281531, 563130102, 765864900, 467682737, 91466952, 618045296, 504501205, 820356683, 801198074, 622250546, 435242918, 764534304, 947378102, 12794531, 422745029, 5104032, 934813231, 910335881, 13837632, 424525297, 477459624, 811001686, 884327677, 841781466, 92034006, 585583151, 689207815, 890647639, 80451014, 860625126, 977427438, 450077595, 783726770, 661710564, 125197078, 723159991, 818261361, 468789561, 511067745, 750505941, 812440656, 460619598, 33176394, 353038993, 554139747, 716699178, 266918356, 860493060, 962285169, 218172241, 228848829, 798042505, 886019321, 642226750, 254612732, 442994522, 52585298, 108033024, 270378597, 274457326, 290843007, 569612504, 863360621, 587999570, 46365965, 30811823, 442654274, 445552293, 573806452, 821618983, 71060199, 138476472, 310375080, 795074494, 921356456, 130481069, 595677263, 14261716, 419768839, 424027594, 576010031, 60485992, 637687884, 583015326, 663071361, 512984935, 856527895, 955574839, 141252757, 804088132, 12579970, 695868939, 595852397, 472949401, 753309216, 224721241, 991705212, 187999043, 62481746, 637138409, 914100860, 705466059, 308195033, 105863676, 508921792, 91778179, 620393163, 369680928, 653688435, 7507138, 803842427, 489703149, 247960846, 322291521, 595242965, 773337781, 575401558, 41930708, 579416612, 727266286, 146360492, 992730631, 595350023, 452056217, 329147645, 626382428, 163189632, 441814362, 704748191, 173610552, 871854479, 762234913, 473029571, 635323857, 772591014, 822135927, 161996246, 369102665, 797663180, 727442615, 52357793, 735757809, 991643663, 511608357, 520191292, 714930357, 99742815, 88450414, 31142765, 281679707, 854946162, 311169652, 410144436, 810509055, 949087139, 550529147, 318982678, 485854920, 953733949, 909872098, 369123757, 944911268, 919676488, 91420052, 635552713, 836487757, 780352000, 551570699, 263043487, 177685192, 128453832, 660709468, 928430985, 981675502, 8676125, 784783481, 793328653, 71200513, 627518716, 679138927, 246561877, 473750227, 747574876, 679610595, 405012647, 780463976, 367447314, 183422569, 110264129, 298664779, 518475798, 297451559, 238210441, 808080653, 593802555, 936959408, 431487313, 875386959, 708762050, 466212044, 708798101, 405109151, 174317543, 452837093, 377262575, 90743505, 51386105, 50929982, 390004089, 353792013, 657092998, 240228143, 829729587, 881578702, 922884983, 160050631, 569926835, 954060401, 375339762, 375037782, 232694251, 841634564, 733631418, 233373672, 411629921, 474541907, 253268408, 115393246, 837305904, 808405059, 882151628, 279754356, 276647654, 878316248, 174538354, 399074438, 446989836, 308890507, 460981554, 768507059, 783784291, 119750720, 77402773, 540352829, 5051922, 721623079, 470538046, 5705658, 252667414, 180167786, 166795364, 501003153, 187170923, 380792981, 726490862, 392436595, 296707578, 778107330, 647862360, 800780390, 555487000, 976150747, 273678128, 367001129, 540973728, 555313708, 41474629, 841696240, 692728810, 131060859, 218503516, 851305327, 119561582, 396232586, 8292236, 626872084, 916913671, 904647831, 811855783, 923090354, 726767157, 769402176, 71154921, 476888872, 920450359, 83900416, 9026590, 925309063, 103067792, 606543827, 669922305, 379700032, 911620418, 387717206, 907906240, 667667473, 411259220, 758278, 878637634, 675222945, 360815412, 467186434, 172535893, 138259936, 489909312, 718796972, 27639614, 403121837, 490954982, 240368108, 661130824, 603165659, 449093813, 814612883, 316143427, 184805161, 619957119, 929534679, 576313581, 363570938, 102657987, 512632423, 510512998, 565817453, 564842339, 983459617, 363383478, 762365347, 622549698, 720134901, 261641993, 873984390, 470941012, 167695615, 330594049, 128091398, 798574837, 895667994, 200887940, 485157800, 201719717, 910957698, 120954093, 927511202, 836973746, 625328713, 615679929, 309337102, 375612638, 146538955, 14092204, 219174029, 741223296, 756256133, 39230440, 186828296, 950998755, 322730004, 818599814, 533886789, 561641043, 230079548, 167457824, 996311375, 248631548, 420260652, 276880489, 688700907, 659281313, 301751044, 91049041, 542603665, 820731746, 422497728, 197149950, 744609040, 90485984, 511464797, 195577160, 588087089, 979853156, 602119714, 326876798, 821009038, 951070535, 721539804, 454886736, 220561870, 488505650, 635611960, 590166578, 761417137, 384517878, 814656384, 410891337, 514371272, 898647370, 93904864, 647868517, 434329535, 179626168, 332083660, 951645327, 643390678, 133591070, 340198437, 918210396, 483653971, 286766857, 233426018, 418914166, 227064510, 64555490, 8359653, 514193466, 898273965, 383912817, 691562248, 788047186, 447859916, 597873738, 431607118, 591813319, 462397168, 638216503, 669521061, 858871508, 699379952, 391882566, 762092628, 30388081, 929876699, 473638416, 605008892, 508015660, 535117861, 28754898, 121969707, 487436811, 651295332, 985597791, 298646007, 412429875, 173469252, 257318237, 965571799, 288808342, 408315056, 893885361, 679598612, 620134893, 349287401, 856854346, 395397385, 107286436, 233336641, 609044206, 503766193, 598828841, 771922012, 771656101, 717173929, 303948257, 66857167, 169974978, 206670614, 708812766, 387190446, 672541387, 59027397, 348392305, 163165658, 837935065, 200958301, 745090212, 892960935, 545182464, 444733327, 321338672, 728467103, 906036797, 131257499, 790215394, 176303008, 249051961, 211311309, 192657158, 375793625, 835283368, 992954442, 138008422, 583782005, 30963656, 968100707, 934796658, 660044830, 594182516, 217776871, 649028743, 197921830, 96196489, 792086145, 316520596, 380607794, 214229668, 528232812, 902532851, 534574889, 563123630, 779894090, 348460146, 748802672, 949626821, 465236296, 902179908, 47945485, 345490644, 599603293, 736109568, 671572037, 608208260, 239948363, 974174258, 729939396, 911198799, 985608453, 377327765, 628049503, 770841591, 131875558, 65183803, 242902604, 484877804, 318882296, 906994094, 827065639, 712186445, 661942800, 970026730, 718856086, 950123348, 118598066, 718853489, 214368231, 459650063, 681706681, 930489764, 862955337, 695258311, 182531026, 792677781, 109885590, 43723960, 961024794, 629146850, 185755189, 865308478, 817865011, 483633320, 369770577, 492062613, 716971715, 485009167, 6693956, 915132931, 4881316, 255624676, 846672963, 993309133, 409592496, 63698356, 802733551, 479686717, 98100639, 577428781, 680175275, 729306688, 352280350, 737324502, 230683817, 52605552, 837734835, 590738645, 999180215, 27306975, 293981733, 724084983, 544933672, 701875149, 97196338, 325305378, 204716061, 893746400, 549248173, 562667342, 154189907, 132095671, 974858792, 581024175, 648205083, 194024551, 975075685, 958925803, 224748165, 952036181, 435804025, 28831948, 565405867, 581704314, 451476774, 796647126, 994332650, 396602122, 566219154, 481613668, 895191604, 671396701, 105288893, 129933137, 88781099, 440942406, 984834402, 18313691, 200565737, 431171095, 206436130, 805024376, 741694047, 899493442, 226436094, 885464670, 912858651, 714883868, 69601439, 571861845, 159219861, 914281729, 767147203, 799685488, 989598270, 177522002, 286985375, 672175446, 784099950, 188304657, 35136094, 72521530, 705778671, 911337554, 733110750, 262771202, 492804159, 432703606, 63504764, 579210836, 222539205, 348524088, 93763273, 679483392, 200254238, 666792741, 522327153, 240145013, 398973739, 439746914, 737980643, 605552438, 559185244, 805735944, 400111049, 416121077, 543935790, 627374686, 592716708, 965922586, 696712723, 857601611, 327961471, 225222922, 667351241, 908691327, 897467918, 690055600, 412133739, 989293905, 432160956, 376306031, 469570827, 198444886, 518956118, 402391629, 769056369, 339814956, 134429921, 989643318, 83544761, 120278797, 690476583, 379054244, 990778504, 36504670, 444755627, 978318992, 592113257, 21769748, 724005046, 436506655, 541310505, 5320560, 729129984, 941814195, 701215426, 42020342, 616872918, 489423948, 381746021, 135039421, 274356292, 184101225, 862588245, 291584806, 147112397, 743961178, 389308910, 86615714, 289105770, 499270210, 37141984, 989267319, 966362435, 752732972, 714333119, 972417338, 869679820, 799514544, 640977614, 856573374, 598814386, 918072685, 628776876, 275145091, 36986232, 220079074, 387456913, 490384315, 409656089, 361776840, 583343070, 46544310, 790598376, 248390360, 547476209, 585644750, 296035175, 519351542, 366490974, 709877163, 903400742, 463714248, 626104211, 911976560, 281305926, 669256346, 62122198, 946133748, 249401983, 115365278, 720135364, 298388761, 989367405, 845176705, 452568355, 54420579, 535198406, 454540743, 8961675, 791152845, 119023164, 934476165, 205110089, 670115708, 770443038, 745748500, 807615356, 127259724, 796484362, 310435296, 321276656, 901867904, 234299167, 254923902, 677955594, 87001950, 950311922, 63419176, 159073081, 517388864, 36924060, 452482878, 571028022, 61490743, 140744971, 59238474, 881191389, 486200342, 167349848, 709433290, 599144561, 965927044, 491408515, 559476633, 156744633, 946126114, 867726917, 495099587, 614624981, 595853525, 512659444, 973315591, 436407274, 946152014, 122929430, 436552772, 72610468, 46697830, 685438288, 308639322, 323045292, 52356202, 52484646, 478043682, 104025880, 294579572, 271141539, 12035814, 833025467, 59940432, 942950523, 98881380, 168495454, 577339099, 728396085, 770283581, 265068521, 598848751, 620221139, 503224228, 489272070, 401361413, 941606055, 441466760, 391320960, 982596339, 146535201, 365201750, 227938053, 452557295, 609687316, 987843282, 306204050, 951654283, 431436643, 940445320, 451066345, 877867124, 819408952, 318688112, 232471267, 644669024, 525228718, 433717886, 347301125, 303832408, 994659263, 809147211, 260809304, 177172386, 492853320, 962612450, 737881853, 219691420, 843773288, 843881291, 936511222, 575419726, 789178587, 16382020, 335951644, 359034412, 65060704, 508278423, 981364777, 800036580, 620879687, 608983849, 563421802, 638565189, 397774872, 296466110, 696283790, 19790433, 466744365, 421249411, 888984419, 992889990, 331817372, 396051071, 698330787, 16383428, 53133439, 795840565, 840795819, 229243273, 100010528, 45294036, 913580454, 317470193, 164494964, 765639418, 428647066, 329243469, 240647994, 112454057, 669807048, 233241277, 41850518, 17350593, 715346906, 10813629, 476007519, 490815735, 543493766, 850777171, 214796016, 369696628, 830067701, 276175391, 278554465, 339527708, 177530850, 367957338, 147860052, 796227958, 527281323, 9501139, 478092720, 686280047, 557384121, 752112896, 483479726, 275029136, 992611317, 356072398, 878039999, 417571651, 519980127, 305480526, 726331818, 723964751, 431098319, 684669981, 776300639, 986929164, 138965358, 337669088, 197119503, 815234193, 876986849, 307468698, 376445925, 298754644, 18046219, 13502537, 384033162, 387280603, 915474723, 618099481, 516192856, 128521395, 682039950, 142513575, 53214862, 796436611, 677028943, 21319965, 492258089, 500452256, 970886653, 851182126, 520883748, 278530599, 836972795, 338040569, 249622789, 740888885, 461956812, 690534368, 96854774, 909133175, 173603800, 300852290, 882210657, 697285903, 55654743, 696334763, 486274890, 3915635, 663061943, 95102354, 462885874, 16231327, 140594283, 954056686, 391714201, 756266437, 951231961, 392645564, 104747897, 73963200, 256129894, 787435169, 530987208, 108556213, 270541095, 293758199, 279108716, 130389632, 124121557, 702881184, 858748451, 296041333, 389643035, 397029799, 832720320, 197135453, 109612530, 852442131, 113854545, 903823202, 304985079, 302717796, 215859548, 95596895, 184693138, 280040661, 504805381, 12785377, 177582394, 257657656, 572440056, 668280165, 310475984, 588079245, 494686990, 392207840, 109029307, 472387250, 650904689, 885361475, 581941698, 187266450, 110907003, 439368425, 537381996, 448206335, 677253219, 983741996, 69704887, 452404277, 117630869, 904096386, 649034193, 215194925, 540186399, 294497587, 797358592, 612397632, 782286746, 238067232, 687590875, 895787320, 954057286, 623819191, 7087911, 877955923, 947134535, 628317788, 639001757, 849532847, 444323851, 95386276, 801541894, 289527045, 793170377, 499082221, 874694215, 712198894, 804302963, 37404812, 953628981, 98799232, 843017047, 80477041, 281127398, 859325090, 204439155, 73799623, 13612414, 249405248, 952954109, 8722100, 693373187, 469841203, 690359332, 63114161, 506035475, 979414137, 333100656, 772300479, 26991722, 458587972, 968451142, 385380639, 141742557, 441320529, 940251425, 817801131, 114717198, 674168960, 462214051, 156910856, 873465722, 99199315, 94748093, 629889411, 205572123, 6250525, 737990187, 728138355, 684505860, 759895416, 450959690, 237645160, 447109741, 785524879, 997465065, 562019995, 102594118, 445586574, 123140098, 80428447, 649195758, 847994023, 962782465, 916969625, 247122526, 23633619, 417675679, 793069284, 761598211, 844989936, 923548254, 833276283, 942292891, 270300938, 949624197, 268284403, 963673288, 508351586, 735546612, 541154624, 752344173, 465046676, 570902579, 980818383, 148930697, 991924523, 272023655, 947774430, 660393839, 585276898, 668743103, 14919376, 599307152, 928372028, 572273974, 674856819, 769152619, 664463042, 863668562, 799264560, 710477540, 210003404, 274640482, 781041861, 245817901, 659093611, 147627425, 394443641, 364410171, 438732415, 600452737, 142802285, 580128612, 117683566, 749033205, 833112640, 818450377, 160962033, 172999421, 213619670, 60864060, 517957699, 502551487, 288068591, 941015390, 489865526, 885506254, 70974784, 408784300, 706354227, 207021662, 707968675, 756961013, 673229429, 45929618, 91305218, 818630149, 639173086, 7045677, 704040105, 289202724, 67203034, 426127424, 453693996, 638384587, 912580721, 397909113, 52148364, 274290961, 261413418, 621356274, 136649330, 230109537, 820679215, 520401053, 306741443, 745534803, 432987275, 406421220, 104939927, 617711762, 228001094, 346447354, 150752871, 542119408, 933464282, 881247641, 816914244, 740711696, 950949987, 897429908, 720920449, 672886702, 730028802, 15842391, 6190587, 274918536, 49002099, 140744023, 326409246, 247667220, 876552432, 64258048, 75725397, 933368207, 919000324, 279938866, 5026682, 751752463, 578262367, 323697074, 881928274, 891993363, 657332787, 347298671, 670204036, 251279624, 279829048, 903865116, 781139778, 207391829, 329072144, 376659493, 55047650, 874047625, 728627364, 954034330, 248227132, 267954878, 985372581, 585448787, 98827446, 610415863, 590501109, 664211091, 948358616, 205389004, 879096171, 585521538, 655563755, 576205134, 360578239, 134589585, 279775044, 20857520, 626014632, 429861363, 401406245, 662129626, 98648682, 844728357, 255338722, 271285037, 375502006, 740536911, 491388603, 60385414, 783955867, 131405692, 171558142, 930812796, 887843141, 978936137, 170733743, 413311820, 329255224, 309560055, 382167370, 757529859, 467651581, 581891826, 240329890, 822302131, 887756582, 84026961, 987383022, 841906334, 601165364, 625275433, 724992604, 609196147, 202822846, 286712905, 501782922, 964592472, 305097557, 503921369, 739355359, 631752794, 442432954, 767800844, 565917503, 938304398, 764030834, 797234578, 74884373, 318494825, 48290450, 961223956, 152968288, 118415253, 903588782, 116013051, 872310463, 106222407, 542887449, 583843952, 866350793, 808106506, 494271286, 308549869, 760425707, 828127328, 916866455, 535744439, 890150117, 993640663, 624716608, 717870653, 985214928, 316249386, 650023783, 11181697, 344913270, 514728432, 504409006, 374611160, 837578893, 772619944, 107718330, 140229580, 991177055, 372198883, 499329755, 823202121, 148453532, 568341337, 510876087, 336806524, 569214912, 894502368, 104565177, 132106888, 694846122, 172817433, 396336920, 800343365, 746855206, 174702751, 282437114, 56312164, 589437268, 83328344, 362593851, 351979163, 612124160, 573689174, 156806847, 746114843, 279836111, 419311056, 426945193, 784503863, 769802473, 940072507, 116723753, 525424458, 351223742, 897067441, 635490000, 808921594, 28944741, 571844819, 772222113, 548039098, 673256756, 811445294, 581762077, 650240386, 170564625, 732220129, 533260253, 433046666, 849368654, 135714803, 339169936, 958686502, 591237590, 163377115, 691755786, 514076498, 643543218, 829293493, 963048963, 119146283, 99080734, 375763420, 198306837, 7335011, 136047427, 582250350, 257767342, 366042854, 984774041, 533361792, 919241132, 261078939, 650235600, 406948485, 554070715, 278758843, 254147564, 39512757, 962599316, 111449128, 963982851, 118243084, 913157730, 540107323, 368738609, 144840987, 61954164, 922473958, 292553101, 187345449, 837557172, 772056038, 59005406, 129606061, 916297841, 223116712, 825033361, 93788768, 936205, 458297791, 259209236, 805075669, 8122501, 405330893, 299199864, 26269936, 729440271, 716840729, 846163991, 924203190, 25022354, 243622831, 738802849, 518024030, 849184593, 42119736, 642502278, 6576378, 196636988, 686373546, 184141189, 246794630, 230800894, 66310867, 144145342, 484626529, 783067222, 92443396, 427916479, 979338984, 85189866, 766433201, 170156870, 854602300, 676948110, 747070781, 162334248, 92806211, 434304554, 674637414, 433628868, 719428573, 746706679, 724588824, 603610806, 86212412, 691581447, 121412193, 182991920, 797357697, 914607050, 318906444, 605990199, 446008791, 694717642, 514675868, 648557376, 743594354, 990957197, 590532604, 651262661, 27880566, 370348812, 930648853, 479716310, 804877888, 469926270, 553955868, 198175514, 241110728, 731821444, 913243630, 106198122, 534076181, 66132404, 711100994, 583892779, 748044301, 546426412, 199984491, 150176851, 972283946, 952864507, 448656579, 274246726, 493037974, 93523908, 734284655, 204790620, 375610323, 642700589, 700191425, 223136625, 978860410, 661267872, 938039158, 889379382, 951664230, 450713132, 280878642, 124199958, 866357112, 535123196, 952479386, 473893666, 365982190, 562960392, 58460548, 865290485, 769506846, 415852587, 271494444, 12964872, 840844860, 690864035, 174624962, 982214675, 473049966, 479729475, 50150774, 321278637, 885646423, 927038843, 777935197, 666559841, 739276436, 359235721, 550573428, 434624032, 168419780, 358543106, 941489544, 747945419, 821112831, 728054260, 912606796, 513290843, 23464987, 336075085, 704702277, 986754284, 17956757, 375303640, 854551885, 926340772, 811315780, 272129176, 550465126, 736251349, 178457916, 182414983, 800403281, 594734255, 166876302, 247582982, 457598200, 628658901, 513993440, 934179088, 453418328, 960682607, 922027175, 58869112, 252443166, 893887938, 796751567, 57715445, 72627272, 375364607, 135926053, 947740227, 439450589, 328098564, 625225677, 984633430, 386665981, 200856494, 627677555, 862590181, 113770523, 244625531, 857075993, 795765117, 559555608, 944405191, 752964555, 315469268, 785143258, 53907914, 714752770, 241743414, 436575470, 918800957, 194818140, 339008571, 165326863, 390198315, 906103986, 535341032, 709732913, 787370134, 376222721, 109911026, 702809516, 281504760, 920149505, 905477971, 864767794, 490868717, 455389299, 128144, 512373800, 326140844, 657188328, 110140322, 610517764, 898739815, 517597957, 51582661, 352012857, 566961529, 548732020, 412772880, 789853368, 693404889, 273690768, 715453983, 848976673, 131254754, 261955859, 687648343, 544642311, 315445105, 59595648, 198283471, 832149506, 509941550, 818685538, 939834024, 213752606, 619930820, 931080129, 575897778, 152337109, 985289795, 40644788, 891975684, 775751909, 900692542, 261150786, 395629982, 708896360, 952310318, 457722007, 724909702, 574933388, 912271989, 990780637, 983924418, 405917383, 470587066, 334558335, 173714703, 854561295, 704817036, 327063224, 912612734, 804375625, 387592311, 478114360, 216830172, 872375284, 487065244, 877198248, 935526509, 802036024, 663302996, 965626066, 810287243, 784008213, 658008870, 744432527, 1746620, 518646429, 499971162, 491022313, 235176063, 264815946, 934463249, 52978687, 858592251, 189200924, 454816352, 272281582, 359301540, 33549375, 842253037, 829456409, 590558620, 443763359, 855382881, 658237187, 106135930, 827401568, 225417451, 12222717, 462223069, 986966019, 658703019, 665923774, 234090458, 74266217, 45439451, 733110680, 536244038, 832962930, 215416608, 957942852, 75617621, 49940390, 567571374, 730642548, 538142231, 903287556, 250251657, 254811054, 83674222, 144805469, 452566231, 787503957, 731782702, 912190269, 855348333, 75713169, 995043040, 623292862, 821557128, 130257727, 406344841, 440995519, 176796030, 53768525, 445627238, 862336002, 493629353, 145089675, 631626313, 387968102, 833280788, 673782472, 934838193, 294052455, 187187019, 451045733, 954490489, 20662471, 636496725, 417418266, 962725863, 866411865, 394167678, 428278725, 611779769, 960726942, 717146855, 796273121, 644414108, 58579885, 759675678, 234359496, 671151451, 883225254, 239114693, 505474190, 318729520, 78299924, 415376616, 5618475, 727306917, 6887992, 55725901, 631880311, 214186643, 378773563, 545051577, 618788036, 485919465, 379535964, 206992196, 148807734, 898537181, 160955803, 211575915, 831500853, 995760538, 666496812, 67601777, 957191011, 346174918, 77925202, 444038033, 695628854, 477300387, 799633783, 876909340, 819175628, 858238434, 756123962, 766846303, 227172319, 210443946, 651148786, 983497396, 17733400, 702290325, 445184132, 932814003, 636024226, 212579401, 953615111, 818164345, 698938812, 968027339, 118203820, 115037745, 379238646, 456287140, 578631426, 124572364, 149879493, 874263634, 368731158, 846262862, 400706919, 621219613, 437433167, 810620295, 363614773, 408463998, 593480431, 268982311, 639467776, 976000977, 474535630, 84270356, 917053711, 916811743, 131577590, 122821759, 498577386, 474385792, 826633038, 323898962, 634068541, 959703867, 660071850, 91497372, 36743066, 159908994, 946116337, 488054211, 639785384, 746392857, 75249477, 837890009, 735470806, 949647, 862898253, 223675093, 417893387, 28279852, 31407549, 469280489, 685765968, 824068510, 768457029, 193261854, 801031003, 149616165, 974360379, 26819877, 190179310, 100315309, 261869796, 672836096, 344790764, 67925073, 814358003, 690561885, 782693915, 976643262, 190028546, 361704228, 683355059, 234438472, 758408166, 154697135, 985301885, 201864681, 638216980, 479450559, 525111464, 381448845, 642313716, 401465494, 965815977, 931585538, 662336812, 833602002, 588809384, 113892321, 502154309, 473404748, 592429893, 199386013, 590199324, 345480239, 759579567, 538135917, 164030483, 384825183, 623381352, 157291037, 932033184, 648261890, 460618846, 872803106, 234041365, 908938559, 741354071, 664986296, 637058606, 801131576, 933530046, 807128498, 489417544, 642573272, 872984716, 182373494, 925460015, 925679169, 832655577, 862891457, 424546550, 38958061, 183679932, 340550895, 563851309, 845102484, 970637968, 411693965, 979108128, 699983636, 606798293, 828626967, 711494377, 658559926, 499326174, 875932451, 177264634, 843638244, 964817793, 176285125, 244291375, 607852666, 66378661, 603350658, 502778498, 807428574, 931891883, 21736890, 931128824, 957780123, 75058053, 753460518, 764754828, 772430400, 398811855, 934794563, 591193840, 43768372, 304066373, 433102868, 573832366, 72849132, 843414802, 857308404, 661485608, 216118041, 311032682, 454991719, 860041449, 438691962, 429674467, 868141131, 481909067, 400458790, 67990910, 890015412, 811292732, 580182708, 920273502, 742783480, 556151348, 597525281, 871853732, 206336466, 501906426, 626825489, 329911983, 279021082, 876016330, 571784024, 302902203, 306829874, 885740245, 381297171, 183539279, 507413826, 433563498, 552774721, 895997178, 254767621, 647344968, 147053133, 261200005, 690420179, 907487751, 593338155, 348277528, 534937510, 203125329, 326370472, 608691576, 552899841, 152690427, 274732077, 438009266, 912204769, 7232563, 94428208, 595845549, 56525875, 901833478, 964240780, 636399805, 438130451, 892766072, 851751873, 836294046, 6733892, 186992813, 800761274, 423414808, 283099072, 211017987, 944176176, 981376098, 952178889, 928805509, 323328180, 680191457, 911188182, 23082834, 535866739, 915189659, 427193501, 210498361, 696681075, 121688120, 97733731, 669443686, 327948507, 208449454, 505042234, 306597908, 837390299, 859493453, 406930568, 696502627, 48793112, 686698873, 561496354, 756758124, 74590835, 88360963, 47118867, 565291108, 934944683, 106260891, 598421575, 643023796, 721571782, 95633887, 784383575, 772119375, 88150363, 553754964, 223557225, 135458328, 503955104, 876987767, 935576968, 477011394, 938422535, 749548525, 975340830, 162023928, 267972503, 573895069, 624380395, 768833559, 326704691, 13370490, 450730554, 310291573, 125593266, 732934822, 811648093, 419159071, 30927135, 98196588, 12636199, 357126666, 279143301, 413081972, 594332804, 373514180, 780975990, 585768933, 595749539, 869082882, 989231237, 613247582, 225447237, 10606319, 438623478, 3050802, 346351351, 612539995, 930230714, 244967033, 966137732, 561551458, 470570159, 67196742, 765378426, 114547005, 339516757, 240449681, 954473689, 435618592, 985870651, 589565007, 114812624, 617441986, 73050199, 315697386, 728381851, 457903776, 598584080, 746624206, 140484414, 475222710, 648714186, 551620926, 302729363, 460982248, 931316474, 61212458, 114056578, 234037358, 218088936, 974310693, 747942273, 644444564, 39568829, 101755122, 3450880, 327361816, 484257842, 717798973, 995392178, 572957166, 522804613, 646208591, 700564553, 646726822, 793463967, 795283921, 157039175, 114490411, 370836412, 217194496, 222496451, 623011468, 274523119, 425360388, 47596807, 151399151, 75957462, 14474551, 797462140, 965996683, 70580111, 225488860, 213990673, 279835262, 796588512, 838017328, 700181504, 18346381, 86251544, 25078843, 524816810, 600904716, 4809338, 667658058, 942187897, 876123381, 440567911, 647372526, 100922234, 973558438, 812380962, 503896784, 222704366, 774966714, 94852968, 802637437, 74865609, 546175348, 597851691, 801538954, 914541039, 761171328, 284375976, 894795805, 630338799, 423139658, 4404492, 437268695, 167034889, 37926692, 794650117, 859752754, 812163478, 686368018, 304390565, 852076170, 570023082, 165348092, 542953527, 182648262, 929027538, 981085666, 401959143, 309707655, 264946540, 453144457, 786078294, 621267905, 72358081, 17810315, 888811463, 307725587, 673846097, 494684342, 878595800, 136121935, 726077233, 54204647, 520736964, 552724323, 519890073, 984400123, 278626620, 135799927, 346865175, 626613325, 14754436, 858396262, 677954437, 701443983, 382451334, 501383946, 948142246, 795556431, 967558890, 313448189, 452894689, 998035196, 73418426, 966545731, 786833779, 526500892, 340790274, 173858987, 776175005, 597119613, 314213652, 958674837, 702244038, 110855902, 792666810, 934480517, 604894534, 75893050, 489364408, 810726938, 601126059, 247603142, 374249052, 513239652, 827261121, 741653326, 835415497, 795852876, 523874408, 545703465, 852307279, 764924862, 273750308, 277759274, 589653652, 761459720, 541918916, 339754163, 949329133, 61955154, 370950809, 424883504, 605899012, 740515773, 64023187, 691469772, 563604660, 596116233, 805552630, 133533536, 942879327, 998187024, 548333395, 731726922, 934053230, 870095732, 288078763, 822034970, 831372970, 850501617, 11307114, 374490294, 568979819, 79182546, 541538608, 765896930, 919763295, 852016777, 516650115, 151160465, 525859134, 792896629, 691280746, 139378516, 993835614, 983140991, 165788713, 4926976, 185291067, 602533340, 264521127, 336491300, 806964082, 160252201, 869288303, 871524040, 52572359, 552981092, 359115077, 574630339, 484720469, 959062198, 993122204, 347885991, 823556378, 327226903, 904182244, 853696648, 539514081, 160334799, 2060987, 51748802, 547943894, 214641069, 390081818, 80353420, 884556530, 999759967, 243532104, 858467330, 351481584, 618630834, 284856171, 228044256, 565426595, 685289906, 498810319, 705013475, 422726243, 821024164, 101720861, 896926237, 880448028, 666898610, 622458278, 347337925, 739796727, 434488966, 885981105, 409981963, 802031094, 740764517, 170286642, 606338468, 702657765, 381309947, 785014985, 865363235, 656997708, 797146731, 167171973, 698150871, 351883286, 863780922, 678674246, 420521648, 117577560, 309081949, 482318394, 432235676, 11690767, 86986851, 507403374, 950801086, 13367426, 669673196, 283320384, 313893087, 423345066, 126636316, 454538576, 232573370, 836864757, 986026893, 372803308, 21452325, 918142186, 234143198, 352426693, 529154632, 311663642, 463497918, 9819957, 919834710, 11122903, 969211219, 295645792, 393870514, 308484448, 727715944, 993738112, 243265100, 981322853, 409956515, 711189162, 186702834, 918304438, 77222410, 996686607, 939450995, 158266955, 45516510, 215468476, 359663921, 776692975, 332801148, 423896622, 684328186, 605661062, 94437968, 663454713, 523444730, 394748589, 919488304, 440200996, 521463919, 535602639, 287587781, 414455469, 238842394, 387823221, 921839886, 734102951, 956487213, 320319644, 223415277, 419913218, 563491126, 78733108, 249540948, 599640998, 189576281, 2187348, 500708521, 577484698, 101115950, 696415261, 208540351, 395478676, 989571371, 999565514, 650088351, 179498850, 999369358, 353145359, 457839539, 251553636, 979237955, 626706084, 181804120, 702378029, 806786573, 914146593, 867083305, 893857967, 905097822, 715290449, 336040173, 57509646, 155643433, 546906404, 95027388, 255541326, 156783272, 108795952, 53793021, 990452401, 322672166, 930859622, 71545478, 896253595, 327017972, 985117539, 682524335, 877958900, 787119072, 117773319, 356518081, 502336855, 217998650, 693972476, 711945132, 157212166, 757590114, 175126291, 192070715, 969272482, 411163017, 312286826, 383014515, 68783673, 89321767, 588036299, 466307046, 340451738, 801229824, 213128093, 551173788, 981086419, 99280477, 498536269, 977688758, 663890007, 406893922, 478499100, 970369448, 789709367, 724301734, 349937657, 726581104, 124022766, 177667646, 272040645, 519183916, 116024677, 640290234, 530204287, 946487727, 185873275, 599533845, 933073093, 376365966, 518616782, 450410718, 781979956, 528381337, 370200623, 300069941, 757129022, 884995561, 772032853, 208578570, 332118334, 276973712, 670425264, 826577172, 202804870, 362262766, 371596830, 971896151, 271659824, 444314118, 472937806, 248423570, 783803075, 255294082, 567547489, 228890724, 986119229, 22106939, 723654428, 644300667, 590827073, 313844595, 637324774, 862134718, 307022608, 889809692, 258530248, 540041432, 363409665, 196051090, 585998162, 35386479, 998227861, 107733558, 98160948, 249910055, 512160649, 869768521, 610096829, 483602390, 343379896, 91857756, 689135059, 501942550, 324399822, 891938431, 785424237, 377005539, 114505111, 678654985, 290988129, 39825403, 155703020, 985531993, 845793046, 681517488, 704200680, 48306515, 354697590, 959274391, 930030312, 777131555, 198325842, 633013764, 483063668, 610706008, 764538455, 999423514, 532043098, 659000995, 466473380, 582737715, 123714269, 89127772, 916956007, 132954873, 417662780, 269481116, 701989675, 556391960, 440897738, 674443758, 846249685, 37760843, 433868545, 823169099, 827013958, 671549713, 43617808, 439773625, 579652364, 4552396, 342641334, 72573140, 872009485, 752718819, 103784812, 10106541, 400058409, 599256280, 880390032, 825013845, 743297775, 171431971, 464522590, 776913796, 24148664, 449348142, 996999994, 411540507, 941913972, 470589750, 338389092, 239740320, 438256538, 670760871, 847212393, 304403138, 719342425, 131713222, 474775484, 549664169, 243810144, 262635890, 354987596, 713060577, 64899539, 919516151, 569183953, 598448057, 805985374, 477615559, 358917171, 808149085, 792122499, 573496730, 470136604, 585220640, 484363838, 326189402, 671922423, 413257907, 284946200, 278339993, 606866458, 597247190, 809638725, 232181045, 826836301, 755662956, 475856057, 725413448, 128363293, 574728202, 630301846, 90638492, 382433642, 316781701, 115985031, 619618859, 572255705, 412378085, 761146379, 959343906, 489098740, 63462645, 505122452, 500702564, 238072110, 353005686, 259790128, 693988097, 221228902, 159250506, 720667805, 280438388, 385220447, 670521676, 361080229, 244184855, 946514119, 183981419, 360925388, 747120099, 913149486, 379222916, 900037541, 334521980, 489218873, 99308046, 766176268, 922401234, 269050143, 648402239, 27174951, 958974686, 337618452, 493555333, 36039780, 471858599, 148036550, 145060739, 68598049, 998363386, 660159449, 644493161, 651764317, 583942606, 793793072, 60512849, 856828111, 696305565, 846009284, 922238431, 865327091, 849669173, 426402592, 649454033, 731316408, 718149506, 358447150, 636521396, 629514771, 681245465, 925388588, 253814017, 492651731, 251778882, 198884039, 839436984, 514954612, 688782407, 475002910, 323792635, 300007222, 585730349, 719087440, 130930921, 754427526, 463202907, 942528788, 676275894, 431248642, 264803726, 31317271, 274364216, 998873248, 796444300, 417625072, 459855248, 762055426, 750544845, 655202562, 702626287, 565737405, 373118628, 640262243, 968173851, 910073315, 695356333, 625390810, 334699258, 167388948, 903932358, 546240842, 492590920, 57406121, 364288965, 916474265, 632298341, 756247211, 819771098, 288089982, 824840398, 938390741, 162483353, 921817972, 223947430, 342936047, 14097244, 729971609, 959837203, 578646257, 273383539, 348930666, 693244535, 776873003, 502063776, 219784169, 266358058, 18995500, 899355345, 463537073, 366242043, 876607147, 591716698, 652520814, 140804855, 722787221, 816159534, 432744075, 877094828, 708456029, 545677039, 948358048, 630487708, 421866775, 681447621, 725107488, 969710984, 280343690, 396888021, 728097957, 925986290, 538322328, 997229978, 840902883, 928707498, 786176667, 518386420, 141406190, 461561878, 83919297, 203535191, 977076990, 137478349, 722323748, 359853314, 41029136, 751042281, 199312043, 593719850, 842539648, 222961653, 677480640, 806385499, 187133749, 733320753, 237614325, 470387201, 107687562, 598466051, 46923413, 228544834, 880245325, 161110629, 687099490, 433999783, 405110443, 66059405, 149490439, 843112018, 975306157, 223412549, 109932514, 117548542, 704573, 364630814, 597120391, 588855364, 694353931, 17184937, 369088352, 790546835, 532498984, 557835997, 842815930, 610223826, 631258944, 493461637, 236091639, 378523823, 163968523, 308145712, 707154039, 533241946, 538755530, 87877062, 273417913, 450751504, 409525374, 779899648, 819592400, 625070560, 31695504, 916755868, 973655640, 300278234, 765403958, 332413318, 137028494, 816018648, 736981086, 738825179, 510294018, 119862344, 115817478, 591929385, 739503385, 981183356, 527784779, 827265200, 939253284, 814778068, 14448829, 663761660, 762216448, 776939311, 537750829, 433508121, 480810655, 420048435, 902654847, 898042022, 741417757, 379096994, 997338805, 775025414, 19973964, 209509752, 718499439, 5538457, 810366857, 992500197, 979744536, 623769665, 562259500, 160208005, 893260988, 152619034, 159888260, 277904053, 703591488, 557443532, 165182384, 696018546, 253412597, 720959919, 829028255, 700640771, 161810796, 940807610, 925941861, 936793446, 380274324, 858767088, 930254138, 328845110, 691736662, 203326521, 627498889, 230990476, 297418715, 951566163, 678050731, 204965278, 224228126, 823811857, 13532174, 142051260, 190135359, 148077162, 822188463, 700264849, 127341492, 72058626, 681414865, 9886996, 634840876, 335452365, 720162088, 777110978, 100080183, 40419893, 518005217, 541022845, 420914107, 954204102, 533806988, 915557079, 965272431, 657251567, 506000368, 685958426, 394504416, 370120104, 35307246, 162769452, 655107080, 500883982, 468207636, 621855487, 280969282, 569614232, 114713467, 992686238, 52402082, 274910579, 337156150, 154699178, 798506344, 976106077, 901972591, 688385173, 665073757, 424408094, 703256884, 271217701, 842464589, 719470942, 491457718, 846026844, 752000021, 54263079, 137312176, 746050951, 214127940, 430657240, 545890288, 827845889, 688317080, 329252333, 692628742, 930716609, 619855043, 487810482, 643397393, 972259167, 300651037, 752228559, 222013132, 842566622, 198890645, 297799217, 128028266, 608971128, 720805466, 93921412, 506729367, 143412235, 238815486, 774291167, 665333122, 928607556, 499960938, 958848937, 246424173, 518112701, 235910777, 958869944, 954485408, 113946942, 546097415, 777181671, 701875422, 83448335, 802279664, 33515763, 612473835, 143198854, 400417423, 837805319, 811676612, 369920425, 600401611, 303944397, 958286399, 569750914, 4912024, 47902206, 925819736, 30165830, 457584306, 665147021, 429214843, 689811405, 284063520, 433317127, 121867327, 729244924, 236823810, 925520484, 274029728, 678192678, 54198190, 315751817, 826677353, 881781084, 349150242, 539541782, 101822686, 133124002, 664355973, 742120741, 968718616, 639196127, 886699829, 680112684, 329328302, 856297457, 402550461, 659182758, 516506299, 463138567, 54411466, 444304379, 289532918, 991178056, 17241315, 446058111, 686915068, 717111333, 127157365, 356591217, 109914089, 592811833, 553086438, 104022096, 673059591, 89201852, 906524880, 3873515, 741732668, 658302296, 680257451, 388418299, 362696606, 904612378, 764364333, 562771762, 731646923, 657269410, 141460809, 51484046, 675813496, 241645361, 433940406, 403274966, 253982014, 349007182, 408985462, 827582801, 693455540, 171234442, 698819932, 910489638, 218141144, 766733153, 40656834, 481747761, 461804844, 737714732, 202053060, 432046633, 756829370, 962176916, 768991456, 285002713, 666405382, 198662874, 162517325, 289155855, 291136102, 44144405, 955378004, 612977486, 627338449, 628738447, 531178948, 879008500, 700340215, 425552138, 100287680, 790984597, 455821533, 956992783, 85965431, 938472236, 111539521, 404285736, 810252396, 148941466, 386085005, 804915417, 383041160, 547375165, 12358286, 122221840, 178865830, 206357651, 235735230, 626844821, 244987122, 322631949, 520911596, 726705894, 467651132, 990062106, 931862161, 547100921, 676720152, 91258507, 855083408, 447030109, 775746737, 3251020, 838727372, 459125934, 295882831, 457060340, 652983607, 43060576, 389725555, 615086363, 254451501, 273942898, 917983633, 86808018, 858372794, 258068483, 387332583, 650280365, 849829955, 8150628, 519266540, 201006736, 785382852, 784592620, 670018380, 502969165, 939627407, 21458807, 845422967, 525862154, 839504242, 251909838, 788451784, 870752982, 648213873, 15497051, 767082007, 513372966, 975090262, 136760488, 412213075, 780345530, 207075571, 289558798, 270522455, 893593372, 953124841, 417714533, 402632782, 966638967, 806725607, 377741070, 358487857, 721361440, 633293522, 593759800, 563246230, 546523881, 766165248, 341656784, 154279304, 234543974, 689307549, 106012192, 122458688, 297953969, 99466901, 376257304, 750989974, 454424055, 652831433, 39982221, 914255350, 192008856, 788518332, 464210492, 366208112, 598999538, 626281496, 363249680, 833859075, 602125618, 738224046, 477257692, 427920690, 432352380, 319703799, 925455729, 795996684, 899656114, 699974781, 181110796, 537967169, 195181629, 236777250, 691328561, 110934143, 632353994, 444332752, 642142208, 4548596, 318666435, 331502811, 856154284, 527724712, 63217063, 585050792, 228624635, 597041804, 417198092, 390577088, 81574596, 259828965, 923188789, 213000962, 132494747, 951807874, 548011739, 273689215, 494093074, 267365157, 953139574, 642790570, 81764118, 588415348, 42279639, 889582851, 209371186, 526672676, 688753637, 436604166, 429840129, 79379676, 573603587, 50383346, 745146498, 32595290, 275348699, 63639620, 597298238, 445451283, 475572906, 918810347, 783236265, 237720705, 689343259, 880186427, 253021811, 803177851, 322721598, 497701566, 503963588, 766577813, 737168121, 28082068, 841415968, 36481970, 64948215, 76239253, 791951868, 574334124, 726684835, 840131395, 237774370, 400226122, 3479365, 97245856, 646003980, 905680829, 32409503, 868904042, 567595752, 721528440, 586111836, 206122211, 685004323, 326512685, 534667752, 549070878, 721603058, 294567299, 606678933, 420305863, 8337232, 622652923, 899621528, 679857551, 892320321, 531710424, 756904418, 299602096, 749551702, 851628831, 616257827, 78868717, 672527296, 65501941, 5763763, 737229537, 709913383, 807111439, 290641796, 78608111, 317860642, 750164047, 645467100, 62604168, 742943395, 599254825, 156725393, 307530815, 537079257, 699277438, 330584301, 460610120, 244222750, 907038939, 315606561, 213240723, 948161228, 331523993, 129906885, 257579228, 667218005, 897940992, 903834691, 825400811, 85930343, 202051882, 988240005, 952026528, 353764638, 680078201, 722578345, 595656695, 471191164, 24241815, 887712171, 91320974, 935829511, 131201212, 287326992, 737680043, 450246867, 623581962, 593318051, 450365699, 694446997, 154174820, 550800730, 704279261, 746088713, 345834752, 702932600, 93274291, 234506753, 750934437, 513256057, 556979214, 879338892, 340866986, 885216976, 724482459, 91639374, 89752964, 186025185, 137724891, 205056598, 703036079, 780730703, 991326919, 154096047, 107205895, 676647559, 503843992, 550728038, 943986305, 807949239, 633242762, 154886830, 9077613, 778289758, 678462888, 525429683, 431605616, 782907803, 468905957, 122298105, 988897912, 136580050, 595328236, 731418132, 788784451, 42302143, 407586049, 797098596, 358046069, 119340207, 211123164, 737246475, 475488987, 719901184, 707096202, 555160170, 316340238, 251321441, 197526331, 772542378, 980702234, 733055571, 112041930, 323878006, 366163316, 536396223, 186563805, 105734321, 194251700, 326960261, 612730545, 982394301, 525901861, 250959445, 908318254, 84970171, 21497303, 24014026, 100788361, 737334464, 709079096, 624572213, 95994449, 878115376, 174597373, 734268817, 469531599, 975925271, 310765453, 372873336, 428850957, 906976570, 849776785, 271767523, 225070411, 619738668, 22051660, 525415087, 750289918, 299614868, 393718924, 917438898, 511710197, 646562776, 91709040, 25603752, 144208815, 984218541, 19011872, 463536092, 587764734, 593682874, 264199758, 63973096, 794936918, 261897538, 681604343, 623501654, 682061137, 782368123, 646817431, 492597071, 283178743, 893852134, 85779750, 490783572, 359760714, 478266955, 624191904, 134636855, 320949951, 258800179, 129955215, 292707574, 511395302, 808506634, 398144327, 514586306, 603174119, 821393914, 772095132, 852728680, 69556564, 620190280, 449585456, 754226301, 276094281, 32643167, 375204111, 397158780, 461208091, 594346259, 41597235, 314976128, 762906625, 782939129, 90029201, 283286133, 902180007, 868846467, 28558693, 649275184, 535525616, 490160355, 409245062, 507651735, 444769197, 950488668, 438441029, 528814145, 89694769, 427827661, 655126689, 196770713, 623501177, 500819704, 554841073, 767302831, 599787590, 330866372, 520929271, 217081006, 311053718, 714238538, 979256152, 198863663, 291937476, 91446659, 376941283, 293058880, 496854385, 915032368, 210169758, 345741242, 102355312, 109852529, 489591055, 662612033, 908235089, 400272955, 796306056, 546352942, 18185784, 341587100, 874262221, 552156852, 807850870, 73536113, 497898218, 885217841, 188850825, 210730971, 888963608, 729022014, 222444246, 161985853, 351261486, 33604834, 295378921, 497188424, 347834574, 633751430, 631769105, 319441238, 191521801, 946113019, 390294680, 882069150, 983733104, 126549724, 233748445, 660461755, 8020256, 764946599, 389739248, 276727819, 774522997, 122942490, 781783866, 926251624, 796759170, 179781244, 704126410, 450809620, 748062607, 9461673, 363456664, 995295365, 234483492, 444686914, 108483867, 642105974, 120971143, 42118970, 858846147, 985554278, 263330818, 216512626, 279102854, 556755198, 577866665, 474898143, 973401755, 51487199, 788416154, 916385544, 975690936, 713679171, 353063513, 397685181, 889069264, 911573719, 673673712, 994027081, 960370499, 742438787, 732938233, 512230624, 545672357, 264196572, 898063370, 592650945, 547994932, 508004561, 753295079, 552674805, 41205243, 216889294, 216489144, 354132374, 287070095, 400157942, 779874133, 768481508, 587641022, 15773562, 605078518, 661218921, 517469392, 60265623, 450424097, 778890148, 158506969, 813193159, 231499755, 270289011, 823753366, 639523731, 320917616, 839613731, 587273004, 305964220, 71723426, 486730817, 867768495, 349220603, 834441586, 758663508, 741789945, 614267731, 87445428, 525782334, 285825272, 258975878, 160298946, 317989238, 814245181, 928885594, 473292632, 782806035, 4980673, 776096023, 378345151, 312513464, 519050285, 953880656, 59366687, 472119009, 268134824, 812937806, 441323663, 311248197, 923574090, 164071585, 306873369, 66743087, 697782358, 384272647, 915474100, 971406565, 326911268, 630188945, 966920631, 780020334, 594693036, 529118940, 944174532, 782459790, 159046912, 296339381, 473608796, 881423665, 981793855, 940362688, 87035636, 263399075, 95882669, 877670762, 547726563, 525459221, 365506161, 655446248, 70542212, 526503807, 650330498, 40745419, 687485033, 75330348, 479247731, 981444579, 637090988, 852987311, 415332451, 374370643, 873837492, 379858638, 291828111, 981800438, 391131101, 118072576, 154024764, 765289386, 620076229, 793810325, 761545559, 643233281, 503447643, 99838927, 907350725, 329818124, 84209080, 135526893, 60514559, 874179232, 887448724, 49269131, 386126149, 247825133, 404962124, 756716212, 48540172, 506441198, 935632825, 714702474, 785689200, 392953680, 883786459, 938840752, 254217172, 343743825, 543776531, 321863142, 768152062, 458024978, 20295264, 881784683, 515561191, 824585858, 662570842, 995409444, 4257463, 910012241, 732298601, 171166525, 630641984, 69934625, 330570378, 408534553, 542569131, 973310431, 295941340, 403919975, 28392852, 900443516, 791826546, 986460358, 812497725, 164019176, 344345790, 19678779, 379022096, 164074598, 187284191, 328287487, 607018002, 519645479, 433726871, 311524054, 915685, 182319162, 600800099, 528453773, 318263259, 429983348, 64275440, 220405035, 91169356, 476930655, 362065355, 589670490, 228728988, 271386672, 368906066, 173603259, 499036210, 174401641, 128395679, 593067848, 78036915, 910696155, 75241706, 253161102, 254303631, 874736188, 434742157, 852537831, 965219108, 115434779, 409104952, 708351178, 234952347, 572404176, 552388471, 994989367, 48910060, 762632308, 352469095, 781144603, 294211285, 69182581, 66095781, 930304589, 90940867, 68411469, 325842887, 394093303, 604662289, 834477609, 407141825, 525999755, 283518046, 448633028, 245262958, 207834903, 795039353, 54193715, 150245674, 556746961, 688013696, 408549643, 491069246, 146604748, 369008435, 902393159, 139907861, 483575431, 963728090, 546638781, 537498175, 983510081, 989471443, 482730006, 298448730, 361248766, 159472323, 993220801, 378435790, 831634461, 442490356, 178254657, 93046537, 626341091, 560235639, 821773887, 308596000, 327867312, 75991460, 515683050, 215192464, 698626102, 366331036, 982728957, 260226385, 646160627, 992326389, 988732867, 3778542, 879848203, 489874329, 16676678, 738742063, 406391869, 349124849, 253593570, 721046976, 407864742, 919224809, 564056806, 148451461, 237413103, 25653206, 430321841, 307562761, 507351679, 484187762, 166497044, 933461438, 454319518, 246575543, 661026050, 422298521, 801786291, 567978744, 654200948, 643048958, 609805546, 679479868, 117631697, 729352523, 765449055, 15800834, 887208116, 10685095, 996873989, 151505253, 546029462, 561668782, 501160413, 33793018, 22720170, 274517096, 65905680, 501908032, 799002170, 485834009, 753955707, 134213750, 71076154, 215080646, 396180314, 719708200, 905897914, 407053888, 370288631, 302357070, 681901242, 649275024, 814839243, 527793100, 201661423, 164492446, 157645120, 974294446, 703644131, 76218989, 678392727, 650254699, 109724085, 296007114, 737525083, 174765096, 253153893, 699328417, 896107116, 518296554, 812986861, 838049065, 599273674, 76815592, 231212768, 747713495, 704820579, 114450650, 311645343, 884547878, 73863105, 896594139, 778510851, 700838229, 161560781, 867885813, 330886722, 416492725, 390217064, 983832022, 119870044, 533751307, 502526900, 833640958, 823574293, 912101599, 931899234, 765337891, 795227636, 377530332, 916997370, 925085685, 939692930, 4907299, 31041085, 706467616, 535198998, 844375436, 144417626, 731713934, 623584277, 122752062, 258540468, 607048099, 313103473, 864360656, 579408033, 848493981, 605299615, 285825598, 740979046, 366897377, 191198396, 384341532, 668460465, 675741079, 154882476, 133087775, 312527948, 149493762, 101183605, 596564388, 453409815, 426554927, 842276037, 251005299, 787625074, 185751567, 23698280, 56812389, 597189629, 592714201, 449348828, 66053777, 316027121, 430223146, 547329870, 787490378, 21986671, 42956703, 30905842, 717146601, 915927217, 594251739, 706787189, 39996214, 54010832, 375177581, 89290748, 486668237, 677459591, 309142123, 256884586, 371262469, 350466118, 286491097, 130482184, 771981223, 727424234, 289400293, 161839011, 883426250, 50743309, 885285643, 256116455, 449484377, 929622423, 114253235, 998736172, 775268442, 750154189, 939184031, 533328788, 156808726, 955970807, 593879303, 687675494, 813171381, 194752923, 228351484, 321169662, 434719, 963995079, 840475162, 648778550, 828054591, 833905324, 447271740, 117945852, 452255258, 170113881, 221061491, 100548218, 935162433, 589295971, 6957618, 281746764, 683951801, 196005839, 958185385, 916817825, 168649520, 672712423, 863078194, 185409930, 80659503, 980478270, 300738500, 274955357, 124100001, 309443141, 425259397, 819575706, 601696695, 886004632, 175775315, 327626651, 972625247, 276856909, 16299986, 542861629, 289306486, 441797547, 871893536, 624392453, 819631571, 244585663, 608886923, 417713238, 592535409, 143298112, 748005952, 675021688, 769083334, 221038306, 129913682, 830391717, 413128923, 590381344, 675351175, 601392607, 987184484, 804790328, 11828495, 469816252, 916264014, 139163856, 802494019, 619105345, 434324650, 354709651, 861610309, 455262122, 142010364, 846651014, 354523428, 887740662, 403995034, 243143607, 294638783, 696528554, 607304042, 270529832, 206541931, 435055917, 200749555, 492617840, 400314976, 568794830, 781123648, 158642391, 431615161, 832052647, 842035007, 115430555, 63979460, 377503527, 959697980, 965820117, 7551991, 75814506, 274962896, 516592798, 186360715, 887706678, 308841752, 672337071, 712930799, 12056122, 17796926, 359958034, 885359698, 780587717, 740587016, 666332726, 328965525, 918258683, 341602259, 752147157, 599165495, 755188079, 423507879, 833886238, 922949252, 171463351, 666473566, 454472946, 514201215, 874654144, 869056346, 260302158, 191210080, 819287368, 926972772, 42504865, 342241787, 635916227, 983435213, 701450729, 268853183, 153726569, 487907541, 600135261, 865409529, 524046846, 860502800, 641170531, 228808584, 979281945, 314304261, 210684641, 348707738, 396580173, 862390254, 922407947, 627617350, 744287647, 319779148, 134189333, 14192325, 432186573, 150266732, 513415237, 658009782, 807335110, 439999916, 342222815, 363060170, 753024119, 969690695, 12024723, 975943658, 166951297, 676867372, 179262431, 171755499, 654775798, 478451911, 761309527, 108427504, 550204866, 1258037, 78363397, 599177391, 479457860, 841468534, 90723807, 269579515, 983915838, 229771702, 497058346, 455613914, 139342484, 811616679, 907730408, 27335303, 841697384, 837585540, 926311835, 337035075, 353775746, 250684608, 141694486, 621950416, 976978192, 936302599, 789107092, 94536765, 479170216, 829181601, 21466903, 770894966, 770706882, 7648554, 546965749, 769061560, 275691783, 722908760, 496406005, 389097633, 264373164, 515678861, 109602267, 543566237, 794133373, 186442973, 414078236, 200036856, 156370565, 540867263, 457193814, 116381427, 35951076, 218588111, 682574798, 232696514, 331373998, 363478956, 554908724, 265613723, 215560224, 669912524, 396174740, 494927893, 832142517, 778736312, 834494325, 191850979, 457832576, 278475020, 318528436, 690725601, 18405244, 111667962, 257662874, 533042505, 354252595, 835938841, 656824387, 659770140, 694305691, 480543503, 581680334, 937223000, 913823876, 682200996, 712439432, 145451533, 870862351, 602257452, 732509858, 893839732, 102901139, 177056626, 685991369, 565910190, 381874886, 569359285, 162560652, 687726480, 648317643, 965383578, 996726045, 228615634, 786538101, 570489899, 166374625, 15726393, 300515797, 236257887, 129145120, 469054604, 343959593, 318430820, 569164373, 706050642, 70745452, 719201281, 613601437, 778126088, 24601213, 208133358, 261259701, 400844846, 646898471, 265970561, 211969992, 988051639, 920718136, 974367612, 242786836, 137647890, 712100912, 138867571, 967759381, 956247497, 965570022, 841055990, 512306574, 557859322, 118097909, 539860287, 806948822, 29522155, 695871402, 621252376, 444823230, 326124400, 295723153, 676808844, 996060302, 269330615, 689805028, 963767258, 6423487, 398234993, 8790494, 965989133, 615259711, 830406995, 320746479, 129938280, 494058968, 635958541, 996441238, 475660862, 376481067, 355670971, 468566189, 977942346, 169593493, 330137695, 810621650, 369897583, 471384240, 855777646, 301807133, 37743389, 32709523, 633595885, 142232622, 595531972, 634352267, 96052796, 712440592, 917799579, 335360660, 86356734, 710679453, 923131875, 962209982, 44312267, 807146869, 560411324, 770378179, 396601999, 508348019, 61695296, 607546872, 830881179, 917930455, 951409545, 778145553, 992284986, 971960151, 789959228, 964662372, 363418168, 374294889, 252296484, 513235425, 482102719, 684278161, 539810300, 816557077, 656867502, 16875535, 542764403, 800992569, 296463472, 967743716, 333965923, 808779728, 838888069, 620667372, 771202547, 629970558, 825213868, 342763766, 488307388, 885405956, 183111723, 969966745, 216875764, 741804614, 970473321, 751708411, 359943755, 532974711, 197454008, 522864213, 656318562, 815296092, 138519011, 463915820, 938833319, 484481066, 845663567, 697389521, 919801308, 445275745, 309223896, 930266874, 497260701, 241886925, 447863281, 12394826, 26954300, 509501018, 167042723, 430315307, 100988947, 497415059, 943735962, 848354417, 972467438, 948895226, 794237276, 326990814, 227323249, 546677624, 272940644, 549509889, 744384791, 564012724, 411197522, 255627667, 759685536, 417729010, 776074716, 703236453, 427344787, 765612867, 130429166, 943148008, 129226290, 530613375, 129877702, 484286411, 63423406, 794393335, 452407737, 441269923, 682037794, 36085874, 646994715, 784642827, 344279970, 166096477, 939400690, 600143088, 62246923, 329602014, 840412363, 601949799, 277728064, 314253481, 570941879, 853412071, 768945297, 749378521, 326304636, 989752900, 460815364, 594024554, 472288269, 92487269, 209139803, 524843587, 259425178, 265886553, 49852834, 80775899, 918464984, 181021776, 394900246, 202895167, 353676254, 381567906, 75237208, 202789165, 891465443, 666356545, 21181269, 471156278, 952806709, 864297444, 164438135, 5298417, 714758761, 15452171, 807819887, 108190916, 143169718, 272433126, 878237405, 569641271, 137791495, 245631804, 990403713, 319763610, 430394493, 323793257, 562355843, 752048860, 17271752, 244345556, 605368213, 904673021, 59948698, 853810336, 156205888, 858922582, 874311435, 373239770, 634823999, 127855832, 325731718, 12852721, 524100257, 569514318, 550542423, 454919093, 834627243, 412271116, 213460342, 441485902, 601940024, 155129995, 198098172, 721509212, 747155266, 590423615, 288432101, 532301209, 531296195, 26612416, 402094076, 648177927, 270354573, 981413887, 873118533, 968934176, 266018729, 315610411, 149923648, 315942690, 547281374, 65459451, 251737362, 271866793, 562743345, 524388694, 772243145, 486636815, 112506241, 810458789, 823501117, 465130780, 198130727, 291877738, 598504732, 82094323, 15251948, 414518517, 27322114, 698324051, 816948722, 102016397, 256788155, 882016438, 868509873, 239371232, 334540953, 236576233, 991423558, 65566276, 246300260, 957516509, 744689854, 83249576, 801124475, 875735878, 473980294, 143123305, 653104382, 102479196, 733118597, 723088314, 260973486, 434219652, 398214201, 986818194, 703251034, 50975657, 607879768, 807963377, 483131002, 143234675, 714039808, 292468892, 460473041, 321722840, 967851827, 726347120, 669095348, 128137610, 147177257, 365815157, 973147220, 384972736, 613896566, 955424188, 603382727, 500238880, 89120220, 406962307, 364177260, 91170005, 23299284, 919103623, 98816297, 79027514, 624476174, 47258723, 787055954, 79480747, 266922086, 416808460, 219861043, 593783723, 331491287, 874479275, 735342708, 409187890, 70445929, 551772088, 461407109, 246074521, 387267497, 692233798, 374910415, 35168241, 587193579, 502523872, 806617260, 97641485, 899167655, 449720949, 865104390, 234365298, 141763440, 681112134, 864459972, 288752330, 825429593, 257919888, 90997994, 683443075, 798963900, 558955216, 810283195, 684838617, 607280984, 647051042, 156852087, 732972040, 625593467, 998896908, 935734856, 754748476, 335001953, 646704848, 285071687, 487927145, 916309725, 235815105, 424713067, 10500960, 530470023, 532604964, 636417422, 153650029, 147894464, 470039399, 522625913, 166408050, 628550909, 643419659, 588247763, 653420788, 199984981, 426883504, 760930164, 299611733, 679483009, 843455927, 315027787, 365205858, 496654748, 942060173, 120781511, 57297429, 135487755, 813851165, 362861477, 33968303, 388736330, 283528780, 781867293, 397760320, 751846597, 976272074, 772567648, 687777450, 977869329, 30129868, 875642801, 69977761, 203945342, 618647393, 436476263, 364898730, 153868394, 743869909, 457597180, 294569082, 434975968, 164426537, 331495345, 465163691, 143419544, 635147241, 730157253, 233022692, 636176075, 743426127, 786865152, 761350148, 604794010, 221890751, 293193564, 935232172, 379003448, 95221893, 438780864, 966102965, 853197046, 578970555, 252094454, 317185999, 585476185, 47755852, 147287711, 386861457, 391650465, 241504428, 664900050, 433232462, 755142920, 672385066, 374078630, 89221839, 346489025, 611147651, 146736559, 176271439, 920410036, 745383366, 704436405, 235195013, 732277568, 834342037, 335749925, 591689795, 389869669, 169396700, 909391186, 245534448, 845269616, 995650947, 992606949, 449090806, 824025800, 132482355, 599581739, 161792276, 943090239, 502659084, 25083205, 301697525, 30997672, 250417078, 608677105, 729788531, 460619351, 426684579, 162776778, 344910996, 416275222, 973480234, 475543907, 682413411, 885428515, 343350473, 877851848, 555086123, 611874459, 248832373, 562296376, 53675413, 860492985, 317454338, 44246790, 28210473, 826886942, 351529414, 630201947, 179100497, 540779245, 347417702, 507084504, 950698553, 520563588, 996377417, 372974497, 911894638, 546680955, 720222370, 586309232, 921841346, 771446174, 924977431, 631261301, 362680946, 617453781, 74918994, 720193248, 959002244, 736409572, 685968763, 375664828, 320995478, 340331590, 71362241, 65984903, 874217592, 419243753, 211640614, 217085639, 398635345, 18922913, 546250245, 353007584, 930093463, 285428592, 122440164, 733734777, 984697398, 464424194, 668006203, 599647844, 257381846, 124904927, 417258421, 538811115, 712134066, 814459447, 883751822, 87853521, 307923305, 649210144, 550746092, 357274389, 854029407, 153530058, 717687128, 206626068, 333608656, 182118207, 719098043, 569183228, 653557063, 859803448, 537167450, 511386424, 210730668, 259372983, 742381563, 504829707, 21951387, 623647093, 59366533, 623108495, 67595391, 838253798, 991804101, 568841253, 513191782, 981798046, 553392962, 943770371, 198926462, 392599624, 562871253, 429311663, 74174771, 215610757, 655233326, 518892415, 100505828, 375519191, 276956879, 787989474, 602049660, 922832649, 421671325, 181392153, 883656828, 254601569, 248682731, 40759522, 461720003, 526604863, 489875024, 812617258, 252505391, 918640690, 956448396, 416046109, 862890560, 677619843, 309458501, 512896693, 343130287, 281922810, 230140871, 240740045, 3659618, 533953352, 540667173, 177218487, 628419403, 743930853, 473359171, 930302747, 825079257, 747665929, 600937723, 911163243, 87458911, 896012148, 217233515, 987597236, 445216700, 735413846, 545816352, 287474444, 552660786, 750022769, 810728483, 773024031, 786350031, 621917209, 296882877, 369735972, 769880594, 677215026, 190349879, 917898667, 990453425, 894848994, 422102913, 296649985, 843547494, 838501289, 573345871, 523731453, 969674788, 435824950, 668245263, 341664627, 474187849, 965851408, 555565890, 964466081, 929811336, 340163910, 594106928, 493041767, 414187821, 102982070, 394087796, 126315292, 95194380, 970100481, 282542906, 10063499, 164548920, 276668767, 336994464, 39109529, 863392863, 481134212, 310216551, 591992551, 682373509, 680534973, 846337154, 2528134, 21165865, 345347428, 316738298, 13356375, 107903577, 518193470, 430134913, 651260357, 391606073, 636515312, 941964416, 226575906, 796212603, 60059831, 61062815, 967591181, 612364170, 728039973, 362235256, 211340906, 802153502, 284142123, 427594710, 435973246, 187489853, 456383162, 919215190, 719053046, 707237633, 45821477, 700608221, 72402405, 972420226, 849636528, 932475258, 27251319, 85765720, 257534267, 642494246, 519417011, 21662063, 533038421, 416785084, 977150362, 756456923, 111916983, 525662954, 580324068, 742737754, 331346365, 887545102, 453229682, 85538712, 781343865, 483089987, 402480452, 46766220, 998706760, 48523715, 91457402, 277214462, 439070817, 257377411, 964988375, 991428928, 495381355, 232321762, 357197334, 545991647, 323498161, 377875342, 964333731, 274689352, 345228970, 530102678, 439438053, 957098389, 852091117, 320274992, 396939968, 526363901, 978154888, 271141007, 503418387, 507152388, 743178898, 851223180, 845885363, 652183882, 441360063, 42418752, 147821122, 871921892, 353071106, 120444440, 528411462, 956329848, 870530601, 892381166, 584911331, 826928555, 572884179, 37622817, 34275124, 187205983, 772077582, 727922406, 421672971, 788606048, 216308252, 863133020, 186842813, 777447504, 556816717, 171996264, 785762914, 483784044, 42362889, 808090855, 708430054, 329900116, 717128792, 333293505, 343923907, 327127139, 321845876, 375433552, 309394376, 519168222, 8737552, 700185561, 248993978, 289659497, 5656122, 693774251, 690696040, 288648080, 586876687, 537586612, 241874360, 821597053, 817842865, 459058317, 175531960, 240137235, 473478852, 626750655, 419223150, 483822621, 212357415, 447966771, 615698045, 782078460, 957423836, 476643786, 214674317, 921170567, 176711523, 6243298, 773965522, 437918088, 803397554, 700280337, 246421493, 520502535, 178076431, 527805351, 882957904, 45427649, 883750095, 949773870, 46688702, 160706605, 229685624, 551478335, 597594190, 145130408, 711870550, 893173314, 274768322, 88211418, 924726269, 543563562, 976568404, 346017471, 674003274, 887758530, 470198821, 962724890, 992887316, 124701043, 467688329, 906526889, 88645247, 741175543, 723112129, 696359418, 289572981, 129244692, 105297690, 875413628, 982821517, 557510247, 309370189, 543716021, 618117834, 454752986, 873791007, 816556273, 921466469, 938364893, 711076341, 525192047, 315807931, 227285396, 143442499, 227566815, 507862555, 65322123, 276595930, 92839474, 735443525, 628473991, 634965363, 799633322, 95912996, 489068424, 241674659, 582436636, 587323722, 586032825, 701638126, 192762200, 270144002, 402890686, 345451425, 948253840, 657746862, 869512286, 542675983, 751681202, 477710805, 144872185, 694865003, 942374988, 876669858, 309339781, 600982751, 954576421, 215781629, 997631452, 615139031, 290709741, 679961357, 928684061, 922269583, 316948456, 762209552, 932577669, 672410239, 717057068, 578763289, 909350104, 864395090, 680602097, 584680987, 463183040, 157256876, 133475190, 264485157, 923450949, 350838128, 378701013, 529091375, 66528020, 511554389, 77874493, 106746218, 650530993, 863656908, 931709234, 818108426, 171012842, 604653890, 807955373, 388989990, 980117638, 485748105, 309141484, 55621010, 319286115, 775183290, 965962034, 191063066, 669277800, 907515656, 69790554, 701255511, 889807021, 21280402, 957165616, 750052350, 57265342, 51659482, 712819559, 18114716, 299300978, 602856128, 498582076, 91004696, 332040462, 475448880, 951626134, 239010026, 890773523, 833626228, 295151359, 701344503, 791350266, 776771474, 326449048, 862481831, 657618329, 787258158, 844146836, 392584198, 637740174, 699399597, 817426124, 157905643, 849042111, 977067410, 387622359, 483310119, 788689022, 626293479, 541832404, 495136032, 549341571, 785058664, 320491137, 598430895, 982475643, 194480492, 382742986, 61159643, 533185500, 151768326, 956821099, 803692921, 37186578, 283697452, 927453308, 594056158, 529493037, 197853836, 833026407, 817042617, 910443490, 632813503, 980530246, 305291803, 870552066, 854935068, 273106503, 281943280, 346605810, 212504207, 876469712, 10895561, 468808158, 69804619, 760761350, 696996310, 31972986, 717733749, 761347994, 521037746, 988711377, 109000569, 618819526, 428406655, 754498768, 166074620, 22925425, 932068443, 179218242, 713610392, 899378657, 774154639, 398145520, 277939084, 505136991, 112608905, 157728506, 221660694, 302263324, 834047534, 303973374, 55889269, 101817633, 591496348, 346412814, 387049385, 358519620, 815118182, 797454964, 192676420, 899124401, 370329948, 670228669, 648822750, 207983789, 759172656, 886501076, 664278366, 502903278, 458445132, 185389131, 597278580, 114393930, 305323087, 274747426, 103197476, 743980078, 146931463, 372035834, 856042796, 850215185, 438320241, 105891660, 396136034, 643810905, 244957388, 387707239, 763773553, 166816063, 633921395, 116731651, 834152589, 625029898, 544309860, 466459907, 562300648, 859447106, 94774542, 706317269, 663222904, 582992436, 835988426, 424035372, 20835434, 842251734, 827260238, 224277954, 722115391, 865245723, 931716277, 492026964, 225362755, 880399835, 784173572, 750449962, 588142590, 880180118, 611730421, 335768802, 194162721, 454164699, 296530127, 403448540, 497398632, 859067519, 868090899, 412255235, 409178863, 107548392, 331353187, 73953862, 229511889, 551105670, 947256050, 112567625, 788981515, 78729318, 347920623, 477515284, 835998301, 907120342, 495808732, 834644316, 629664334, 344053758, 954178751, 272132985, 492220538, 651545652, 622303472, 190563017, 315102598, 826244108, 423833818, 890670382, 682830539, 891308358, 836032125, 661717894, 159400400, 284847188, 494730816, 574735085, 985801129, 308121935, 733209961, 75212225, 532226826, 370059834, 98233136, 359604907, 801201983, 805078840, 378860554, 807478219, 176688446, 226761298, 586351970, 398985854, 787901214, 728740919, 292605179, 153042478, 447526156, 632042388, 282973201, 276696798, 697081260, 692581213, 445556318, 821731389, 355141493, 227755726, 39419621, 65869136, 720767794, 95198296, 790978600, 117029460, 582940601, 429375483, 861175311, 752768579, 150762013, 971340419, 8335303, 22352526, 849323126, 860197669, 93262522, 481603567, 577879205, 722738117, 374345144, 992666258, 637057391, 107146660, 961807268, 164369937, 921146988, 917158544, 660669006, 828590304, 705507709, 334974869, 498493242, 843169242, 153610832, 409003063, 522723318, 402192924, 157245035, 801287097, 777631418, 916046830, 74241565, 446903601, 551361026, 657540384, 307074370, 917821599, 68429958, 508975126, 416082677, 628649275, 351211719, 206262774, 217750086, 742230112, 383532275, 950849464, 34248168, 618200285, 337518133, 629911311, 834933637, 139654790, 479336837, 397245244, 845384197, 206249123, 225984507, 242970653, 188604684, 206727096, 24130787, 170967570, 787826170, 355189035, 742019492, 288969868, 403880754, 444438450, 667743904, 24457658, 701618695, 626371599, 137941019, 550614629, 517508722, 507908666, 566726393, 229721208, 151765450, 660176152, 913113917, 358174860, 225409565, 655689154, 185013020, 949760213, 445382208, 628396521, 815633738, 400157000, 102823199, 594757866, 805924984, 857572418, 823505409, 557156265, 422723319, 499790020, 459606831, 190648343, 975359566, 697530063, 189366596, 981031194, 664196327, 835330706, 387432169, 27480698, 277727785, 804351577, 759393891, 981019948, 37153091, 496222027, 567486576, 667476919, 601276780, 882044244, 962992195, 31313091, 606255897, 550461517, 369932350, 604520099, 706778003, 48549863, 401470273, 533178135, 158233665, 17306823, 644749013, 223239738, 915926521, 526397444, 4289510, 427051715, 213751738, 879801156, 731812440, 768002113, 688139568, 29096459, 562864723, 562455434, 439852004, 225164088, 509592258, 571556707, 891744281, 591898565, 156868998, 212276022, 612234690, 808419930, 678550102, 569687101, 392766304, 497006942, 27058573, 325658870, 534329883, 91416715, 841760202, 20568520, 825943142, 394350461, 951716960, 696207052, 446238572, 527985820, 877860832, 65248266, 839637351, 736139784, 85381336, 185456609, 917599988, 296043650, 682220480, 528885872, 233521931, 167138566, 59844825, 757113679, 698197999, 467753462, 533265800, 923968776, 112668931, 529524248, 51317879, 459903613, 382984399, 733605411, 410297208, 365250769, 838945277, 883149606, 280914513, 439654191, 717253148, 688765757, 786944068, 802442682, 333085773, 775061023, 991986002, 732612736, 338881723, 633115917, 569951051, 854902468, 483234462, 183945923, 295151676, 668836663, 86324893, 183389387, 942328581, 183775241, 502667005, 656355906, 777383140, 285749300, 222516621, 842505645, 589117947, 725808570, 216148720, 342815791, 540262138, 657303248, 846245266, 286968415, 644161133, 730262897, 710127379, 247419620, 185436062, 370368784, 123142963, 936926544, 634290638, 875593314, 944518004, 323050149, 84541421, 316050758, 608502128, 53532724, 142730507, 340685518, 23842357, 209165299, 585102154, 630153313, 664053455, 446110325, 413962127, 699261402, 484261187, 633941222, 244671271, 845859972, 663279909, 503440502, 32202519, 191582553, 53428890, 675504622, 31742027, 249652953, 61066354, 711807136, 940503819, 369406733, 934332390, 623090055, 454572429, 500514877, 99511384, 791880369, 536770652, 772609712, 948068603, 967870556, 218532861, 83884159, 506474015, 380382694, 551511569, 155544539, 904746709, 180016231, 403197939, 447258020, 656994630, 735736394, 835371155, 369008727, 229891304, 848502329, 621518285, 578224451, 863432308, 777563186, 229194795, 271844849, 453698106, 103686484, 576180491, 713864643, 870229107, 203857524, 629397094, 129354912, 730325575, 21159826, 732862182, 477929147, 408036862, 155178939, 843440150, 406075550, 171209309, 315842132, 809573120, 137373459, 597156193, 99964224, 563399163, 16315028, 721436478, 384943301, 695223733, 200025897, 277574200, 309620369, 333759281, 260993744, 465982155, 33724461, 136546066, 394537026, 904921186, 244658002, 521115964, 279647266, 706923770, 775444846, 989191635, 45895206, 954920131, 154314424, 473169092, 947120191, 735077198, 665879228, 361445358, 996257639, 919551882, 23898072, 710438956, 122135554, 115086019, 113627160, 376743477, 318529132, 230016092, 396716132, 523915496, 589079256, 444744247, 764805776, 636364222, 714243239, 630247455, 887348943, 644129102, 285724803, 544936487, 765710285, 119813657, 11861890, 453957087, 856034105, 440416985, 549001517, 691276153, 354323455, 470017072, 147111557, 250840497, 319651728, 66106194, 707852269, 259593510, 434174041, 957421441, 279177557, 411285158, 754634448, 728781256, 206292242, 919502734, 458693012, 191702042, 408254403, 66506285, 416067332, 587609759, 946612881, 943904877, 557094369, 80240006, 635425030, 911695571, 369388542, 609147963, 70044267, 212250872, 741998696, 638006424, 379123934, 963376519, 614408156, 393510970, 408813977, 438140034, 598826652, 622432689, 804399680, 29714917, 783549682, 273521539, 623764706, 691640268, 936886362, 305442068, 974912101, 217174150, 256027003, 690294708, 884982823, 649206794, 792020271, 928869218, 31690688, 169838964, 484719565, 284775382, 874161063, 471581134, 329851928, 567997470, 780821216, 505704938, 352345506, 637282999, 772298002, 18733367, 564988322, 597320282, 992962720, 775898926, 830488700, 647870492, 369589048, 126200112, 993909688, 530894469, 334567279, 80869097, 662251385, 355023367, 462536390, 121711719, 802368654, 399713769, 577435562, 56223737, 66676688, 549470838, 462741005, 60661448, 647962023, 558112280, 191846, 411031765, 423651158, 194144249, 419489003, 421469687, 282273358, 173759421, 14784999, 46309190, 772912698, 836144250, 306701194, 915397952, 846332056, 866975640, 934724123, 373056322, 526513195, 834291192, 958828254, 738213985, 790929744, 784410028, 665326785, 904376168, 998950456, 41032006, 391967378, 580688605, 404888497, 642806528, 711401798, 39353219, 809528312, 976400537, 479455127, 437049741, 781013902, 775260221, 917768276, 808459515, 941570966, 861831291, 924158845, 740946012, 466507542, 889840738, 56586951, 712948542, 793012693, 704090977, 149878230, 807393750, 14593205, 285246312, 505014649, 188000683, 484869056, 916959004, 713636002, 597729371, 850891810, 619686376, 128286951, 270007078, 629253865, 600323930, 369524940, 42342181, 851778807, 693214805, 839704923, 614524400, 9744649, 282842321, 75077013, 361601615, 349816784, 49275298, 641246871, 657424667, 812228515, 196740563, 141465516, 318779305, 676435027, 19086820, 595986372, 870927710, 370120463, 171079900, 279945842, 357858170, 235538373, 994162186, 238088806, 351656518, 575791492, 782581479, 995949635, 154630710, 360476888, 28781054, 484555276, 973056647, 331361812, 938905937, 323563772, 79469805, 781324261, 343162250, 429411308, 689985444, 797651625, 578872892, 936282908, 473389215, 876264645, 124380745, 653135235, 212747819, 900070598, 173006997, 182968396, 510167794, 47244892, 637662928, 289540588, 408658997, 714631607, 412347744, 369044751, 426980092, 423597969, 418054909, 362216450, 422778018, 490177985, 266049531, 801744400, 639752503, 904122148, 226364606, 975184087, 412382680, 351463017, 876224263, 786677986, 513019482, 358481294, 812381582, 293433124, 804795013, 498689181, 813377274, 40152456, 144538363, 661671337, 193128335, 920478821, 686579481, 668306431, 814387593, 562997814, 815785023, 516144330, 595885772, 519428614, 961641932, 63545812, 653037399, 897852866, 385631846, 759834324, 746645135, 864026327, 713590816, 693932841, 800610584, 652738698, 1077375, 527605622, 219503504, 421241018, 409261081, 414009138, 306896745, 640065221, 284472731, 732544227, 316492278, 438771700, 821755103, 326912242, 695955252, 236796958, 730667787, 100990691, 666630529, 2555497, 711137690, 910655809, 583484124, 182553985, 77893561, 912672418, 996931989, 336902127, 583431685, 656957647, 229092907, 341941204, 724755457, 702446281, 747286106, 913587511, 270172517, 979757584, 344684104, 318931268, 907921144, 261785016, 935428736, 372493979, 982545107, 255833104, 589687880, 597027922, 45449951, 601904971, 794548823, 938638850, 493432468, 770277103, 446092427, 683021918, 919238139, 666535817, 692145394, 87766324, 966271890, 650172108, 131707335, 733256925, 73318337, 38111705, 749386652, 207169044, 409924981, 207826073, 152320698, 398878332, 290805583, 661679016, 602231248, 233846257, 458287480, 803260749, 52696610, 256120979, 753879784, 452130159, 753290900, 471695934, 598984187, 126799759, 420494998, 952060996, 949870499, 890712900, 777625602, 974453552, 935369070, 573930311, 922839334, 867859737, 889371137, 88883815, 358231754, 92776303, 946449481, 79376495, 717784401, 80042311, 544551375, 779724735, 119155924, 997725460, 362801352, 985710517, 392538536, 177709025, 41860760, 227350888, 790902513, 922062356, 784546135, 855521081, 510623076, 759737763, 671796142, 145035469, 39038263, 696256573, 908449016, 496970405, 715036016, 758252507, 207596946, 408861419, 388894162, 402301789, 831674552, 850531404, 947131950, 985668026, 116092544, 316698148, 683248668, 743183166, 492792154, 813957975, 102202080, 805799646, 76041235, 123383796, 849521423, 813240502, 883716584, 821054315, 385865495, 991708487, 604949142, 976918783, 76760653, 4398677, 506712701, 679768506, 629055548, 628997573, 88219256, 398768654, 111099012, 763324717, 221528235, 320079234, 194346811, 467295346, 41658587, 574527953, 443379785, 672310266, 71757809, 691129467, 106349564, 105950934, 530700678, 36537696, 778021000, 730291456, 627986830, 494741401, 536977741, 253770301, 509474360, 939004375, 254616180, 869973200, 932003692, 238074374, 738831821, 847383997, 646312100, 754246564, 957167418, 197784115, 275596584, 244973230, 685078907, 435896372, 173634832, 973171429, 133216218, 8606263, 51739705, 762598884, 367944696, 674554097, 782607538, 917203831, 607580253, 213690571, 645555025, 94975554, 5742971, 459508552, 896111920, 457694056, 940427156, 569623402, 343518757, 220206760, 525809758, 193857723, 507446241, 129553204, 572426105, 487207070, 2230172, 147071893, 357513367, 17278171, 868059679, 27405353, 441585879, 42005011, 395255533, 655302257, 45223894, 162451152, 830819067, 657350693, 102624129, 902112087, 872931380, 352543966, 943965509, 591715313, 152552585, 278673618, 60170904, 621144876, 521089093, 300698568, 64524392, 146719871, 981613469, 344977936, 127998519, 228594165, 692736389, 411376565, 329301117, 79625177, 49922849, 680490468, 104659876, 772927572, 803906410, 142373863, 684990539, 757813988, 24531394, 277220478, 969014098, 521564488, 11199740, 997745157, 668633927, 581134187, 965547151, 251620444, 918169303, 345085125, 696775914, 153477277, 441678796, 947608135, 500509919, 307870596, 510284818, 995587681, 102177890, 583863761, 565546506, 743244808, 958468223, 905160889, 730068996, 78824262, 156023316, 702004096, 853069783, 326758285, 5252377, 329257532, 842670801, 575604393, 949820285, 181940313, 887872676, 990924437, 880038383, 902232684, 248198338, 320390826, 177955599, 790899719, 52975932, 42996655, 387523255, 442250692, 616813079, 768341285, 381003336, 72126545, 670680223, 176666102, 983660482, 881483505, 271287115, 248525783, 440008834, 111502900, 785704373, 839371690, 362833224, 613090624, 452783543, 774603493, 75336769, 680422050, 902051108, 266503609, 111687891, 195901337, 59675207, 678049231, 314095944, 667115257, 94910550, 255072435, 308352304, 472881073, 261567138, 641044620, 53201419, 309938312, 901606328, 613360112, 382061792, 684339204, 515219396, 951367481, 50115005, 868956981, 349322216, 3405992, 971207933, 580586527, 998654343, 777334548, 942689851, 17585394, 380681617, 384323560, 411763298, 581400586, 804157691, 757949821, 620563202, 111831282, 645384129, 933191359, 119627805, 598217432, 687846818, 268047596, 507816791, 724295752, 595937683, 478923854, 296954554, 150676457, 786149171, 790437173, 34989440, 840722364, 508308660, 807480582, 823034309, 554187998, 389281230, 795929183, 808668877, 560345033, 834570286, 183537075, 159865029, 969469119, 2224132, 328196629, 733334314, 568267584, 59913181, 93987006, 791878801, 710527964, 155943104, 294918036, 280578765, 949072219, 320511827, 269795717, 29411372, 723914451, 442006458, 83514395, 696161608, 432886615, 156772445, 659391884, 192273978, 681409336, 963027144, 738932146, 512382063, 996451730, 489368926, 578980212, 858708874, 115544945, 651411177, 561825263, 413640639, 908220356, 352981218, 938913663, 632188717, 936528535, 175900919, 856145626, 214148477, 890344051, 537721910, 427336331, 362835544, 872156462, 108547626, 326461950, 721513495, 119960563, 942801832, 749615667, 689937326, 193984357, 168605054, 198333807, 199504369, 239157674, 578514105, 600912225, 669545343, 456335830, 718466602, 56070562, 769260908, 867093036, 137646891, 118209142, 893005023, 99513405, 899821983, 454707527, 16026833, 665767140, 939419323, 730121595, 903828323, 612165997, 350289527, 274295269, 129414690, 372670821, 635980789, 960496357, 455078325, 744521911, 180379429, 944938085, 697597112, 20574192, 473768165, 766584445, 454288667, 220883958, 237670817, 571826289, 391377442, 48359416, 312127389, 695982149, 377585159, 245127727, 633891911, 770007385, 893835807, 409175433, 638354651, 185618887, 453243846, 59872575, 182268737, 971180327, 287049911, 836354591, 737276683, 282644106, 616666032, 405969180, 141988306, 972215272, 93219570, 354273947, 762373365, 13687106, 837348836, 361630904, 631402829, 653198766, 289375215, 406549402, 507762413, 262165250, 271445052, 667396102, 804127833, 895618835, 898320004, 24806977, 399695868, 871904054, 145024158, 386052781, 901090265, 276070662, 868022185, 363973842, 73567307, 367820860, 449179204, 372034281, 480473031, 119634576, 908095689, 925707310, 600712132, 924153247, 168878145, 454329110, 641977899, 685364920, 854679055, 687874292, 712947900, 334484926, 322467250, 498503181, 584015690, 301291445, 648896344, 255657561, 421554729, 17433142, 932757, 687897967, 160314102, 870958177, 635500700, 377160050, 544728566, 422510119, 761264050, 393924535, 890723086, 682099923, 937690832, 451342946, 702868571, 220891606, 650516339, 529001210, 857369680, 745031037, 207877586, 86974890, 536665830, 798876203, 252594134, 468441651, 768679732, 601270394, 213699507, 953363817, 258744395, 441090966, 718352580, 288089096, 51740999, 724597620, 486618994, 268862081, 220786220, 829441538, 225410622, 549000024, 106414785, 500723121, 116830096, 482170592, 108289166, 297762309, 941911062, 325522139, 26390062, 591361707, 216449419, 346185551, 317187942, 263590340, 61128719, 541785485, 889720409, 491118247, 947411756, 336180762, 824591980, 526054964, 386148038, 681590745, 241701421, 328070409, 364075603, 237811732, 642644596, 590185743, 167647102, 47516357, 794859884, 678120160, 997436528, 526942580, 110145358, 985918592, 901780979, 538977040, 564208507, 488474549, 249089797, 861238305, 860189150, 838857716, 317336745, 240621818, 461362373, 3164544, 477376779, 858721303, 514571467, 348316855, 982571738, 132597152, 865293556, 14474822, 870328541, 405713966, 986424150, 468116478, 238965051, 173465601, 684856965, 995050850, 147280496, 857732698, 829046740, 25660702, 609004056, 505297752, 64477384, 689678541, 572209838, 142301235, 587133530, 670406019, 114660128, 421661333, 571650298, 627804459, 338649955, 138551970, 288877267, 608080437, 660874949, 933532405, 411603942, 882626025, 387487733, 187149257, 437197554, 406082517, 116499842, 815786555, 852274671, 174755293, 734906620, 344633546, 464108198, 629624835, 663338445, 8028953, 949271699, 183575040, 922648744, 626927930, 444784375, 879676717, 282730799, 713033135, 290487608, 65546934, 161745252, 653238727, 686186872, 646816464, 286232195, 516206062, 885902805, 212534029, 617025957, 894518529, 219355310, 869526605, 171213287, 692141203, 85911091, 631558720, 194328881, 790093414, 891163407, 491477042, 914559879, 281670347, 893976665, 112607850, 5802802, 573010436, 575872454, 263201192, 69876078, 353547406, 286780186, 859848499, 538437367, 842136903, 791525525, 783663628, 588282169, 500184761, 428110625, 877331943, 561099339, 104432496, 735002434, 251661673, 104288920, 778670066, 371274212, 796843507, 705755553, 648887052, 960793010, 457170627, 344976834, 856642994, 579363521, 277805307, 196038289, 833772957, 956044344, 900600879, 294061576, 424459859, 791330694, 891021520, 551301038, 561519458, 481095502, 11317557, 171981662, 991407040, 503388435, 254235999, 202185665, 605651550, 813341135, 803077669, 497858108, 34409712, 496023837, 621383091, 753653226, 379701232, 955216355, 601943575, 713973122, 906576072, 934965793, 922548599, 711142003, 537069615, 722773702, 191344648, 546298941, 642744663, 641502935, 836987446, 660378625, 22062485, 56559278, 918313840, 300151238, 280442754, 20440332, 256521838, 133330941, 588229590, 283880345, 254505472, 433813194, 843619799, 408382359, 611336309, 266427109, 970582202, 817418702, 873319250, 955843963, 800393455, 435524485, 589939045, 677915440, 360364185, 804703028, 113054108, 770645308, 871867210, 617893939, 440308129, 998287135, 11821293, 312362198, 831135398, 491958142, 313622559, 238525429, 960573677, 518106239, 604738408, 985729654, 45780160, 633166103, 961647222, 448156123, 888894142, 431135298, 128627482, 856052894, 488759480, 266865142, 81621972, 223588556, 105274029, 760931200, 3838950, 149589708, 94952600, 783524634, 317466424, 24036246, 466866081, 747903574, 762966817, 575018165, 37378693, 499753477, 866325518, 591309250, 904119171, 966476638, 450979076, 289239710, 818495735, 663279664, 554564359, 761142238, 368170336, 919598450, 575318618, 780930903, 763848749, 800686387, 97408146, 106781783, 702113332, 159151609, 246142306, 241451091, 346699329, 773722503, 212163729, 700305442, 595303617, 362649736, 641492136, 484772217, 683373406, 853804186, 513159723, 198732175, 114799695, 154033111, 720860683, 357728649, 862545103, 867518662, 131050978, 393076285, 417898525, 548207979, 125558268, 563666810, 502390328, 124260808, 896166567, 232905775, 556434597, 618381704, 734526041, 925812035, 716148881, 928015553, 625522514, 217963708, 790941806, 429738916, 624681247, 4710504, 221059946, 469644418, 783147229, 536848127, 681190909, 179452603, 949594072, 162506223, 471251106, 395046456, 617176025, 916607709, 299785469, 996172162, 133054830, 294356172, 930607250, 901691790, 794543098, 955767121, 724314428, 649904695, 72475554, 521827896, 256531, 670837862, 288666737, 973047827, 490727436, 299831770, 913544162, 784686708, 216719991, 874400719, 283509522, 100314159, 496767046, 853319705, 686958266, 629031088, 420406796, 559378657, 487177553, 734693344, 259705496, 994376678, 256511820, 44461210, 307147300, 485191477, 641127719, 577157253, 630095584, 733525251, 891496402, 306310501, 479069211, 292130660, 344283554, 678929726, 904522339, 162093367, 186966060, 569178057, 859563435, 368325850, 572300544, 442582679, 902807731, 221585277, 740704499, 194859116, 214352496, 673435803, 948287434, 791740926, 638136333, 347143016, 795311209, 290169633, 435537894, 15032266, 807615539, 812153359, 854680987, 924114999, 12608600, 188446803, 170177028, 331215149, 931222329, 390896268, 803971659, 536351769, 992964304, 820673733, 662638496, 846929915, 531622244, 607407400, 233256913, 583989213, 626949418, 503373312, 184477484, 116311002, 657257954, 735917047, 915785600, 137947390, 643811860, 626407049, 37954918, 472088085, 699429634, 198821875, 507788261, 292615457, 207325789, 457030667, 653818110, 224334690, 394168047, 64817786, 465574063, 60791056, 210762167, 508782442, 890048401, 790767411, 423623013, 154290909, 118272768, 844729224, 50476165, 152606823, 749442477, 540721630, 613223861, 37798389, 944110026, 637479117, 387913302, 843077201, 928692089, 100725113, 556563843, 268134415, 109417084, 265615257, 48929975, 699841247, 798996543, 342200602, 367103013, 19188684, 895472081, 859752195, 857091773, 374623908, 96888726, 694377897, 818175932, 53315856, 740470941, 95394877, 797547760, 969132042, 13883214, 16061646, 694708402, 169365116, 116788398, 878344347, 228231764, 512153843, 117230545, 507135859, 383440918, 264043360, 936746094, 304426522, 701271715, 643154264, 749284975, 782431270, 366171307, 886460657, 36941979, 700861113, 52174, 319341558, 39293807, 778270752, 822154437, 315355812, 483983173, 769078930, 7067506, 476384845, 974573277, 353197167, 945349363, 152505868, 508570169, 265390202, 265402597, 853911692, 328978725, 311958341, 255207960, 451069932, 507015012, 534934423, 354119948, 966749968, 316361257, 888796630, 881575321, 68735716, 792194874, 675179006, 499178406, 104232328, 746124899, 206931465, 370913693, 881570057, 313139051, 585278256, 18494989, 565494791, 827745552, 311414640, 559454033, 368146601, 318916585, 127571181, 225268609, 667260338, 264896649, 174898571, 97462462, 820885652, 326424796, 951568754, 277762390, 263401898, 465111486, 485482474, 768750628, 47425961, 523233334, 945838748, 616944610, 968966914, 24390132, 908982212, 843183355, 756974493, 167476249, 453651996, 427415349, 246841629, 126520603, 283678102, 532932831, 449661686, 281682753, 35269425, 825281631, 758238893, 809822649, 232683147, 38056732, 449282426, 294596170, 331548128, 832522678, 881189152, 5150569, 667563313, 555300295, 302754691, 524274043, 173451699, 475544735, 692712319, 994084198, 530984527, 847728943, 834426004, 918302567, 901911204, 597786647, 980780630, 617870210, 115236487, 350739861, 1780225, 742550966, 961919125, 284106681, 447055939, 77208062, 45210271, 765207116, 940888616, 463227376, 141899823, 544411228, 171356426, 790832916, 911561992, 302878028, 917776585, 806286573, 146435692, 309830611, 947853625, 685714607, 148538585, 511341086, 258330665, 558420892, 544122128, 813752700, 400255417, 756546174, 451765550, 299706097, 821068029, 477795832, 123722981, 932149776, 791810862, 229344944, 365263684, 227718193, 168154580, 51193030, 900791240, 934152094, 475768460, 533854589, 636511658, 414588216, 707952426, 651418409, 157444780, 717915920, 46600556, 996939473, 345458935, 70728448, 103443509, 319753687, 600659658, 730864207, 908309120, 959763615, 460908870, 166739740, 707187454, 824435584, 196194860, 376766267, 986891632, 140430021, 579899276, 491732006, 821074862, 973494790, 476881488, 272307516, 283727322, 220449021, 773674847, 93601365, 621074839, 202117326, 119637048, 674830145, 810106933, 481447518, 803830049, 945456237, 916003200, 25535362, 824449134, 530097616, 727392150, 938428160, 80095320, 639834876, 556356035, 486439537, 171381091, 605608344, 501048719, 853072923, 587598666, 779852206, 61500340, 597071729, 779072618, 373168096, 758408923, 898822660, 999885469, 317984127, 335949387, 590955691, 763961152, 366621851, 714634543, 547359629, 439536146, 69868040, 321879563, 321608155, 863645441, 352657963, 929974347, 125099091, 575498883, 205051626, 234563509, 444063211, 386367709, 845238006, 163982636, 77249537, 800447932, 658554869, 919304650, 138881782, 954096235, 385334733, 219587155, 30972668, 49343684, 947250435, 951499653, 752826212, 896721692, 266077152, 823380340, 658243065, 447015723, 375976060, 537512356, 326568726, 418408341, 449324651, 497727888, 904962037, 113199263, 548696327, 46358583, 642110680, 54718644, 273931576, 289183163, 387582647, 47284917, 316564172, 771173971, 985313509, 380172696, 928435437, 989044280, 221517153, 781491673, 325042355, 437603955, 893057978, 628467739, 916900803, 390905880, 342815351, 26846632, 983744206, 160875061, 746536206, 833825429, 960804257, 88865612, 239869161, 349729760, 870217393, 769951275, 109499698, 966364967, 977586813, 374495472, 950619793, 623834095, 41022633, 626402725, 451993099, 186358871, 947453195, 825351625, 602494245, 831678306, 926487974, 700860762, 961951324, 926503622, 567990992, 662009291, 61306070, 195501803, 439698308, 938141359, 711690296, 757647638, 959581703, 245306, 101908831, 491659637, 553065805, 959339470, 453424815, 967571488, 457699744, 687382688, 16480962, 951874950, 470904204, 108265259, 371884370, 235319999, 85984081, 977000725, 545550270, 135651598, 172399525, 349826023, 777419969, 524228276, 489155161, 546008805, 911458941, 444381564, 577926525, 535007227, 128746071, 464691665, 810686203, 749440126, 905054728, 311148453, 486293235, 821464024, 179288146, 623136038, 607469447, 664156943, 767964312, 946842375, 7310621, 490395901, 654290005, 734620147, 669898777, 343818483, 705945610, 839029046, 41731016, 84009135, 608137546, 5841778, 51191479, 401247410, 926887173, 209871109, 147174759, 741994451, 817197139, 702335666, 927948906, 173719341, 152650091, 728059027, 476767946, 520056770, 535182478, 54283048, 341168709, 847745103, 78014318, 235955901, 978779050, 86640419, 5719620, 153659774, 606861591, 29367977, 775581272, 542236829, 657358337, 653235564, 725611293, 670488237, 193808787, 272361249, 192886656, 955299702, 279311805, 628593409, 791354828, 19495290, 462213075, 34927233, 278324879, 681878021, 4037965, 835847255, 398172279, 947641842, 605259511, 840853361, 855604576, 813219069, 468177414, 159351976, 299449199, 77816968, 62908674, 920657859, 780826614, 202267195, 795679145, 525823513, 566129609, 894534525, 850242113, 265466968, 467119594, 925985870, 6675213, 700688295, 818727864, 157737026, 357248845, 415406197, 463245507, 593081977, 970818855, 481326953, 561172710, 237434729, 148152743, 829188088, 817993200, 666811197, 169683277, 28406755, 402998747, 736524012, 263904222, 348194780, 534256993, 49617248, 456641431, 829387831, 148068322, 511003282, 444972647, 640441611, 821220145, 541933395, 196966107, 175206553, 8759861, 352041831, 666077237, 928290465, 391437495, 829259582, 406055294, 335408068, 835001164, 619387312, 571395708, 379957046, 863620444, 334624604, 638580400, 1159590, 709019816, 455826750, 510401493, 771055705, 276702483, 490873853, 760350159, 729016590, 846918595, 722665246, 243805240, 182673808, 898016498, 373584765, 895779004, 298979792, 469783408, 522854396, 901203656, 965553098, 807282442, 787832162, 768823348, 406758742, 147725342, 87915231, 687994214, 984621062, 584105970, 700274564, 476048320, 602146278, 442528729, 392386867, 724523963, 169580299, 510564459, 654642833, 649417211, 614774229, 400931387, 685558529, 953428694, 774788278, 509081446, 931512761, 223072621, 962026130, 964803940, 334763576, 239457356, 116587423, 4653317, 191029543, 689679920, 437179808, 16048433, 655225739, 235236077, 688516073, 890021650, 970278774, 462522296, 210434020, 156482985, 66498127, 331135660, 832961998, 316147637, 218626775, 174672950, 230830727, 803006210, 551160923, 462416981, 617733457, 173915534, 653967699, 595704389, 119706510, 326363587, 983804811, 237016983, 758692261, 903013068, 230140231, 582709268, 389937200, 297872764, 44549464, 494289498, 358504059, 564451808, 728659470, 311327352, 236841672, 103477755, 281175843, 542961920, 623828897, 350283154, 741490114, 355818171, 140051675, 370912440, 603409608, 60403441, 580189831, 161556543, 617600604, 537335254, 170019451, 602296315, 925106244, 723019586, 490309668, 72517206, 40795220, 963280371, 324785326, 321404844, 858632886, 164864752, 252611078, 215154086, 625122842, 42963895, 720408226, 397719938, 981108861, 259111468, 343526539, 754509143, 300698338, 772282670, 777481230, 945981107, 425009763, 554002379, 229439482, 199706101, 846480677, 943100569, 105286970, 929345369, 727057754, 199304338, 246705370, 840671213, 975936468, 791040979, 704248241, 156253511, 567441327, 529172735, 568451717, 975665746, 806250287, 161295673, 569282001, 65419437, 974822902, 414482995, 959897657, 784643155, 449342422, 393869418, 694217543, 140138032, 458391350, 535893311, 917580436, 644576738, 809957890, 814315340, 67545985, 825785754, 858265676, 231625676, 777744488, 500535440, 429362227, 60102190, 741272496, 693298645, 630358415, 54748585, 315491196, 887280768, 783505310, 586630027, 631459096, 718379090, 863464630, 991897003, 316539268, 924561746, 705820738, 304233533, 180470471, 664564940, 723837047, 61384671, 821796843, 626167502, 796511714, 140200623, 26206793, 366680783, 276303805, 793278038, 299312354, 834811767, 129138354, 503560233, 449293011, 797748381, 309375838, 744384458, 347302299, 186245929, 667264109, 458401226, 440984882, 792504146, 735626915, 114668184, 710027813, 258750080, 49438046, 62703781, 828362501, 159522241, 440984527, 40088025, 593240454, 318128882, 336991491, 78258448, 724747835, 860610111, 652047457, 440227212, 374894532, 879875719, 321249892, 481052586, 446375932, 164660307, 999698454, 451970795, 966629675, 138713173, 245789631, 23186619, 399988804, 892993648, 399284463, 162557457, 659210003, 5798439, 515562795, 569125298, 865193401, 811957521, 714327553, 629231596, 248202653, 13140644, 159953169, 956406692, 1800538, 701077359, 433337237, 983960585, 164418474, 281071662, 436021100, 228575504, 260880421, 696167939, 612934885, 673420873, 330109124, 946112619, 592306304, 731939091, 541236905, 784234838, 441377102, 474626187, 885048771, 935324661, 325388519, 116985556, 113582699, 442383435, 894164712, 50246546, 481977073, 400244508, 562943376, 381497203, 363298132, 149540845, 852593638, 628104765, 869460049, 942236070, 300727807, 650441034, 1432923, 118925911, 781572288, 122928973, 466656395, 549161773, 496445761, 798541410, 29969711, 121151615, 386795706, 568654273, 187289078, 773749560, 452753124, 17038410, 94155299, 563309401, 18455009, 926881235, 22510, 606613272, 123598144, 252562254, 678513336, 469040844, 168130835, 906933067, 541766195, 525207300, 719226215, 670574739, 442670630, 254083411, 498996994, 935481594, 556247171, 668371220, 965839128, 13146699, 246351271, 517620437, 773240651, 859073089, 64037285, 934848915, 808073951, 162663477, 843785387, 824024392, 348065374, 385646499, 1997571, 233108004, 327014008, 326277619, 256081483, 443634154, 592299464, 45580395, 429212395, 131730377, 875974532, 808295507, 845527200, 740710538, 729384979, 51155741, 415907741, 661688706, 213060145, 876460449, 167013427, 19041034, 878201949, 380363515, 505158445, 803833512, 630526182, 793487005, 234838632, 619600382, 902077913, 916181288, 502728355, 905347101, 264323933, 697470136, 818402408, 476936172, 864699692, 484227957, 379650763, 363819258, 600209894, 161565211, 703518013, 801029006, 525963427, 397134020, 477483907, 66738398, 943342720, 8448013, 406682590, 62632260, 75681908, 201454271, 465751952, 781113778, 187855002, 274331512, 174642855, 906384880, 441751331, 624695269, 563502740, 340485571, 752210343, 730984181, 670161811, 911047581, 841291394, 519776798, 8812594, 976808712, 552439512, 612499776, 718115061, 751698530, 901354197, 862786934, 47939067, 378088197, 128794833, 588091365, 240847880, 242795663, 750442637, 137455787, 235522127, 838420510, 151131263, 330579194, 918477440, 978956168, 214815492, 222188938, 57718771, 355125201, 14033665, 863728334, 846192280, 688557035, 749912842, 459984068, 8736172, 568452135, 544608530, 646436145, 422976819, 635261378, 217013641, 337838156, 343633758, 157683337, 98633018, 283541694, 487974290, 230025072, 582769843, 185798150, 421658371, 950005936, 444964092, 332512504, 83544129, 110936440, 147897023, 395844250, 656560065, 798670712, 870920514, 874930464, 843904463, 28116004, 694976086, 994093543, 390471688, 390434388, 412935576, 876272796, 951010407, 728083168, 614874517, 569418865, 527227008, 293508816, 762991624, 481979947, 506644394, 50498286, 838546486, 567723408, 594880387, 52687687, 345116712, 713346121, 913442893, 886383290, 528377994, 753500957, 108021178, 669834017, 801370189, 787519704, 483910389, 174490449, 268290955, 894984401, 349411886, 46023491, 259001593, 982443270, 332537719, 580537852, 138751687, 630298003, 492670464, 884965218, 17666331, 18199612, 1850254, 862621513, 945935613, 290298026, 818577422, 809173766, 978963594, 691163527, 504569627, 506672584, 798974597, 467743189, 94031693, 617244214, 142168146, 14704664, 787726840, 630765674, 712690057, 78482497, 719082896, 300148590, 60400766, 214197742, 407970354, 961913196, 219545541, 740454879, 409419876, 750517674, 165288455, 809999632, 517101241, 733337923, 469845127, 230721213, 655707134, 276706667, 892140809, 313431289, 920582547, 731310303, 869001961, 908054085, 818471086, 409376664, 736842217, 890586145, 358464865, 582499706, 793961215, 264510718, 668410664, 407636344, 973395638, 118707103, 396181162, 925700180, 185830852, 826354060, 427453560, 196762246, 977680829, 89105525, 678903090, 864370629, 640437819, 768622250, 598574328, 36070337, 233898875, 434830801, 992612613, 832775914, 239828592, 181714639, 437216668, 756169887, 876939576, 145075481, 546643882, 828047395, 713934654, 139733222, 754707551, 927582117, 263748036, 656722443, 214159139, 658041927, 543062562, 774145118, 172826382, 966963043, 251898274, 499709299, 817014816, 921937014, 148539768, 963606163, 574164355, 49187227, 788370798, 871499987, 322417408, 358329992, 911632798, 701010713, 897301574, 533462538, 345181352, 184094614, 733703829, 277409758, 430748771, 660461406, 395015430, 548954671, 233422313, 705979615, 912921848, 269356400, 227222364, 427593413, 319276117, 784816575, 654492259, 150437757, 514248315, 803726692, 346423597, 589813338, 665302282, 715281384, 25655266, 29021939, 360686967, 263596230, 433263300, 536045065, 654626731, 658940080, 305876605, 769292302, 998187265, 175919720, 415266115, 61280296, 677747220, 730677696, 778071003, 988151206, 62425271, 898466851, 626612124, 982851215, 524050171, 190540635, 911860741, 501453559, 790626986, 80101488, 494641202, 804966450, 161336940, 172715029, 544097015, 36115244, 650087245, 901258219, 228405181, 838160595, 899217153, 444583481, 68712486, 417076491, 125925421, 576567857, 204100111, 158816345, 346516149, 424952607, 727252490, 613165289, 375485506, 362430594, 313372186, 512857948, 442719957, 527009463, 749893458, 363526063, 912265033, 939737267, 615078183, 167613195, 821391453, 219542948, 244209884, 679940074, 550837104, 748854598, 372587866, 67608657, 865972482, 597104200, 993440147, 482918702, 712103578, 179284344, 199204102, 411585956, 936315946, 39217645, 358126227, 467144040, 583834206, 828398491, 960645681, 740175218, 40100901, 615651522, 293108490, 693175026, 824817386, 636653153, 732041826, 670795300, 579438093, 45986134, 31079423, 52284724, 86517929, 844696484, 921147155, 923983671, 45513153, 833538481, 520778337, 722457771, 314307782, 127245330, 783416348, 13192895, 340541586, 386570465, 387048105, 654613425, 780408459, 386882100, 955636423, 786797355, 716408843, 426073479, 364279489, 790921942, 581661790, 910107597, 288498523, 878769328, 614013314, 241899541, 338925123, 220675757, 423101570, 683648914, 4759855, 941518919, 224658876, 70621425, 265942162, 210366304, 421861527, 878829073, 412594026, 821327935, 492131458, 518956902, 692484597, 813518951, 858672412, 936924396, 862799439, 99975106, 249991109, 723962965, 696745513, 181098049, 129711925, 491170049, 435881710, 413758257, 78771589, 113347618, 925401315, 112322295, 297121624, 298266327, 758827769, 976080252, 281326438, 392870520, 152385565, 67580000, 728807347, 43669932, 443414674, 11832934, 458765400, 266052986, 528163894, 126295493, 139776278, 672924827, 754833762, 941803104, 316854192, 674361455, 234020300, 267669597, 984501026, 209823856, 448729498, 558740539, 533090594, 459225336, 605359495, 35106812, 34074060, 336520297, 220804367, 245513416, 115341692, 753069210, 651111115, 216562798, 969660575, 63258085, 619400664, 441523033, 397582286, 575551764, 347716810, 343258533, 238467159, 434048775, 369059893, 425491929, 910719255, 328405743, 521212419, 885166379, 281401522, 454339908, 472457255, 877827319, 365603321, 205862471, 816631702, 210403823, 94325997, 543211366, 36918198, 173985475, 508773272, 629130768, 587862424, 92172393, 414347009, 921650143, 408204081, 309773064, 114648126, 999945813, 555813118, 628693564, 909415562, 27243219, 179255738, 695829966, 853065383, 829484196, 372331780, 142114315, 614459965, 839172567, 692831171, 456183668, 624019813, 841428290, 371358621, 671744576, 479217731, 997266498, 620360749, 562043424, 571808755, 448052556, 855971007, 637377558, 668760349, 106650692, 272640429, 639074249, 724449903, 159001722, 580937938, 798995003, 498986140, 593203251, 589107134, 207019911, 145617965, 333895336, 878881486, 176214356, 56195270, 787871080, 327124773, 188509491, 562273719, 834134493, 956312904, 325166148, 266681917, 968749120, 602584589, 421512580, 529993333, 727164421, 275621545, 258237989, 756018421, 352890038, 289889806, 887410462, 683695136, 738465095, 679028798, 322209112, 620294327, 159968292, 83142916, 806944858, 217107109, 430146713, 385919450, 763468342, 835442850, 832833187, 444688008, 972706288, 986907099, 885600248, 819889329, 961293595, 677229650, 1751903, 51584662, 411575254, 102409515, 517367153, 400054754, 838925821, 533246262, 110194146, 461980322, 720796841, 755077756, 706287792, 90445062, 899197295, 885168474, 196085209, 941785910, 400171933, 70324857, 610034678, 464467051, 419750251, 823852083, 184642211, 265679219, 89796023, 868694342, 636260689, 771497899, 451116738, 776235532, 54888515, 182269999, 889178967, 869401734, 608617398, 731032524, 139760279, 987225626, 740377528, 605237353, 727780994, 150984804, 7285017, 311202579, 96624161, 746462741, 973126643, 775388055, 893651189, 189415045, 542830087, 301974203, 373382749, 364417385, 692432943, 974426501, 126075815, 675989359, 840486300, 92604885, 372394870, 408549069, 378078149, 79737890, 614928000, 520614159, 851718440, 642190660, 867444757, 37430417, 119676825, 723601353, 615352287, 585014422, 736598770, 824310517, 866751135, 685434952, 694052930, 209590202, 855584005, 432977739, 70926232, 100113922, 85958548, 99288728, 921776155, 776247564, 155835614, 956980842, 130434005, 702457912, 24861325, 106754608, 590727851, 710006729, 181051732, 687764977, 642632551, 889895768, 653257504, 932702886, 19995349, 985083615, 801820888, 593711627, 142301400, 558272327, 684646910, 785716422, 534665862, 749757886, 713571780, 728854649, 901392902, 74967144, 503234418, 243414509, 349777296, 179061040, 210085298, 609551936, 787950037, 464954458, 999577141, 303244828, 909088497, 943944072, 464619613, 225585021, 630293432, 947018922, 945498122, 111637026, 690195401, 70189209, 178673806, 685029794, 929461919, 234002390, 645660800, 757206050, 171979617, 566140984, 645507455, 331518291, 946656184, 852693557, 979448618, 493241076, 929708005, 42357044, 44456549, 231286880, 33825415, 253203188, 952963713, 785593887, 842261167, 938278664, 585471283, 238278217, 648586726, 423042431, 574524260, 863490344, 218866034, 447833284, 456911774, 636592175, 468820098, 539195129, 97363179, 796307914, 174090084, 483888240, 344023975, 197200996, 449235116, 285125310, 348554311, 824838721, 422184065, 131654580, 137897965, 212907521, 557483597, 508949363, 506967136, 576665517, 963287724, 268670891, 642951349, 744582169, 613051313, 48034396, 143403862, 838180577, 150425930, 476786885, 480690443, 786610411, 708043534, 653484357, 560855151, 492294, 143248867, 13396361, 205913198, 794286113, 717148333, 65785163, 623172244, 525011686, 334517728, 318697268, 404316196, 155321647, 448069319, 824567208, 238392099, 71073145, 302760733, 758084350, 755255539, 138767017, 755084959, 905553496, 316726905, 21317678, 867865846, 133299116, 421595327, 658518124, 203304330, 906971181, 126150164, 874991206, 675155960, 514362977, 560291771, 259164997, 762184765, 34895039, 930552548, 100055368, 499270837, 775786117, 684760192, 752947165, 842814111, 679294686, 939187990, 237588513, 538168167, 222524663, 204615145, 177217148, 415696622, 342260833, 399415846, 566714463, 283333052, 235755647, 679078433, 843357252, 763086756, 688963596, 661816549, 140925637, 435807258, 51624743, 12674644, 713059256, 11063192, 26817258, 842897010, 933234480, 762650953, 799340734, 916522140, 649435956, 467929421, 22898540, 286444877, 779867904, 81375745, 360090234, 668627352, 958080765, 465074705, 947476600, 152631363, 758482297, 58636619, 52196835, 703765754, 224166339, 934428915, 651805807, 30836387, 407557408, 462360262, 642452009, 498359359, 954476264, 142697787, 54714390, 75871584, 183465939, 882096646, 916450339, 706979554, 867588747, 138051729, 7942470, 657635443, 832748002, 399623652, 658490397, 970398275, 594607264, 202366732, 357166860, 983827644, 494270448, 575111191, 269265800, 552361092, 539958395, 662332803, 690186256, 573509863, 579290018, 185820738, 516010864, 61023598, 866729704, 14350412, 808496030, 555656584, 960665986, 875214298, 522180595, 730697563, 521786552, 678767140, 371299202, 860536916, 872384136, 632372272, 747467367, 818366887, 762263470, 165915725, 961371602, 621694977, 928392160, 6675073, 693441791, 991472068, 821198970, 431556274, 588943683, 142084069, 214632104, 305862659, 563598472, 635550384, 557210208, 771249779, 987461101, 292071978, 995088376, 867609344, 494668655, 225125415, 621352350, 57903545, 30365444, 200359174, 878163757, 35284013, 557009390, 30125852, 255578644, 913725948, 710727204, 18737857, 701397151, 404535976, 810281847, 524915271, 738254444, 46972667, 946568136, 556285625, 772174140, 388695260, 349778042, 890766490, 649971207, 488399819, 571912136, 230670738, 736360577, 439334357, 517108809, 70934493, 513551188, 853825185, 889670822, 114232234, 438039580, 313188414, 878962505, 309480816, 648387013, 567918781, 34496167, 190748141, 794606640, 274416863, 441577725, 843298495, 861751981, 281880542, 637950713, 840728301, 976084615, 862241142, 64175879, 300291453, 521616718, 947101195, 594048550, 72095654, 962829006, 320797272, 698137991, 481433626, 784303959, 443866160, 985527245, 325308043, 947868088, 957284823, 472776698, 45713908, 266845133, 716348066, 682721865, 352161718, 3066812, 193106318, 450058105, 388370286, 357755391, 720474159, 313335797, 669985688, 522856453, 97897107, 88781009, 753024114, 628564487, 58370243, 578090135, 164904613, 132136620, 999428607, 944752848, 64654825, 826605685, 549736113, 86806134, 915917223, 459307796, 514614468, 924695494, 195713260, 570463351, 187397503, 803345268, 689723253, 402722774, 934510594, 945646776, 492544906, 648082681, 706828882, 345169328, 695969655, 548373647, 676626172, 512437096, 117348681, 864334573, 841828006, 971714298, 564159809, 390578020, 401932563, 908418709, 27367107, 941070360, 325475333, 668615149, 962760144, 205378398, 327308523, 361611545, 359101178, 149623386, 57469331, 11611620, 381607066, 699572585, 960032831, 942246363, 885932147, 994370876, 717478549, 891258660, 315717547, 47608210, 768224200, 596061276, 999366446, 525135046, 955098501, 653368886, 178812308, 570807507, 345662192, 905383439, 770750262, 194591400, 613872331, 758837298, 567799595, 803820122, 294290461, 722373745, 199064925, 475775153, 707459891, 369932790, 349775845, 346886767, 936989908, 464253970, 963013556, 251863937, 82135210, 831852973, 348872091, 120370257, 451788186, 695130274, 742857010, 145652753, 419616725, 675386231, 689974324, 987591946, 741764820, 209764, 609026395, 482774477, 981361770, 76039669, 602867261, 841954885, 679527727, 118307418, 267368457, 829612610, 984284132, 594451500, 894062293, 877434070, 330897346, 470370967, 80484641, 577757508, 525942618, 679293754, 689688336, 524903534, 940506543, 372735625, 377072805, 310136042, 175399259, 130243494, 592038159, 49174879, 105523282, 655612408, 67884130, 283466660, 305729474, 345031265, 288497038, 111495872, 408737589, 180138719, 922741430, 527190534, 119587849, 461577939, 657524377, 405169277, 530323767, 55966130, 590156078, 669316504, 778631169, 87381552, 894408731, 785623094, 664983279, 562899087, 199726930, 186086130, 161752118, 666343297, 345967650, 358633531, 738562132, 903324954, 330865056, 437289855, 880311073, 545486348, 797855688, 26366249, 318886601, 493521510, 204824249, 59108517, 11877550, 613716659, 461102686, 730462318, 942724958, 283548752, 493848453, 77071196, 563441005, 81987496, 195068099, 561780671, 311920118, 728043715, 392596891, 686333847, 321683233, 500346301, 42455543, 854654433, 115830694, 980260202, 541859886, 961758262, 179762862, 67717213, 137097738, 478946916, 900336402, 223525822, 41624364, 585925980, 456717741, 548396189, 437886682, 17756309, 102969119, 145415273, 176205669, 992544453, 381053449, 794697914, 907642751, 295710597, 807942330, 162314573, 113709028, 544638371, 454599424, 453607196, 423145288, 705944215, 420368198, 172072519, 34530252, 733335608, 769922190, 675449266, 572611883, 785318963, 172172029, 637724621, 28747201, 37615900, 810251993, 439382245, 80687336, 300740736, 565807374, 8544057, 740384145, 320907531, 830237847, 79845243, 372484726, 627897781, 805200494, 752512083, 795663262, 68268221, 265428604, 978548221, 984328600, 395696543, 396337068, 423080606, 315465944, 634137996, 273360431, 326254238, 893463395, 100586958, 843884543, 349724622, 325365831, 807462581, 578730193, 793481305, 544929845, 285793819, 381197496, 230067314, 98658689, 209499665, 838270932, 53632159, 528506311, 339170364, 334247742, 675222621, 407601580, 845786946, 12524298, 271044579, 763953488, 403492333, 410529497, 698123300, 806360695, 543679687, 444775862, 720561007, 475992080, 695049251, 634908025, 317818334, 80121275, 951210470, 853857806, 809123569, 808113850, 732918785, 599831965, 392948221, 242839751, 239893108, 326758495, 163216352, 246130869, 635718001, 963977934, 438750680, 778662056, 61695418, 340558820, 543688250, 777617632, 366254566, 606706942, 878401583, 44297808, 467738182, 641136715, 20691496, 267573253, 517836479, 819970655, 342904441, 37795897, 112639560, 992968274, 113894543, 415496185, 666750981, 323298208, 106935932, 313079675, 828665106, 564644621, 262200298, 641962656, 961041334, 942419248, 357423213, 39207898, 111402746, 391132529, 157917361, 801254159, 820993338, 596024293, 48982810, 363741284, 965798, 953443514, 799276548, 454406269, 267631107, 602115798, 113914584, 358140218, 359822979, 698925026, 956716823, 457601584, 391186157, 302309513, 762792379, 429548845, 80536703, 434828272, 858624644, 955698418, 457265018, 128155782, 907260428, 212331719, 61507406, 748674099, 524159883, 993576611, 321582353, 378917542, 415042823, 766785234, 294859425, 465396228, 622184662, 28934113, 987635724, 167873436, 755081882, 784225041, 630861185, 722910102, 663313204, 652098439, 336587198, 647519702, 656200733, 590730325, 169471638, 628295310, 589517437, 754112689, 887365741, 894697059, 163610773, 686084689, 526587401, 823238737, 668822058, 900596152, 39241297, 602373626, 972497089, 308607788, 694792669, 986115580, 729065024, 47136479, 203177813, 985803027, 241297552, 259460911, 482389475, 844024133, 561357497, 160943141, 487763517, 362120375, 712415426, 754814377, 244551087, 745507366, 862868785, 127226698, 417726995, 73099690, 170033374, 106256575, 815182203, 25058520, 289031787, 829735770, 844380768, 76475090, 434867359, 974509532, 679253023, 522161291, 250652767, 226843350, 190914171, 191659520, 800701807, 859069605, 911246591, 409402460, 2895710, 473131589, 418382985, 894674697, 840267839, 774451509, 395878484, 693553812, 787701136, 776167479, 347527486, 39683676, 181838384, 179047875, 839149072, 540795216, 222016853, 171788171, 740494186, 299793381, 187906052, 536471941, 672277568, 614095087, 510637984, 859655035, 162687704, 729332442, 545621975, 732538538, 399274583, 57434726, 167951698, 502072687, 423950658, 59799772, 88377062, 249062713, 95520325, 840713974, 686254991, 780065371, 495825227, 827320292, 304883519, 113768778, 211577457, 528218131, 72141764, 764620339, 612399553, 681847101, 189627490, 979214196, 522714496, 231403281, 225814864, 196364133, 159429215, 31127875, 220266779, 612941737, 738923025, 137033709, 738447729, 897968025, 544614634, 989081975, 291566305, 22187998, 764217291, 887478231, 362082326, 711244750, 825360423, 95158020, 342234423, 445539431, 115831325, 390782216, 461055478, 808145794, 103455050, 71831567, 330782523, 469665026, 371704191, 488992247, 161238455, 186716423, 431873124, 457132372, 634723011, 875934984, 708496418, 761129219, 298430180, 59028843, 975364331, 138820157, 690594986, 231166613, 962213584, 20498980, 111245895, 839071478, 738261430, 636718593, 793330034, 222971185, 700989273, 684680963, 492745159, 422577154, 995534570, 442434480, 974735548, 964217304, 403652299, 654165724, 600664394, 707316948, 257622430, 564758851, 284096752, 552582418, 923906164, 654620407, 26512310, 99229737, 983836734, 722897856, 339732250, 853506727, 883590082, 500538922, 403091453, 462299572, 813831027, 845254971, 683174359, 224688873, 323253683, 873143866, 979932464, 137690994, 615243394, 721092892, 258338434, 423748815, 874574959, 334350251, 987321672, 588314486, 761226932, 271045115, 9760290, 773905751, 161236752, 137841537, 333384476, 107232652, 219202932, 932084270, 111248222, 646184419, 116484407, 427476464, 959079529, 350655142, 112756648, 424274200, 656608336, 7344543, 404969966, 922072624, 464326006, 677958509, 957318417, 99779502, 165050934, 867686825, 621647787, 604284162, 494338976, 191489804, 678162755, 233831561, 575080834, 869669228, 259801912, 475366492, 674456572, 25327033, 735665028, 438431342, 779218484, 879243341, 921865118, 147955568, 47967757, 350686749, 807114640, 725603369, 381834798, 552448457, 159869269, 949885795, 344630430, 668427459, 586903189, 944428974, 493138956, 991981666, 974271172, 998509736, 12354803, 551211611, 747433421, 487546933, 256442455, 522690955, 698553146, 625725704, 347075273, 805334553, 782441428, 160688357, 885603733, 65140719, 259187309, 536479536, 850998413, 356247444, 346705691, 719714965, 769303269, 634316686, 265911805, 860066241, 765110321, 373882384, 816905967, 460251983, 139322664, 462477819, 70062823, 648400408, 223850681, 728476265, 819198746, 214628694, 84704714, 510523725, 298267579, 223541283, 72531240, 737233294, 732930107, 906435661, 616247046, 139867357, 968008030, 370115184, 29116614, 154446663, 483836454, 797473285, 162965333, 32506777, 529694829, 80404820, 675332458, 116039449, 244964608, 623730281, 717510358, 113386381, 326820639, 556981864, 873363735, 638973693, 50363294, 119912954, 942088291, 873602352, 557809258, 427999790, 926900763, 338198791, 127053015, 920600378, 165900675, 856226839, 504776244, 620183839, 401324394, 53398215, 488601746, 321985035, 318079825, 383345120, 837516432, 70539661, 938043051, 880565303, 522800677, 724387480, 930166666, 344493856, 815990590, 985891288, 110240513, 841299078, 767609738, 940436704, 571109137, 428416026, 664084273, 919680264, 485741675, 416005474, 155492315, 24867068, 36502275, 891986621, 446911400, 932948187, 852468294, 25314866, 745306980, 796540884, 344523951, 856197029, 434474015, 881945631, 794890461, 114296268, 596106596, 294736659, 249995857, 995680521, 227070569, 527343873, 670806448, 947401426, 543391316, 995404578, 48958703, 580095376, 525002060, 67307220, 203008673, 173163472, 708058745, 670528005, 643669651, 315515231, 831192304, 214138013, 653316420, 154069127, 49205334, 968750562, 580021428, 384464383, 83718634, 845243689, 246028268, 357794946, 982544949, 30002232, 677247901, 660805847, 353353989, 834110946, 132583857, 81944575, 839768786, 129082950, 888913822, 225508481, 932806499, 444820751, 587484953, 707283225, 116870267, 225607673, 93898297, 729506731, 31266616, 825858088, 383135139, 839075882, 214022259, 524539610, 496049317, 352799262, 789758535, 118356748, 390225948, 832275627, 741384640, 523304067, 77720196, 807073402, 380176820, 492150175, 191657472, 158569352, 179484008, 431419958, 647443319, 9980253, 439075489, 293122590, 603141503, 10933107, 314987159, 512057400, 918753425, 603428600, 430823529, 299031786, 984209991, 400122023, 25500324, 839422443, 219114654, 68059027, 632925110, 277814103, 765225014, 952561714, 128731091, 55018752, 464032797, 458565964, 61204402, 461389455, 928705779, 732368784, 384934545, 259564763, 475889587, 287093961, 56852298, 931529435, 783664970, 114445710, 182421604, 651225275, 796094443, 207050060, 174797919, 977395657, 821228210, 623241379, 472005499, 80559147, 923755864, 781432138, 507928559, 138141091, 595737587, 173968146, 700908714, 469544299, 915929154, 465609879, 398238119, 207019429, 382594205, 877566673, 425349305, 932033648, 703905847, 837238241, 919429453, 752039191, 677798299, 534451521, 140587944, 453154907, 324541063, 395926093, 421922159, 868007657, 837109490, 333181946, 381737458, 770879541, 144894358, 389860964, 634675382, 76061274, 421492718, 773391086, 645720844, 710725725, 224366468, 764741186, 32824306, 471988441, 359572042, 719311187, 633016983, 650379703, 695781137, 854578213, 265020912, 144957779, 384377617, 719459838, 436437357, 714845360, 92347547, 334466, 596631119, 393901054, 967185435, 85166269, 364447878, 770860732, 322687068, 263539535, 51757620, 222205363, 337471782, 226043191, 908694822, 585145558, 123922692, 433896359, 652710875, 810923127, 954522949, 739081021, 407346506, 44577429, 761632275, 819681922, 213788269, 138523071, 569442733, 603702620, 679164683, 156243916, 992912166, 400047074, 24962107, 993203762, 725572139, 351096801, 101868231, 922587830, 294063286, 811576802, 396608415, 177025111, 873827912, 90973637, 62345763, 625537135, 447741622, 26787110, 460661622, 832990394, 425828130, 141633119, 899825300, 170553927, 913707186, 876708304, 115144887, 364732675, 549141997, 206847871, 760936615, 568709851, 310912000, 793924502, 541955965, 585792080, 141831604, 474257487, 731248629, 277100387, 18599991, 225609129, 294204649, 898339538, 564744265, 236736987, 437124663, 975068147, 216868251, 245626247, 334610073, 591315708, 752811765, 129959540, 479325653, 993034953, 578356719, 400766932, 693878458, 84039906, 164521815, 106546955, 990277192, 272405946, 609083968, 445911080, 211346159, 510164847, 561240763, 869873798, 996559770, 8139799, 984664524, 536218926, 204273774, 215692295, 475297533, 869673510, 57383470, 325082785, 672320447, 972192283, 480071102, 988891046, 512748905, 734083155, 976532094, 651733076, 349940342, 66451928, 157308460, 702153927, 519212320, 976827092, 598309427, 635154229, 960972827, 242610777, 686362190, 904811518, 616678741, 29242748, 801506986, 650502240, 939916222, 809996916, 66564878, 627498831, 912245487, 617683515, 130213985, 260194098, 226096929, 850584939, 627481424, 673550955, 629587341, 269806145, 848029557, 201728477, 340050404, 167466188, 820691298, 761878127, 224614227, 233849104, 844919096, 470855558, 744910936, 779400909, 166380655, 904530757, 322460978, 153305703, 71539048, 347307922, 845189027, 35922515, 639324095, 696997581, 149988194, 513966520, 595453000, 619394299, 530817578, 623530356, 489279780, 753114330, 756904586, 356481409, 10906278, 865209073, 503202502, 839910797, 246283332, 608783053, 403118419, 212506811, 467023242, 593745595, 861019771, 593648482, 35869262, 122847597, 255116457, 854063489, 547247872, 210987559, 595956576, 742781487, 398651085, 787789583, 817130142, 967621987, 851268632, 158333008, 495009174, 389953953, 913396639, 66374591, 27781112, 392782327, 350675299, 393819630, 573825442, 165974023, 275568478, 713409336, 170827084, 930915340, 246794868, 634357051, 605980516, 548661321, 616264246, 9023235, 469920265, 39376162, 324412061, 286855141, 637200436, 972131196, 247260496, 960216370, 912880377, 434999832, 441040924, 993566617, 570179851, 359813890, 11287837, 706322858, 489865184, 200598341, 78510105, 145963951, 927458910, 891015769, 778274178, 137684931, 130894541, 818173, 889187991, 300811316, 116911225, 458621986, 507246345, 769322614, 771266402, 679255079, 369093353, 714669633, 166483797, 645893109, 553744137, 329636517, 642948792, 260993612, 879432078, 14822397, 502528672, 485869033, 849084650, 302179909, 294693138, 127916508, 113240906, 67422954, 599755407, 447019261, 711299566, 448712591, 342652408, 709067927, 376847975, 574468759, 33132385, 712055456, 373302121, 383703233, 163397872, 378239094, 402572132, 484732024, 741447613, 481933733, 546750982, 784966522, 555515653, 232976661, 630093605, 109657230, 99489543, 145264207, 132386222, 956633182, 793948751, 774599128, 405213190, 512595844, 784233099, 305336991, 260801809, 718869904, 444067715, 574179959, 245138965, 195232509, 776289602, 3436084, 523078254, 460679318, 272407971, 639935240, 967069030, 294569804, 840245432, 217146142, 363820843, 76070551, 664692616, 664813205, 481095258, 719713445, 387836194, 514703180, 331552413, 871203413, 131542095, 129749527, 593028587, 222994373, 828890381, 991190180, 99733511, 811624044, 977364499, 510856918, 141806706, 433486318, 224784146, 573435367, 584615452, 162906992, 259502454, 659268477, 308481009, 445729240, 44940037, 397338754, 955172633, 825024626, 793122706, 825464061, 494399652, 877063499, 274308298, 380032215, 88320581, 733451222, 716370982, 605240966, 992538942, 290312026, 226240457, 564433497, 125763151, 755684643, 350048139, 494381794, 640923691, 170592214, 205775695, 629283737, 940545, 530592003, 338460503, 138931061, 75847999, 159489951, 141088268, 755037317, 721088314, 133685813, 646657444, 916655959, 287901726, 534624663, 140794916, 347427477, 556451813, 973991679, 274197222, 532760673, 27244321, 970526488, 137934560, 955968350, 687298939, 110001234, 485339499, 996406445, 423770174, 248995852, 867974992, 221378501, 139890797, 290118774, 65292352, 679505832, 823345483, 312654059, 79199416, 399592412, 749529654, 371147984, 933114400, 782903040, 289940994, 495025662, 452150564, 68855909, 955540515, 910386960, 771126234, 129634650, 660859941, 879625832, 743029445, 353337336, 529847928, 720744496, 785485982, 196526714, 36953478, 785123986, 7073111, 699120660, 683045516, 281806329, 418292585, 398533014, 997287517, 170696992, 876381703, 858983589, 117105645, 474357604, 752571373, 706458543, 519353146, 625685557, 756548837, 782351311, 236165342, 530355748, 730460866, 586930095, 600580284, 927936256, 728741627, 222500780, 482766498, 799571643, 951135345, 695478322, 854268265, 140912106, 901770405, 926415046, 949206843, 347570614, 114704111, 217761453, 298983150, 725803616, 121740714, 80832430, 497603120, 267093935, 49075741, 709688326, 626185338, 109337285, 319795942, 267922669, 304431036, 516155877, 142804521, 161268974, 273004386, 80029908, 340568239, 462307866, 9724180, 565604160, 56873912, 507493462, 297839927, 81047903, 239603093, 735177317, 972437025, 785640938, 964591148, 11416490, 664998976, 72476435, 695460148, 306048015, 986411100, 483642422, 398197675, 361997423, 264851027, 759235345, 45309975, 851585068, 126476984, 668776570, 996417554, 412709413, 777234840, 547607554, 705943884, 178725617, 180796704, 71595686, 750482920, 669449362, 360833692, 968286431, 845888117, 409983963, 570770285, 925389140, 525800106, 234889568, 724440728, 475901400, 346914652, 852529708, 982076427, 997428981, 137851869, 824453498, 5974051, 285980603, 893875945, 357423291, 902818898, 726516833, 115090715, 804477004, 108452692, 812975797, 756210782, 782479344, 938882963, 966275435, 185641345, 398235121, 959530675, 420077094, 465298624, 412946992, 806997299, 556504826, 137110669, 831211529, 797095181, 255659970, 185622005, 795220290, 257966099, 494639558, 645169637, 762434446, 121432508, 269623186, 157418360, 888059383, 129330744, 260831737, 791212507, 603014781, 131564819, 698010753, 153826, 774847240, 582438526, 405522126, 194064521, 772557353, 728477826, 128933066, 582470766, 569993049, 510129270, 43612109, 559814552, 266202379, 461651281, 577399848, 689252324, 90935698, 269881232, 133555996, 637903022, 3591900, 980127832, 547967379, 819296139, 695879581, 396191560, 706416772, 159320827, 115517685, 708086103, 104245548, 661719008, 802440870, 362810499, 827684236, 861671134, 18413407, 300549796, 458553154, 897935673, 335935016, 42162566, 86297264, 939945413, 742972491, 647573564, 94418482, 498904194, 646277701, 704551093, 10792680, 988972111, 57613309, 956650591, 85311080, 133658694, 130036219, 210023331, 92049493, 563811341, 258919463, 331762469, 293462228, 364951244, 823931821, 526631248, 44179980, 38896430, 210604714, 423455390, 970551915, 805529018, 173998855, 199608524, 159888455, 115893453, 688034669, 494278918, 928098092, 237685034, 315591672, 152855983, 538873229, 340475888, 704948521, 811239228, 96867020, 930375863, 392849913, 142190471, 187532423, 851921220, 586681380, 218171480, 124029339, 497588578, 621894996, 622841736, 488583599, 659306179, 931848687, 87988138, 207085895, 129048343, 115271887, 817213190, 600334391, 831028932, 607291634, 593000859, 795258183, 816164976, 839895370, 12684212, 902885052, 953731121, 213850637, 69965923, 804257152, 957053781, 313225020, 259193606, 17201787, 431922953, 427926984, 139803619, 518360716, 276076155, 288747004, 38161067, 100777182, 943063142, 237348275, 903619581, 815504458, 990088102, 45668579, 471913036, 519333018, 905904946, 326088413, 587614394, 644997772, 332598861, 362908617, 831084933, 982637361, 726620232, 427157943, 561692638, 391580666, 969864727, 26144438, 774826556, 630452564, 547392769, 299759298, 764803860, 162163538, 773810101, 776055377, 695714117, 248639234, 65906117, 621547376, 23203154, 322921733, 982870418, 785346797, 361925859, 514129091, 317356270, 976280926, 70470760, 229201335, 355706668, 596429855, 934187503, 133976423, 989551779, 79592831, 872049150, 969611724, 956339582, 169307732, 11886293, 749960715, 764399282, 77188616, 430784144, 837380454, 291716946, 741741604, 955933950, 238689605, 596010417, 494667366, 508911751, 807821001, 465180674, 338844272, 370035945, 517225301, 370026158, 122106117, 167759546, 413509407, 676082802, 250007186, 570476063, 937176351, 377522789, 739478051, 651879559, 644622284, 254946659, 299846761, 108796844, 539565571, 213882611, 771280563, 832617875, 673681035, 1369073, 996588142, 479157609, 650088162, 741978892, 371324153, 53298390, 403479093, 250611686, 335110933, 527574605, 140430891, 910803009, 250841457, 341479240, 563112892, 692690204, 701025567, 830225155, 505277884, 583159346, 418065838, 414678828, 599231207, 663112412, 280651636, 328916806, 630558702, 3384421, 71186900, 181986433, 327046689, 319826973, 529136935, 503698032, 536751907, 456715952, 382056423, 718123807, 147005360, 327071971, 332334265, 538638220, 477905813, 386129925, 273942469, 217965127, 978081212, 149976922, 888586177, 322958377, 199215625, 474988251, 969057674, 231914171, 876937740, 275980478, 250529644, 220438613, 730903123, 306200417, 380866922, 2358134, 847735053, 230304374, 519594719, 659358162, 835612476, 399153776, 281495075, 142639694, 41712896, 237201968, 442072673, 216361196, 7184235, 384031158, 795317441, 817244293, 533109318, 215941149, 42805378, 199303182, 531795730, 55497964, 52601204, 455329906, 538007142, 364723098, 51563585, 988124439, 455509465, 144975437, 287066141, 140205041, 284320908, 629832139, 780427027, 853074695, 854012530, 212288064, 596756493, 741311223, 750233707, 379317056, 498640495, 131634018, 181083504, 427833974, 761611103, 801192462, 578827798, 198673109, 197524947, 341919116, 206059380, 611696381, 442149980, 973825909, 441584214, 921384359, 705495820, 523066126, 139262915, 526868470, 972197435, 413059090, 739387567, 860842695, 913077652, 965485852, 780755387, 847616372, 962201443, 708498073, 665082079, 158759777, 502181704, 274031471, 224474382, 759669264, 116728569, 865151326, 607291193, 690293861, 415515297, 823442252, 390067815, 102562873, 843702770, 740155330, 28266473, 500136920, 15646102, 173254807, 890033451, 650003318, 514640390, 437741032, 285804345, 533245604, 823557272, 362541714, 182596589, 627811250, 718955863, 600324858, 403007079, 997495097, 658185692, 605388888, 631383623, 136517397, 175964956, 288488867, 87400554, 950691332, 624046375, 447418593, 995209761, 915184749, 953496612, 135746255, 12590558, 720278181, 891437500, 353968137, 107083388, 63769610, 863412368, 344006592, 246317008, 138437368, 282482510, 329269398, 716155282, 844654917, 887331441, 626585517, 776153964, 865748626, 98111489, 112858207, 852850664, 777271997, 791209100, 630376507, 311280660, 739865326, 639640301, 369877151, 767917224, 953685360, 519414092, 961910868, 860212515, 712092618, 164680029, 858661733, 498611191, 642951080, 742932687, 968624799, 528313278, 209987041, 375577127, 664995916, 680198608, 513542736, 447882032, 886373040, 375278682, 736994905, 979678960, 205775468, 367607857, 640483297, 83351504, 315594459, 920549648, 193711658, 555618722, 182308093, 772583573, 686953648, 600910545, 200892903, 312984563, 111115947, 729038123, 589502183, 259066031, 458857404, 142674304, 555727164, 12995237, 186519366, 746601011, 604658331, 4175185, 940490624, 869966994, 199073092, 569274701, 775916750, 531793093, 917961611, 188934658, 161218420, 386655464, 354905589, 357809496, 450316119, 251924449, 899024055, 403428748, 396301453, 949008223, 514193803, 527819429, 920513958, 943910264, 917106386, 242699726, 618015298, 285604788, 842018209, 602635705, 924630533, 263812483, 880836158, 300442380, 421672445, 740110239, 489251006, 762515731, 652060424, 960866930, 792837571, 650983820, 660721833, 495511470, 991488417, 542960469, 616164553, 818229375, 265757307, 996485408, 51575249, 725743201, 368041141, 752530413, 969575022, 446791792, 881232779, 936785487, 235507420, 845430768, 623795986, 137143359, 174380004, 377985638, 669547200, 286793324, 883958947, 778546217, 89231636, 526773228, 256261299, 648484175, 724162132, 484057709, 497063895, 918699486, 934807862, 16500587, 304336038, 266334967, 388390597, 561788078, 577116728, 394180415, 489340534, 521091308, 964620113, 234810907, 704747381, 917727493, 118015444, 583368739, 341464399, 39496131, 78690303, 177850761, 994483069, 945145059, 148808502, 80797653, 325134815, 716277816, 270866183, 107893226, 882379399, 889418010, 646798234, 119360257, 967390581, 486245014, 102761557, 571760802, 985815204, 885120349, 534968122, 404233962, 438200778, 695370160, 649181014, 154726804, 838525156, 206363150, 761743040, 919812457, 56367928, 302054181, 808290920, 473398630, 667381115, 804788767, 861892446, 112171387, 932290092, 616146169, 315144680, 147366927, 896472955, 559088928, 161201093, 845422329, 303715871, 350937090, 177891932, 744957911, 969394957, 648332113, 138038232, 146681079, 495682536, 976187890, 977379943, 117839740, 586613711, 829704852, 777557384, 582731313, 276791116, 257587735, 218809355, 787183174, 281101708, 790683188, 759486635, 614349894, 170032496, 501662327, 621193441, 591750012, 373560827, 92348645, 836235107, 473193133, 752044567, 248287911, 20166266, 648216997, 508502910, 382433086, 73621002, 527968019, 477234245, 60404339, 727102659, 521303705, 672414037, 956549687, 404911390, 236011044, 148397835, 251051614, 362471413, 790522687, 863978818, 265546579, 822254501, 701926683, 677536472, 532517177, 485621596, 322585280, 42083317, 230971041, 42886353, 669896694, 676597046, 855477837, 824583329, 170971790, 398032985, 740595447, 152568406, 336834433, 66472965, 568883701, 516199692, 814011925, 527882913, 646378605, 548187478, 196287579, 781437513, 110295209, 758091632, 582706315, 830365442, 624607556, 164076373, 458485561, 367985656, 862555879, 166209731, 712605386, 322053687, 947150510, 503246912, 979762578, 302454591, 391447562, 841007658, 423055957, 470766870, 194767137, 156786946, 4449157, 610650076, 735304825, 881537323, 196695988, 125251173, 539773201, 265602859, 281464401, 109766001, 756271176, 471292794, 907770667, 871522573, 585396243, 635911938, 178122378, 101672715, 315250164, 17999428, 29745930, 220371534, 610225433, 670593561, 877282262, 889701627, 818158103, 228466208, 779698109, 170664718, 622435713, 981341094, 640632256, 687233728, 394864183, 596775456, 514989872, 925421342, 862525585, 561811030, 218789063, 947343286, 184426024, 477125902, 73094834, 218890654, 516172662, 79547598, 547669633, 58281471, 157797764, 541363276, 962562190, 304700408, 961323984, 928144003, 66129150, 906867682, 749673055, 905950585, 595427194, 71783837, 939246005, 24199275, 25165048, 893201640, 546233450, 778381616, 240106252, 276470824, 249686426, 757539566, 940423693, 528680155, 476508554, 398126338, 386774251, 786138376, 421402271, 972495436, 33580282, 376835012, 700109162, 674192341, 161889124, 573143837, 193246100, 300065220, 411338423, 490653085, 994226049, 813382967, 343509784, 48826667, 31248075, 389906817, 498807067, 410841394, 741131553, 836610799, 10245102, 140605052, 512186263, 770576920, 469171337, 928329032, 885778101, 6953405, 324062624, 149426607, 643685442, 802574639, 398591623, 346447279, 424409807, 158853544, 424527280, 798503496, 360509480, 187441523, 39654856, 772263783, 896752979, 636615719, 878127237, 266961616, 513864948, 272944663, 764634123, 389209995, 844111493, 107415607, 432577988, 875429362, 747904022, 305742080, 657177437, 409323505, 824483919, 838068962, 136755597, 906669627, 30123011, 852487720, 61452768, 832808752, 844289551, 221747146, 82294768, 514709421, 640160547, 26204110, 176628113, 329369042, 329002, 235604171, 194652078, 852378113, 450418456, 984129865, 768118777, 132350130, 526013640, 402002547, 377840736, 74345293, 847425797, 76879767, 641996192, 482964688, 594178786, 4110521, 901401519, 851193703, 518093369, 398967016, 4127337, 268786707, 545414918, 330466396, 901503283, 289335197, 642875006, 129599450, 62199908, 867736413, 9527050, 17132486, 74958511, 689099460, 421400523, 60804740, 220685518, 488320893, 355363982, 988334512, 101182407, 994415476, 706540318, 668492144, 326326308, 509381196, 106689912, 270012750, 584946969, 985925816, 806149339, 103865433, 284105914, 367587528, 565138408, 486463042, 516846455, 675742862, 23826481, 731739506, 683260240, 847350705, 95655839, 103256977, 873688546, 59112311, 836341314, 668563023, 607392394, 488480222, 986134723, 232360079, 700821243, 420259918, 180274340, 537594947, 797667044, 630191490, 823648921, 11560056, 221753345, 927260692, 173000542, 943842177, 202098008, 544690063, 610142221, 485506402, 376540915, 426472196, 990521101, 635414318, 40473524, 934940665, 626463249, 942566438, 51805593, 870608739, 750895055, 642452770, 543793183, 1439559, 53474361, 672093391, 598494367, 23085741, 482965959, 486938185, 498733946, 496552870, 205004365, 94274522, 513880574, 729236531, 541377342, 826130406, 441731996, 95299450, 769374903, 249039314, 672648967, 773519880, 693681734, 792789200, 484830582, 225340296, 571065711, 253799473, 861307742, 716829907, 816856955, 201626759, 682249889, 731621778, 613997015, 430716617, 917471428, 198431457, 807464152, 51452056, 862265074, 711588979, 370822658, 119808966, 582521918, 695707505, 89552272, 695180038, 745463684, 985529043, 445975214, 611916657, 679376225, 265203539, 6915063, 442596953, 769315495, 567363787, 630999417, 524361345, 723372854, 892527307, 222893702, 700812399, 352835535, 841602532, 624807958, 172562428, 244590009, 478005955, 393107820, 419960342, 76644971, 609914934, 240451785, 88611857, 726822035, 545657729, 28976483, 390004482, 242459603, 139185290, 43713517, 814189805, 865134372, 602700895, 575808611, 389696353, 97630926, 262847881, 719109448, 751828641, 936030473, 364990919, 776492590, 26877497, 681581481, 298808639, 248649756, 835462357, 432334555, 752966759, 54817433, 925125619, 534675978, 379015465, 149653034, 964870777, 125732944, 514896471, 82825560, 837864760, 422717596, 351183953, 464109268, 878412683, 120778303, 53890524, 935841507, 720946539, 312426899, 64678508, 853983580, 525068746, 777570782, 141988708, 819800720, 727013810, 860194647, 13301837, 723418549, 393720178, 181205646, 182607266, 969327343, 132136681, 336555585, 17505213, 116782046, 759744626, 501088298, 590533499, 470997438, 968207079, 919514010, 771511297, 50582293, 603365664, 893090577, 551640671, 313975202, 407347457, 199587689, 280448758, 741343902, 267223739, 626347930, 743417949, 165953194, 733579009, 3501322, 213908860, 657916748, 281604568, 938925906, 865912439, 852192740, 268906859, 203537585, 233814080, 858416703, 36965273, 866495922, 189983086, 101229992, 713479048, 243773837, 94874689, 765627146, 813801245, 87389782, 440690804, 290418924, 58471384, 353849605, 116360545, 391364864, 621801347, 148355661, 41610322, 681113157, 191633241, 560336152, 146864877, 590348838, 547866649, 912171986, 764667523, 687428289, 525488451, 380402348, 647680594, 113774915, 138230425, 350411921, 691630181, 605319907, 575642736, 159127566, 842821796, 920329277, 776699578, 607190427, 70010014, 770756603, 764176281, 67221545, 862748216, 730513087, 240820573, 194554878, 787813296, 743491335, 828693706, 918497407, 601881535, 598019726, 288163640, 323957602, 489283669, 50147966, 347001780, 916846244, 280137139, 793252715, 972192906, 389708028, 147556370, 204610672, 828063835, 333172173, 267499754, 497839695, 686175659, 480805858, 52008401, 199479796, 640314600, 230207642, 317516735, 552348857, 447195081, 126633219, 919946716, 762569608, 468383739, 199848757, 88001456, 429413982, 170393732, 91576933, 446437556, 79507802, 383497736, 807281287, 980431423, 686953020, 590644041, 248871080, 774853820, 227262513, 971840175, 336286104, 934600333, 594131574, 878194787, 774403065, 388883668, 520959494, 333478083, 385362861, 155428744, 58370923, 91043293, 422866249, 333175762, 192750067, 34221946, 991857741, 55334700, 869989895, 991731788, 660659745, 611020754, 975370765, 344021843, 35107255, 788450783, 491337337, 766261174, 429768673, 414692101, 247446362, 440321770, 246494526, 233772303, 776506641, 701946409, 114749470, 31834697, 826818285, 442458450, 668039923, 885363961, 17680527, 763346557, 855565296, 738463981, 720400059, 142615713, 821648825, 498856762, 441885502, 832356926, 813217021, 655765573, 228455083, 729535331, 415772928, 701731853, 291055503, 735436120, 360281581, 124029356, 848433773, 630576232, 24437730, 733508435, 552861119, 951841645, 39221172, 620676232, 277641664, 544290853, 942886990, 910442340, 589662942, 499675774, 833499185, 149222153, 94749765, 962970996, 538950094, 583614649, 869434576, 337337029, 53564984, 876218311, 168093792, 829978349, 548033207, 242302398, 997134522, 610745810, 84267965, 924661810, 997022589, 683148147, 780795740, 313050437, 348479896, 956568446, 857015037, 124061070, 517338083, 938759437, 362183034, 784971999, 658162129, 576350385, 481216590, 732508910, 769658964, 659046274, 786184898, 517749307, 998016562, 852576444, 366326996, 2543634, 130836156, 780134004, 115677055, 11036906, 243537800, 134239262, 649834534, 931355914, 765883632, 289977239, 65655104, 843108201, 758717926, 880500955, 184844469, 918589697, 605721569, 418289580, 310224917, 296684107, 505834413, 380357442, 120075251, 382266636, 917601649, 759720721, 719789894, 80981072, 341973519, 571012199, 964510362, 963830273, 588531863, 310087728, 386388852, 358896704, 698198297, 116438818, 212377313, 575769824, 35446229, 896151832, 195780260, 759756316, 80846548, 552251370, 172024195, 546677865, 949246754, 700995755, 355264618, 749670917, 478202135, 619770563, 331630594, 817425829, 371966205, 181265606, 312967460, 141892100, 837346709, 68622483, 752457434, 642187253, 638276904, 403143266, 833129826, 594542083, 395881429, 447285827, 403413474, 964207863, 221383512, 208932188, 618791345, 608990100, 336413624, 670010442, 793911500, 15588838, 444061962, 563664033, 285104192, 426949105, 21040836, 278624633, 401900636, 8016621, 592551247, 309514306, 637362741, 392916218, 314542142, 419677158, 231074224, 942560731, 263826614, 854364500, 475692329, 893804823, 5905918, 195335155, 306995636, 225769671, 561901477, 891796598, 594882429, 443967531, 581346535, 196031806, 219236703, 848605426, 574223982, 192500455, 338787612, 704026878, 139829233, 2396122, 711243593, 234866472, 556095051, 935687031, 263904822, 587014891, 353482121, 696447120, 351848128, 645253864, 681368338, 439890641, 400050317, 285883219, 469707458, 411997015, 716316554, 796061073, 420344800, 201183327, 214260524, 878624172, 529392712, 150283815, 788195530, 607615548, 342715552, 306274551, 588628528, 22878765, 14518669, 775898964, 770597940, 894199423, 40495727, 765015460, 538202922, 224489024, 633480399, 644488037, 945631662, 896480865, 39212536, 668574134, 668135972, 755691856, 922797129, 454869576, 320763446, 752416687, 615245465, 24121668, 716532571, 879317366, 668922504, 104103129, 286057137, 21807333, 111385570, 841259266, 797794252, 199113607, 312481287, 932514339, 145313517, 301085314, 102063352, 62950865, 1606428, 104339560, 871453339, 184485494, 77034243, 56778480, 812701132, 55546583, 89738615, 734003059, 345085425, 981269466, 607197463, 463933727, 482640879, 663982436, 263750726, 829119363, 109578102, 468090216, 704566530, 198801639, 611869654, 371614255, 946776853, 417418529, 521237989, 437305200, 523548125, 258480782, 378182663, 776977233, 347636625, 266654158, 986659393, 157386550, 948181081, 586071764, 956308138, 260296256, 977165764, 467012336, 628941750, 860328937, 848984527, 426434503, 532772133, 903970307, 326222863, 162662774, 586278830, 567360338, 735612263, 76209663, 424894499, 836819826, 139479153, 791387554, 736252217, 233718408, 583994006, 125862762, 295021202, 420030327, 752427538, 413785394, 350385602, 127943380, 538774448, 223433346, 568527951, 134024991, 892889162, 563554745, 138597777, 852609992, 182733528, 958114440, 117793837, 767031619, 136882457, 482100699, 753207508, 295376644, 947667895, 821008049, 374429588, 767857250, 612578617, 541394622, 559800539, 158341977, 479855742, 598756665, 710920409, 484933244, 537634277, 259547308, 518590904, 525015436, 274747760, 300376750, 576243820, 714927930, 944467414, 241592281, 16721070, 612691731, 569284177, 526891665, 62941518, 963202862, 197243884, 102612903, 616828248, 217225918, 404407769, 28003917, 42783521, 469832439, 360316315, 411078277, 896356328, 236151665, 913933849, 321342942, 158696138, 430282331, 626900303, 605878020, 894127777, 748619728, 323823594, 800973609, 208049208, 813451663, 813113413, 2710, 943044544, 709328271, 885441563, 938509686, 508987644, 827309446, 493837909, 844219484, 925713296, 594164796, 676691055, 105033545, 649455870, 173261184, 375378, 933090663, 24827900, 450987254, 353049104, 939470500, 99301790, 702383115, 299582951, 191530978, 162377780, 540633224, 94091018, 837730184, 148023153, 503652556, 713707690, 918357379, 99359749, 275853723, 110460558, 254226043, 855497672, 775789116, 729279934, 554151011, 218479347, 477084977, 603200632, 868698357, 446100347, 867535323, 761775372, 292283328, 176526348, 368766677, 300833760, 267250974, 883415956, 938461731, 913764543, 940026978, 154808497, 105125645, 682379729, 171493413, 940810360, 367632407, 541494425, 410930906, 496383783, 809463362, 11647881, 352579372, 944079824, 122656701, 210976380, 53760842, 214980596, 660040085, 612297291, 780755782, 604690189, 450363453, 559450863, 484254733, 385839676, 861149776, 812119737, 963614802, 173503082, 992375571, 481364593, 846654937, 27266292, 425365987, 669164893, 676363606, 64899264, 644693609, 789362964, 263606336, 910559860, 98080359, 957525073, 594815860, 387563448, 250097662, 213977382, 834493046, 820736366, 80562243, 389935779, 328797594, 864399894, 936949930, 224790193, 202508061, 796559210, 378884553, 900600784, 627137231, 857668393, 126456403, 290682765, 144430214, 530073997, 344616626, 367356548, 383522091, 402259928, 966324435, 613515353, 68258215, 808962324, 276404331, 917857567, 883982022, 360755761, 13011957, 294994852, 726835371, 332638841, 667221827, 501764579, 393531998, 352259896, 306412455, 625762180, 885995278, 635068438, 256588091, 923132823, 37535006, 317901161, 800789826, 506447550, 19972838, 487066518, 332766651, 338813541, 924571133, 608265886, 998462769, 478335319, 671140921, 668123607, 106862264, 947140227, 521525303, 774463611, 84473172, 74213784, 181720308, 121827022, 206395590, 886864125, 705519295, 224278964, 457408207, 773004752, 196729924, 215481219, 943208159, 171473926, 128598608, 604136967, 394920377, 825266923, 675129511, 145724236, 980505605, 896125195, 364234177, 880570729, 672047677, 850791313, 604182390, 637045335, 614496363, 776116662, 800037791, 455229436, 508943136, 95336466, 965174073, 783869182, 880753792, 697845019, 259013066, 120961067, 84614801, 889406852, 637453014, 93574659, 133370387, 585540650, 438062682, 184596199, 471655817, 115687818, 335426297, 97194715, 308477878, 901567154, 968935537, 343079586, 231404243, 452674534, 433231090, 607699130, 799647533, 892412162, 955816152, 766632778, 250300111, 554523432, 294318298, 673790884, 934356804, 900942887, 402043989, 70619615, 218402973, 319527698, 479730296, 595232548, 952958189, 24008450, 649068775, 8984854, 520219559, 361595237, 268878798, 246365551, 560565020, 884936078, 761771623, 852745937, 826519838, 851357399, 413892000, 674675475, 897152918, 201871489, 796209798, 557089504, 439358273, 583875127, 835021666, 687690228, 968735805, 791946158, 707899580, 223270298, 687398618, 362321361, 922715118, 879151354, 60932340, 590658102, 632289574, 767161052, 612731477, 996841452, 389026489, 596323895, 197895575, 535335072, 540605172, 40718996, 802658280, 994741452, 940230499, 672549983, 943938400, 402421644, 281260703, 710505579, 847129070, 13936152, 299954468, 993819608, 905113847, 913265619, 664122310, 295923439, 561124152, 763384596, 37534547, 657585397, 436665625, 175407622, 481678153, 602601620, 543689812, 15950542, 419322861, 815714706, 574822415, 161603059, 399194942, 839244057, 846611460, 234706529, 579448905, 998200515, 716289694, 124022009, 950740361, 986439575, 552225735, 199412537, 129767461, 724003590, 156986081, 338543524, 723586900, 978814487, 672878137, 109538007, 888244746, 855080102, 777870862, 198589453, 248552024, 349122007, 939842524, 411782261, 110789577, 753985309, 839992034, 588971875, 322571571, 871314795, 144767042, 687841289, 893158924, 821313913, 496689746, 336132646, 669728042, 3265679, 746398868, 438756527, 51834616, 284935812, 76618445, 982529068, 852147742, 222147842, 390546598, 841603242, 535780437, 297977875, 734525982, 9358484, 784940973, 154937339, 563456714, 313306476, 515219875, 167753221, 915383898, 185962487, 156126447, 138279592, 587954231, 952066704, 506483635, 918154416, 106624374, 366503276, 906433809, 575786379, 737828182, 753659077, 116704407, 95792908, 100907326, 485865637, 197327345, 769894068, 359729491, 211186360, 774346086, 235669682, 986644644, 862355802, 655110936, 867641804, 391190550, 668606407, 694236473, 933547017, 906918454, 606937553, 418761593, 581163728, 15692976, 184304468, 539977265, 99187864, 487804003, 58811735, 560743009, 467404033, 41767092, 32161502, 184755023, 647086515, 642055123, 192849409, 766973094, 105731402, 150951907, 335132752, 87023470, 148753086, 27359358, 938821607, 708989749, 903743715, 377733047, 815340757, 329490397, 16522139, 866118821, 684315393, 608721622, 372718422, 765136567, 413020670, 298888617, 566188676, 93037172, 909086106, 101590080, 772957768, 868600959, 991877577, 220449604, 161223500, 133662846, 930483261, 516056791, 417819643, 866827570, 425140099, 678722374, 906660623, 21838298, 298016331, 48551181, 220180430, 794329620, 35996221, 627917716, 371990347, 931448475, 450094487, 637319175, 108180004, 215840944, 158673281, 665100497, 268738125, 649191641, 532538877, 46032875, 472017226, 387228588, 266636376, 520757205, 583641077, 209394206, 571776481, 361347409, 882308492, 17389530, 753173910, 960859398, 970288890, 417542029, 15384929, 502712282, 883637010, 147072839, 495323529, 530487301, 476413981, 206881742, 67354869, 405518035, 623735451, 408342676, 994776551, 170886886, 735382010, 706126167, 33373557, 645187962, 800287605, 311857993, 900974526, 381194287, 626427295, 355820660, 20452111, 427021039, 459148279, 458063832, 328203441, 2051144, 450904745, 152381321, 60271372, 94782013, 728811472, 176507744, 34412779, 227064514, 159925741, 147319564, 919777168, 75858375, 284130663, 110046378, 475750060, 152056533, 438571477, 166860781, 528728072, 927270384, 370012663, 100781794, 520726354, 815998997, 294040693, 14025567, 400611543, 82556784, 204559931, 681679686, 673964731, 770682225, 548800871, 176281614, 136996681, 766471914, 906739590, 317627107, 14043257, 433569170, 264696555, 373329371, 506652027, 9649076, 27246040, 507102836, 508288226, 387031872, 756741504, 464197975, 613712543, 928964474, 130817421, 774543424, 660203568, 682593817, 590618587, 758565894, 629505867, 731354029, 958839492, 249694421, 655268908, 581226427, 226614771, 601897229, 763307241, 821801486, 75967642, 409631256, 235357873, 571102948, 507281543, 595674248, 926273118, 572166703, 280818592, 645831983, 937994066, 493746427, 943147937, 466290904, 827628067, 717779638, 319306592, 207351634, 600623510, 670965971, 254651117, 653857053, 97701405, 295202779, 697626848, 77356581, 441757553, 814659258, 299936983, 5716070, 809859313, 48013850, 907888164, 253555186, 851721391, 914571909, 876873344, 498208317, 423882927, 892919340, 670052165, 619833421, 628820732, 400670348, 423943592, 321147597, 339814180, 609047272, 289724703, 24900625, 19953790, 171739270, 65070192, 247191935, 266147938, 612120217, 949074334, 187697439, 558801735, 109648240, 187242599, 487689446, 670684757, 747898420, 695909778, 833571694, 413960, 756106703, 108981530, 791736686, 379618635, 677512628, 321034378, 207929226, 545437079, 913853384, 530386477, 459862664, 940534601, 913746214, 478627282, 503000051, 497669377, 277585263, 185766089, 636706959, 480562760, 465117897, 734425844, 697085630, 869932031, 684981263, 149334511, 37633500, 412770264, 422320614, 138430249, 952222170, 239903707, 738759899, 370883428, 126593969, 90538228, 140868802, 145187088, 688487614, 107105631, 760948394, 413100188, 363189991, 835254735, 734176499, 351362864, 556452865, 725395558, 422777390, 868548348, 528349111, 740895495, 364584290, 984897271, 124983884, 661522051, 39846131, 176327958, 129473841, 65912500, 6516631, 129631687, 49715702, 574259136, 230740396, 196340792, 813280806, 643754302, 391955119, 277410580, 346368017, 152368303, 934446905, 36217827, 411494611, 772042517, 1790746, 458178134, 139859489, 107830383, 220106281, 974314659, 740494780, 670307101, 248044849, 932748734, 838961157, 167435267, 70034546, 660156880, 591434239, 47833126, 276440195, 299674345, 251617376, 86386002, 238788121, 186719172, 505994524, 19194636, 789038739, 30421055, 55365338, 693265570, 27098686, 659854291, 742241772, 462603157, 542120465, 238084270, 948458984, 587998489, 841093560, 576780377, 502313349, 127846905, 896478166, 311537015, 82546792, 187717622, 630903326, 885714474, 462291328, 54423965, 960236919, 993668519, 745282490, 85661626, 736271301, 668556474, 910816873, 282212492, 611021192, 122110944, 131288545, 655588492, 887879587, 753379186, 678072488, 79397557, 484997256, 717401315, 270256400, 690733963, 852805575, 147323761, 93698572, 98792542, 34129896, 78693910, 93063117, 255521005, 646599270, 343812108, 825695316, 329705981, 703738877, 145162945, 937665696, 470167039, 343889775, 297251672, 592085356, 366202767, 972623038, 277132649, 828027135, 331202431, 815214002, 682349598, 77910438, 663338069, 751371742, 288041789, 32463873, 778999433, 280792107, 992353663, 630554102, 128529586, 769322111, 510949801, 714790161, 46861951, 902580051, 792380536, 859907668, 343973237, 305671621, 114025056, 687503643, 953251321, 155032123, 401462527, 232958325, 120774644, 77119096, 290745424, 168208367, 275295016, 414559929, 555881948, 861376160, 987221467, 439661767, 405464235, 835538369, 647617386, 174748068, 386475051, 79606148, 222524991, 550160381, 93028512, 513060569, 42031513, 953382218, 766037170, 629845825, 619894409, 344486192, 863710543, 969856160, 20350740, 215609367, 760471153, 926393903, 570434438, 819955111, 282361859, 512123100, 475588823, 744004303, 359954388, 760344870, 312643574, 367763710, 787757485, 691594071, 227156055, 471140108, 131896510, 678180704, 937695776, 992666059, 703700697, 934611494, 709194557, 309459684, 341101248, 695978207, 270340242, 350611402, 384324462, 703843964, 466239353, 81273110, 301770237, 521853617, 541098573, 359627873, 968559013, 729980556, 131397355, 112641895, 156389654, 836204432, 533504321, 900477420, 781904407, 973668873, 169536893, 961483836, 858598110, 424988520, 709811085, 919781900, 390278429, 946204381, 989609953, 669363982, 895295755, 638717369, 416458088, 533685704, 903497352, 157543776, 877182810, 352952586, 655180101, 50816962, 580548057, 669906017, 805970850, 380753324, 297691926, 760730323, 884840782, 29516799, 186629352, 542106399, 279987710, 147282296, 837704134, 76945592, 977468991, 144263435, 649888480, 773842602, 528887336, 249873762, 873064275, 588449516, 584427116, 372880422, 847309023, 974149128, 140780773, 351358519, 593019770, 695372023, 869449117, 291962087, 486119244, 689791385, 945151481, 840460781, 304242874, 117974094, 33457149, 346973341, 82585250, 653594369, 595511948, 288803622, 839024391, 732863073, 903389711, 473263082, 140370249, 598914214, 369070263, 377142794, 47929665, 987102035, 865626250, 776148583, 280264414, 502041836, 414343830, 93478511, 541045205, 210078096, 562222389, 911352409, 453456236, 387516934, 687905529, 536489143, 564752033, 329776154, 541853174, 974202777, 861396442, 872744143, 812953556, 888730109, 146247320, 79319242, 900232833, 830463319, 201062856, 326613233, 808523021, 372095568, 559509281, 376212287, 957107313, 782306241, 692586551, 671850148, 80745034, 152419436, 164454749, 187321034, 113259113, 940347768, 970554427, 590717722, 993579531, 946130881, 721158516, 590883727, 723087135, 258056292, 960301534, 533057457, 550469432, 246421380, 413595440, 162905535, 497060046, 479538338, 38802753, 297745511, 604118973, 21552394, 947627503, 308207196, 30123071, 850528284, 124578035, 207758929, 582145717, 290950615, 90385166, 283410590, 612932416, 12793713, 641589758, 423704992, 939635574, 159728146, 941642952, 552435152, 391583982, 243413931, 328989137, 47284351, 940846672, 669462939, 966676795, 137320589, 742004977, 299356139, 272720196, 123593292, 167373414, 585274221, 871360505, 376145655, 26697529, 678451635, 913351868, 430242761, 306411431, 487446508, 608750819, 25200322, 100127408, 315275296, 40381538, 452947135, 394591467, 231003644, 428505156, 451134797, 76790813, 543033640, 799595322, 619508634, 77846292, 69558762, 47069989, 155808940, 373898026, 370138351, 849995462, 310468124, 12224418, 46984300, 485191576, 231054974, 722840217, 576210826, 87697811, 373180062, 867247250, 737221913, 798043972, 124809631, 280372755, 449535006, 939176576, 395374859, 686978811, 254635339, 17694246, 689494726, 96314757, 142724836, 179755703, 173917326, 35641901, 664257870, 688274108, 610260378, 774981732, 85944566, 899495062, 499054268, 468001731, 636535834, 223313484, 92385823, 181100579, 976848291, 414615847, 954204217, 528759238, 538314209, 720223291, 201991395, 277240767, 933203168, 578996745, 429019107, 679885549, 627040337, 34331197, 744699435, 977238888, 848197785, 545053571, 222837087, 822800377, 261068351, 459932048, 945012011, 254030289, 905629240, 569325632, 487567365, 565059350, 997495579, 450052981, 410484694, 290462789, 851739297, 390591002, 399138770, 188113428, 879790252, 824555097, 555864741, 425152513, 74697337, 900068813, 595048064, 555800941, 897323676, 965294257, 284451088, 732517168, 783224613, 996977202, 383121781, 177075530, 560911279, 204146100, 824745307, 95649990, 351427626, 604836453, 803844919, 99618005, 627644898, 792067899, 362975313, 996690008, 201691923, 295078257, 692858119, 821359073, 220990049, 282555050, 523887715, 493049530, 185091054, 696768162, 31034037, 287635295, 210672858, 574110913, 44064650, 294018640, 294766625, 134340047, 488951596, 594949254, 173579055, 460185253, 282920052, 150828201, 513207352, 710149589, 840276017, 644242919, 299943484, 456752571, 473276603, 153305917, 472881413, 916523135, 990046784, 340212792, 77159473, 262942729, 570901206, 852640528, 621926034, 817234138, 425599110, 518781015, 92341406, 877935955, 466055780, 216253495, 818930753, 821850228, 984466439, 818608647, 941155559, 41396374, 903065006, 53536512, 414895693, 371117835, 900667297, 328912664, 446356012, 970106327, 345668101, 290755363, 829941842, 82324730, 317802871, 550673630, 806580856, 456356340, 284183778, 809548748, 820037900, 757708339, 593558719, 761156154, 899559996, 180491877, 313043814, 876932424, 365191943, 760255718, 122676322, 274097606, 460865076, 336234416, 878388354, 942202341, 635576880, 548039782, 664099974, 212408911, 901108764, 850026744, 249827305, 887481272, 51188996, 623525486, 141980930, 301439798, 374961319, 771090705, 193587897, 552883695, 21644674, 690660553, 762484390, 175233298, 723708285, 737682082, 730007934, 420357968, 161953487, 819198860, 264192979, 98313886, 907607869, 478834488, 616752087, 704131710, 34837132, 672730731, 266029254, 912326049, 986315177, 838518935, 214388759, 745954006, 877895129, 771267788, 513002764, 291293116, 522554462, 7157694, 711069814, 326202185, 167927291, 903998165, 396690814, 141586935, 355881162, 534095884, 778992754, 223966099, 199130769, 623953705, 184385554, 928370294, 864005664, 858487882, 35845808, 942014265, 221938019, 114267708, 615936437, 544588645, 908091285, 554259701, 885135655, 974137191, 607857948, 354836021, 86334266, 65542521, 954812799, 238403003, 989895058, 642416873, 898918480, 261644511, 805619085, 125628910, 480450938, 692847750, 611322114, 779971621, 236065067, 520109434, 366750260, 856027539, 806376201, 962946127, 624458954, 1868752, 601499301, 502862208, 82926512, 29215780, 770832234, 888356109, 375720560, 251434210, 364494864, 335411571, 652148432, 538647280, 82174004, 789652642, 656116659, 104213551, 875971084, 302460264, 820192168, 114875823, 942295652, 690069311, 129131296, 53130640, 62189966, 801048556, 954125602, 353680056, 262937736, 191762371, 889246956, 454467833, 367073674, 372469964, 561567394, 96990164, 295832637, 182894700, 321712487, 579240353, 225764559, 395063396, 430235046, 964384181, 216443618, 467349915, 709081798, 959819667, 118571035, 832833933, 882072100, 749507908, 273875983, 851588505, 666024532, 476877733, 689600988, 411557260, 700643999, 848679996, 92365410, 979654248, 261543397, 624060987, 353724683, 552521917, 515517602, 358340722, 511980870, 529805556, 812442502, 72165516, 4992418, 317008986, 717758273, 385631691, 170556132, 341779826, 27449208, 515190440, 223563860, 881524564, 783297886, 331310767, 465585770, 429071035, 146135947, 75509419, 189487509, 315654915, 575455636, 12261879, 678173129, 277885088, 123969017, 615375525, 13671744, 652490966, 706445397, 972117645, 605101077, 260820510, 463118262, 423039475, 838664062, 983748339, 659534663, 496227017, 506242223, 320395844, 770249531, 787223632, 167509934, 550195795, 375659756, 91576089, 641402322, 235637159, 508968758, 458252640, 516062628, 483894439, 967669120, 780379242, 387549294, 6694759, 655805577, 649150067, 755926391, 253842035, 86167563, 746564520, 124707652, 565188792, 770747380, 231985918, 626728690, 507651941, 190992046, 993886893, 318289037, 980063317, 206181187, 84873794, 39080366, 362773374, 531013590, 16594153, 740292201, 738558793, 659486229, 843822601, 386430951, 842525564, 843021623, 131957607, 562188630, 664129732, 875336880, 20487998, 580481755, 526136157, 35174365, 87202201, 288700528, 940604869, 665729864, 519272604, 879771922, 932716798, 999083891, 544947212, 885075665, 796029620, 895400137, 46741150, 982584693, 907699108, 888786978, 840315506, 16216275, 206010055, 829005700, 310625418, 42481240, 819085514, 538545710, 539802870, 211127438, 217658377, 461965363, 721472420, 387961881, 944686471, 818079921, 315568407, 404900317, 100600930, 175315031, 607880818, 266854483, 911095146, 889687462, 542709777, 351662211, 393842499, 460961352, 123211071, 292201743, 772985630, 545389333, 697366560, 74535023, 680063797, 14178046, 575415667, 160302530, 426742251, 563243499, 656611716, 454257458, 529042306, 967851058, 200165783, 915839918, 912398938, 135225015, 630752887, 304983530, 377269347, 911574845, 378039693, 256122576, 851183582, 204972224, 737717920, 305155120, 280003770, 308318197, 670828590, 913103512, 331683886, 536289184, 760405495, 935951354, 795944460, 678920349, 138483125, 202430858, 235625922, 157882304, 326959731, 120068462, 48955171, 686560615, 174698092, 512212961, 627142686, 718930351, 427022298, 275201985, 142023104, 364013867, 733950684, 588842328, 112544886, 949843668, 243117524, 34122398, 89983390, 683896460, 733633231, 502168710, 607736092, 275941242, 682749886, 74687102, 381658463, 398821580, 30986948, 306687527, 408339949, 379460286, 327467534, 930030351, 68804048, 569704595, 498438126, 823604303, 40256592, 455993053, 519803430, 103152567, 367718816, 756193801, 74275376, 626062908, 121056728, 19779343, 89870703, 421732905, 265514878, 781657186, 547029272, 122547804, 842026464, 779433566, 819792490, 386990195, 501072426, 740483214, 751224811, 234562751, 809992785, 443935572, 533851121, 919055376, 997597921, 418161517, 83188439, 529362738, 230046358, 301705495, 480756122, 488345828, 485859377, 255295208, 715049088, 304428117, 593214835, 480276128, 72398280, 649643286, 102693182, 355203773, 231789206, 730667688, 448007093, 651663151, 976724515, 172369764, 547425289, 109222276, 364869927, 233740576, 150937429, 404847502, 377851892, 596440539, 955342523, 713762128, 314079127, 876489231, 170888280, 458763083, 329891261, 109334399, 893765936, 97117103, 395710400, 169976545, 611786404, 757610996, 720482335, 798945980, 607948558, 710057597, 210349773, 929342998, 76297248, 559302758, 557062878, 161816083, 714802265, 930710648, 192288677, 337507442, 567061172, 185497179, 636521434, 858030532, 517870738, 173572963, 284792348, 658945671, 958216945, 99209643, 844265384, 194031839, 186391317, 511949670, 342397568, 141344147, 838895842, 804301675, 171599261, 588403022, 245167240, 333530783, 812664448, 871849866, 856064113, 257870892, 809179697, 745485049, 946028899, 626048946, 365355732, 586323227, 907671178, 78717070, 61086485, 957520778, 201629165, 91378722, 156700708, 235176682, 153223608, 324580436, 115101572, 726724014, 837711974, 338325261, 782338009, 215077025, 515495552, 438457895, 117129776, 694596963, 189454071, 16050532, 440597647, 870013145, 161606303, 139613582, 614593664, 285958350, 600349454, 291022452, 474630249, 729471241, 34860796, 273770149, 749033285, 424915824, 723763694, 255657928, 303688633, 837562626, 987340822, 643271042, 293789939, 272174359, 208595403, 79784461, 779774550, 812123649, 204240313, 752932493, 935679680, 189880330, 265586115, 646614873, 42413744, 634409777, 880634957, 680938290, 20994445, 867623340, 485970475, 554991539, 203205021, 914207708, 962514527, 388061599, 469502726, 627937964, 347867192, 956400358, 226763163, 476067183, 789123090, 623123257, 278814605, 709582229, 377887363, 808187932, 932262383, 788506444, 516549584, 930270520, 853862909, 729590247, 569239259, 746279391, 372016213, 478586816, 588670857, 246634976, 88687636, 178325395, 131154182, 38258003, 529747324, 887679083, 742428013, 424942835, 477462075, 569514702, 610897924, 979378971, 182525727, 930712614, 115785574, 494270527, 795780800, 982896160, 729121290, 746470151, 858905984, 433760540, 961477825, 783264418, 883194408, 89174916, 938958753, 538246705, 65958021, 838390447, 353335180, 989178923, 895258152, 354593894, 279454723, 768680064, 11568657, 637596123, 830483033, 202449342, 159713092, 53635538, 959257957, 213136942, 455545673, 304435748, 788333832, 275933015, 514431389, 107244635, 691347275, 900157282, 906154642, 601922324, 490966031, 419224649, 476526135, 964091769, 439781730, 241858684, 956158239, 733587639, 823202450, 68714208, 558700001, 406885032, 109790885, 234285223, 866748387, 541817825, 291060847, 234455136, 272249084, 378552216, 788246077, 384286704, 756688241, 704683613, 362317787, 1191152, 774688392, 820304301, 632410420, 919803407, 856699552, 285057166, 462123953, 899874465, 908004892, 370646410, 111262132, 410276714, 294866884, 273993285, 514680590, 225228348, 371428284, 869344626, 563932922, 15091910, 335314280, 857680198, 146402294, 756979576, 649063890, 120911509, 702662070, 767512742, 935020658, 161584091, 102701935, 634395360, 712801907, 1699104, 290012883, 926138802, 653577285, 864526669, 818939290, 432904189, 687207215, 605717337, 466799390, 476307901, 20032552, 738599494, 438847768, 719777338, 754300337, 662259918, 590558929, 149383936, 224643258, 836974077, 582778113, 50224439, 98356771, 569326393, 880918269, 822576241, 359151799, 896646798, 843150284, 748220166, 709387106, 11386592, 567868261, 773187272, 656097355, 900576562, 987480479, 935280819, 446173223, 583006420, 450105356, 194370281, 402239021, 718322924, 539779688, 780177616, 163407497, 482265724, 236459540, 260357962, 587348915, 137071004, 446761881, 890437811, 204100066, 207677567, 968169993, 574056555, 156711945, 947447736, 35630727, 227506545, 69178724, 469214300, 999049987, 438654164, 583877738, 873072989, 847841260, 309843421, 35713538, 485955557, 591330453, 233771973, 756063062, 929413073, 943353625, 129730078, 346716356, 603458703, 10773024, 637144821, 939295328, 205276488, 776373081, 494609255, 970132284, 801258175, 397208758, 223103106, 101786366, 522563040, 45247694, 572105600, 966239644, 964836410, 269374103, 431242782, 414048471, 284773536, 543451153, 517848965, 883344368, 549593036, 474082628, 759216260, 727629355, 709795934, 820269968, 361826005, 432835980, 8845751, 889835161, 562225087, 71341279, 175502850, 716199425, 189394569, 910957655, 616476679, 763928918, 779708708, 422473446, 488488759, 588630670, 131414188, 151497536, 986118026, 892935594, 702057830, 245896072, 753379266, 43300044, 883773778, 624451899, 303155207, 409521408, 916729785, 628213999, 770606192, 89177860, 321548873, 644178414, 229363543, 39477946, 402413955, 783039250, 100042027, 280543853, 955629116, 779409773, 908667867, 406161168, 14441743, 15153012, 821072917, 839792057, 191794400, 643488481, 193411046, 488485455, 18605714, 673340202, 893587432, 9933297, 993863225, 818891206, 534450662, 898629577, 741644824, 184024384, 489331107, 42887651, 111418364, 765744933, 266302662, 894590774, 411523991, 731825272, 880506152, 80394795, 110599834, 865685355, 565138830, 678490946, 629643026, 382826993, 289561076, 101434158, 379592863, 800640022, 80264204, 1322522, 35211668, 893514663, 951406666, 945160247, 625130494, 871756127, 758865921, 849199515, 427135788, 265031293, 181230624, 685879095, 517067298, 384519285, 941647935, 861601884, 754358337, 37464794, 956801532, 702634885, 603292979, 740991118, 901665017, 736947797, 364117207, 887789721, 815423338, 417806789, 162235017, 77699406, 947382992, 291973235, 765642300, 213910178, 387302357, 668566482, 884614286, 126601220, 355899053, 607638698, 838268007, 827830634, 391983103, 92619544, 274955059, 298789277, 799609615, 704358944, 901530232, 553668294, 580042128, 681727635, 74496023, 780156780, 53023896, 807439677, 788780232, 297567424, 735254509, 812387923, 334087952, 773790204, 772728074, 875965020, 433942874, 570727787, 112869577, 650238981, 492247281, 651245248, 834200358, 580677247, 488046755, 770711172, 430366590, 220287623, 849531178, 60207521, 275037430, 598462157, 903885942, 802371720, 280304468, 618931964, 512114134, 243314342, 608297767, 762430925, 887926897, 410675602, 986547565, 519500946, 258567894, 66170938, 875062547, 849367291, 135055491, 136671676, 300610846, 531525850, 846659031, 711687262, 943556624, 11749174, 416815551, 850457994, 573375680, 157986667, 471674586, 915328762, 17543812, 355002633, 217697397, 873809733, 769057058, 563499137, 496362344, 535201162, 301683020, 57519577, 237461709, 975284482, 831060702, 643785486, 712616450, 425857923, 244803559, 176657003, 951848931, 194932834, 865999097, 75460336, 286610797, 660373910, 238589928, 258519449, 185328626, 196232864, 327578478, 297385240, 46571388, 964897408, 535746320, 45353676, 672082714, 24891854, 409027130, 944268368, 902093377, 618313534, 969059134, 929280678, 491019542, 804609809, 985347652, 312916726, 806878457, 631423106, 363322098, 709897979, 487492555, 966513965, 56510961, 92527793, 314130686, 855549128, 699595983, 743149843, 326840426, 982348235, 997851752, 292545600, 656027604, 804297081, 391110613, 397392835, 513097445, 654360106, 823221161, 769299962, 437502845, 278157641, 909787660, 66252397, 297715184, 689843483, 633268530, 360161384, 651081902, 912533156, 840571084, 927131656, 443853324, 697214572, 655999264, 338889966, 454276952, 854199562, 467281048, 306546409, 798975854, 255718792, 20237960, 208515219, 138717387, 432078775, 557787099, 921714255, 881880602, 166453575, 377486158, 626775750, 663237500, 722110415, 748382438, 325699707, 946008926, 745346375, 856984535, 352776950, 288712384, 973294819, 239845730, 840261865, 715493549, 676835296, 798415773, 578280463, 178877290, 283874755, 716628075, 254758888, 100873720, 688310326, 443111903, 402682970, 790350205, 684402215, 57505574, 118174305, 847987666, 365802769, 608864676, 576697543, 288275508, 823763455, 670649892, 728069790, 980552938, 146750950, 19677974, 454004720, 863973507, 233534138, 47046401, 101941094, 390102118, 26768720, 912702447, 416868468, 826465406, 906862038, 656311969, 484179918, 152493081, 700266527, 567900002, 296902798, 77063053, 339401586, 648483537, 587326111, 217874454, 282577585, 131287806, 485197952, 61394413, 292979095, 32373776, 878727162, 596716356, 912569209, 907440137, 622731534, 102667390, 442013749, 807336255, 336573005, 630083105, 102593021, 194343637, 619634098, 666561933, 463487621, 187088918, 290577699, 647584684, 944387705, 696010127, 805868836, 35590379, 72533622, 61551247, 530573668, 836467528, 965516358, 534568935, 906043601, 952662125, 374691676, 468176712, 819457205, 999913295, 589249660, 846375716, 729257309, 574166686, 458978744, 689486538, 241955923, 624935817, 896132035, 595039835, 807470061, 98929439, 960647229, 622348446, 765396288, 814487016, 300909548, 977744668, 886842132, 869828111, 255497719, 501735645, 681524183, 58016558, 842932542, 949382875, 321499171, 707761243, 462065210, 187318961, 357505608, 399014688, 1941570, 989962170, 148000143, 314072652, 713710247, 725373492, 836652904, 310124180, 109416999, 759536420, 985427552, 376638238, 926379210, 451087388, 203207682, 86546250, 566610149, 162922848, 665816701, 820161324, 659597736, 340135213, 154985011, 126535700, 71547955, 707490695, 629541883, 870652589, 347462955, 395056488, 907996790, 18669180, 733561186, 209239434, 895059752, 269305613, 168015373, 655426104, 1762966, 356233307, 642460535, 599435235, 515411166, 524857451, 626083872, 221338995, 730983383, 747478928, 16849582, 990933881, 526288392, 54771834, 76107437, 748137859, 443523742, 889149009, 968679412, 430942118, 960378461, 787128005, 303723015, 363697909, 882061414, 492803669, 673902482, 629041220, 436698886, 310396115, 161768298, 381015015, 192461421, 93288483, 229609819, 511026012, 875202139, 624797682, 125331508, 433250542, 541098209, 814988095, 388545170, 419890380, 504628460, 162390546, 665070899, 267767674, 86211797, 993281979, 787003906, 36870300, 503180633, 228353477, 48685081, 88225926, 755296845, 643780449, 986119129, 856679403, 408314180, 595224787, 155215987, 470105454, 334726219, 63552474, 359297534, 555311387, 539117463, 536010676, 279637288, 156649247, 865427084, 887644252, 793664424, 539067768, 783717524, 229096712, 532855296, 966473617, 617678349, 951020642, 297228623, 61232544, 434360941, 883822694, 265829776, 490952897, 311788721, 436000223, 764814527, 898975103, 482272397, 953995379, 441325789, 748623939, 176975629, 29733686, 418389621, 149437914, 676454064, 627445739, 172607754, 945392489, 992206389, 174770773, 544101901, 80987372, 446809847, 600842991, 118627233, 680260727, 47177128, 903855612, 918975263, 421418911, 801199882, 401464036, 573574874, 431206397, 623076205, 302384627, 26116958, 722777415, 774311711, 713774032, 262558356, 430539877, 638709657, 555944126, 211891562, 506574257, 239744859, 139693279, 321347249, 409635940, 450553610, 85223890, 845876502, 170363207, 627723417, 944982661, 970617839, 667411652, 379234293, 518911839, 827328999, 270371428, 273854631, 587670826, 565405009, 595274768, 463938003, 786969686, 112178204, 4540142, 963686654, 148251623, 758911768, 193298748, 367191539, 143334566, 745418106, 180214960, 910584878, 776146148, 191620699, 752667498, 710399851, 505183593, 800944865, 678202796, 142454510, 309743943, 723557914, 187330242, 186074696, 688520383, 513883971, 215822164, 559365022, 418468558, 768083160, 203105171, 417211802, 743808633, 890658303, 463287834, 420446941, 193638762, 344049417, 144755030, 639577788, 349855474, 169412918, 751610363, 116382675, 725923163, 697825468, 219851560, 284410777, 885326475, 420550420, 859830494, 156979873, 796285428, 827330164, 256211190, 152132237, 792190307, 375133813, 586328080, 271890184, 893513738, 708463713, 944836789, 178085488, 155519903, 70387907, 229968572, 813652395, 501282073, 509276659, 504134415, 366696530, 583528974, 724484470, 360845327, 570053808, 721975375, 714690140, 140853273, 86108583, 909111700, 935242074, 249308076, 427293188, 163516122, 850202680, 962692427, 749678808, 290875849, 720295950, 957360435, 539259298, 132646988, 981919126, 162246711, 545869698, 467334137, 802331385, 975603917, 806047798, 52232827, 70613419, 264912781, 710279873, 463432148, 738182389, 667875019, 228932570, 454641957, 328894314, 990200194, 745760631, 708935542, 578488557, 453124172, 737141793, 977348257, 435417346, 884947148, 623410896, 124033473, 170342004, 595131492, 610432935, 692371607, 324747956, 990975599, 308327765, 154646495, 567763665, 972672195, 465535766, 688187664, 697858887, 103825683, 868020819, 218127371, 250434569, 550639514, 100731396, 586386052, 83763987, 940660114, 836742306, 382338734, 936931774, 260417510, 709312598, 8643220, 431013417, 501453297, 536076732, 655227565, 341581227, 464736154, 436192048, 142550885, 149643434, 919952146, 400991682, 165941944, 387959984, 806187219, 271404879, 755433650, 637774756, 772194357, 602146191, 32400395, 41234884, 362212992, 303481418, 249213439, 201123388, 752023493, 297868692, 755568646, 823024181, 863404008, 590383749, 523102598, 77594827, 996579790, 820895204, 611830853, 67912583, 912921166, 392766632, 120132623, 20599970, 228297803, 833967851, 136002670, 396012133, 434256556, 231550851, 388008909, 388112517, 606436743, 339808613, 825348540, 582772988, 536344744, 786903716, 9607446, 241569626, 473693694, 133630262, 745244707, 136679501, 727341661, 899624681, 855207781, 108421624, 516586118, 395422479, 494042382, 858041487, 422258389, 32436965, 750185018, 777543880, 832621737, 523119236, 881785134, 436064633, 12394594, 820814683, 234618751, 999566214, 269215377, 141612283, 959808789, 309709592, 586468817, 342883206, 952902752, 255021790, 230921952, 91976627, 651896067, 950068909, 849467738, 864141274, 356691428, 509280025, 806358550, 250723980, 263687391, 392902062, 158553696, 149456107, 979894095, 331779083, 572308465, 374982367, 967914054, 416847456, 305309197, 226611627, 656459221, 146593216, 929945824, 736412659, 590490803, 850885541, 454091860, 236558415, 64752035, 151709893, 66934902, 500172542, 273320698, 276374997, 135028395, 838961465, 958982446, 561960127, 593393728, 837317710, 974132923, 556366430, 722465450, 866070919, 618813606, 75575259, 167468382, 686295438, 181004540, 992816300, 954354763, 366880120, 77860761, 476619229, 178894577, 101395020, 783441406, 334676481, 956012181, 631751125, 911748884, 614492831, 832664174, 217386184, 651345919, 281341912, 419001035, 555615352, 345350535, 802067618, 432623484, 71764772, 81852050, 729384220, 670974429, 428482393, 132623867, 95893330, 672986621, 361507605, 90937793, 686434848, 172459373, 901640143, 34739901, 591595684, 783812074, 960921958, 24060354, 351017432, 20712072, 258919919, 146052086, 352217439, 480664503, 684823705, 999996477, 949209056, 391688713, 962100411, 68271822, 273236522, 469590171, 982442508, 820787714, 837684026, 702231841, 226328880, 623582596, 223086714, 872976817, 947491876, 589161863, 430100099, 699593858, 518452805, 951174221, 532597292, 16884946, 438207937, 913957451, 857610722, 269543834, 115537973, 474610290, 988688839, 713468934, 582253363, 515355050, 861503742, 470247125, 914561586, 798650030, 208979426, 743805861, 725153954, 937936901, 102007408, 709536146, 327083862, 854983222, 945705478, 300421106, 639615867, 272949803, 742192223, 791968571, 953367502, 914743159, 614692675, 292414033, 490757721, 24349039, 623420236, 868534556, 592864809, 188832296, 101475343, 227826609, 386501519, 447548119, 475058948, 94988138, 940140129, 689526334, 739136876, 68231597, 120140227, 909835007, 367639584, 340185061, 66806448, 578398168, 934631856, 322067857, 297022486, 990374416, 285566328, 291269478, 784797282, 882342316, 235394260, 127454936, 701373440, 642531056, 733305413, 329601439, 781189020, 109601525, 516017691, 544643514, 475271833, 124988784, 524556721, 976517366, 166042823, 592532847, 278579780, 786091860, 723169279, 930579145, 305877433, 127534925, 943366346, 712474653, 953227560, 413016351, 400224179, 398290331, 629496686, 674372898, 645855751, 486106823, 622935045, 764398934, 10358828, 487430643, 855914959, 349660968, 616082181, 666457397, 443539959, 665776883, 351300447, 766875532, 624387706, 440391825, 796960794, 745261030, 729492616, 351049868, 653264751, 260112379, 510762288, 508960307, 429888400, 57559257, 920891542, 680353251, 215709532, 579030415, 875278725, 878504641, 525023050, 888763168, 818338133, 211721096, 240948553, 727125718, 505996134, 320302081, 563573512, 794614682, 266028919, 608859723, 398739805, 141769057, 795546698, 845360278, 678845774, 309440004, 652862580, 104497110, 65876023, 234979572, 69663129, 106940162, 758263728, 728089320, 643100732, 121592094, 801402592, 546471180, 371522850, 216877610, 141024390, 492598564, 738088004, 343488699, 459448851, 515784923, 939811139, 213070831, 541855226, 687202163, 408103300, 602879976, 561376329, 221541280, 778995542, 264538572, 985623751, 882447786, 484681241, 403559311, 326332077, 807601039, 565880776, 156154020, 985316070, 439517066, 815820779, 33251375, 237158364, 842476742, 885623843, 181823093, 161492240, 317490677, 466644165, 254202242, 213025385, 134111616, 382111622, 266486357, 325485038, 893910633, 212753282, 258778916, 217837801, 234095669, 209628905, 58835394, 257964818, 457772576, 646054964, 544900481, 799696629, 214359487, 301482745, 101745039, 845591815, 354415619, 25426746, 535964615, 233933998, 486815338, 619888051, 132627232, 675160513, 174392721, 919832562, 216560886, 337422486, 746503336, 992163412, 533254819, 993492774, 837142622, 261160270, 176555529, 11880622, 675569046, 580314258, 876640115, 346686026, 615443688, 659161894, 199894781, 411265293, 214954091, 31920216, 16524380, 811383726, 490016467, 200501222, 927096446, 419844125, 214353567, 153816260, 391355215, 931350562, 947523105, 466938313, 918541532, 894352270, 521440564, 103080536, 187742825, 286297881, 314708152, 882337915, 731788915, 581419769, 496974704, 955191330, 730487540, 700400577, 368221413, 111767182, 796368100, 990024108, 974100216, 300930485, 503030718, 943814335, 77041108, 486731586, 524205853, 958361378, 332650582, 115481430, 679318233, 228762024, 580520241, 543811482, 685351081, 303449032, 970811396, 861022356, 971131642, 954053023, 134611497, 319929102, 567792811, 716845690, 927131614, 876803953, 178012060, 109244075, 244790444, 710392550, 228783483, 305036362, 561701065, 686126797, 216545937, 489320185, 887130801, 975978606, 149070765, 754390270, 245213160, 36999206, 383248131, 468572588, 818018679, 849689054, 851546914, 437997677, 190705398, 307723191, 637623289, 82651821, 842316842, 686098627, 641007129, 748252485, 533980099, 69708485, 227489274, 550937934, 512387986, 663798526, 645154743, 495285905, 936432350, 767091394, 123910064, 494805504, 894612840, 297758593, 934682176, 455723789, 642691591, 848478565, 338616704, 520383220, 349099225, 783623311, 641599198, 358476330, 71492441, 39160518, 356041367, 910084958, 45841875, 321944755, 127413042, 448833677, 339808747, 452489331, 246691037, 673762256, 383536890, 782516949, 545377682, 876477550, 748120496, 15707503, 783846056, 978219018, 5742696, 757576325, 572976192, 784144886, 869537398, 747591910, 922952066, 258278957, 829312918, 886640026, 197356372, 219293489, 847107407, 877136148, 822832689, 229747876, 314891289, 207659629, 374447139, 89272776, 474880714, 508121944, 504355821, 53497563, 906629511, 20491517, 381951522, 324762411, 248660325, 466511883, 911160240, 111312617, 429000344, 138888380, 690876714, 991098312, 95811878, 668474756, 370054475, 277797808, 519599544, 829431760, 383726666, 873710720, 874394914, 833509067, 139666110, 393077225, 987048863, 388179636, 137747579, 594060671, 726294196, 517677150, 353680317, 663953294, 883883559, 602264976, 447877226, 961007485, 966156496, 666403561, 743773912, 217310676, 866728843, 249964425, 255371007, 547061769, 803059445, 410285250, 103139066, 40918091, 936962931, 554234428, 34341090, 993330608, 38991210, 989966946, 488667437, 583440042, 364234226, 137478516, 944369778, 950741222, 479087840, 258636030, 753594158, 934510142, 888455882, 697512529, 641501196, 532488241, 491980739, 463058386, 270029774, 588504, 737120283, 297682951, 189279252, 508828805, 940358685, 449608072, 221297814, 662612947, 48283622, 477455622, 685080414, 451270895, 934858050, 685192922, 643245098, 538160576, 422974809, 784920106, 512163041, 723029732, 655179541, 855055183, 442318383, 810479008, 83075277, 997623411, 249037361, 568826230, 652222837, 115044032, 777043313, 169446045, 968254451, 925366707, 837553804, 979700133, 911809138, 839910211, 311156705, 317344813, 378783697, 84941345, 96530476, 600630992, 861219558, 944256874, 800167177, 920084654, 948831215, 88897873, 132063494, 717049458, 229492141, 680737568, 564873935, 676290364, 19145078, 760807268, 365732014, 256075686, 767295485, 657707115, 946683793, 75936858, 832915018, 95910821, 119582484, 263410317, 394624798, 74816102, 933599666, 364742570, 711137028, 697855365, 327549822, 480261865, 701388303, 608103775, 846146487, 421153406, 421362566, 706088407, 623648229, 808783492, 28223308, 927839304, 856542370, 154588326, 148656376, 543712617, 879949108, 554183877, 777436968, 363724273, 108481472, 329755616, 464630756, 696288953, 165908600, 702167106, 530130784, 437386027, 961122736, 250029074, 175250020, 301682138, 134597632, 279794042, 161417960, 981601985, 35148579, 35502097, 825356371, 192213261, 934316446, 865088033, 233369520, 369214677, 878817832, 575390074, 841240293, 461319621, 403239620, 142732188, 990412180, 652699079, 21703413, 724765710, 287725636, 311603174, 811070443, 899995238, 488590392, 951335233, 354357362, 335582050, 523869759, 418550780, 803356397, 323793847, 814427873, 528041077, 16343603, 168691258, 611042165, 416641296, 187803130, 713678535, 713243055, 68610718, 433944898, 34495303, 335654539, 592010158, 730810683, 605928676, 937619300, 254681240, 150395411, 461811074, 879552205, 560672062, 506028627, 962707418, 341566685, 325276820, 60551381, 335771876, 536626566, 337990277, 143046413, 274623497, 11683232, 835335425, 343372241, 106241306, 87706395, 633349528, 893752785, 26338499, 748004465, 147852353, 415299689, 899362805, 591187873, 158532374, 826912837, 61754609, 751710308, 45984276, 318443244, 975628498, 856939356, 244644835, 536633766, 722044344, 789113781, 85013428, 727540510, 831472353, 588820000, 587847152, 874034743, 698965094, 383813387, 278077668, 940403, 66559034, 535099890, 247038450, 689225231, 615827888, 408788270, 401859830, 54408114, 765555818, 760809149, 372116350, 306827546, 702017605, 420271058, 390063087, 652759715, 590917546, 775250851, 272003395, 351309579, 141395749, 642810182, 825649439, 188082526, 400733313, 870771310, 35087116, 713977300, 714196572, 372568415, 316536055, 655338272, 731888044, 412507636, 84321499, 125378423, 93085513, 564287079, 923693049, 519379669, 525645545, 80802931, 879960070, 581913130, 14869869, 542862836, 274666596, 957130928, 391201321, 618107450, 310662053, 520293926, 557646446, 841658629, 153042600, 278400198, 807685452, 43165178, 627836140, 480053699, 443906306, 915337882, 432270530, 673125883, 111980658, 105470286, 63899207, 668218248, 31347233, 763316313, 667359882, 635742879, 395327130, 173580466, 15786431, 211625162, 302756833, 365188650, 842719525, 414223004, 522772896, 304002476, 683474782, 879931459, 521578836, 953699981, 166311247, 244575367, 12138719, 196977007, 610656978, 840000617, 721727494, 606289700, 668497549, 14519496, 96072652, 707501767, 543206860, 845213097, 162307069, 144862768, 759347244, 530503351, 516472750, 375717721, 21226443, 813591682, 995421979, 548457538, 87402088, 233507244, 786436461, 131971069, 933815733, 356917491, 209062552, 644373137, 957863350, 146805051, 360215941, 699436711, 837456888, 49487230, 863765972, 172611161, 658290813, 684128955, 174291666, 838726274, 256327805, 252887248, 770186590, 105599550, 979798534, 232862515, 949394554, 874036173, 991396887, 739598103, 403630506, 210878981, 149957581, 558680963, 351571241, 209674414, 6743606, 958057781, 181228591, 134267823, 200730203, 555761258, 274364409, 1501807, 238981401, 218321669, 696588182, 213569146, 740925016, 247659467, 591013668, 869220547, 137206701, 724752166, 229175414, 101445240, 405501354, 578264730, 563739634, 498022482, 56463795, 220379806, 478562642, 512993299, 617471134, 307187455, 880135919, 422261979, 840447681, 135101187, 830145216, 955313758, 574332335, 46878521, 397844466, 919210715, 539971964, 642008012, 601899210, 143714809, 764543999, 927745164, 333980572, 591870451, 248055541, 220259485, 51849910, 264587018, 190870819, 383361473, 127708320, 44610819, 320228349, 69603673, 765726986, 169752300, 503684843, 588579769, 482145191, 957998821, 850134562, 19643551, 264405548, 748306346, 540342475, 781844686, 420183761, 791090214, 186990898, 618855953, 435383718, 323820863, 28003141, 307245816, 923764109, 835815422, 391092352, 149630966, 235514996, 110656886, 795599917, 63308545, 931365607, 430518685, 791345315, 815105008, 848401096, 385174107, 639639842, 147571726, 329471665, 260337842, 475060910, 716558028, 223106018, 575656510, 736029740, 359571191, 523157959, 555017870, 336336284, 222540443, 994898957, 660172594, 875504421, 702295205, 784713114, 347824258, 866530447, 608351670, 918568627, 262642082, 380038652, 322402027, 633328315, 137754668, 713246843, 256593174, 535983969, 294675677, 975631132, 45203797, 206531392, 350750731, 101711282, 153585589, 224393864, 319234541, 377967304, 463223457, 990125151, 351755198, 879753903, 630933474, 11108405, 732537579, 228167700, 683791039, 404752150, 553492991, 432266475, 503730398, 519699142, 624752817, 625624779, 223013623, 114898811, 993773827, 687900665, 177096767, 777121891, 296302197, 294613374, 717707532, 910963275, 434990272, 157198217, 62485477, 821407835, 765698581, 872225382, 510987836, 124202915, 740776776, 494606480, 472832329, 983714113, 149006589, 847113574, 299953328, 94253534, 947208972, 96809081, 799432529, 512605854, 331923375, 532000589, 54197375, 654056329, 757127285, 962118300, 882261497, 663539874, 561474275, 450891576, 912834458, 951560431, 239674724, 589117743, 168024061, 121822288, 355352673, 893836325, 572505953, 41206454, 257150903, 961980607, 430008122, 704879655, 448982786, 972160210, 232737520, 665973907, 90163162, 831259712, 991504367, 889763044, 360622917, 999323497, 511288785, 430758690, 505547372, 78827307, 81627593, 915108466, 518966713, 145384763, 270298229, 263500494, 388516166, 966781463, 22506809, 41320689, 22066323, 521915887, 105064125, 97932561, 452749287, 875798342, 792375844, 978270212, 639376811, 947198479, 163820885, 232094941, 429423804, 238553545, 829215400, 748013675, 37788875, 258219544, 70759888, 254888824, 791611966, 709616385, 104816394, 85046507, 216011139, 211144208, 248655986, 868739214, 792231243, 144489218, 512682267, 188894737, 350241195, 156031805, 560427824, 505086748, 707043848, 82793164, 260062968, 815729490, 914941221, 173875196, 140495918, 701255695, 437187999, 831262762, 464040748, 360978835, 220446908, 933715399, 611129786, 685738526, 170226988, 109653437, 2291372, 160640745, 837695558, 16331459, 56484372, 670916065, 577266123, 500460187, 201894404, 140453024, 676962934, 705984970, 724489383, 728073129, 595697273, 542431455, 983816537, 905466614, 647995741, 70231115, 796467673, 890092962, 690088192, 414079249, 653493129, 813328584, 105113440, 865125674, 176534021, 364370320, 413358888, 543954550, 220378908, 158303029, 143048898, 369483352, 99763398, 798412862, 483602778, 49990477, 669458800, 818777548, 919917591, 616525070, 491755575, 23884653, 925080472, 60863246, 547220297, 288856012, 481563830, 977939785, 869273648, 856517640, 10150028, 128038462, 63668764, 346599224, 125166615, 155376592, 879165130, 303384151, 592793859, 359635612, 22902272, 670848425, 614064882, 573310441, 456268806, 115907060, 385870466, 82556265, 854554236, 667183967, 420308034, 164821092, 940890658, 610251116, 411796204, 781594357, 902696268, 8331214, 239636712, 300232011, 980902426, 432451866, 997815131, 490692222, 610871750, 871715092, 346075398, 76054108, 101035269, 593140555, 185950060, 265662027, 915640410, 717647302, 776454035, 483798018, 526479053, 296473085, 64412458, 631266007, 80042408, 809084660, 152957813, 687804940, 632266082, 254131789, 398998773, 691836091, 351157616, 564064143, 86816975, 734658515, 181458230, 245685772, 963394937, 908085983, 972672960, 395880679, 225534671, 339973442, 273473619, 838163761, 871050122, 645777347, 282869690, 311360845, 749480044, 533698171, 972335949, 771151626, 418999146, 698050647, 880796143, 394271411, 28366614, 994655984, 687451963, 335043002, 897181587, 728440625, 734509148, 188220383, 797108571, 436648321, 359081664, 538004702, 10547767, 839294204, 88795503, 924913634, 27160764, 324955262, 923491615, 968407431, 307153550, 156055278, 735009937, 626581107, 836766089, 949850390, 833716449, 768492321, 8174051, 118931016, 77857658, 780657854, 134893414, 254193014, 203828382, 717820997, 568823389, 730009730, 315276412, 716948742, 144179603, 741994719, 237086423, 662208862, 569282460, 459421786, 498793254, 419091598, 180140439, 270385929, 494575907, 22075928, 552840701, 600327056, 886271524, 493730086, 758657255, 269627522, 285133632, 456022326, 998123358, 103971955, 273578730, 672564731, 645464769, 589699737, 351298149, 146336767, 634791208, 56086265, 791192656, 824855243, 717836053, 549490192, 293596220, 421701702, 876310352, 265145571, 109149543, 54700046, 409771807, 11633164, 788940867, 759032493, 692693364, 429211400, 317237154, 650420502, 996228614, 790520375, 832502212, 125361073, 477355245, 15434963, 693503561, 203541835, 934177190, 60462654, 254763363, 929600690, 746130410, 494330845, 671350829, 918288606, 835676905, 838629513, 890877491, 996278947, 362965828, 296042599, 551949280, 674775641, 404203868, 79777027, 398414871, 826457569, 692971896, 955375234, 488535972, 18337201, 277759975, 967967035, 586918025, 537279364, 522137033, 857864080, 244536423, 573737197, 812986457, 418408539, 612817229, 227272461, 7889703, 114659358, 444062722, 187575393, 119874839, 953082991, 827469199, 774443426, 481002143, 405320122, 276231091, 736495626, 232118164, 566388613, 176267366, 746985838, 5452037, 426280496, 228926132, 328456039, 410285335, 66839027, 867509533, 58282035, 726956967, 976058801, 21572698, 781239064, 624553643, 79889107, 230552613, 152542775, 148212981, 162387653, 510083343, 332166100, 282299949, 954004669, 25835621, 445820565, 213980824, 790401265, 160812887, 600871890, 175305384, 881425832, 802701257, 953871010, 69803339, 884050251, 420622148, 28827827, 188534648, 522444355, 79333609, 723348211, 455626632, 533909923, 881907116, 710303787, 323422944, 595906323, 730917101, 973749019, 357451538, 897234665, 620716733, 493322092, 648501226, 943935191, 174075128, 436155333, 882077630, 40536217, 731229250, 353297153, 505491094, 323508918, 845651739, 308477264, 942476702, 697305168, 809168663, 642093027, 743600680, 106496336, 61051573, 511944177, 632862979, 865492900, 649942264, 320500557, 242893824, 281588295, 5252569, 338967292, 976017028, 909774485, 352258005, 9789064, 998918292, 448653699, 196680920, 868541148, 912339721, 201210100, 883793616, 36915707, 358981376, 191073575, 964811752, 469631756, 912207726, 147158932, 882157570, 134230013, 953529881, 709309598, 432262855, 739514272, 472865879, 572682149, 10478001, 203066966, 335547193, 986928939, 698107898, 318283688, 151593976, 362622152, 240555238, 224419683, 402409454, 113221657, 753740100, 312154832, 297225837, 132288962, 449289257, 403049007, 294490874, 704751492, 661391955, 823714542, 377361782, 704941517, 86064791, 670899620, 49118778, 581092743, 169053022, 403198484, 655098375, 215470260, 237861495, 111753792, 570639492, 992073937, 6280404, 261988219, 814385528, 158170166, 516990979, 847511595, 266756359, 583441141, 782751962, 588707769, 86274161, 820080485, 281980848, 761898405, 656549997, 253347139, 832030097, 542848627, 149389271, 989945502, 116314444, 869419491, 569475463, 671016311, 725349964, 500081439, 321198521, 46489676, 255882101, 568219823, 91421414, 66770492, 972584994, 494450758, 348434884, 838085663, 550648436, 983579133, 272791279, 62300476, 844418485, 120105908, 482775530, 448212418, 269745718, 662522588, 543246036, 1905327, 354534521, 615359638, 119435652, 913170936, 589416220, 932427790, 782951484, 393862083, 673487904, 708466848, 54294490, 668930848, 877631941, 355770450, 605382678, 258041222, 807896916, 54098714, 254477828, 865715392, 850269018, 596893434, 60339430, 804234408, 912893437, 491189818, 308623067, 207815241, 361643316, 147353218, 773240133, 344269674, 515865025, 312690874, 228069971, 451568304, 679551858, 724466787, 900842555, 21710973, 985132636, 909060266, 492254714, 176628300, 459468548, 312729252, 275168329, 526494438, 131793973, 612792738, 426549366, 905083838, 782377136, 454155923, 410414177, 725665816, 642635866, 549531019, 457796065, 550046702, 663525090, 529519633, 193656134, 373052753, 101016608, 346273782, 570345371, 480298706, 536951426, 225050757, 481887261, 270633956, 606896822, 947341691, 769580619, 14449991, 599919579, 166365826, 645757341, 13331554, 798532309, 748409353, 841248518, 739592336, 64838903, 322798884, 956033382, 751218387, 985846031, 385235437, 694704256, 802411527, 919723761, 616383941, 903239272, 781480497, 373215933, 240068202, 703776118, 616916240, 531989018, 955647733, 634512335, 166417770, 781834665, 948672160, 38921510, 762766113, 113609500, 366383555, 553353437, 493973677, 892185654, 379353995, 919929811, 421017273, 196689193, 643934233, 49574558, 308062367, 317211351, 285022997, 572404899, 440996355, 945135775, 187900075, 366602567, 567850339, 490665493, 782939333, 727516843, 659871894, 939267442, 33093067, 269204563, 570480630, 698642413, 987914170, 280551198, 782779908, 543225070, 689007702, 624727970, 576443271, 38688598, 112840210, 421956632, 425345567, 274725516, 768185818, 438561132, 701305169, 175555331, 644877468, 231037151, 118482392, 745701627, 667658056, 198203385, 201982, 133812053, 44547849, 624686673, 406307285, 387775625, 244587256, 721227392, 135046838, 164078635, 562313636, 526835373, 696733466, 304852359, 820963015, 618525079, 249155303, 288587658, 530237468, 410837497, 501218822, 107572800, 144120880, 304917303, 279765541, 284714569, 109371618, 446077037, 286074034, 604302011, 926621337, 461784195, 311052588, 767257020, 400215262, 338941549, 488541326, 906410996, 164740618, 959312705, 241601438, 235115570, 610559622, 42987769, 965882928, 676573861, 155329198, 954387970, 260856822, 683050135, 124773057, 696294542, 40374343, 232598176, 814117729, 994606665, 467616899, 772833583, 419934609, 97806286, 666811913, 581414564, 594286862, 934406051, 759796039, 476189391, 989071831, 766248375, 844013734, 312162641, 83462052, 337999060, 396875167, 714564014, 792662632, 313107908, 857432652, 803791178, 820699870, 582761602, 595273397, 601803075, 718291998, 453185247, 313259743, 51866850, 606886802, 86963585, 593274717, 400058329, 731612425, 408715681, 91848566, 333257862, 347507958, 889703272, 706848060, 123840593, 151996207, 826428317, 824957690, 872953840, 512554961, 467307115, 832872763, 674029446, 413556257, 464414892, 589317612, 816574649, 571303464, 785914539, 216562006, 155804033, 976478944, 156121891, 860950746, 797839510, 137931463, 23230015, 833474061, 135769533, 974419430, 392524073, 224700815, 300376759, 531225176, 793784785, 169969898, 220530579, 93916233, 569268328, 820574420, 811267312, 495097536, 960617328, 263044024, 672555256, 154297748, 688716620, 665425222, 542927593, 89262744, 366194064, 172938164, 894457754, 433744416, 978723033, 586677760, 295410260, 201431439, 462275243, 957029879, 878887004, 596057499, 691596619, 176307555, 595199780, 675827111, 949838274, 281134568, 144536809, 520496668, 364458523, 949483483, 784044365, 734083065, 514516390, 254204693, 608671405, 844324245, 860323507, 988460609, 317789988, 561974949, 550940834, 293834510, 748089581, 702474016, 180389401, 571947778, 44434432, 514559770, 496276782, 450970556, 890330712, 90323186, 713253402, 847826887, 499571397, 659394514, 145777408, 176982137, 305083945, 64830846, 618968339, 360126994, 114482695, 440928110, 69056571, 152837565, 649266165, 334156291, 699355624, 305109632, 742655465, 381813464, 683502540, 393423109, 182743101, 988779769, 90263941, 273252965, 721478708, 925770684, 208513635, 134332559, 657541263, 161399286, 795150701, 228090682, 485498057, 706858905, 635045569, 168465433, 584152390, 115090468, 425980774, 632936662, 679463712, 765504475, 895693793, 701493872, 692407995, 203225892, 940653762, 460133288, 215927740, 711713769, 515241489, 603765942, 162007514, 711040804, 219862407, 547177258, 641378043, 596008911, 268174247, 488811195, 556357157, 647958147, 344677268, 35137877, 954029818, 523669878, 572047628, 743709789, 991768517, 870708596, 812991017, 971208277, 249144838, 96434603, 244254746, 114177485, 891614812, 3467073, 796971012, 324326464, 789224671, 387832243, 851600153, 902929621, 833735238, 914090021, 144978334, 342493036, 177845564, 614568741, 608605764, 782955211, 993450598, 384195457, 142554111, 874957136, 650967702, 673633337, 784171306, 596806661, 957212686, 528394280, 229366430, 153975397, 165470283, 161683265, 422757036, 952386063, 703813417, 29148987, 979865582, 422640023, 557734712, 847660837, 340428328, 544469227, 781863819, 230354097, 936076850, 316677700, 418192930, 876737726, 757928634, 675410218, 547157865, 345415273, 948105450, 89278276, 244086467, 929872416, 469869478, 814919172, 839269037, 403837580, 805769768, 680273075, 815177178, 899106101, 640343671, 904207392, 945281407, 90276692, 492915965, 114766635, 662893248, 695439557, 914149904, 511162367, 80248926, 327404241, 906624200, 963012985, 631391108, 315217859, 317419409, 175965754, 371030648, 363523521, 422294139, 629151235, 763227903, 437947653, 532059727, 254615480, 443921609, 545678842, 448971577, 742988226, 440876824, 539293550, 33814846, 303231260, 84260098, 344936867, 522753502, 799907204, 143849363, 549495881, 299890933, 429347825, 595451930, 268793404, 60683575, 987863425, 271046914, 320800106, 656665072, 270591847, 4573766, 594833172, 892858290, 68943577, 35507934, 103063515, 577977034, 360792969, 307959800, 675487542, 976458449, 675930073, 772304294, 440832818, 596370939, 8779169, 274084772, 813809880, 92742440, 262709181, 504313483, 36478146, 439636844, 963075911, 840610822, 79620199, 319231357, 438566051, 319602422, 560276187, 891680522, 676888972, 56879284, 758091917, 126952984, 280638300, 219765477, 276536557, 596252689, 356309214, 429545461, 906842027, 875556563, 985060252, 295648461, 317736895, 784737287, 936241004, 400751741, 579830243, 603469101, 914332010, 147282344, 7771100, 62809532, 790936411, 414790860, 59237214, 239798012, 134184605, 464641292, 155880683, 420480336, 319940123, 697901688, 562141080, 771705987, 72657335, 357607435, 757226876, 154785717, 494926313, 222390414, 183311377, 978913692, 588548312, 535571339, 422747478, 395636991, 609981966, 490380030, 497853315, 770232181, 91531038, 205505798, 385869711, 494382870, 119562964, 912250226, 262185630, 649839956, 180869894, 556872458, 621121517, 640158282, 568826972, 762215232, 882522492, 618993264, 961691023, 23990610, 647174551, 927439073, 179235264, 617336286, 551722372, 254514034, 689515625, 434321264, 279269945, 456067130, 481209697, 105429116, 904116935, 297945234, 269932010, 900637878, 330942774, 255755896, 360003802, 307944806, 239388427, 309810446, 300992030, 757268223, 753034980, 155206344, 273718899, 961019119, 249331941, 206082608, 455833724, 43000226, 730222660, 195549407, 76328345, 560815684, 965227086, 732950286, 733924457, 282357260, 286385309, 446881863, 311594164, 287093373, 777357604, 221553829, 215405622, 865521813, 966716199, 479461674, 711469030, 630799015, 864802986, 13142152, 387856919, 456829664, 361508074, 99922323, 991466526, 689012257, 984818999, 903236177, 731568883, 626227455, 254515343, 188547639, 912580145, 36258756, 972170308, 299928731, 707185089, 243963849, 257543622, 756088890, 162608888, 956044159, 429723305, 798991483, 415180470, 590674640, 22363902, 7985013, 85218847, 784462769, 641986804, 771507081, 77081238, 119585369, 701544597, 292080335, 449730238, 589412382, 27711868, 908337706, 86936896, 765405065, 68512614, 846809094, 469627698, 710725791, 135010507, 440134712, 521203984, 708081306, 983302458, 551530307, 962013009, 297619034, 11647074, 786292972, 616665529, 848943717, 832758220, 48204419, 495943664, 929998191, 738248712, 465080445, 710868043, 243986919, 637939749, 862998150, 237972456, 762370381, 747504007, 501359223, 690469009, 493481761, 986228088, 476461881, 683488960, 398803532, 434298652, 37841105, 115802130, 36320555, 273689601, 398197490, 895940796, 324725819, 509043802, 344891016, 387102256, 631768941, 511205269, 867844191, 103608766, 237506213, 621859225, 51120941, 576200847, 304496953, 695315482, 97481225, 954926231, 841719793, 83126661, 478464982, 189935418, 701366110, 321062600, 458621462, 961001420, 854584556, 883265454, 469726532, 239945021, 925182257, 810397648, 803322846, 640024844, 615478940, 657169082, 497246789, 514283536, 668910448, 994098593, 224354807, 965801421, 354675633, 563061044, 937993563, 501148720, 903549515, 167111493, 197825822, 161201235, 712497631, 980497403, 39820940, 214598736, 828977644, 493152, 14811430, 249071937, 914888654, 801278802, 16031645, 208265255, 61556758, 969930203, 900447950, 218390643, 543810972, 308842132, 678251629, 96030488, 602098650, 729679351, 30880619, 563639011, 786949433, 643985518, 739438706, 595700463, 764110001, 646535690, 63429668, 480902132, 145417095, 791743207, 387859454, 141987939, 641064382, 821168309, 166915247, 56719489, 26579401, 819907320, 983014034, 926653931, 179053962, 602317940, 536521555, 871172520, 79679288, 628042505, 11542968, 303045035, 560919708, 988695428, 15947894, 704358509, 735363051, 13709377, 790260891, 378554870, 16788859, 457628176, 619791466, 632545475, 426928552, 824940659, 701201341, 684861597, 734222835, 21069680, 266211034, 467743755, 850046906, 929755173, 679026174, 132087819, 864874771, 400595139, 456460552, 624731132, 803316005, 354293272, 582733621, 984475244, 988308022, 21070106, 909189189, 344058670, 935343653, 352164342, 232155124, 381154602, 772878175, 759748334, 313343846, 553822920, 744177712, 967123473, 202080187, 214005429, 118523968, 895471405, 737711414, 765639186, 192139335, 888769710, 573720320, 742891116, 854082922, 131681339, 345366099, 438638823, 359249012, 408078766, 895186298, 860951391, 606075974, 352157970, 828816831, 907682813, 626228294, 482425224, 344328176, 56275699, 632332072, 652615061, 412423506, 113089706, 521477538, 103668143, 979661872, 742472085, 787650266, 121890144, 897687833, 421464096, 52293105, 592282911, 704645947, 265855768, 441332006, 312765304, 955818503, 473680529, 389291552, 972753435, 91466998, 618579220, 916699465, 234090887, 271105446, 526444282, 436307103, 433352309, 645187387, 769232732, 408437598, 550612089, 650795695, 56733121, 591064912, 391413809, 407676567, 492934263, 215743364, 58683253, 728484954, 358679287, 553169070, 465254350, 315179685, 38792385, 115323934, 653329536, 584284254, 824981025, 767792785, 165084033, 921673863, 917875116, 185398187, 672032101, 200325509, 637568592, 163116956, 120677764, 560764438, 698377836, 842852326, 314591900, 635538841, 181803782, 685576983, 379837017, 611191791, 496689393, 847110038, 57531017, 713863123, 161958506, 895768103, 630089485, 18002702, 286263039, 534149134, 440307974, 843133940, 175232909, 656361676, 429095320, 742491452, 822722965, 738796248, 132122139, 538525053, 227341727, 42470618, 325027696, 336212075, 116282570, 417632290, 300466235, 206256793, 626120130, 250705621, 652783728, 489623706, 68538779, 788205770, 820451386, 790057531, 642232808, 630486215, 504032821, 720624862, 786232263, 676048400, 957594287, 293273644, 980146035, 247561469, 281416004, 760124379, 409633960, 613641581, 236649285, 127109073, 938950755, 867707692, 604689380, 705963950, 688659975, 674662863, 972078885, 336527468, 950838294, 774042050, 156255415, 369092092, 975329539, 439995659, 595923262, 530523440, 486877323, 404363710, 574910307, 569753044, 539712531, 373199836, 175340018, 995304002, 695497343, 266059658, 71783186, 481533963, 273375254, 838662635, 640449048, 642237917, 223016693, 757971756, 971080912, 159192958, 329056957, 409671352, 598419509, 844813970, 482787197, 420968444, 842369169, 78351704, 262717100, 375838592, 762743995, 607419412, 952869224, 678588052, 893973125, 348534129, 794747434, 781271340, 228527636, 563430834, 711289753, 169342225, 512242289, 238999514, 391487369, 116559242, 555731306, 647171317, 958125208, 379235015, 962648967, 716113506, 819887124, 434396756, 595990516, 798944178, 176878629, 901017160, 538459440, 955506590, 153563242, 812925146, 210544552, 223510998, 571146241, 256927635, 395216371, 722525024, 349443854, 273521257, 532302384, 999075272, 505671034, 645058716, 295538126, 505516455, 444380771, 287589754, 141937546, 10210194, 911098478, 810088254, 960848693, 218105641, 891109575, 72972091, 134574009, 960940406, 631560954, 974985288, 69281193, 125023111, 420198457, 997898887, 617443441, 882367843, 494068802, 247945958, 287772453, 941543546, 181253469, 925108707, 197571773, 598038211, 938345482, 346931810, 965571990, 240455710, 570347858, 243492045, 714393087, 985569024, 50276651, 452728537, 799002806, 225275785, 125628764, 453799043, 273382288, 249434290, 644313614, 297564559, 368462686, 200480831, 311436023, 937192478, 917980433, 324246501, 395030629, 404787534, 830722776, 877677947, 713124203, 525939332, 860721948, 806773877, 57558046, 2032724, 695958821, 880249686, 621744624, 994055173, 213585037, 510029312, 468802579, 753570070, 541935131, 182095761, 928204058, 933816065, 292517990, 575464556, 660738860, 718748502, 800680410, 951391455, 676525344, 349627990, 589826441, 503931289, 284306844, 748321564, 29818211, 80516408, 888241371, 501865890, 389882041, 899359686, 590914705, 361273468, 611753591, 288628307, 287539567, 294398069, 722389330, 937305468, 21751896, 868719272, 498843956, 900323592, 537147122, 77387999, 799208018, 31951193, 366651848, 237819073, 313313809, 509166738, 247225539, 804392095, 700001139, 661975585, 685608223, 825562761, 113159680, 952325689, 849092559, 725112544, 398716989, 663605798, 67989105, 462180710, 14517079, 165457615, 606760382, 683280231, 801259334, 70176461, 71055454, 915459947, 792138970, 860526370, 651292090, 296473644, 628248194, 227125720, 869263655, 773219487, 147351593, 257874009, 812791446, 828847280, 13945435, 490817822, 971300589, 134520225, 445668455, 675975173, 443499075, 533314518, 110900423, 279352396, 694496366, 968624571, 886281587, 478612652, 140567692, 565261103, 164095543, 595817008, 865024986, 911061997, 812924164, 975191608, 891645029, 879887569, 780606605, 356778508, 383791625, 554203434, 185416037, 18883646, 724968646, 451969967, 292095230, 597256939, 540343545, 232785945, 179049602, 331911343, 78241200, 809728452, 858226316, 960158223, 211461343, 128433990, 137387423, 997910442, 145056950, 412051845, 304905936, 429948309, 218054443, 200440999, 481499045, 770845166, 182285864, 164535883, 415158610, 7777648, 761740945, 846094613, 179852674, 255051729, 97620928, 858453601, 31986436, 320088955, 976407406, 621670772, 393296091, 760555471, 302567490, 976847234, 618900028, 774138304, 154586941, 330220296, 279147499, 25637466, 124088465, 854469854, 501399188, 960596568, 804588365, 271013332, 999789740, 60922121, 967890007, 167616829, 431518849, 294444508, 676837004, 506621060, 480730270, 587393180, 103270538, 875263354, 861496330, 449360876, 329448235, 951524939, 941185781, 585099193, 881062858, 365648040, 289453281, 75104940, 921799634, 594723742, 505857790, 524000790, 922200034, 45156535, 242316168, 517356297, 613023975, 64902625, 428011365, 626950761, 578486867, 190637549, 179943424, 287939754, 205113677, 163213774, 560781837, 273736018, 15597232, 112005900, 91942326, 34128105, 525393581, 390369757, 988645289, 624837980, 154152051, 167788878, 587650252, 830043401, 254707031, 315911074, 601922248, 23750619, 499259742, 678979096, 506052711, 671350039, 868074175, 133381509, 53605836, 396468504, 957115445, 479130080, 943441017, 407414633, 873801023, 770155955, 10714301, 329347219, 726654145, 140193016, 900182587, 708831405, 917329369, 368828621, 898233766, 109967183, 529031488, 930852957, 106404231, 211699041, 6368844, 97140157, 162612827, 880564265, 527492208, 25430297, 541611805, 263821605, 928896926, 953778413, 775742209, 73504554, 91494101, 293939436, 697271871, 789307035, 531322860, 573972602, 881522711, 857901783, 546493718, 705822855, 212547425, 21840735, 566157785, 144973855, 316412739, 772081754, 625321554, 432615885, 637485683, 646459522, 500984217, 637050023, 994981460, 814591212, 384303860, 451568750, 467216043, 661573622, 865664057, 130662054, 571502276, 586824318, 344539115, 393652482, 478471106, 700488787, 295545073, 616716361, 416953178, 747292127, 541771307, 541775224, 846333610, 572394452, 323132001, 420227586, 821290623, 397334922, 781953248, 828021367, 90461542, 530157594, 726608444, 633800202, 426052106, 77389271, 976169280, 238526440, 586998846, 87946056, 960933691, 836097506, 123036271, 900414883, 656098118, 276031327, 260530865, 217641827, 3169637, 387605309, 343407787, 279648771, 711495683, 443196398, 423423588, 79330217, 390265174, 383865968, 287271562, 642350031, 260921621, 975205287, 336624514, 219637056, 555795223, 450824399, 648012738, 614432651, 723387878, 552489617, 412859446, 788562870, 666596426, 294383419, 283408065, 118451420, 470671518, 598361850, 742154348, 827289955, 639972776, 78105898, 757378942, 382020739, 732124425, 553244477, 927811926, 837078676, 245321396, 929447187, 814223135, 208271939, 28473997, 992363787, 3573920, 201620653, 167028461, 758994217, 658866121, 82308736, 866275776, 197134464, 751659065, 271491920, 179988083, 721287870, 312446838, 376160720, 613188284, 868019688, 758642756, 192400988, 900418881, 579738558, 805114135, 303643013, 560492018, 199385835, 607792250, 962225540, 793656944, 273512308, 159380063, 388016252, 860157643, 996621498, 825045479, 426105022, 202093406, 915855956, 487748914, 355700011, 805599482, 968987926, 181790335, 253024047, 663390504, 68657167, 276083759, 399331674, 730206102, 933039920, 398420392, 558399692, 58512015, 226877141, 796025727, 712445065, 689099847, 767411186, 585458622, 443757943, 895808378, 4556243, 873242381, 893811275, 562050812, 756624047, 867885410, 725724826, 149456270, 867303550, 459003475, 180599960, 204856939, 618769809, 83194757, 280549244, 78412625, 455777448, 757985139, 16386484, 501132657, 838807536, 79221215, 478476254, 152734585, 151400946, 891455119, 44622485, 690429232, 235724789, 802324678, 106744032, 905000008, 699079292, 222234376, 821640402, 795387024, 204877568, 827477374, 106978326, 455867141, 539247228, 196200490, 727920481, 398235143, 582758067, 410420243, 816681052, 754262069, 723577726, 773282838, 394976570, 439626577, 104470908, 294219385, 299013066, 405379097, 138864329, 557629660, 278637917, 595683647, 799026614, 397277394, 318444264, 863415355, 829271992, 806590793, 834764175, 72235526, 475171810, 671945684, 537690723, 511938831, 948734333, 810999315, 591559801, 849764495, 9181830, 799219042, 630843317, 573095915, 246610597, 326845349, 661795079, 549831385, 506961523, 345903242, 851017069, 828224814, 685929878, 145109268, 847133634, 914754624, 230700340, 244171248, 196969958, 623802250, 55263414, 489940795, 325463098, 250730842, 416406078, 718277639, 690184133, 722612062, 183938104, 553692456, 178218219, 84690420, 959680563, 685831638, 222803696, 525913448, 138017888, 197360001, 568671770, 905492037, 174697286, 597961390, 733972867, 714417913, 361430829, 573148378, 305643138, 755492969, 585627320, 607962119, 473984643, 922488151, 134567986, 930217955, 898718263, 884928556, 493043242, 398872169, 334817065, 67520607, 462801258, 352907228, 803339585, 336660903, 243250286, 537063219, 591106619, 298350112, 683899221, 654819842, 830824178, 624541434, 926978313, 54345109, 118784905, 266305698, 427937394, 240826180, 989303865, 363119596, 887278054, 386173600, 664155531, 871341584, 153015834, 466900308, 472382630, 837251985, 704298396, 961784536, 281258402, 754060019, 743770348, 585091086, 625297835, 545404242, 625866605, 654837056, 148507428, 763105454, 981924333, 658138456, 845315090, 921291514, 87499417, 177872981, 375202029, 388119782, 178973470, 999585703, 456326003, 650645172, 258759136, 127827539, 143589100, 610110111, 944562632, 50432259, 5511695, 818352677, 653627275, 527074526, 583829939, 413730370, 603452018, 483928746, 56297243, 504813878, 59859029, 807504263, 285467198, 10235744, 564306223, 236191134, 622491869, 589504286, 578368451, 650660710, 674004380, 236285798, 845525353, 704745435, 578119894, 417114027, 378286483, 471250773, 356471191, 818015612, 984711416, 652641270, 423643579, 684551274, 776666368, 783264984, 290338062, 279846771, 970537480, 654346238, 575185340, 112303966, 633084293, 997263885, 443215238, 157912665, 440150059, 783026926, 890974665, 507907798, 852985938, 472138414, 211608534, 543665939, 289583083, 466370938, 541120768, 438390847, 782288325, 907173518, 288627512, 210030364, 749906772, 210809116, 33277701, 221209149, 899081997, 898769616, 250073099, 467336820, 923930472, 860345893, 557150315, 456125730, 510182567, 63223369, 907226042, 728989686, 372119110, 319809395, 17023265, 589520412, 428000385, 705325946, 184541153, 599574359, 655285296, 14653920, 626502553, 734742382, 742673064, 825185027, 674704092, 232098887, 763877516, 348046973, 969517778, 609459064, 241237495, 358942358, 914709671, 195359223, 57043425, 871308960, 394126044, 777414623, 547956533, 803766099, 149826771, 636834736, 492179055, 640862072, 448324516, 637593437, 235437558, 906670193, 972132521, 22088317, 202031399, 987092308, 586622836, 642878566, 747999922, 599027452, 863699250, 891259267, 760904565, 496648760, 642367690, 278565160, 961899157, 947638027, 375511828, 655167123, 438475097, 767895579, 343268117, 786057591, 241029214, 871732484, 101469621, 462179126, 868520938, 898033825, 271041178, 848508449, 402643121, 497559163, 158698109, 799589192, 503335635, 6151545, 18615103, 119237002, 824422258, 836887470, 413348091, 338287841, 404861296, 622696549, 641413413, 398038350, 185962939, 409769001, 308307950, 544093040, 232020932, 217794535, 333010743, 332620309, 448718963, 797751655, 420711760, 740881880, 807932516, 189867567, 664824316, 208688378, 348479608, 732267565, 287707331, 954556856, 124556812, 279215796, 576458633, 721603487, 579625483, 222540110, 664105559, 544451770, 83119208, 931902833, 859121424, 459603900, 927027243, 202232129, 115354863, 237146539, 916409456, 615724551, 753718840, 35256458, 764332392, 958396254, 794818889, 832028000, 494382429, 811195545, 977955044, 662094528, 85245022, 614868093, 493634086, 390626940, 819405630, 202260600, 932247446, 263769477, 413221521, 700896528, 160598709, 959283872, 390095206, 993717642, 174093381, 858491569, 543165670, 864186852, 583076472, 197026082, 521121530, 864124893, 214572050, 193424935, 683209155, 108986754, 903539196, 521424733, 560933749, 159602128, 689442709, 88409124, 23681734, 979898304, 551026052, 741390769, 910975983, 170117601, 641358762, 993745120, 216642389, 514405785, 812470565, 706979575, 542897337, 799082988, 222318067, 592373309, 777216795, 861998701, 152571140, 467999359, 293145647, 788182165, 267179372, 541753912, 802177412, 26096755, 552743393, 21429254, 573683774, 949470539, 883245601, 486627050, 224502243, 170568718, 353833749, 541148699, 309524253, 313569314, 886620456, 907913802, 872192724, 609847624, 489063331, 106434774, 258097809, 204993718, 705631133, 638829000, 477762618, 996815951, 264329563, 790526731, 691946999, 980332422, 203152666, 289805224, 783885566, 713637701, 47725339, 305319032, 558206416, 957033417, 727371062, 265644238, 404699622, 256100947, 136498456, 938571908, 411990321, 927381424, 644570632, 606496699, 657833286, 692817172, 282358557, 764503900, 154992910, 406468682, 311245417, 973820603, 843847963, 227595946, 33028011, 261032810, 841709811, 938970551, 228888912, 309452714, 967546048, 220434254, 532775037, 633793607, 694325130, 210889075, 939391829, 192776602, 651243916, 160633331, 119296727, 747117067, 53947992, 200682056, 819337697, 940026525, 700199433, 743651246, 616538672, 353000010, 29936347, 408031166, 561028377, 111201522, 973864270, 545679320, 207405710, 41314353, 245164699, 904269082, 294401736, 218413894, 321547702, 80839370, 376085534, 500538855, 1685916, 568274775, 686641463, 990429073, 624762250, 844183519, 329033410, 104173241, 122265716, 43797609, 649276437, 395313956, 144274285, 307430512, 446634007, 135629571, 652233262, 421809897, 507387653, 249408819, 8121556, 845842142, 17688669, 961199142, 535356919, 805179055, 556797412, 778434940, 801774514, 595006947, 541726761, 277427804, 635239552, 867211096, 857519219, 499491099, 537655810, 444989542, 825980771, 620423215, 113979565, 10402568, 757637965, 393946409, 239851066, 985932884, 546873683, 981790271, 393983567, 198950752, 885513115, 768845135, 982599499, 197458074, 838784050, 567010865, 219558276, 274830004, 542041133, 843817129, 414787805, 462023735, 592602763, 78511243, 92578786, 890551222, 536995383, 782783249, 534307077, 713044944, 354670899, 799753593, 986634437, 337855015, 574899145, 453626229, 654810087, 756544728, 446670816, 227774963, 639025959, 914982682, 685056743, 153906137, 892087180, 886831800, 701761205, 299125746, 373052968, 132736248, 566035353, 596139243, 943898984, 605101891, 169356856, 381132797, 828008718, 883021366, 310803581, 37863142, 40119635, 716842994, 438311059, 49876391, 893071070, 853251930, 838644355, 823756646, 184006472, 927157876, 359290634, 599568466, 677393452, 187579887, 65222430, 423332997, 126424313, 816688354, 684672403, 851073804, 944145093, 78532173, 640352652, 25552782, 7430645, 136957401, 15219441, 407063319, 974007232, 45424881, 48024636, 223082674, 79762858, 872946966, 714282752, 226305817, 951192498, 893931534, 474518065, 427114102, 468748132, 732727037, 932052628, 356039043, 342731890, 108205312, 119234932, 450841752, 175226388, 552469331, 241518199, 523585337, 126526621, 707222557, 809833190, 749285209, 552402701, 473542884, 841035990, 84280117, 658309833, 192666731, 252247866, 439983554, 747186910, 913010961, 916048731, 842907965, 947635577, 416306382, 101304790, 309534689, 567812565, 806633036, 251125683, 401969963, 954504208, 424724159, 887672221, 257932764, 934441787, 319301480, 349222592, 356748849, 548744445, 873301563, 630147092, 135155565, 153403775, 220464548, 355293180, 284784306, 620826125, 610410442, 365669202, 574895717, 427470594, 807386390, 504385412, 120883207, 588668099, 778925034, 750380779, 537252004, 772404688, 70721691, 465575537, 929121750, 371013651, 342792289, 200333062, 703648668, 750041851, 565734910, 76668592, 218285420, 37764498, 701528260, 942047408, 13120188, 487619428, 708713647, 223306804, 818786481, 304929790, 262252210, 21970729, 865993190, 909824268, 279535889, 550129416, 887779506, 436081276, 606466501, 321276086, 533915809, 258813766, 875880530, 413906276, 919999731, 270000132, 290559209, 709301175, 763708205, 87792304, 30074543, 814755449, 192108941, 718170146, 858348583, 520274996, 899376539, 970968377, 730973805, 703100094, 89322874, 310149718, 767835847, 821631641, 445871104, 628976623, 609420526, 34713432, 10119723, 384603051, 19120596, 760102605, 32807791, 663705902, 11941644, 737565426, 759509766, 280922645, 812253802, 377836389, 942187478, 986372976, 631730065, 412960309, 298891425, 422917826, 992110052, 715723918, 791842244, 585004021, 330548044, 200441409, 804690875, 314985304, 933023793, 630968255, 913258477, 287120396, 960882297, 720662253, 183325539, 635701161, 579035885, 228130110, 296169197, 495201552, 375343885, 614900394, 988420513, 777367831, 851173013, 128914734, 616028608, 860141712, 222388973, 7448349, 259049892, 734933774, 662330458, 973387287, 839193004, 732847099, 613221340, 248797366, 692733048, 592220028, 446635530, 129824031, 546377666, 550756176, 55912490, 620442720, 625358017, 879949757, 721371707, 778127694, 180482695, 446582056, 536842599, 143513944, 419947029, 837985791, 741801141, 103403319, 467281020, 203020537, 200150786, 578030619, 357278026, 973288580, 507272270, 579680701, 918591672, 645429223, 775452781, 572090388, 775442670, 834945896, 966770319, 896982190, 372963157, 282941948, 990965532, 179241793, 976249739, 302151621, 241810693, 102995852, 842375952, 691908846, 737834706, 897355233, 513811588, 559284616, 384519655, 362133962, 270241831, 912948175, 815713405, 499937479, 709777077, 989441550, 545361891, 868612227, 429059683, 971439279, 624316713, 104456310, 76838364, 39380877, 5984357, 954077644, 203595519, 307882198, 448021509, 454940756, 497617954, 397327017, 553451809, 940183253, 760199615, 291809862, 866089195, 157357711, 933604251, 269173759, 219895936, 351521951, 516377988, 813553841, 332596826, 218465364, 913775476, 110228291, 38906433, 989943430, 119174579, 916014085, 824173810, 779419074, 495162840, 344715167, 102296252, 909321157, 555864966, 411736243, 548396477, 696463554, 821108827, 297212005, 443687110, 172955126, 721131197, 438750237, 223265121, 791230630, 512368749, 596587054, 638112234, 557407519, 815242203, 950201044, 142275393, 588438200, 257581325, 678798146, 509034050, 743255724, 27833994, 270783243, 658804338, 288870353, 384648423, 237870219, 271796622, 918016191, 723092701, 70503240, 813598926, 383734564, 396555715, 624921997, 127835932, 767141862, 605178011, 349879685, 87932169, 60391546, 278725906, 524772447, 728375759, 227138408, 671993104, 542473960, 745884420, 55585104, 576098614, 536761165, 346848299, 1523614, 760398302, 809614234, 693732958, 124341268, 228342770, 741508938, 535295038, 652591140, 132791037, 76435470, 119453980, 137126285, 645417150, 920453752, 314683933, 336786726, 112321430, 610139061, 28295573, 777207739, 761302024, 73610600, 107231764, 251222114, 908762194, 899206609, 746026592, 412113758, 873005110, 734039287, 614212811, 235439764, 248397976, 442026268, 252711388, 317637659, 183686313, 579843294, 161715854, 455001024, 580730306, 356308267, 24294513, 56109713, 616818855, 618926623, 521653973, 953282552, 673877610, 772501170, 429834884, 147651059, 592329163, 487802059, 776223630, 372068203, 655361947, 18575760, 10897938, 965240622, 997046899, 841002098, 459758085, 203545196, 752981224, 596503756, 775048507, 134261199, 204526045, 380205583, 642044238, 979916065, 462231353, 410740959, 486921440, 98710964, 313313816, 224696679, 116606227, 222702904, 215037187, 220464184, 159705834, 103673454, 263988146, 57143748, 770158441, 57421262, 976379307, 896325244, 110315730, 300598759, 420021598, 307133332, 475579649, 261128670, 140883040, 175598988, 231763398, 759913899, 628845115, 417191322, 907986599, 929153462, 543990840, 111702023, 609320417, 23350703, 773369047, 881599370, 701237013, 623244121, 702317771, 768162287, 141142940, 273583119, 227200966, 450045555, 246408664, 196991454, 89410535, 878894257, 612656426, 874747245, 683706667, 641400115, 768853751, 4812835, 169603937, 211507658, 36893138, 933863256, 420893059, 384741785, 34460480, 904136263, 658488382, 453647386, 896789620, 853490688, 25022668, 645868646, 66240218, 170072597, 928486667, 589148500, 44460768, 190417089, 243011290, 111343784, 151348378, 978073379, 928469404, 290309409, 76729948, 943164744, 439929595, 383851617, 884589397, 362872803, 613744838, 996811260, 275086350, 738762111, 16337239, 981101818, 849449408, 242284647, 836312681, 464991980, 608222183, 278684581, 404463024, 473331280, 367746510, 483760630, 290529830, 660356302, 559752555, 457856932, 140596636, 417235033, 822811906, 437921185, 653273319, 63559588, 548664422, 590681015, 210194489, 306252167, 556781322, 271237109, 685422192, 708818398, 588447011, 135877839, 474650615, 402640294, 556247111, 546760971, 327029157, 526282455, 840251106, 180361606, 342802895, 143077502, 451457603, 931063822, 898306207, 896945978, 422079349, 620176385, 676143872, 638602233, 982135406, 474115330, 74524785, 89669362, 331320614, 933661080, 888885480, 771157245, 280947196, 38792814, 904127170, 861740736, 646220520, 347366782, 293660492, 349889695, 976995600, 40588498, 899183158, 992861699, 924892973, 949531354, 442283397, 395093541, 844341621, 73792235, 468300297, 157035250, 21346074, 424634070, 47404537, 612204873, 263683229, 157378953, 596082564, 8929315, 111234860, 755277008, 988327515, 92803000, 447246076, 995590463, 868747528, 234564507, 171230780, 578258606, 824973999, 214560277, 478117447, 314516500, 990817342, 911612237, 462074355, 551878703, 502087650, 474053118, 181194936, 720749270, 833891360, 416004627, 581394310, 442982864, 695146402, 593844375, 339947639, 618240446, 743172085, 882375417, 50810052, 512412036, 128906345, 52329805, 608612835, 374789206, 115496210, 600687432, 812672242, 553151722, 781628523, 847654633, 921207599, 222163600, 77159719, 583036916, 417951350, 611027060, 637313837, 13021447, 528204905, 41767624, 347319883, 696846789, 962135735, 166439396, 630695457, 492791482, 691003231, 988165317, 458259190, 549867467, 7534533, 229238931, 478660365, 413093198, 843863016, 110783904, 196377511, 448293168, 126801809, 544048776, 874240691, 79990832, 733703030, 304312479, 143130040, 819856040, 415722077, 721296110, 5676117, 464013636, 48962607, 675078892, 642483226, 185323222, 695093867, 902353737, 55701796, 913702730, 31913393, 111854042, 347829530, 832059277, 655741194, 95992685, 439022372, 951325551, 918481992, 605147704, 441581918, 217851086, 441204426, 919184012, 741381535, 618353956, 726135679, 752625510, 485829296, 115400115, 852384953, 367412404, 136009242, 104933688, 644542469, 178267593, 34143884, 580560876, 798857241, 74706886, 752606452, 604800674, 394930539, 937673707, 246100860, 68491210, 592630727, 605918493, 78721029, 229978327, 901099960, 552148164, 393906258, 940217946, 26407865, 186370287, 422350154, 567595759, 959983916, 49719532, 828518695, 218132263, 257437780, 6422148, 841083560, 507243157, 174742129, 255484749, 507412438, 55150540, 49622102, 612477551, 194146126, 768193734, 537619561, 432856452, 156762290, 941965214, 160151918, 543896667, 19479734, 925393007, 230398270, 658583190, 880350422, 636379074, 935699695, 614507756, 270773462, 734748035, 524675960, 129752768, 376757774, 723599768, 21931591, 294958096, 984300699, 802514065, 567635950, 330646576, 104569182, 600962752, 657887055, 77968427, 524015608, 604082627, 662691285, 618807801, 620268155, 395085986, 333849838, 703916352, 568635764, 375440150, 586207366, 146423932, 647371475, 140837739, 426084260, 882231056, 514487916, 109128654, 491449453, 22265024, 999091451, 334898393, 456749328, 729319755, 796795105, 577358476, 88378154, 657017162, 838145288, 498668277, 274214221, 631892211, 419814375, 431138361, 177591798, 247596504, 373107470, 621484632, 312289824, 541554157, 117648140, 558785719, 478681037, 292073442, 666573275, 279484219, 395123661, 518744539, 816009437, 764347255, 948204193, 465636687, 924161771, 796780104, 512839546, 917795425, 354163387, 587326367, 790230699, 857225271, 610543877, 907770576, 729116272, 617825244, 835014862, 90322497, 872934952, 895255590, 443665629, 956072638, 991571671, 723056403, 523158689, 960862986, 624575576, 191496538, 482110104, 569407093, 585164283, 369722387, 370874440, 429232323, 81414589, 353218299, 389705972, 97265026, 829388192, 753743200, 405171013, 853389878, 232671725, 572345746, 647699001, 858061427, 437062431, 188502737, 575068585, 701885160, 226824551, 742374846, 658911669, 319625337, 144849677, 67186849, 592954231, 265122963, 812775866, 2970116, 789794893, 953250713, 381326185, 848202475, 638278704, 458261827, 12565337, 741338962, 450406128, 589655507, 833650924, 211129726, 31722459, 514630303, 497163789, 372255375, 179257916, 986114283, 853521166, 703682524, 947446377, 314220669, 196474392, 301680162, 131320255, 489798899, 87671151, 530174391, 232948242, 987978012, 514501118, 688904148, 876202802, 770820058, 147946164, 601463263, 89917823, 764716850, 921499724, 957274445, 577076508, 277065510, 266718026, 390303325, 608709591, 776877711, 375243235, 430309048, 482021041, 679381420, 788419431, 914586950, 539774019, 580613263, 327458479, 528102066, 815411945, 340919571, 567625493, 990945463, 273862112, 407303713, 698937850, 211234899, 703664061, 968586094, 927593386, 281798959, 271695774, 942652996, 77438268, 797332262, 655962560, 699788351, 345419553, 872675025, 829758931, 519438949, 615852289, 418102149, 224705558, 246325792, 958514446, 695511324, 877322535, 722818263, 120351784, 266143437, 291832886, 581193113, 568454998, 63546610, 601459605, 36431964, 346389690, 772430213, 186349840, 614509368, 638616662, 997801785, 193714342, 452527690, 878966144, 399669882, 965281697, 991507235, 548888780, 175976468, 516101210, 987054855, 719485619, 604168869, 693268283, 872016748, 875697421, 766707966, 346179245, 553992014, 967529785, 997005973, 827191957, 692098160, 959384828, 151898984, 451316827, 687637403, 203608337, 35515810, 286333104, 194482907, 124289639, 983902473, 962210797, 597576957, 890277523, 752594226, 26633198, 596111409, 328639341, 837414430, 996535043, 723480027, 744408431, 763561281, 737289858, 486453707, 946169990, 677633922, 72355866, 492783242, 360501818, 749265066, 90570820, 537995593, 884940306, 644874702, 369492484, 127181630, 213068827, 641794337, 111538960, 501025767, 994038197, 447141585, 893789833, 165621895, 991958314, 273174898, 131504238, 671601308, 945237167, 802298643, 844698861, 535923056, 560126042, 90314343, 994449757, 152486923, 285927767, 56307290, 885737904, 109320731, 179576459, 385803734, 228038700, 68227980, 125750725, 271639157, 472084121, 439677775, 740670642, 887224821, 65985782, 48658089, 1778881, 682427495, 571927770, 681560426, 540901726, 553684983, 214989940, 799630330, 450860973, 544787976, 137164624, 308993213, 526946443, 800601186, 243620114, 659339978, 229967178, 79667650, 164657518, 858364014, 752173010, 117260464, 614116909, 943142097, 309100083, 688418850, 237630995, 331457905, 978821443, 318306919, 324044559, 38550419, 712126009, 943339826, 317221413, 705567724, 533457034, 382571163, 217282568, 550082875, 608810452, 335763048, 545528005, 875832796, 583017412, 915821235, 570943626, 436996821, 681065984, 260257548, 638252628, 678782617, 30794082, 532398994, 171052126, 111218191, 644999638, 62114817, 515623717, 294518076, 257032946, 430302626, 950764486, 646120271, 664840220, 211203388, 737098448, 615368523, 772862289, 375763331, 604919407, 920474735, 426855786, 391945664, 459828284, 303796696, 653504870, 271611844, 344377345, 649334372, 811158180, 982156274, 341265317, 202104033, 942329886, 122332977, 901119154, 421604152, 421335640, 697346887, 308840738, 690653624, 549560251, 136781714, 924585308, 944150054, 467715845, 566438867, 530313995, 417359711, 493893173, 161272258, 10693220, 244517162, 634498746, 618302472, 837510663, 768680297, 388351939, 71612907, 342936920, 875908897, 372738827, 659868009, 724300752, 889376868, 59627040, 72882965, 338491279, 415215721, 325840394, 586931538, 530921647, 116725582, 487205638, 973414235, 690808280, 151689169, 579584849, 105851444, 721397772, 624279660, 894203400, 327846849, 694116157, 228406992, 250270473, 85093208, 140651918, 618410239, 294621990, 767021025, 285177683, 451078829, 74227565, 912477907, 601887343, 465203370, 724250782, 720277486, 290719493, 884736338, 757644166, 24566459, 60896013, 449534532, 556124633, 646894763, 745419652, 281484112, 623749853, 513162792, 62355831, 803744541, 988196610, 172275384, 51425793, 834936492, 309674820, 460718721, 648800572, 738940624, 635273198, 8618727, 128522776, 695725567, 296040071, 773214391, 201278549, 122413121, 402345673, 27739522, 214224761, 598314254, 369916067, 583742087, 178910712, 40838165, 414910297, 429596978, 992164246, 384117393, 271542776, 483425687, 893192714, 176253660, 618227751, 889185912, 906955096, 707484302, 128839711, 830111683, 982573798, 383252221, 813787301, 267788529, 318706957, 659488991, 999161440, 657218560, 6309444, 58826041, 826200495, 18699612, 785036967, 920338531, 100986723, 680563088, 445511884, 120792882, 121829028, 339791335, 910438548, 527792421, 17846993, 110318046, 638787410, 685841358, 257410477, 556042698, 621445069, 861438525, 132242387, 638693250, 157257463, 997588889, 988609157, 551143143, 551275718, 259564541, 425208685, 133124031, 505847423, 525708798, 226608094, 285458380, 692487398, 258852933, 787308074, 749112260, 631577444, 53018236, 754825476, 502308048, 566534986, 615905454, 415650150, 633940312, 159898508, 922808215, 501822785, 218810526, 349327741, 502292009, 949535023, 653423940, 406429810, 692460583, 989006922, 459568033, 194675128, 379161472, 775131691, 776529907, 598306574, 837166912, 225785540, 742298073, 220631008, 631161115, 312496960, 304488989, 735831035, 233793623, 652443010, 675616678, 320304326, 338583986, 403120727, 772551703, 613381061, 108129589, 747558917, 843160777, 150502599, 653398286, 934408298, 951637554, 956528616, 423830664, 194989160, 795771541, 850300506, 74357170, 357980706, 362501762, 47973323, 867687748, 632360028, 83466364, 50203295, 668572237, 452760995, 495228060, 247887256, 716706257, 942610547, 88786358, 317385998, 901168761, 859719437, 767453169, 932697551, 325109590, 672378638, 217865666, 894728343, 329941129, 280216380, 397587346, 888874570, 992974305, 732618783, 513041320, 479461215, 183060313, 296425030, 551823049, 629490119, 718552615, 739974278, 916736026, 194772657, 453414409, 558803095, 22961358, 76283816, 905236565, 370638429, 995639071, 906426635, 74082329, 146479626, 377813532, 120058264, 515198013, 676748038, 289735142, 487470632, 154337480, 840921284, 833742093, 712993080, 484077978, 657194688, 610396504, 755226518, 680297419, 136408750, 914837280, 698325264, 430385390, 141521661, 254363471, 703096932, 675894480, 817519482, 758044661, 391387485, 977266145, 85263266, 938420847, 338911089, 125919264, 995702437, 769574953, 144099086, 733369982, 590757077, 477079565, 770449046, 806761217, 145075493, 222307850, 895529928, 28655419, 586230121, 725057124, 494285435, 962877803, 187831953, 415433146, 477436906, 873053653, 213159993, 556304927, 766787453, 790730490, 276064321, 229647727, 8419344, 207774590, 90244860, 819332862, 895292595, 605160881, 810283704, 969416176, 548813995, 416307781, 645445408, 834465874, 513488303, 386800036, 176492481, 217058639, 641436155, 883155702, 454384226, 896387578, 707656003, 562355517, 6583812, 715819260, 951237448, 990826553, 305090357, 731750958, 702898534, 435954715, 65829787, 720892491, 149047656, 112800795, 833930065, 453160400, 382621640, 574485455, 521547897, 533082344, 690292559, 794751853, 513021503, 519543599, 98235740, 102367874, 831672510, 256369170, 129808009, 785473995, 11926741, 334720275, 985878139, 625484903, 111879441, 888801848, 678388373, 88648815, 181112465, 908593411, 298588432, 700924048, 342881970, 891869197, 490685177, 524141965, 257327622, 476710128, 498734550, 5389762, 739452326, 196055680, 972601575, 328847800, 707251283, 977067272, 235079905, 545556349, 486898207, 779639914, 650315902, 847368248, 205142006, 342279792, 512092239, 382300983, 714355229, 883322572, 935974690, 700611521, 393328052, 695330244, 664089185, 211839132, 915849905, 9857653, 952446563, 840891270, 899595053, 844238706, 753475284, 444457947, 617918842, 110180654, 655836565, 288945031, 638326391, 791439140, 334295503, 900509881, 832101819, 930055934, 394116155, 469122416, 115278639, 965064137, 384772691, 959209948, 939174604, 897959575, 833966567, 71187473, 747732122, 566900004, 185558109, 486114863, 36586600, 176137955, 244266676, 501774584, 771114973, 169917051, 6806668, 267166590, 638539205, 310444478, 419226230, 395173275, 155858884, 193190616, 25630558, 157282299, 754643871, 441820302, 565015025, 167624781, 115556945, 993094761, 884738615, 50897240, 341685693, 289368280, 367078537, 524423164, 404620324, 582547953, 784224100, 222697946, 284079482, 531635577, 887963385, 481692624, 368886585, 746147886, 855194714, 888596807, 978053430, 863321396, 72600294, 71185043, 910807972, 520610993, 586253813, 708321540, 197000472, 383923532, 161689065, 2220520, 993789361, 265338345, 485445663, 553525090, 35824756, 929344200, 213951505, 800673610, 856067085, 665450984, 207831811, 486743627, 683810515, 15088210, 542941137, 681785504, 81012002, 114661130, 992283360, 573503101, 353635580, 776405571, 385635151, 683156071, 209176505, 351170588, 626981758, 301892525, 88337094, 433318034, 618545005, 761868169, 198722612, 439837386, 935257362, 382214397, 333352781, 823197434, 197950217, 794628224, 255865782, 740069360, 906454200, 309242992, 405605560, 395992296, 303365620, 13485713, 305460949, 650741758, 787169154, 524774148, 897314349, 746781660, 671136014, 510809313, 253697932, 711983407, 8045705, 494396804, 975162389, 946982071, 560405663, 719202908, 394315117, 529483990, 274238866, 551813966, 622072945, 61501092, 407543787, 604360234, 813265264, 77764610, 766269900, 10386203, 191253138, 395386631, 590862007, 443613512, 396407193, 36639046, 620809204, 765157430, 236459675, 5415196, 530964909, 334671070, 630181810, 32798201, 720711307, 732279338, 1127294, 429349869, 251335222, 705433166, 733020443, 56863213, 169623448, 787029124, 932461046, 480011028, 790979323, 125128030, 207771526, 236011256, 49405320, 884495611, 149814336, 256913985, 272831664, 768792764, 193458139, 274497981, 355055974, 52455910, 375214109, 470859519, 462124455, 976743170, 959556788, 867978771, 900632164, 938708021, 976569171, 858769243, 100102080, 314306190, 450203324, 246082723, 322426377, 131612622, 373503283, 734175275, 175471432, 979893674, 298089487, 518426294, 761708351, 992780389, 35855947, 220700886, 509986523, 342332549, 176161106, 238563405, 929525601, 205171539, 459915304, 513920214, 106435259, 202304858, 608965302, 595507282, 920150847, 269178566, 834420113, 782919260, 820126167, 979793086, 802906998, 491670593, 826976589, 902721168, 952052354, 76776936, 742401184, 423433073, 66125895, 688987978, 628100230, 385819131, 531204065, 595947503, 15275759, 467141267, 702518259, 888776366, 96118077, 650804038, 884865913, 883892227, 487646819, 712761568, 658928089, 466786875, 108865158, 330412200, 194266144, 249343774, 468378585, 875211460, 428890312, 376503654, 567248681, 122722289, 731621002, 477869391, 90792278, 261511537, 162384829, 511959241, 923724953, 933547559, 552611797, 847595024, 630840742, 626241493, 326448146, 196479204, 932633275, 667048564, 635836645, 50021780, 553699947, 609806873, 372827857, 98431218, 312571343, 715419371, 289954436, 802373873, 171751630, 394120344, 484771902, 508374487, 791644460, 148966956, 679216853, 330690524, 173838099, 518279864, 13907114, 629395868, 66819728, 732927584, 940991385, 742295416, 646092761, 945402536, 400273760, 171385668, 472377730, 62558679, 449301565, 567946798, 740019912, 826908898, 800655071, 189514439, 332478724, 244401843, 957409508, 354399802, 4270805, 290227470, 511457457, 252920180, 348640399, 293407155, 472194391, 61482603, 29563446, 490997617, 907575365, 268329192, 414658262, 206906425, 757748380, 98609506, 596349111, 268285677, 430464750, 106885289, 344541882, 555096297, 882482720, 399853797, 368680563, 243089315, 436453511, 716636501, 844159184, 560557720, 654751160, 741421702, 592572653, 319574891, 260406545, 752407676, 389227588, 20701201, 729785932, 28723266, 278850745, 403510870, 475782, 593892179, 817706960, 226729438, 597046757, 993323867, 635811624, 775869952, 471886679, 957792468, 660860706, 984891410, 622867663, 6719035, 711723331, 193632074, 813389359, 174292884, 729104329, 934230140, 292659289, 53353493, 225439770, 112826909, 454062686, 304182919, 947883986, 87018140, 182585545, 158180072, 906359142, 40669954, 518896203, 421886145, 435328806, 494447954, 529275402, 297496778, 122499916, 199267727, 14636458, 881692844, 549468570, 687905816, 916982213, 872948616, 777011412, 681568187, 238985064, 866896735, 648404590, 331421476, 717390153, 473462287, 627076629, 675538192, 531281468, 608152005, 853326227, 897157446, 16214791, 769908770, 146629569, 313318917, 593831986, 392565637, 494418435, 962928049, 183846655, 861512018, 489822445, 84237989, 780338218, 412513740, 761171504, 684716013, 917668286, 224797874, 525403582, 260216674, 730433174, 805887570, 277945972, 101476822, 43863764, 839532660, 349395493, 277100371, 277017934, 546224526, 973446, 293829746, 116396930, 196294274, 360218172, 490388435, 346773660, 574334366, 246564701, 114123522, 720076297, 355178151, 435127761, 563625781, 453806866, 538527295, 306588081, 59034239, 444829723, 224988677, 63113973, 725757893, 269398463, 218124976, 748292482, 475313666, 692865309, 916373488, 703923945, 529613423, 1689334, 450546034, 618312087, 106830586, 183854841, 810941203, 168789213, 919162711, 625674221, 709192713, 262215033, 161187860, 184253673, 127001200, 510204996, 259347594, 722768841, 89094008, 254517563, 530583410, 189841228, 242693267, 298887338, 971202823, 489334053, 248340117, 697007777, 146579497, 229761303, 287744006, 120970181, 391113304, 608389469, 523084851, 129052708, 142628426, 97299039, 589218881, 271698027, 163276565, 417599176, 952944257, 164385792, 86751766, 324456069, 979738499, 37751202, 76891224, 38384240, 781134362, 837366164, 397563020, 492726675, 573832097, 700311907, 990838437, 906965538, 708095499, 135302887, 751968634, 761604951, 462930078, 357549680, 635057132, 439106279, 134168618, 67738272, 878668707, 921147547, 92972597, 335016474, 873128213, 178208876, 370902920, 152536991, 805740355, 594909801, 865258343, 461640465, 423829129, 955678599, 869766333, 17236449, 570884257, 750086615, 731910637, 504421771, 828744106, 290010255, 71791906, 860041026, 167054696, 658795383, 413122630, 61160341, 36303554, 89331021, 983976211, 692521115, 861988496, 476860047, 576871541, 794547802, 855161593, 363300668, 7927021, 995239143, 630571763, 103070121, 328468357, 417700305, 520643391, 378706957, 683785837, 441817912, 880095944, 448244826, 737742460, 37284905, 22050093, 281584083, 915820477, 47822594, 805872006, 274568589, 611086629, 663151168, 74176334, 811599358, 980597278, 57897190, 237400518, 882774852, 83820272, 29714261, 941753907, 954591164, 913285145, 68208747, 134539625, 870231929, 161644675, 752800482, 178829461, 240030227, 539387547, 300279839, 163821381, 898887005, 431551906, 972002381, 680983110, 716238985, 414848671, 982600423, 812272477, 86102147, 313859032, 126752679, 867562124, 233453184, 953826346, 788072635, 572335369, 587000114, 877457442, 378995878, 705091528, 94199228, 662313155, 144172689, 658303038, 406360588, 86267625, 621164761, 549643294, 527824352, 864274100, 370019917, 347257175, 798747926, 269725012, 915028742, 326712368, 959812712, 457446885, 199754329, 530405995, 406314024, 43312134, 716247851, 140201437, 310243901, 385576784, 959033760, 193852, 651606272, 214977433, 645930687, 96666771, 378944920, 198714391, 479387394, 301541593, 440618883, 536518000, 491847671, 62959213, 90340409, 381151339, 171112216, 195570253, 51699540, 51812765, 721660218, 638603386, 979102027, 493054679, 630576205, 98093432, 71109343, 771932012, 114496254, 760755514, 42033510, 454493748, 721273925, 469373613, 142498313, 366481610, 185671994, 717276849, 816600781, 665389150, 714192995, 993934449, 55086653, 583868891, 193713942, 789468313, 243256754, 101819463, 199889783, 627575049, 700212015, 377751513, 602957984, 121053098, 86489921, 177664388, 598683862, 51223606, 580336902, 267538478, 130602627, 142547306, 223708958, 787775833, 137345291, 805339062, 557220401, 557545013, 65983325, 866755079, 539290910, 160847837, 127623826, 186331589, 345472273, 787500228, 246722353, 579423878, 707598672, 696821165, 549219922, 853663174, 469665446, 17427670, 645612695, 893011602, 730106620, 190811736, 5339280, 65564337, 533010551, 531906575, 800866997, 617924018, 66829253, 301105267, 606177216, 605334673, 977910674, 481215573, 599209093, 173260912, 323567657, 389656531, 901575003, 202952264, 367936432, 531921355, 763291503, 214371357, 534266547, 725739726, 244410292, 129172918, 315885384, 486952000, 843439616, 366735593, 892030913, 388260638, 296394346, 123046656, 534221503, 667814777, 534418023, 758443037, 76103107, 78485255, 511085311, 900172111, 637700658, 862110923, 86968474, 920372841, 572873840, 741810364, 84481804, 713350740, 179780645, 345392649, 260353930, 967422289, 739960586, 1491639, 574330369, 147615836, 716548003, 375512186, 539240582, 185407154, 802064260, 84255675, 576059129, 74880258, 497246717, 451471588, 493104742, 827777141, 433373597, 609979668, 634143981, 757086244, 700459738, 237687832, 654915804, 82560532, 448407680, 519363684, 351253770, 536296715, 125331571, 50076786, 13911421, 815130041, 424447914, 88634914, 310944889, 932136869, 138891296, 138830417, 535923825, 63411200, 306764858, 565082812, 450259608, 694610804, 992232095, 707758375, 497981650, 370441905, 107592790, 477445099, 208609341, 967115531, 890273243, 738620466, 52667887, 244459985, 758442962, 263346286, 28857631, 215680676, 73046511, 279654393, 737845376, 721367691, 410226654, 749548852, 246731474, 523347482, 420861474, 76491258, 406047500, 155324073, 975646954, 137080811, 954519187, 518853877, 379118160, 178857646, 279697947, 209594086, 816147875, 399474728, 533890105, 622592434, 428619818, 529460745, 809172877, 409648296, 927588506, 86368644, 908812462, 252970719, 567771049, 959100081, 561222456, 414832075, 599422929, 762563561, 203732537, 236106685, 694515790, 200322256, 611101659, 79230374, 37440823, 324825175, 647946783, 230576992, 257902823, 966920311, 349078575, 774731184, 16928447, 252508189, 179057106, 756724870, 507395486, 95246678, 503620948, 522798257, 651726830, 317166302, 658943946, 255509719, 812680394, 644191643, 779867932, 662712658, 382012964, 614733105, 50324444, 941056036, 485593777, 988461476, 140299730, 871390629, 676677446, 835078131, 385381942, 333830261, 466503443, 591816236, 416830451, 407781195, 549240798, 607107587, 914923247, 518757647, 737003222, 786793947, 402896353, 422560230, 58482512, 31098145, 60032306, 562429805, 926864539, 636844314, 803926650, 889835492, 866661103, 990663951, 801965002, 106896727, 809481484, 582672733, 670051557, 154586919, 354826503, 213656630, 635296105, 987458336, 678262688, 824753828, 707892343, 248669493, 556139911, 940348875, 218947712, 591120876, 876813924, 586565609, 807876307, 729305082, 868183321, 549142457, 844252755, 933016077, 950352609, 967419183, 919076123, 968366782, 78837819, 347812052, 443249565, 473043283, 642751554, 804056446, 672211828, 847344264, 106643697, 166313183, 250395787, 944997098, 563077073, 596907208, 338676235, 85813861, 957260952, 32718931, 692317793, 96845280, 422867810, 82549309, 172947489, 821799439, 171621862, 490746498, 465832757, 267044076, 561546363, 999858465, 785631533, 859813925, 82937858, 333947252, 502499954, 789538910, 516761477, 352251254, 892145033, 661692236, 551787512, 284152670, 574744611, 402166121, 461674605, 755171443, 706192305, 249632868, 939053009, 229132506, 243073932, 514883519, 353074665, 618533564, 614645369, 499077255, 942398178, 564352361, 40951435, 567647471, 275453846, 513950465, 204679278, 704180395, 5450380, 807144763, 545416486, 775851172, 51716174, 999691665, 82073589, 540706068, 71333591, 301099783, 18903592, 413278202, 242772911, 581303767, 312775218, 727713980, 953113020, 103520835, 434979972, 169772509, 59860473, 359309032, 339877937, 261458608, 708120831, 568774497, 257661427, 117858329, 655315119, 388109421, 124326744, 384264229, 208295926, 86693780, 349824500, 781429625, 874967637, 280473291, 54952301, 82204721, 698820461, 406008461, 527049469, 430392138, 95325322, 275535290, 482206918, 899659255, 647306386, 91327998, 115134691, 47273820, 277371768, 816129246, 907282462, 304548794, 644311178, 417750195, 396595598, 622262536, 326999323, 213047683, 988531533, 296744986, 731156419, 541032308, 393084623, 877180632, 474511828, 959642369, 459260649, 433573492, 826386475, 692534268, 138671879, 168844251, 376117341, 715602315, 933216214, 170092339, 168310541, 420530003, 106863044, 50375887, 396970336, 746214186, 179164190, 758398838, 593337217, 310925807, 858406741, 24714086, 8272198, 563053916, 953676909, 453547430, 548390837, 198437743, 753992781, 14970012, 326198641, 553612751, 874046263, 424080197, 745668036, 120757935, 259379656, 326729249, 766101705, 152816317, 445245580, 377584682, 999339790, 185726518, 30490916, 363231769, 169560189, 904203159, 429218985, 930352879, 869224981, 977778870, 793435491, 801761234, 593923429, 920156720, 243566682, 72608906, 554759647, 634487869, 348353070, 519463740, 591666957, 629646216, 189042805, 245743407, 685304729, 342241766, 667466267, 765184307, 39825769, 21829852, 553655874, 554065178, 226862096, 355733990, 492543601, 343344909, 644185600, 425126194, 959503566, 508451719, 412362966, 406232262, 140480772, 240440083, 211219401, 31388906, 830148831, 331093594, 554571960, 852286703, 835533232, 202663413, 686499899, 440942785, 271266655, 487715004, 107214938, 597904713, 373517811, 761823576, 848707702, 819718387, 71973535, 215328825, 899781147, 827224487, 455935084, 921176855, 193613606, 233462740, 526225935, 90705378, 238115276, 37186869, 755496038, 573331100, 310923535, 302166767, 566757340, 790047449, 306851796, 21122250, 969048542, 499691736, 93239408, 302291065, 137413096, 866168024, 806086457, 117508942, 548010289, 767625100, 442644521, 850815008, 709340930, 687054564, 544588649, 543716971, 376568206, 872891926, 564675138, 523585603, 81891156, 997711603, 288343429, 550209308, 695759155, 330290138, 763214865, 934026670, 692472987, 928871605, 626793060, 439789474, 777181257, 180776077, 6906514, 254788612, 320321556, 462345545, 603427851, 873813546, 43277856, 452993751, 256235277, 342889780, 187838221, 505886261, 941522281, 204503168, 530349619, 174919189, 753896593, 466204231, 744632471, 338283109, 152764596, 683235186, 992385024, 86292559, 730606516, 973742717, 298177312, 167225011, 10547514, 182365452, 134557785, 980910712, 771744566, 472658622, 595088170, 746168485, 754173845, 857563917, 715265355, 577797766, 915381216, 48221632, 907624971, 598514733, 816027689, 397609778, 569919265, 923745427, 901134345, 727301741, 648206973, 285337000, 586058296, 457824374, 314287925, 40588132, 126620075, 268702717, 824303028, 565632477, 628764506, 352580763, 971113762, 33948644, 731122546, 295734128, 467485572, 615886714, 580327690, 586910995, 252008007, 983994618, 863879227, 869742289, 698806848, 231833044, 522423318, 18026435, 30128225, 532913016, 753134878, 210401902, 328913919, 94386799, 158331371, 115732448, 44045871, 303788347, 136930104, 942735685, 740623491, 370760646, 618987785, 615936493, 873443935, 856714538, 803590679, 154384, 79971096, 414771678, 691846566, 891417746, 700407825, 557501311, 453577831, 549681723, 370683762, 336560326, 632733, 199907132, 587019806, 778752749, 734702919, 426204515, 234676138, 114429949, 279411580, 6386349, 655208882, 272559648, 805410333, 747375200, 873612853, 161400551, 599676614, 909819800, 693659147, 802149418, 87773619, 299920038, 183020436, 699573407, 554666756, 624773088, 525084320, 49163355, 707594604, 741914600, 488125689, 270369341, 94924418, 498459184, 242471606, 755049432, 586632581, 791653890, 69895868, 1441534, 594667882, 980628351, 556810806, 405826926, 402264277, 483390017, 959074905, 900009806, 83662254, 474916328, 112593888, 543335576, 685806601, 347476638, 586887880, 765320821, 277247926, 614464660, 632261085, 347406460, 116941837, 721583434, 261364287, 205869151, 727251113, 456609429, 749292399, 932603440, 922121566, 737954850, 481590486, 386656860, 181901863, 780444445, 117174049, 676675109, 578298098, 315930500, 388698653, 492064984, 514904861, 774566011, 280596872, 242093411, 736055493, 355510634, 628691058, 114998216, 831304264, 192236067, 430691803, 714715045, 31717850, 402338209, 778251420, 143259487, 505516215, 869033841, 813416637, 247457434, 472756769, 479601371, 692417238, 740260960, 780820630, 869166581, 436161127, 244286829, 178008791, 805894565, 838542606, 183140386, 677060134, 413594396, 905129690, 923313160, 919176129, 99686431, 472132222, 598213992, 82780304, 915590824, 858178635, 512398646, 317804160, 308935272, 32099516, 300471074, 785543645, 696966702, 479551338, 536897837, 663718933, 361711201, 628166561, 723250663, 757338341, 792085841, 987635725, 135123291, 233539886, 51961144, 909392169, 867378013, 845181923, 216598619, 478491381, 252401186, 134817264, 511172338, 886622962, 678117393, 683311921, 430662937, 14813003, 288647888, 49231533, 218565286, 723902997, 215897675, 267693169, 929266759, 106665170, 247703534, 883256455, 285333192, 871802446, 896001432, 148261066, 15656275, 432374093, 780181238, 841267880, 765206901, 931482754, 870055640, 517976916, 932628808, 663497062, 496141340, 618099866, 645607067, 703557714, 217112715, 441681289, 489486264, 161194798, 798132594, 246064746, 291600839, 402033254, 280253961, 10001001, 268444825, 307921855, 870554338, 993153193, 700873179, 465769358, 625634121, 631940180, 626026859, 724835770, 415162835, 198805945, 640112049, 516810716, 236169416, 740884077, 738753123, 212074525, 522973135, 52800012, 370805663, 944929104, 309648523, 112656849, 916390331, 712179739, 654148457, 928720293, 275565179, 642545001, 896816728, 661753602, 363763216, 38703895, 608070977, 753529702, 648935807, 175802936, 978561143, 950267759, 13496273, 840638334, 787158756, 140677612, 609362721, 614871661, 488184373, 284176954, 243619360, 141082128, 943878144, 931459014, 210157819, 906655586, 400969687, 735275330, 517560516, 171080274, 366659467, 186491135, 537394062, 123333022, 737896622, 558490503, 564232575, 143438564, 877935933, 476842885, 998754746, 685635641, 201963109, 276427039, 886978586, 466567058, 4644606, 291204123, 845797634, 709950577, 107625497, 42196681, 732843584, 593235750, 46502276, 498545395, 615440767, 859645608, 160217188, 749005411, 873300538, 433268417, 518415350, 9333832, 43062945, 484873766, 776347516, 745535266, 322697875, 3291954, 811247265, 653151407, 382021950, 970877684, 992645585, 498357817, 439160706, 875043274, 577768090, 114446400, 443081590, 789247481, 636889167, 894184965, 960156452, 303650270, 97966189, 728385010, 89584392, 972232365, 785375497, 317032502, 493286580, 891422371, 732244857, 111074815, 696919437, 504028631, 984594643, 415231669, 186202145, 350158978, 283469428, 454337146, 757303903, 611086151, 410324039, 866684784, 942977426, 557172692, 659788731, 877977766, 587689714, 26044987, 814826475, 173263019, 716527767, 648439847, 435655954, 299622441, 706713560, 657309280, 139406466, 767999448, 671326224, 818138996, 968011736, 808322206, 514252, 821115839, 676562650, 291185581, 79171031, 370417054, 944899305, 708815514, 252892682, 403850251, 785609557, 555336504, 601007810, 750811048, 554183926, 687526756, 876377161, 722170499, 823673010, 445060065, 190346831, 599361689, 70053892, 929071994, 101837526, 931335332, 718750535, 470428356, 521362745, 835843888, 31529946, 513774106, 556158357, 778974111, 189030702, 911243910, 992322859, 734710007, 766598019, 256127416, 394998964, 511275669, 570587640, 130014336, 67520462, 141310720, 66023839, 269903344, 838067243, 699693530, 4555645, 697877626, 668102727, 902717141, 45044072, 886369354, 283268490, 912485049, 991124178, 330836519, 985491279, 774375368, 854249882, 52865899, 731691829, 401194543, 579252447, 258485398, 85966257, 309879552, 525961139, 891465756, 416572838, 335191611, 203290000, 496398299, 956306039, 37609306, 112035187, 51045600, 151761804, 535476937, 441611979, 583922903, 864913290, 146138539, 954159002, 64788074, 657936591, 456919238, 146939172, 448099972, 56892905, 900641658, 633968277, 142680638, 153529626, 160886346, 391265089, 473527374, 231625660, 839643231, 233172691, 501248632, 130087518, 970065329, 510523273, 998134978, 71661243, 600950839, 844661982, 276993337, 503398243, 820316721, 559479071, 114072310, 635897437, 980678243, 981538965, 948486342, 603521374, 618416185, 139293867, 859285275, 411869239, 141158589, 873626246, 557025866, 724329087, 337883324, 324979432, 524748312, 77025909, 401675910, 187895591, 721615449, 925232170, 942576644, 581927510, 257232155, 928479564, 574332222, 599904382, 725291829, 371749944, 546969669, 42598582, 844449298, 737115537, 686682253, 71727946, 494142741, 519246344, 538935959, 701134786, 278375932, 216095200, 548270237, 437754984, 909653655, 671879809, 281367416, 768359351, 645067632, 418332026, 782778835, 165876066, 302114536, 646624798, 766173043, 925129187, 813257968, 535297420, 18065966, 948405858, 920652433, 689737511, 69708994, 904913255, 903334931, 959941159, 939922616, 491400678, 358123986, 877955876, 998579329, 773844547, 657678956, 310542377, 465225652, 877130920, 436647852, 955424999, 759031110, 466011452, 259467166, 258160068, 942483695, 878658665, 842053996, 284975956, 212748399, 121411537, 433693013, 269773246, 550979937, 980648809, 305808174, 188328029, 822502689, 184001895, 537818942, 991327719, 216189989, 300696855, 159225957, 603770106, 291140036, 278903702, 285076012, 40208654, 200390493, 135129166, 227492052, 817266722, 549638879, 855638779, 869540700, 658703484, 433758759, 240681190, 109097700, 152096262, 28559103, 187182583, 4287652, 288954957, 457100278, 459122766, 312507885, 311124327, 243166022, 211287806, 445554086, 326039015, 240604451, 890533439, 699866867, 473313222, 969998929, 567972899, 641028404, 96604714, 244119342, 295882268, 70946453, 314613196, 332559355, 591821933, 684899283, 17542653, 921341298, 156006191, 533358513, 362100485, 653776585, 134483657, 204948816, 69387485, 599486643, 807259700, 897623141, 636516332, 543637781, 517532878, 906282978, 635327721, 6165002, 178998979, 262502110, 118336989, 425206720, 470396127, 159357085, 533625420, 765121609, 506091413, 449235237, 970437076, 31459729, 291339922, 552829552, 646081119, 590855551, 912254663, 695657485, 430826019, 856508046, 229034957, 632927847, 822293509, 330523653, 818357913, 664744103, 264309166, 910506428, 851055888, 754918487, 340133714, 21253771, 135586041, 214311783, 369230771, 208609432, 830565624, 143005024, 825196497, 119434445, 570387528, 208714547, 14725221, 131590760, 38279008, 424461654, 290593606, 602976886, 773685907, 296862972, 887427825, 469166719, 147566076, 326121355, 166389129, 2408094, 661645192, 421871084, 559554244, 448688245, 975772920, 588248036, 957899840, 353269186, 818675899, 439202649, 209003060, 577858619, 124096876, 510306225, 899417408, 834516631, 542705308, 882665928, 32165667, 633368376, 683597681, 133778735, 448092700, 313693462, 128798793, 176989410, 72135898, 191424347, 56446716, 591902739, 542458348, 800809807, 619738455, 674010357, 745997583, 989830294, 791392516, 333565953, 548644147, 146415982, 999938496, 25033034, 889532013, 390225567, 537161874, 685317869, 176334962, 928531936, 356818601, 558199632, 93326434, 331061710, 549054969, 275568747, 652877412, 972209686, 782424211, 770519890, 956711251, 481407926, 673454821, 935638198, 384954648, 436564785, 408275206, 654720333, 681081733, 898031686, 907706038, 119743993, 273398247, 563591510, 345783067, 648275562, 659316818, 211415328, 732163968, 289382636, 707593835, 428275955, 522812950, 283076963, 176055951, 709823849, 828576641, 897072459, 355522199, 800401894, 190814627, 765172763, 248404950, 685452805, 138117832, 411919367, 329223476, 682410203, 653566407, 942345617, 261608846, 831569863, 655367412, 33469411, 319632962, 238490354, 186984615, 482787177, 139536192, 235654233, 711740667, 491617058, 818788048, 479053299, 428362667, 655111678, 70518122, 646209083, 758997537, 11726322, 655827726, 938842121, 202623686, 258467563, 952768548, 688479434, 574775808, 578177283, 445246001, 350533121, 208745027, 824466148, 546002971, 71821663, 545460385, 310105258, 677596080, 335026988, 557640921, 997951145, 481084783, 25077653, 496230391, 516127897, 447925472, 714238573, 964945817, 291089508, 600488365, 591287464, 170369186, 600727817, 903689869, 758228038, 665987503, 723413938, 931436346, 787893240, 894304277, 375648339, 499084374, 952638747, 349002848, 685931535, 639370749, 946984967, 156826975, 459774116, 25712007, 188270036, 454785595, 279491781, 334483128, 856098197, 293305701, 607963812, 320523230, 447997378, 564238135, 51309220, 717356038, 531604214, 443070999, 815856866, 677495866, 639061079, 102355116, 731387433, 968562384, 904292152, 976840666, 964462158, 106133954, 577352076, 778057465, 71885604, 981198514, 430140146, 385690630, 223761279, 46401085, 35021935, 650594545, 878612445, 677236797, 526244015, 879871366, 758570322, 58323515, 451236154, 439754689, 218301865, 13051869, 584514210, 317049320, 665962181, 30527053, 717849691, 35561295, 710132013, 957276393, 226243324, 265412745, 451176623, 239803219, 454139954, 515985774, 873653674, 982385176, 171913918, 240393142, 311262312, 240555617, 591925615, 444942505, 125825472, 25566396, 590030390, 663930750, 824897141, 425390098, 603963105, 406020447, 811876898, 696754807, 446994812, 648633892, 278898741, 100572907, 534340865, 307295459, 501904340, 879045351, 507456505, 893535601, 746706718, 860694751, 196939861, 813238326, 396196392, 655605215, 913471055, 639509824, 26025794, 411741702, 505537544, 134068342, 643024342, 276471540, 264828962, 885064466, 99008182, 121271941, 793562393, 951566923, 913930247, 880980384, 65843921, 134434272, 139585258, 710772425, 777863849, 773100304, 696375636, 309687090, 655144638, 476076943, 131994917, 103924256, 76895272, 454931777, 847399645, 544849066, 679871667, 406350706, 253999371, 781132121, 272242573, 578726798, 936827478, 184323177, 671240506, 737686824, 963564427, 939194783, 288542455, 305548312, 163398741, 141851137, 448329597, 823646023, 174325638, 439167206, 817852263, 490517854, 376139339, 154450561, 976869231, 829538745, 222310353, 130364638, 751315861, 692451971, 610929938, 690601173, 242928203, 152220237, 731246911, 928702021, 563085978, 532692447, 640455263, 761648481, 38622568, 104646531, 931708843, 926160295, 364299790, 820770007, 836759768, 209279524, 472132070, 352411874, 224633280, 81459400, 431687192, 421624957, 414852570, 644705294, 420301855, 25351509, 380165498, 71568585, 733558334, 931247683, 32313607, 254365595, 260161358, 289580864, 62420725, 934856458, 72508444, 102896657, 297250849, 951391121, 888557345, 467736351, 158931623, 749435270, 897439656, 14973860, 875917927, 147693298, 859574261, 129941562, 559453804, 713626789, 12742519, 541020617, 113895903, 729712534, 573842712, 217250903, 997253549, 683655491, 587017387, 303699164, 399914386, 388520555, 968926636, 31398107, 127122437, 82325186, 357149746, 896903254, 245674903, 756634807, 700376909, 49072077, 103243335, 16145634, 11912979, 86850870, 120431917, 922759428, 164694480, 824027242, 637870736, 623485564, 876318145, 838440167, 244129876, 84416969, 655268211, 1110029, 379938251, 267900502, 602307340, 25442027, 140741721, 484630001, 535393376, 247960178, 396287857, 909129714, 172324817, 668821339, 614588126, 443967699, 938293892, 817838593, 375529377, 457506000, 791580371, 849871863, 807106836, 625446683, 133099448, 636209570, 114862161, 141651881, 528171842, 183977517, 192443762, 489562262, 658011556, 304204761, 864670740, 711143861, 467002169, 227178803, 233003839, 522628164, 562683235, 49008017, 546654910, 625607656, 476430348, 194956151, 157840575, 396972040, 526533585, 17778986, 533333995, 761007457, 818355398, 660734274, 323960232, 299574059, 960088712, 279789518, 339124305, 140882022, 295264584, 603040349, 897318391, 157518539, 953899607, 936686137, 779600902, 675746371, 82384067, 459486832, 59483399, 236980234, 199441839, 35087301, 324015369, 716932447, 516589071, 505240019, 867487682, 58885948, 391261365, 361438023, 813536033, 930002855, 825141866, 718384112, 43117658, 595792232, 822237396, 706252379, 269081690, 477374972, 553944506, 511678263, 42268413, 404725567, 556480370, 68553964, 430207452, 113574901, 579510806, 691034174, 410618242, 727724576, 980291777, 238909624, 699869024, 799055706, 127873552, 277964793, 159349189, 17641875, 559993724, 515665718, 937393717, 640152574, 662584630, 432028599, 384022521, 946393015, 713610193, 152551836, 493533652, 409887710, 5655711, 770683677, 843268710, 661693028, 286913887, 390177854, 484716208, 91194674, 446583450, 202752742, 132477355, 28774230, 469397005, 18949306, 494364534, 357916126, 230505659, 53510546, 978113606, 881771223, 769603191, 868895114, 328047808, 937702270, 452369869, 188416779, 236604805, 920891652, 912428584, 142494350, 419776746, 271295839, 464839356, 273600260, 984755317, 830588519, 132226057, 185542883, 26906743, 419905192, 893567100, 955622580, 485946540, 277141298, 806231243, 109335204, 798743912, 666645196, 246563575, 698705502, 287017975, 745350453, 87117068, 269578813, 789606740, 324375321, 783938478, 599797383, 805524523, 700192362, 193472690, 600541116, 4565678, 239752484, 683021213, 424436194, 86619809, 510156069, 255056474, 222761847, 958168190, 666321007, 424103601, 153167831, 298124680, 261446022, 594487142, 415756671, 409463324, 212840523, 467937637, 238195550, 780263844, 649089078, 661693836, 311615318, 379481427, 481630356, 170103608, 450351681, 934025422, 222329948, 521235386, 65062222, 951566448, 894876635, 834341364, 360754094, 453530316, 381427249, 748137046, 803172019, 993139505, 152885445, 528938725, 986169622, 86770756, 441803794, 964387398, 503821214, 222028392, 407427936, 814284146, 280398197, 680530936, 940990588, 675467366, 155255059, 894076017, 655886828, 279436863, 206181430, 333512771, 77598018, 620292733, 756759642, 314947427, 670034073, 714153181, 173774351, 211925637, 268185411, 278911759, 368767105, 205523777, 994269957, 406346367, 266665005, 215621826, 518133708, 733835030, 323150798, 551661451, 661083498, 872456707, 239043179, 828311316, 364287828, 226228491, 881397526, 592446129, 581707216, 438984871, 983860939, 351567523, 137692805, 581152642, 402461487, 533586033, 502668738, 67928106, 39023669, 927718150, 12997197, 365861757, 465767515, 871809998, 510132578, 324503936, 78344076, 35544228, 987549101, 54271269, 213099643, 681891063, 778421086, 887811618, 133543482, 774580808, 948311078, 486534476, 185488876, 95800091, 950244981, 489716641, 557802091, 893346357, 930010389, 611949747, 481463367, 392543388, 622327656, 530432142, 173221709, 276553921, 807439641, 586133827, 297490657, 384445806, 891513044, 787843513, 36769583, 418405627, 952908493, 237310732, 928352618, 934003342, 97346353, 516520117, 826357668, 483068708, 276961669, 368726362, 397161578, 170186396, 808769883, 966271530, 748040623, 882461053, 762654075, 536558426, 772574384, 237867428, 66097620, 892777854, 397413046, 832857017, 408628356, 283175724, 458997823, 928570184, 776120756, 710387015, 260678684, 832177543, 582063884, 883117313, 75177267, 999139489, 225979326, 873832843, 139674266, 557189758, 792657451, 565105323, 943124603, 627499961, 694223838, 658180477, 398190357, 391105449, 799928958, 187117663, 449475841, 856116468, 410426247, 240653505, 767509613, 567862280, 73078729, 722670496, 667278924, 573905983, 504055643, 251428508, 848485824, 496566644, 659054907, 86126993, 845427540, 877835138, 936219412, 470016203, 939147483, 289090392, 34700760, 844691361, 149465994, 592382192, 623260859, 406834, 139419564, 547728471, 644713543, 99882816, 345322445, 280840092, 232979599, 946274141, 453585044, 325029100, 894153657, 659350625, 653502432, 749294031, 384628079, 645856274, 705296464, 608020323, 201400433, 735184661, 955641760, 360146896, 34385144, 386511700, 419714522, 54260561, 760966612, 243904563, 164385950, 534528883, 89805259, 232890356, 647626391, 672717457, 994204544, 872812697, 287152956, 927839551, 999332531, 912620126, 183626048, 405703683, 281714192, 595290628, 48383713, 387840554, 240570679, 148293137, 204636839, 296987129, 165667650, 191555377, 425936124, 876039904, 228567330, 223609079, 417625229, 882160902, 105211532, 519682430, 192445966, 325417447, 135153874, 135959227, 656553090, 9713436, 779297096, 64092765, 339934243, 304051243, 255903568, 380247541, 629265032, 441045025, 263910830, 536006834, 94068861, 124878862, 120685954, 582805285, 506971201, 451542091, 155210455, 43735587, 780879170, 236256086, 423746951, 80609548, 165658084, 871153049, 656446838, 450696634, 178407164, 705288749, 328575313, 642646979, 150941861, 296548071, 342017404, 811817466, 161826574, 172807696, 659239791, 91794905, 841775294, 907479691, 811380131, 330183311, 348001653, 954397612, 5038294, 777768599, 31738155, 125330371, 769420764, 995312383, 929815633, 354989494, 680760018, 822893759, 927266071, 883155750, 806620752, 902662263, 486784385, 328709586, 963772015, 874740167, 581508340, 381522428, 801075074, 726939989, 334543600, 184791165, 774708421, 58557609, 985504720, 962988698, 842402670, 262343547, 586818018, 854144302, 199084395, 498294391, 117065353, 883264379, 148748857, 996896452, 818267127, 733633429, 778901039, 237636563, 623638470, 301682371, 157577596, 238452822, 269170059, 291383360, 984133067, 966316044, 22564786, 105687396, 453831362, 527821700, 135365001, 282399555, 335774592, 193858031, 58772717, 224779562, 869115721, 406462633, 606906797, 972242150, 913633261, 579657937, 987591056, 190953258, 131269192, 671057086, 44025856, 700769387, 246545148, 928063107, 189416516, 756200207, 780554903, 909338826, 55726054, 651609483, 156310587, 813440558, 998280966, 943374760, 106045376, 618940287, 429535246, 438016623, 972469139, 826504390, 901775755, 267923311, 467320199, 323294959, 264076306, 928922476, 563322710, 900818570, 593320536, 491188889, 889867584, 371858127, 892654302, 780186302, 124748521, 294996355, 663850334, 727706085, 472170247, 849655484, 46260067, 116999807, 270471552, 560012591, 962269171, 128869875, 246830115, 759294369, 75101497, 948533607, 814616179, 188672701, 196617773, 705320483, 103420541, 560245379, 573118159, 950913375, 463287476, 181405120, 530486335, 173763321, 624655674, 224547200, 70312387, 797887993, 169074097, 387810656, 758656575, 180329034, 254374429, 656468613, 635173956, 64535705, 495421325, 647314531, 800218429, 388229003, 655467497, 664393011, 731963508, 485777481, 130069751, 37142587, 193914224, 80095644, 214497450, 447997371, 446565550, 839110315, 69917361, 816745873, 732460923, 483458440, 700271503, 973862182, 340371638, 633131231, 202961483, 765471223, 944765042, 26871922, 202016718, 397457291, 248006745, 778305774, 325151433, 664429306, 648647603, 385933586, 867829395, 551412749, 685849363, 586945763, 312831759, 630248578, 160882586, 469818189, 74583889, 3253535, 175575919, 425825452, 149460551, 384277687, 869854930, 178130950, 746512177, 814942642, 325489159, 879836510, 100829456, 165041805, 38594174, 987746603, 756673601, 776426314, 253623354, 307436561, 744430106, 576180479, 933208800, 873423133, 511230626, 712418571, 704659641, 37053716, 57775048, 783476438, 885757048, 282652868, 772203360, 782775225, 429575352, 201788038, 168986770, 426725645, 421622788, 656889164, 118549828, 274773158, 40309447, 493923659, 214969098, 89144878, 402891154, 895905937, 457702187, 339809946, 61925585, 583158954, 587831500, 426318397, 121680482, 542543517, 106199950, 360070106, 698807792, 116540755, 587011544, 744427662, 320054930, 448276016, 452425348, 251522643, 249643313, 392384889, 60110602, 894436776, 60318232, 161569614, 56806162, 926250878, 21000033, 962023589, 83487949, 233556729, 267462774, 600831743, 260982160, 961832901, 206029895, 661885799, 562547425, 310389673, 634417558, 740536745, 671476178, 81163931, 446808213, 571172764, 978028355, 63498454, 44496686, 418079768, 411200082, 487120540, 669352913, 371217937, 867679591, 522859245, 431911069, 851137282, 74769046, 684533860, 739282943, 289806039, 505044508, 652176861, 852258334, 601283329, 922993074, 740017098, 915793293, 739679831, 675936789, 779565562, 403946282, 431404221, 768329768, 625376856, 422376807, 441251556, 895975908, 937316113, 349479205, 833768228, 436300260, 552261022, 615434237, 951768031, 37050326, 521575072, 685540014, 171780898, 744741612, 904797735, 410439418, 628679184, 878988627, 674605314, 807904477, 558853843, 130870079, 76035465, 604023792, 706165853, 746459898, 821916509, 682961977, 777529229, 731825625, 633896510, 612418341, 935502386, 326790473, 83331931, 46965465, 18100556, 946460419, 892747017, 140944409, 748717254, 269587872, 210732304, 295851490, 43307615, 507080906, 390669043, 960720675, 101716448, 896642929, 292657720, 802576079, 41012459, 802246093, 787944317, 476850063, 195609739, 380733063, 948527127, 148898392, 729719172, 479115782, 425472102, 602131323, 937937100, 586142906, 821601330, 78241884, 663777267, 349224184, 963433218, 85528358, 675639304, 362608139, 114540244, 229574782, 235968280, 806935314, 962995262, 833523287, 428353320, 115706360, 623487293, 450062251, 129048153, 400348762, 173436843, 532396574, 679704027, 347823461, 974629365, 312760660, 510154153, 508918668, 109770731, 728256017, 272646906, 741971055, 550349518, 440376033, 441540141, 776919002, 764625177, 165645124, 296938825, 996623992, 629384120, 55483754, 759679047, 576498108, 37072052, 222411159, 292846900, 72785070, 516136181, 628215648, 636679929, 318546001, 229530413, 677784575, 257331034, 557621705, 365029558, 415365933, 987049101, 518349788, 967873489, 31446952, 836523938, 188322214, 423333967, 492026492, 699135153, 656312786, 148741126, 885815644, 737855675, 84518007, 798116145, 686912424, 259230519, 620837254, 35649480, 67831829, 204351251, 814543846, 801714399, 549461447, 623587051, 889771887, 665022611, 127102207, 902165888, 884221307, 393873637, 975306335, 40244022, 250102958, 932802244, 810753641, 993983199, 790305812, 105295359, 965680714, 235026353, 314823552, 805138558, 871355249, 179630983, 965029069, 382989725, 715400066, 794628270, 742858, 298070629, 529087303, 494630072, 599245642, 753826515, 699696687, 805973007, 2247141, 96957509, 852674362, 835409415, 97646976, 643698680, 812380293, 711109103, 159405038, 815697960, 253904068, 838787331, 829598518, 827974967, 491636469, 497817506, 182221628, 805053343, 845695746, 504983026, 65949154, 78488267, 462688970, 353333666, 918641679, 290846594, 319526008, 218818250, 762052187, 583210465, 414285217, 362847794, 747799220, 728827125, 490264000, 15910976, 103900474, 625948817, 371758617, 534603683, 841057115, 690285004, 832128645, 414889300, 745835807, 395464653, 382695486, 631882025, 689080305, 97149916, 994584086, 765035898, 449475772, 462371456, 735726906, 529813484, 970045152, 242701732, 420773286, 825379225, 575471784, 5587425, 598026944, 418818270, 288260043, 352518397, 280266919, 530653225, 152880826, 377940317, 835430, 710878386, 102817474, 672884795, 920026275, 784175623, 419173829, 565821908, 22404734, 252182895, 438403834, 521970308, 138723933, 622850072, 940516887, 237349463, 808414472, 788989536, 316464931, 651755485, 299007811, 58167849, 114807553, 856612815, 913951210, 143876378, 852314023, 767463131, 38122413, 556628105, 937414644, 992225311, 440364554, 144048233, 403586040, 567737896, 261422763, 689927255, 877156016, 836548220, 895003028, 204659638, 800601316, 711440696, 34606449, 664619402, 739763796, 481823809, 735793606, 91519898, 903612604, 770903376, 8237079, 687923498, 694487678, 963474467, 180712134, 351382709, 786086757, 248753133, 858224192, 877632939, 442066533, 629414578, 888435042, 379589402, 781652682, 647814171, 55673740, 864233136, 244562888, 583732721, 150132988, 106998089, 638626434, 14265549, 106109136, 834783135, 441143287, 404915586, 549444778, 218794637, 213636936, 840598378, 706763612, 24632533, 74007064, 775072241, 85124048, 81408903, 813120547, 293306373, 251725241, 538206839, 527143293, 916426016, 695839244, 255598831, 629726270, 787175661, 698690357, 90683797, 997214829, 886700392, 839317201, 684454636, 686475937, 516196849, 536058800, 175895499, 589365007, 367872399, 113255915, 830691005, 523075700, 916621463, 344238559, 887387635, 199649571, 311880043, 177765036, 652728008, 507098279, 190201509, 203536772, 864818607, 268805339, 338185790, 532190221, 342339175, 675246858, 576271484, 946374011, 639020894, 792388108, 582685713, 17849333, 621163991, 340043771, 789179961, 721724881, 546613946, 112085573, 706752590, 352690079, 883635397, 603427122, 7515864, 392970743, 277432479, 661843265, 535556238, 480380272, 656944693, 85003121, 525236572, 244773181, 252174546, 279619798, 109100939, 195181950, 913636861, 538601598, 950894723, 691017414, 972780356, 594033214, 246449173, 182446828, 439693530, 511495952, 935297560, 653858714, 806331087, 220393742, 204362497, 700420625, 503789230, 560872344, 376003560, 815823265, 504933891, 254024601, 23281185, 2085906, 616692214, 324807130, 703382788, 150362419, 759801790, 601229461, 568867356, 499640781, 449673796, 849330417, 179771450, 182376311, 673114681, 808379871, 569516786, 710327174, 660848785, 48788905, 255305915, 384932593, 941029611, 688752824, 389019142, 591987191, 67061859, 560401844, 485949867, 932185729, 18249864, 484410724, 278428429, 530555072, 84069181, 200455437, 444659799, 443275326, 60259314, 424322704, 799687282, 558816687, 621960528, 438703738, 976001043, 969117050, 951196205, 750819476, 552217977, 695185743, 765933612, 933188076, 322701336, 460206374, 305358474, 748337106, 418112878, 488359996, 276367923, 572512464, 901436397, 210436952, 807482866, 885863371, 489957482, 526475635, 774386709, 401542991, 965841584, 248826351, 366548952, 720956912, 847139419, 789918224, 722101592, 687743628, 393188588, 552551740, 470695729, 146633563, 827051436, 851811895, 639021634, 529834644, 60280196, 391043122, 229932244, 446095702, 758994612, 12788480, 291540108, 89504026, 740952187, 947652785, 562181835, 893231852, 554379367, 65564416, 853996783, 670708747, 90546362, 61559309, 774825275, 335659412, 829759864, 197435184, 431955131, 925253027, 535324626, 803480140, 97183436, 337413362, 74764466, 687335917, 68736108, 704904068, 863926962, 446322217, 861104492, 94065087, 891782728, 869379409, 687338236, 260731814, 452432975, 970473415, 418305759, 200465084, 42798985, 352838672, 877144836, 254300782, 146426921, 467040781, 674252842, 147395570, 178093975, 23414485, 93574952, 728523753, 694236026, 760117040, 804307169, 208011326, 725064770, 378614641, 513260819, 468160167, 816467275, 422600960, 294609470, 804484225, 666084097, 487940609, 810159568, 636034575, 588667894, 146784354, 967309784, 71154034, 178659587, 815330609, 574384361, 623447342, 656801176, 793928476, 749965761, 407077627, 841900905, 658813824, 826172323, 76669754, 417378648, 514186950, 678651540, 393709376, 542085427, 478838330, 779531271, 960641168, 47876244, 549651854, 589919433, 331540579, 405975081, 632426999, 697997612, 438083177, 725999200, 468155140, 556110540, 522877954, 446442632, 301485707, 945655109, 911380536, 426155141, 547258970, 811140307, 496056170, 20958259, 323989000, 98776622, 498269356, 985266842, 737060929, 449745377, 546751262, 17416682, 395905479, 360249795, 713744420, 621606643, 851526590, 668205800, 297916478, 489256885, 149199, 753917927, 126700373, 503576205, 766547897, 466374935, 63422770, 683145350, 423489228, 505093132, 923243072, 937584157, 458727465, 892355008, 444055327, 130990692, 232254708, 251916334, 565627888, 757699744, 442094655, 85859475, 899013240, 139605718, 530910862, 575093113, 516155957, 348504947, 198934083, 735849058, 539673662, 571131888, 484601625, 494940632, 634570125, 21686830, 114883155, 509088093, 205870774, 289470533, 412796245, 170740206, 891338669, 26789693, 568903312, 709089776, 790333269, 203704251, 395945737, 487915465, 65948231, 440476983, 219476709, 798553379, 209873888, 106367862, 54819512, 687574016, 619333810, 609858150, 614764348, 893663633, 364471150, 299132534, 833417694, 344948482, 358178047, 657013726, 88167158, 952009445, 960265902, 251174583, 343536640, 691163775, 684600468, 27870353, 327277724, 372515496, 159611700, 311975372, 137492192, 753784794, 712516079, 589988584, 624964370, 374938978, 733486666, 336843285, 875180327, 921196702, 863072313, 868096506, 181357788, 538730961, 650065798, 602844613, 21847021, 67880180, 950937039, 398215458, 76358248, 279182683, 281145806, 634215195, 6832378, 959433781, 220755398, 724026773, 425269611, 872720336, 286687828, 115325856, 454525431, 98059230, 797841908, 356752731, 196319463, 41392873, 169080027, 850998792, 360134695, 119000580, 727643709, 725568370, 75695416, 150845164, 502740688, 306651749, 625764826, 421736876, 875953418, 68790280, 498289732, 535305312, 714123862, 404348291, 834168609, 282832572, 605841797, 797036182, 8614142, 744581702, 732584772, 959509547, 600460879, 122254979, 517165534, 500318679, 732302225, 249060143, 393221183, 630041141, 463955625, 799831860, 962911928, 705109902, 92997366, 371712528, 712643708, 817572631, 695716021, 137524680, 632258133, 694302962, 528145848, 789874253, 430563090, 509000526, 703651313, 421337432, 795652771, 641550734, 9411628, 246358504, 918741695, 788699221, 875522935, 174409733, 194868019, 519888629, 405215010, 350733425, 241739049, 203039135, 667381549, 409331291, 187039503, 106412570, 180298290, 927535789, 584174038, 321455753, 23218280, 819009807, 644081844, 40785225, 239820171, 973427625, 334906071, 122846484, 771898948, 510652023, 689013976, 172288784, 939231267, 663308679, 251832139, 438440722, 163949882, 356195224, 958697485, 889280999, 972234825, 389817291, 614225263, 865801676, 231670472, 163937987, 541010114, 766371878, 712967034, 708096165, 325260405, 798601928, 285240280, 861356839, 979243610, 375770012, 197239787, 162781717, 115877209, 33503597, 787119499, 78036947, 781479525, 147722914, 155683220, 252017714, 363994702, 507535310, 199044652, 954797371, 398261725, 204491608, 81508782, 491494066, 594250272, 349149104, 416443831, 476963288, 645984756, 595247914, 149772257, 514094432, 651636217, 983711505, 164891364, 718240576, 212890432, 730434745, 562231168, 908502428, 217584109, 586064313, 159655817, 181559730, 665973346, 84007384, 409653286, 431192850, 857029107, 777805693, 989970333, 899196390, 652839909, 146153171, 343064624, 225088655, 64701146, 188501674, 515620502, 812734171, 421887887, 161974594, 653882373, 897678974, 763261008, 202505414, 87035728, 505845016, 651736903, 498318918, 826613381, 78062513, 626200115, 784988323, 792728332, 552127508, 353177947, 258155446, 843215801, 815472572, 168308138, 82106204, 806383412, 354717, 687189125, 860778610, 303791098, 525867761, 103647780, 648954776, 562594541, 600292169, 679418099, 631952155, 570913440, 468974808, 230223309, 753745864, 926612244, 244120884, 589412847, 784297806, 241814709, 625484261, 973488480, 314499582, 461144692, 733206391, 672051035, 47854687, 943080258, 621813224, 284513142, 659515732, 5014181, 782350787, 287756529, 965166178, 261803383, 623478372, 379958614, 680936899, 450954156, 352346012, 121451877, 698792616, 937448460, 679116856, 235007931, 902776262, 148966106, 965477165, 354614691, 469138244, 383700134, 869400523, 276357985, 353916767, 923375059, 248667524, 189247720, 529841554, 15484599, 697838659, 521261547, 401239570, 659645321, 848592741, 530373514, 969714784, 164768464, 18683981, 280267149, 748100086, 51136730, 193331428, 231779821, 451710744, 938929549, 132960128, 958548987, 851328619, 62176469, 473254002, 822400482, 123318555, 80439389, 199361907, 903196793, 297461522, 872217313, 281377833, 454189780, 439775177, 219454649, 183596553, 380656182, 755462895, 48498056, 738037033, 900921902, 369901530, 136882486, 330998668, 449896305, 977211294, 890835413, 966600653, 85683640, 616860759, 655352430, 504561292, 17285095, 272583966, 780853993, 536539331, 278987406, 825355189, 934335563, 350066809, 306893628, 821489574, 211493126, 861036524, 979564789, 79812079, 322349790, 604162510, 860309472, 167388456, 643001808, 618593061, 630951392, 356585277, 518136112, 953411088, 637998640, 746341792, 666971680, 486090205, 472106963, 431420375, 97917606, 985166840, 10640213, 444035119, 701514757, 653152266, 422433300, 194467946, 436491421, 336937865, 176450824, 56145018, 707655046, 353086961, 188458362, 178265590, 519742784, 493929219, 866585356, 533077840, 436290005, 106891133, 35256052, 533896991, 863385714, 795183550, 783244261, 527608808, 11850954, 299287394, 253627035, 227742193, 210168814, 487147596, 450216815, 261440987, 799059976, 648494769, 632187198, 231898477, 193765804, 683393671, 963776906, 270985120, 55384966, 810920700, 675614432, 559503685, 291271657, 136664287, 667398839, 436568791, 966916775, 844740088, 819964553, 250536241, 70769301, 354330359, 748619327, 873950001, 439898644, 86217786, 586431552, 152056084, 883358685, 963319537, 511273090, 160930111, 539822132, 343672304, 722051303, 796119592, 813292411, 779724268, 97830693, 767795040, 119618649, 613687035, 312687260, 532236944, 67751977, 873790784, 526095182, 397652026, 402363480, 664539025, 168613994, 676411129, 411513183, 174135218, 58770246, 100388758, 870126399, 457697769, 90060012, 155307748, 874605327, 65851297, 699043552, 914109412, 370435929, 421076964, 172927641, 921893083, 792524963, 53123907, 669133850, 245479691, 224689874, 489345669, 446332770, 20896475, 558641080, 542506425, 108193263, 191684702, 347027379, 866228278, 878783611, 978732457, 403910796, 507486924, 910786969, 369058814, 900836155, 864927327, 170570228, 315316285, 777995303, 943189135, 93937550, 316675115, 877021387, 202304110, 947645754, 691211203, 878828443, 950350960, 513776870, 176192482, 828318378, 569516653, 457105496, 341975761, 908459264, 315499481, 128914531, 676665590, 513016090, 937271913, 964040614, 190490721, 683342268, 409432826, 157211754, 915653560, 858776027, 936333324, 154378985, 160739490, 853807790, 38206261, 935544907, 634266077, 644668707, 242614849, 880900628, 175584155, 385985175, 108238130, 754813584, 325960067, 974602172, 412986026, 274101867, 438081155, 25197722, 832684913, 460781369, 911191934, 577306948, 147543028, 171602533, 461657942, 511259949, 851212658, 651205037, 551778842, 205895275, 219165400, 622396545, 568603759, 645375043, 267991574, 711363087, 730448068, 677641525, 207130761, 670351271, 333405773, 619972330, 360252497, 401494500, 620705467, 159269197, 490403869, 752235625, 203783689, 859655630, 875459128, 265638241, 907872794, 699755580, 872946587, 417846172, 486296800, 723035484, 880097132, 495543387, 528957000, 134153015, 83307269, 939251451, 583870875, 392067945, 43139932, 315486992, 481520329, 582631513, 514930363, 585780728, 143512353, 890344178, 28421514, 371990349, 139595622, 878564799, 975355628, 555430562, 90724742, 101499136, 528641294, 59310146, 716122247, 58284410, 45939173, 539304548, 454433766, 327514334, 619645644, 449716137, 902027629, 974788267, 251023075, 203550566, 169750312, 369391196, 542067172, 717696121, 741333799, 587868218, 373947232, 25997496, 696477360, 334740067, 768599712, 547639200, 260339112, 874440746, 180284533, 250001811, 746544371, 348215260, 499658669, 85849843, 485356802, 357858113, 722975509, 280592532, 362406368, 890302977, 715132724, 85691229, 943087370, 693120285, 956226912, 26376927, 195068769, 639924419, 858184298, 619352559, 553634543, 147700230, 274611635, 335854465, 973479308, 759390376, 488932205, 504749081, 674111144, 191310547, 112246607, 20134708, 762834231, 591185887, 774013645, 89939683, 32242408, 945041442, 418397474, 591120090, 988737703, 162805256, 776639993, 61350996, 796510668, 150409954, 352533915, 779426450, 189819028, 775122552, 473034217, 366263462, 106652282, 863036168, 48079502, 199461536, 566469436, 185697420, 939654202, 856194026, 594773297, 607438510, 280067333, 274653147, 620667914, 178358479, 41138926, 922536142, 861460669, 656794277, 824842528, 694152158, 778165215, 912834775, 190576144, 633501792, 109814881, 672553429, 898214019, 137609151, 842571180, 756664847, 812348020, 488979390, 254278556, 767780095, 728165064, 916158779, 719326079, 746199549, 206143137, 385646025, 504717737, 444648250, 532244531, 199638208, 529855402, 641201063, 523422854, 551965818, 74791586, 779920476, 422992363, 703686722, 962746935, 967275730, 487008332, 952948632, 378171817, 533059767, 639979033, 539646415, 606395698, 68920544, 168009662, 373139051, 768867957, 281759602, 74171116, 886956522, 312380593, 957857460, 467087958, 396538484, 52292235, 82862228, 64793284, 316392614, 827190554, 251228828, 301337841, 787221790, 307925735, 962357847, 267925372, 408274744, 256000940, 169701018, 900645024, 869653694, 61128923, 604688036, 389361958, 885836485, 955784219, 501498239, 728748789, 772635289, 68262547, 139272616, 86552360, 724756011, 986863630, 857288580, 290216, 761306652, 994727144, 655880959, 347824731, 462487034, 513545834, 923778058, 500921384, 809320632, 87950059, 32389552, 191751083, 82736169, 698406538, 685923141, 324089501, 873483791, 334903700, 191272065, 688230955, 183427767, 242442096, 977278658, 306556315, 440456725, 20371128, 253409805, 542294398, 226735058, 860753581, 879358555, 729550288, 171969644, 275978153, 412448362, 704559423, 566348200, 805510969, 705912463, 425877259, 89868343, 854282208, 598196326, 199653483, 696182865, 908614962, 829583113, 900681374, 235629072, 209838163, 791789525, 343697797, 553618232, 892100597, 551056933, 593114035, 847603125, 69119178, 365532022, 561731426, 217965712, 212650683, 485848920, 919861422, 412397552, 497395896, 688877805, 54820717, 143164760, 963314552, 393944077, 465086549, 35006857, 695265329, 192148146, 319183581, 231856233, 26548096, 286197901, 693252270, 584376848, 942265643, 769820858, 118155944, 895663843, 595332741, 728235455, 649354992, 782743684, 440911759, 915642537, 580893397, 532174572, 689051262, 319048624, 154440928, 696001839, 79546823, 390783107, 293112101, 947063917, 314065942, 622995012, 29744450, 555524416, 974332349, 128240682, 709289664, 713132273, 941354076, 739824775, 23980207, 680253284, 417850253, 873841539, 674773820, 304029491, 923698544, 460026876, 606576846, 662924705, 698092849, 667722002, 728678513, 194841188, 169422920, 600095833, 676617255, 919520522, 468842930, 910622681, 974233654, 875104980, 109715083, 922364235, 716491243, 393680750, 462151357, 252442421, 769023947, 654781311, 841402258, 430616442, 586516957, 523634662, 352285071, 966926789, 410770073, 640506543, 752596622, 580944601, 351307919, 272308877, 820695305, 886681603, 778617893, 806024995, 708868540, 938565180, 756392624, 601382519, 525814402, 579398643, 675497415, 826697580, 54982321, 586507507, 614360704, 331917627, 308870885, 32095904, 881520666, 342497293, 698281585, 52707134, 82833346, 312737534, 364683493, 185809392, 809675185, 669893504, 674301651, 359502554, 902535645, 674011934, 510271723, 224139949, 710060355, 412642066, 413304631, 59459350, 166647986, 638174129, 71282781, 944044044, 110058690, 545875192, 111519190, 686377741, 872312300, 871568227, 265267452, 818708865, 761150765, 365056932, 546083373, 177851596, 816075107, 908644291, 910145715, 887858989, 938059207, 520912814, 949356939, 61637038, 470079941, 218885207, 223421016, 102640757, 64873735, 771343083, 186063199, 50825293, 281191833, 220430772, 557951668, 452706151, 917735990, 149430370, 431375563, 682578669, 713772163, 441879733, 170313457, 813522608, 442638538, 183428579, 300869467, 37594159, 416003907, 918907125, 961647685, 696468482, 524751466, 142707582, 163740704, 711359381, 161145618, 803073847, 143153032, 52528656, 652696268, 876394118, 765957893, 356121819, 390419307, 219059333, 834557886, 341070501, 136975411, 842310609, 398730002, 679389251, 853934994, 632675810, 870029726, 814271955, 645425036, 36394364, 944711545, 458418664, 430038547, 9036240, 859513922, 395685506, 387238214, 296362781, 794271361, 17159273, 27571271, 255835614, 400309148, 779917851, 174904992, 47675838, 300185856, 215754796, 116493557, 757094717, 579951192, 327912079, 643342237, 336334650, 315254240, 944392962, 550138531, 850639433, 547301920, 596774609, 568824693, 577787889, 602525511, 893639815, 56777730, 77364209, 378966020, 178454912, 360815928, 219241606, 948275792, 592644781, 321735644, 257530850, 704370182, 351537709, 923507238, 623447305, 311072987, 680745573, 905344016, 658325773, 269757489, 396375804, 437615578, 374106110, 52097303, 436906381, 930834745, 14372216, 907926219, 980012985, 820244103, 288329317, 891358062, 705110968, 41452907, 724724938, 617781545, 563553011, 484572600, 772529055, 626952749, 716098847, 640838501, 726120647, 321641019, 145864932, 179612945, 332585429, 528081877, 450180581, 82016314, 938867755, 613169831, 312082457, 446873420, 685881623, 639970394, 27955678, 37803075, 947690247, 394981578, 516690544, 62313595, 156440530, 356285040, 449080538, 111113828, 852722747, 535877129, 540428591, 175241737, 743212432, 287293177, 994192293, 168217469, 9440491, 980497089, 336817851, 468490137, 456131545, 269030138, 38506620, 671836007, 56502805, 241200247, 769187644, 442733907, 809918074, 334609545, 588721483, 424332073, 397330964, 326787308, 254452472, 784504968, 995509046, 207007268, 666972123, 346859376, 771295748, 412540881, 608848439, 974355985, 14250351, 131523648, 635689904, 111072305, 440872475, 268111795, 567466994, 970421359, 660537307, 436175419, 219246350, 730000797, 673400596, 690607882, 285402666, 99823330, 141460400, 107058972, 454523786, 485245152, 844360891, 651933861, 162360038, 622431822, 935115721, 205968773, 667316545, 522199444, 810039509, 564711054, 420334267, 799411652, 525343807, 942839037, 867567465, 983905105, 974330428, 27498912, 354584789, 112655519, 208666321, 882057262, 134894160, 35766002, 421322967, 717458980, 91954996, 835842479, 174095651, 835681821, 135673023, 360060345, 443996289, 91659162, 258854868, 700217465, 803467001, 522466149, 63443917, 916697673, 831208850, 529053578, 711365905, 923867947, 228186145, 504491212, 314738976, 635630122, 106810363, 946964524, 871328208, 479831174, 77731798, 890820024, 737642614, 931282004, 893295039, 279742880, 311590962, 34059874, 642926875, 851006846, 199982515, 146078194, 138204301, 187873038, 12036862, 449024685, 577503763, 869438410, 205678272, 581797021, 676713532, 475911903, 331845081, 34003506, 41356049, 236718927, 848602381, 180614435, 173890681, 382889789, 869042900, 969622019, 37373923, 608535632, 880378745, 937324109, 364099040, 206923710, 560117761, 562828952, 807674695, 851415874, 974710456, 785549756, 718450229, 154764838, 100406283, 122712450, 126804921, 494596068, 33532985, 26089409, 735059329, 64787699, 663142030, 460477323, 802115109, 109639671, 623361925, 130681893, 992267756, 892016755, 900188615, 722542666, 501888201, 770490163, 385771216, 917176215, 588378132, 976306156, 662484341, 863785488, 151855058, 443464688, 508461438, 233773906, 481568484, 92483664, 832266696, 593292585, 565308823, 303110340, 547144485, 779184914, 536426015, 898950790, 186470768, 818079597, 746396712, 580573720, 512658243, 509900774, 92958877, 88560322, 289989978, 420356125, 770060104, 524432027, 357174799, 451510216, 564294376, 664849682, 586522777, 255792675, 746935947, 751527448, 814520726, 380375793, 838364120, 113656780, 98722130, 128217492, 546487771, 324323514, 154716827, 96773728, 469803829, 784720956, 183485646, 536161961, 309305175, 109170498, 994434280, 338952095, 223720512, 1990090, 885280771, 869657834, 641615752, 243030726, 698038516, 825152490, 84558328, 990852087, 660191741, 791159157, 823773921, 36800152, 774041803, 916641944, 274457637, 306373288, 490248065, 639880495, 361622607, 816727515, 304154, 791305358, 346961915, 187620218, 543050623, 934890757, 237362489, 476393646, 488731820, 607586558, 258093209, 391327955, 224697791, 966724114, 873699729, 153612830, 22780542, 952419305, 215661540, 474846940, 866145163, 855437757, 298316979, 439546002, 730672390, 112431884, 109416346, 301482995, 359235691, 225419568, 547198504, 926506381, 922601582, 103139241, 971596257, 274226635, 731293979, 138661736, 790381906, 86626207, 721427075, 6186304, 734269850, 473815475, 277210440, 90913169, 142934926, 807129090, 384788293, 681517758, 98248129, 831337896, 305564452, 123146384, 25850318, 389477492, 492459927, 981457850, 624651293, 244223589, 592701102, 577655210, 678187514, 49385249, 991042202, 378208146, 477669680, 923010861, 954622643, 647674682, 71721830, 265627243, 154536558, 409218220, 973422774, 447965740, 963820608, 403739417, 708575872, 806113013, 274315165, 277853150, 299439642, 266457654, 581811858, 561855949, 789641517, 883262199, 818834257, 334138052, 290979461, 980228050, 869768506, 375936574, 957440674, 268331669, 130602464, 165537351, 328310629, 385181297, 455392367, 276469391, 356897982, 520289864, 487110078, 559941388, 639907969, 989281034, 255350126, 529601637, 596561471, 961523133, 60439209, 852026940, 662302709, 207694527, 588459249, 877349957, 251777310, 497835456, 153587847, 326695605, 838378553, 670980328, 577075470, 612554080, 251531446, 772077540, 995152561, 730928978, 594531792, 579226540, 380179042, 243227088, 656566864, 143536025, 736218456, 972598656, 11826239, 482200651, 730204202, 57037806, 558274178, 731489197, 553020252, 816993084, 710620865, 404295571, 434982433, 826273777, 324463069, 107934896, 567073382, 543653668, 785205163, 114981126, 809575035, 148460304, 399693041, 486397562, 874533412, 832900422, 233802145, 940149868, 577575593, 64194238, 878693024, 299342202, 368851450, 837758976, 8809953, 861713328, 227478433, 541801410, 438198886, 895349541, 74393676, 798473678, 880383759, 597183928, 449981379, 681915570, 269345324, 263157766, 845333049, 168623014, 451967343, 944730200, 255751018, 329881218, 318747710, 977140088, 824521282, 565775122, 388493623, 835735058, 629524710, 206063599, 836289184, 895936143, 757992405, 832101120, 480409640, 147819856, 413693662, 998013249, 797506270, 864864106, 90719252, 931750887, 678544677, 569993824, 537391746, 100422496, 911846266, 114596973, 953351482, 302222881, 991250090, 642731076, 570329741, 40886472, 32636705, 615616718, 737214945, 541262637, 153315726, 287573456, 502015344, 522145477, 348838315, 924751243, 58610881, 737742756, 765666398, 675167565, 134366508, 267578384, 864735996, 115856042, 681797881, 411252727, 116174700, 984056671, 972530663, 379222734, 336231536, 567496639, 390457876, 143718552, 571945286, 559384212, 814281378, 551182181, 416518860, 477826071, 913027931, 517406928, 268329855, 252178563, 330968286, 686708386, 710859609, 321336791, 675497970, 407638934, 171609233, 840069154, 258948276, 857774089, 663662493, 783590055, 169106594, 577072898, 883013948, 167190497, 737756816, 77641322, 887258867, 462352416, 785957638, 458383795, 523647334, 150244758, 319907869, 602415978, 418131772, 639468088, 670352866, 773791185, 878054291, 555810192, 421082106, 482293754, 550079479, 351308556, 495492210, 862322174, 173840974, 967456728, 737449807, 938082359, 230458684, 272639124, 454975315, 387249591, 659611047, 965186018, 457703221, 672905372, 593302740, 440675740, 591960032, 50894774, 712676690, 704881073, 442617838, 493615329, 928235479, 367604755, 336292677, 242224627, 789911362, 801279551, 293487043, 45082203, 307385723, 439341679, 734013784, 98332320, 90016184, 519766845, 155228569, 721334577, 229518864, 553196525, 175507799, 724173905, 404524895, 153250248, 289914471, 855239146, 171044210, 971253957, 507383307, 642373922, 589699371, 779425158, 117845776, 646808653, 137644881, 900636034, 843073611, 464511395, 472682642, 428590078, 699904302, 401270355, 427507313, 287709635, 67829322, 288589924, 214994375, 618306907, 791136682, 612098972, 954015346, 861989868, 651592278, 122223538, 609699142, 900659907, 739275078, 563005373, 934472118, 889720392, 968721266, 104883989, 527400627, 85997329, 571368588, 475044889, 374631238, 76422094, 805651283, 165005970, 986300138, 741588827, 488690336, 803068671, 186303375, 552416579, 199860193, 822794038, 283333181, 324209518, 737749681, 449396897, 207336959, 892254419, 189204786, 938344950, 330775727, 656238121, 490526949, 70564682, 548667629, 733413249, 64374617, 257549839, 17313399, 289693308, 756705679, 303501074, 78893652, 976278781, 829857993, 537487068, 702220035, 353844304, 741548014, 958804190, 116009071, 629274516, 146319370, 150019514, 107401849, 121143751, 644705448, 410691978, 453294600, 183874041, 947649605, 633358798, 711600061, 272152631, 212256354, 32890940, 866105684, 409771911, 688212152, 185600936, 776057387, 245758630, 882410216, 114753164, 122291776, 380042067, 460230067, 33983141, 755116968, 302423919, 616738733, 539542641, 897790367, 168855073, 933366054, 905155946, 930811059, 785365574, 40690845, 784316661, 604440195, 230247050, 130931271, 875542182, 306943680, 287418452, 654417645, 214931724, 349476179, 393418603, 744535504, 789252937, 817946709, 343156964, 390329580, 217503883, 544618086, 531481839, 651925095, 491653993, 315532632, 894487415, 943378435, 535636035, 466374563, 256028845, 753322591, 313277332, 684488206, 791529496, 383319094, 710330520, 974302186, 923174375, 725559868, 561638596, 128795380, 980741581, 637119090, 949358077, 798712353, 864354439, 448162879, 725336820, 670544756, 692341469, 871515655, 954439805, 79615749, 641036618, 706414491, 551730513, 891103816, 67389045, 731306212, 724112795, 340714581, 665349586, 314831403, 81255154, 368785244, 809875876, 103660019, 863681791, 140642288, 38639975, 55113883, 768336360, 338476941, 646685301, 261716749, 136903284, 761192094, 246087334, 447066036, 461591195, 866962052, 697738112, 430276409, 203610892, 112041266, 322902340, 318398226, 566446382, 111474979, 928658990, 439660498, 144559798, 913028129, 299601707, 521243176, 361412740, 268928091, 320371876, 228753925, 836016866, 479827293, 450086789, 592728014, 984135095, 105635972, 558881207, 3208653, 771921041, 51431675, 714153015, 615099273, 786640858, 124343100, 821229416, 803529563, 716041018, 176964532, 159326310, 81367526, 946679186, 13361731, 28613217, 626307166, 131459448, 216707233, 747791565, 741520569, 116149320, 716854232, 230546027, 533823359, 215850187, 745011958, 47253698, 576758268, 625434434, 135104872, 277177749, 507726330, 884269680, 120650597, 151289221, 114196744, 192951366, 92175482, 131975968, 309226721, 577700668, 503674451, 564748998, 58420363, 404819739, 543617923, 31869754, 861458725, 83347885, 597295964, 130291156, 436705188, 92927528, 228218031, 135446230, 127925279, 504425543, 527223366, 917194605, 653583243, 152592253, 92841399, 92010459, 186318691, 143299884, 182344101, 708481934, 212272153, 283264532, 991983359, 996355683, 67622597, 89555280, 876570599, 342550591, 801142890, 88893567, 634064839, 497202685, 939079345, 545522824, 185942506, 619014936, 263618791, 804852337, 957958757, 27505645, 823719864, 972231711, 110191090, 305421333, 470943498, 373656382, 665604045, 954032229, 882735898, 442597625, 539154201, 516032010, 541368513, 529325479, 43718738, 571347521, 267375714, 161848947, 634616871, 292250055, 836662998, 822382991, 80173703, 612826067, 37029212, 967168389, 658687822, 157861842, 743438427, 297575459, 706682518, 362710548, 732728415, 687226273, 66615269, 575312658, 273140198, 487827866, 180650200, 787464714, 573236256, 668252923, 531835472, 368268990, 980701068, 768510303, 49741562, 612817490, 874962741, 25086993, 651979159, 764300543, 807749697, 785976730, 451076287, 908044036, 563261646, 657230154, 901645814, 557033283, 261336681, 532155993, 76727929, 77012206, 197099448, 180630309, 50497998, 836116666, 186200089, 400489959, 871778255, 862167400, 138173869, 813698415, 655438057, 301732865, 924756043, 414973173, 930306051, 775110287, 196952761, 985984411, 372506761, 629604539, 617678453, 907463111, 403224266, 814912249, 82264444, 853795028, 356175281, 554277295, 614999412, 544127444, 871109387, 659285312, 469388902, 578006508, 939557565, 153654589, 65570236, 461805949, 825027616, 668318624, 341462496, 360154555, 794531658, 683200252, 867325699, 316960463, 888147122, 622867510, 506835910, 665715915, 895759318, 964745393, 147977778, 467173885, 59388814, 26382965, 243455807, 842936180, 965534888, 601782640, 590159110, 619422224, 940437270, 65386966, 487533401, 122478439, 23768935, 35507449, 788035837, 615718568, 842823384, 762740530, 266074238, 63955738, 446417987, 811526380, 694506280, 385338373, 231812252, 85177085, 67584767, 698445852, 593256136, 808992883, 558558137, 840172739, 344554385, 177085471, 247820245, 736274772, 445797490, 402017595, 207775808, 253822367, 871558826, 14471758, 858602107, 934937603, 921446898, 841644795, 443451012, 470004764, 211833637, 564095361, 857732385, 194378754, 654389795, 483802893, 829110853, 477282944, 700948940, 570184877, 352679799, 82435780, 828906668, 45410182, 118132567, 829673482, 293718801, 366775116, 384085806, 61593653, 624443560, 636359853, 355358943, 760410871, 265495789, 148759714, 81720007, 746968763, 433172424, 931424383, 672823565, 295532148, 476899267, 216037419, 621776952, 87022978, 419921866, 236552769, 74914502, 283256401, 945801991, 912163873, 16783666, 11525367, 903342172, 375892458, 157441990, 7230437, 90594067, 654397580, 884267766, 74996387, 467462051, 811710949, 218919478, 655649286, 746982554, 662213765, 498803262, 591851926, 874796019, 666799852, 743010138, 277210373, 404661361, 841277557, 29917847, 700102517, 799456481, 383803403, 18203086, 288082736, 982133037, 634831721, 135313703, 699343953, 830086522, 278783937, 28326583, 565112862, 514466119, 572082327, 132063749, 833167616, 355566808, 808944559, 75554163, 856337215, 637120413, 474351634, 837593462, 187570513, 264044588, 191479688, 887166719, 417530392, 267611304, 396866994, 933121018, 5074313, 113662964, 403123766, 704936338, 960107315, 823219386, 862875237, 329846831, 35778952, 680153939, 633210591, 863992407, 936048164, 45601129, 734168095, 321319356, 434694460, 172505306, 142786777, 936524894, 262889233, 60650203, 767173525, 226711866, 593992531, 204832134, 232169420, 181184163, 169476203, 39270015, 263365529, 89739224, 804697354, 635559226, 776601253, 710165848, 822573460, 345001729, 524135573, 778752195, 40036651, 908400085, 757167111, 622769663, 556175250, 613402404, 315990515, 450364488, 439987074, 857585198, 858508482, 949458150, 810978290, 630884611, 634993003, 476413235, 988484928, 87221869, 278596673, 598769461, 445650145, 883879976, 461838189, 401912067, 499137756, 578298418, 365692765, 543814056, 141210109, 25282875, 357513010, 49188136, 123152923, 105597563, 641883950, 901370520, 579029125, 17512292, 793033817, 854181247, 730615850, 973755059, 39352358, 115574601, 374756033, 942039490, 323321334, 606380296, 526193854, 839938196, 986930772, 294492558, 912739202, 501601994, 911693614, 420792858, 851919398, 485851135, 493012648, 996303032, 321621141, 607047196, 721008017, 424784093, 467622619, 769433902, 151949843, 798081535, 754619037, 629958469, 722377147, 26583108, 404041462, 736857882, 814485808, 608754527, 249314756, 78261184, 258758233, 264012084, 90284333, 830798228, 529924091, 786578549, 102963426, 229614092, 128253579, 389922476, 629739903, 412165905, 87281519, 160391241, 907072424, 154828826, 502083573, 338452369, 214618268, 504201452, 493593665, 970524203, 886963081, 689781090, 19289395, 133733385, 35919291, 589787926, 701720603, 20551909, 197721453, 676969894, 238885673, 346423936, 351826969, 599972572, 264912346, 492948384, 337081524, 534287358, 676304563, 788086515, 690272206, 728465644, 163380292, 739015530, 834957560, 91049019, 611928943, 996222305, 753780993, 650524740, 192261153, 286834957, 769763222, 624051695, 170020852, 720597827, 118780144, 697563386, 994217317, 403923959, 837945000, 776419084, 558819129, 826158150, 470870235, 314271829, 878864565, 37863093, 628051969, 275348033, 604025609, 173038409, 970017767, 486545399, 290484662, 556920358, 557868944, 506684689, 889444546, 438771950, 12281670, 359003499, 467244038, 238493850, 202842049, 897426142, 3397841, 916928675, 172946513, 17242194, 273758302, 735574816, 954551684, 438184887, 150206392, 750518988, 59434653, 352834623, 688785094, 401340588, 270093960, 355810902, 207469491, 804329037, 680346168, 74377249, 631976228, 232867009, 206471861, 733305741, 47787416, 525840877, 662085003, 391118941, 953525767, 711500110, 99927017, 192688606, 262114234, 897516217, 830279585, 497621791, 37291295, 671507209, 555452285, 230073809, 366323924, 966199985, 342201640, 905269726, 126383076, 485830156, 310449298, 595867557, 136961205, 194857941, 723969714, 354596413, 908414832, 283135910, 641988113, 665328628, 216772202, 396560395, 793515161, 903052023, 208518155, 223483138, 699105626, 154365412, 27438198, 994942273, 198562523, 849385004, 612422848, 778193858, 659991324, 498256943, 443585635, 762289765, 933345963, 910916138, 94103441, 343931516, 81656604, 857424294, 502247978, 527938815, 234183581, 840383439, 194932547, 437479675, 204736459, 736332700, 371616008, 301043025, 271971067, 452698566, 339275527, 72287450, 155560717, 150767141, 368079360, 709421653, 825930551, 506013126, 520163687, 366302143, 972767852, 114647868, 702617111, 170009550, 401332466, 318571319, 403133482, 176343754, 727036938, 543974984, 871598360, 296332565, 128843743, 541844344, 527547235, 626961296, 172343566, 576867999, 841086728, 444090019, 821971298, 908516001, 52633436, 781568639, 573961746, 395566106, 490854041, 618954098, 239341685, 578832768, 814150926, 317326814, 646307073, 737936857, 860670805, 164366721, 452161692, 610478006, 339542591, 273298131, 788264065, 322849563, 448517902, 968915897, 605633538, 188764453, 301277582, 131890898, 516646761, 327296656, 652118714, 205701764, 644513662, 492649053, 514231581, 867992705, 527556710, 30034395, 747230645, 688531865, 497845177, 743025309, 117314736, 920198442, 395713056, 938532065, 901398338, 128369463, 512975940, 679030462, 6372699, 403920966, 612543167, 507046375, 544561163, 775204432, 767455552, 151028551, 72429015, 669979472, 466386840, 792027995, 974353388, 659776824, 765908241, 492761762, 515804282, 226585243, 215907885, 178934132, 391013710, 155213734, 654280370, 133317585, 36836397, 947604007, 793746975, 388786540, 562543795, 162748250, 632006022, 455058959, 734032842, 650526416, 297159835, 398486396, 548972154, 197770734, 744192996, 312244264, 602498671, 219553430, 314787523, 926703390, 232189821, 576765885, 514616638, 476240336, 370657766, 944506309, 121495035, 30116498, 2788806, 422907503, 846519049, 3406344, 36520187, 797961597, 861152044, 513111627, 928776343, 887326672, 73890436, 104423682, 537730782, 373044399, 842353663, 216291429, 186407791, 734341177, 646698770, 799565232, 29614170, 538645813, 533725423, 441476005, 944560779, 518781365, 458492492, 275205207, 300661572, 588582591, 346697826, 48490907, 362316026, 131812794, 571507802, 192139405, 979335287, 148666106, 870573587, 279967204, 736258209, 619151977, 279618849, 74534466, 877593814, 313383073, 798148849, 723346798, 759373756, 799400409, 717871946, 918243450, 572338460, 193688525, 601959893, 621484872, 387665526, 737672047, 71578961, 876735031, 557921804, 330743721, 159401469, 467989852, 551579452, 327256740, 120730181, 734233792, 953906160, 29634840, 60691415, 242946698, 856052654, 189797760, 701296495, 774571352, 318045147, 840805019, 641661756, 165966025, 974402409, 250560695, 840450161, 72152615, 851661766, 378060985, 548417889, 849916662, 340808297, 360775389, 736855765, 77029878, 4130143, 45827361, 569036671, 96707601, 703871553, 328523036, 169687621, 906021701, 289159834, 402017397, 333146414, 745442911, 409598153, 978133023, 472898787, 572561854, 892203794, 628734589, 699276529, 726129198, 66499775, 286790126, 858029297, 179864860, 340230920, 875295208, 694455085, 668855404, 691451530, 790658303, 127876679, 689778908, 805398771, 791576679, 108211833, 592418346, 163158133, 35595985, 562596061, 770894099, 700600778, 963852664, 60931859, 147187676, 332887415, 402436298, 68004522, 26428465, 305411157, 233765995, 226585765, 645980341, 813833945, 232548841, 731510641, 492507229, 166916476, 215732463, 579891271, 578837001, 160094913, 543333973, 910148266, 963475895, 325671788, 863994510, 759520588, 441393634, 734455080, 574144200, 28009230, 129618844, 486933240, 741844389, 236581400, 237791073, 68620306, 540014571, 802089759, 80017486, 423260280, 528636031, 36575627, 543928665, 766976678, 231565429, 70648523, 290034447, 998433303, 109945364, 868797322, 246001657, 323432173, 835574302, 188071535, 410378530, 302632242, 151669954, 298234117, 420175824, 51615515, 820783912, 204175052, 275898611, 29128789, 664804889, 272578501, 249135682, 557821346, 790163717, 390709379, 822120821, 284522909, 921968482, 235761487, 616925394, 985096453, 805438787, 241207001, 867327130, 873465623, 236995389, 249088182, 729956211, 437527486, 56032240, 231276464, 207511118, 550430044, 817772771, 283717584, 978443197, 188878506, 60482523, 966403331, 122881830, 708564622, 21394231, 502953841, 733239143, 484003608, 57345646, 914586050, 613507174, 170331128, 123654854, 158932843, 836997690, 550948371, 721426614, 65921705, 377686164, 634567525, 466508682, 185614125, 147073112, 65290592, 291610538, 199962656, 818115073, 937420172, 513679167, 296924515, 178298003, 74430230, 851505596, 847386062, 15883214, 333938128, 822472136, 684565217, 53782414, 806424897, 388856104, 687403731, 835681559, 599400202, 242623516, 3228662, 628615308, 481889297, 746025874, 13502441, 237575921, 33748375, 624257223, 516874486, 193287550, 777050608, 75739558, 601931066, 275577225, 357201062, 341302312, 84199014, 202119558, 132195915, 146514754, 629917817, 700311583, 600271324, 999127299, 196278373, 800026701, 183706958, 879010322, 748457258, 345427139, 187549893, 629267290, 301117946, 706692504, 268568888, 836056647, 741072169, 910408732, 271286839, 815379742, 431502513, 33931858, 932549388, 746315687, 84347220, 232318354, 465058714, 61521571, 748353974, 945995029, 356534339, 729871470, 899560620, 166900745, 189255603, 737261994, 801619453, 503042804, 241291579, 360374533, 147606139, 189028675, 321023572, 642162254, 373100278, 319960581, 255758286, 750581909, 111495240, 881894593, 918583389, 325481583, 684231373, 266044522, 518989134, 897743287, 143896621, 778166092, 479924422, 497197944, 504718698, 22878975, 120318396, 843889587, 442786092, 783197537, 835427045, 612564224, 13666613, 418394922, 14856705, 684442606, 273558961, 517485202, 290923539, 744829353, 920151307, 305740517, 668881184, 836812775, 719090514, 865164454, 687212791, 777654148, 721856987, 51434184, 948996834, 475988313, 824313408, 58882133, 401377631, 41955282, 361840186, 408339468, 965880110, 966471923, 587909125, 130110617, 141816617, 433704225, 54159263, 693703946, 683779112, 913604157, 113261956, 233665382, 588822648, 674990540, 917828917, 137393952, 445263595, 41438377, 89396467, 334714809, 143843338, 133559024, 704968713, 849796134, 527611615, 614720381, 429733280, 355034632, 210168380, 707203508, 77641018, 14578800, 207526649, 85792082, 88052194, 546543214, 198446607, 268492630, 593567999, 705327800, 657759637, 602650006, 93386418, 366880909, 542190946, 115445193, 349693629, 960075420, 157289633, 875976515, 362827932, 107206436, 832815887, 234017676, 697591955, 138372647, 117218941, 823751974, 778172309, 95081565, 722605898, 207460026, 507289175, 106903029, 552358482, 589194316, 650377195, 765821692, 493844457, 579463248, 187559444, 918154949, 931029216, 709650116, 235570557, 635676367, 467594801, 102705555, 21510354, 441613431, 642818051, 170348586, 58245711, 87013553, 871519682, 481924405, 550215789, 590736320, 579169600, 952379794, 570893053, 787512512, 375214269, 846321429, 740555546, 510274634, 666871648, 438752793, 432582479, 673934932, 563491827, 154150390, 607669453, 17027806, 297978297, 689015006, 172505699, 893031855, 1768252, 592285131, 215451698, 191962543, 599183658, 254804673, 35454287, 213433930, 126466577, 312795041, 797708295, 256228602, 463969304, 932814439, 215689477, 442422524, 302731701, 786442654, 168761714, 836047900, 657227498, 248408075, 761521567, 101015450, 995319147, 50482707, 930517539, 624731273, 304985317, 312577136, 97909577, 601438874, 892243748, 846419542, 860067262, 727563034, 836313788, 166508133, 989646093, 210600655, 358670956, 322939646, 105764042, 514065232, 658071683, 745843373, 931457506, 824087759, 133193271, 2789223, 268007988, 128403118, 56382957, 743593950, 139439656, 806499608, 557099896, 560659974, 232179469, 754527880, 451683902, 979621491, 844179259, 257248805, 781974464, 674093697, 491789822, 12357811, 461318530, 257519417, 601540333, 929151721, 145758904, 9373727, 502011807, 372839015, 824950545, 930818612, 434926649, 943946375, 262728544, 557453978, 5535198, 688808366, 691605982, 243795283, 827875228, 11037804, 849636860, 89806374, 918086579, 145294881, 28645592, 604659078, 171810627, 255083000, 612490599, 888528734, 703292919, 978345493, 313182401, 555658806, 447551736, 99561013, 737399483, 403189365, 613454025, 595056946, 289214242, 273035981, 576972262, 725676988, 979875672, 623411371, 804512410, 205643277, 60857640, 632009182, 667741354, 548952928, 356515421, 427778864, 14357405, 547357842, 643050113, 25690355, 925929769, 251558155, 616149682, 629957272, 187031162, 286204189, 307725491, 581272348, 75706482, 157964015, 29167182, 810894527, 827085181, 777701381, 230095825, 987631337, 543449896, 741240620, 827235877, 654639713, 943697148, 338619519, 511026588, 167029188, 625780562, 337391842, 757343773, 294957621, 698452363, 561668989, 101365002, 979318593, 929197145, 716496550, 184722049, 539937261, 39553, 793331191, 952591286, 265352693, 775866252, 70051341, 600494949, 712528061, 954360523, 257559132, 538797026, 989136957, 17044314, 517923053, 777532268, 730500784, 235005404, 547956318, 702657599, 614897962, 506409166, 843410688, 275616018, 518641902, 764138979, 686292117, 866289655, 933999698, 857704399, 466437701, 188983156, 362659827, 672306569, 244986910, 418600931, 954348665, 116429209, 815346324, 322903771, 916697270, 820274620, 877192695, 69899913, 872555076, 272856009, 842253805, 798059701, 817598081, 395860147, 764870057, 627934398, 591152833, 406808997, 257407473, 705711425, 48390137, 210871849, 197754911, 372006836, 907498089, 494243921, 437699263, 154892202, 452040361, 340488728, 207775522, 657677477, 312230583, 213015227, 857402445, 886671420, 992581289, 365814739, 681925645, 995897092, 988447768, 473634795, 828243946, 409762795, 467259419, 394718641, 234461948, 416421090, 574300157, 972848845, 547243352, 724769478, 114284687, 229249486, 235359512, 776461607, 972634924, 775195804, 499569084, 903883449, 86149282, 851666419, 917900484, 245782028, 798318574, 549856334, 890371804, 793796569, 11670519, 745682111, 312215594, 410615731, 646214691, 484029305, 291654323, 359092594, 375356885, 96519664, 581089234, 880624898, 623905249, 207778367, 692744488, 469204193, 72432224, 636807853, 359899613, 908259646, 91325565, 625710308, 931541322, 828174836, 109043936, 388431964, 163828494, 953279002, 22866729, 231142305, 563298066, 21360106, 595945897, 932983978, 4887482, 278037502, 834894584, 777469816, 824800210, 749059061, 369178656, 296781684, 407361681, 930901330, 20285056, 183364201, 24062063, 107389720, 212502273, 964220915, 924141858, 62506482, 999668560, 414185298, 589385128, 476039308, 96856609, 780158820, 966818805, 337615569, 763959055, 469334061, 995695125, 891406975, 760768645, 505629839, 839517669, 126569527, 877890057, 141084427, 629367453, 475767134, 123616881, 597352870, 977387964, 38839409, 115225403, 225330138, 552753795, 234132215, 720696127, 840944039, 552528117, 865256343, 889838963, 150901227, 328198, 743386910, 669532946, 400507358, 469948935, 211418743, 71061845, 976814791, 841972748, 582860090, 705982118, 581819892, 413663877, 7381174, 471079886, 807174875, 347428101, 987257929, 958644175, 550018082, 6970676, 122497279, 807805313, 413321246, 465198568, 727102327, 723564372, 667099782, 25632435, 80653741, 178133399, 8842703, 779920256, 942623600, 601222615, 512799972, 115362441, 671665317, 287320804, 915159534, 238165038, 601530154, 11352251, 314610767, 184293587, 46920580, 515277240, 269093876, 404611105, 903851897, 968789161, 914612788, 365116653, 453624371, 213920315, 368311155, 359425517, 829164520, 836387149, 911510687, 637148237, 343612821, 386254134, 217865490, 882997279, 601613164, 342468690, 778748847, 765689792, 813299618, 284267102, 874496537, 851558207, 309302681, 400544196, 601771338, 613890895, 298189020, 107208356, 212898032, 300302007, 912193755, 203268741, 358250116, 590511552, 483655328, 758909772, 310410931, 344708615, 928614574, 367121160, 171897151, 575280042, 197604822, 735415870, 399100028, 153225841, 893244247, 910310365, 170606338, 867278059, 345757778, 547041981, 748374840, 396045495, 569806147, 857746923, 734642800, 581509378, 611390316, 84494246, 256350335, 814627322, 374680825, 712128093, 784140868, 660192735, 945132034, 525048791, 17398702, 642113091, 70655912, 686785777, 569792422, 91310813, 624736963, 528912942, 858113982, 861172588, 905765336, 335078047, 594835929, 809936147, 761555087, 548835519, 702462635, 874523331, 310637220, 383672166, 48937299, 766329141, 34779843, 83736643, 622750307, 492878086, 211569316, 501272140, 631431338, 191150426, 621697447, 411552232, 963879545, 504228506, 162557268, 890067774, 108367541, 590670385, 583603017, 842332653, 783551862, 97844115, 223966397, 112588208, 732494391, 8438807, 326077776, 701166009, 612562836, 694773890, 898085989, 372058617, 826214734, 870122481, 255349466, 968302091, 497027999, 930803699, 96660135, 561209025, 113215037, 354747059, 300476654, 944549629, 163824250, 233624627, 813884650, 331766181, 39693937, 45510876, 817731150, 360949157, 685136943, 91298630, 735176794, 482071302, 402668832, 275760336, 853518302, 279342795, 708475339, 972008304, 826414400, 292057665, 509388176, 98054512, 213618725, 33491451, 269184885, 417687500, 389984794, 660017876, 127179673, 109174531, 813396168, 22169744, 13893615, 273157176, 465295650, 124606120, 585162261, 228821883, 225854054, 961849540, 399574728, 120299553, 191554787, 729446385, 308873546, 834871345, 747289, 733431074, 411915139, 670444849, 106015013, 873575627, 979121079, 630255268, 881434820, 803184543, 258419496, 827335312, 912933614, 783642593, 804005726, 361801517, 461114773, 931381828, 353680671, 979060936, 76996614, 825337156, 581872298, 938261042, 847551223, 992826371, 436590973, 493284850, 139390271, 123761709, 281813118, 849137547, 390567648, 648183223, 80466720, 727438897, 119618700, 933010106, 441389638, 173921950, 619635614, 805118785, 440106383, 129011548, 92802623, 651069594, 639694554, 38418844, 152892954, 341678452, 336546043, 568819256, 95585028, 605225988, 950241204, 795938369, 322339318, 923703535, 78804434, 518563276, 151857608, 728045937, 550871376, 931814194, 288994472, 241513012, 357688374, 420827671, 89721313, 393180954, 818507745, 436981652, 377783805, 954559664, 339709498, 648603367, 592114255, 463808792, 833382676, 408474635, 993432715, 422521417, 91950883, 297815935, 824911650, 477505840, 54628197, 38361745, 832770336, 539584325, 59431408, 451882051, 371693657, 248915261, 412353598, 458089420, 141451024, 684156942, 335146168, 163153171, 816537557, 52438038, 824152109, 995253615, 89066648, 243573459, 595983848, 341423030, 921854343, 722278115, 625733825, 342389573, 323801208, 798207776, 35992106, 851870699, 45004088, 629847572, 642403432, 356121081, 98653870, 473430489, 512191203, 768636963, 806847909, 667120311, 988899052, 821501048, 539225990, 449487465, 694095132, 441393442, 866039980, 136318865, 753391188, 747445820, 530489766, 484411646, 322011489, 751428193, 62047684, 926393274, 88511736, 60209057, 128315516, 565852385, 934445672, 820559621, 242566622, 9296748, 58035202, 864473079, 702115288, 598843074, 874321502, 883073424, 910158806, 212428965, 227264803, 250766723, 195436111, 260659184, 998515678, 230404450, 514376658, 785022814, 255949523, 180242111, 869166861, 777195465, 261896583, 24158167, 645658995, 694914795, 687826859, 388352827, 594697856, 585329965, 130974873, 897211848, 40297559, 976981827, 901328194, 838666805, 831997168, 722613783, 747861938, 699027494, 460737829, 198319761, 675162993, 14138947, 485377222, 606329136, 251669011, 898003124, 708505178, 756338526, 582306309, 362211645, 546050955, 873493994, 682966857, 621438601, 305941266, 778554432, 425541321, 159632583, 449659496, 233221782, 429751677, 20690083, 867257888, 16441543, 104054175, 759415671, 206018349, 88663218, 171965846, 657682175, 788330445, 973580228, 854225885, 642768335, 614396291, 844123967, 946389636, 670456553, 944580063, 510419440, 926381588, 61166069, 49189223, 268615902, 340151175, 902839628, 960316628, 401816967, 746853465, 734993901, 975883134, 886913799, 185494266, 314661965, 240627246, 714598604, 397824146, 585703127, 139010184, 298931877, 717511651, 945284997, 542935852, 632117350, 378916684, 987800470, 581194466, 955358979, 814189063, 271336156, 48840096, 796091514, 812762420, 59356926, 30763960, 105951265, 708489993, 927003011, 898208511, 49050518, 781031488, 4244244, 438924659, 46096052, 678561882, 611132338, 741595977, 424506206, 325464198, 276287875, 735635137, 845868832, 703757844, 275332662, 737602253, 578813404, 11091235, 848873013, 456758476, 128568234, 725447533, 590046917, 295506587, 409043400, 573486193, 853745533, 519894661, 677503587, 800502668, 505489985, 150209327, 870891558, 484267590, 406397970, 810260462, 263872092, 498152255, 924851767, 45510464, 719388726, 646804491, 93040660, 543807986, 909282456, 403363134, 755640268, 605144075, 769736819, 619458158, 104578838, 751507436, 562999128, 817890020, 60758396, 162682651, 822163562, 80157011, 584161907, 3910487, 136449882, 811517551, 643998807, 558045715, 969486380, 745503988, 796530925, 48880192, 48320696, 373862984, 163445186, 652231034, 477613060, 153792836, 282989352, 626346648, 484132365, 609548427, 969870747, 488489933, 459501614, 634572237, 25386987, 353317171, 452300992, 808296683, 770135853, 989139753, 25833398, 788149724, 553359104, 468207182, 786181184, 787363770, 83232210, 889850307, 209965937, 267490300, 266466403, 36981771, 815519732, 252204546, 580148701, 447927940, 975563337, 794979821, 954201162, 96552495, 433130594, 490033609, 723959784, 752922449, 29699772, 125207469, 182396344, 834853354, 226893081, 460550107, 709389986, 206881374, 858470085, 679623391, 986079359, 764230650, 818544202, 38029763, 68954473, 640828659, 188836223, 429335000, 462935330, 602191114, 365781773, 535894862, 11662128, 594864566, 787961593, 477289381, 132965178, 731051259, 6458291, 294435446, 914989866, 393518176, 942123633, 407912696, 876101819, 407615753, 743414297, 227236122, 579438691, 933610003, 130594380, 537478398, 510002177, 112461416, 744168399, 418742167, 309531790, 31176421, 411763908, 188409342, 735608346, 274385064, 567935636, 351849244, 412036668, 357812649, 871861053, 389624345, 792061496, 64731671, 84271663, 472248334, 425292863, 105727543, 411731749, 307441307, 480640237, 574414540, 405056703, 991365328, 565128425, 758335073, 190185102, 516859912, 245249512, 780084120, 543343314, 19981259, 104194215, 628407842, 701239195, 911017528, 641422688, 98969173, 550828917, 985759520, 968309339, 509541284, 449297333, 91369653, 280975679, 31535718, 479734480, 498221561, 973700109, 310014491, 763728261, 424259192, 108789750, 783120481, 936282751, 271626103, 811518126, 177494279, 810704389, 25626908, 768287085, 273064029, 913602049, 793183440, 408515137, 26001457, 434663359, 507822501, 484539932, 148604513, 723066847, 457507598, 703824670, 265359559, 803720629, 50046889, 489715074, 239572953, 650812951, 693798303, 373240552, 523874920, 349906292, 431698755, 555083872, 956523666, 73614264, 670104110, 853933328, 166257328, 175185458, 407832304, 301614432, 348835823, 408549661, 771651417, 28721984, 613503115, 314011336, 536826441, 311583648, 953468747, 761612229, 370536840, 227767645, 190641872, 391332310, 809462355, 542523196, 541372983, 115793866, 843219405, 958865056, 69775546, 59528781, 525021324, 290101833, 785890592, 120849137, 566729113, 909668264, 320794118, 790093815, 95730887, 268393928, 904422513, 806678427, 971745195, 285855912, 601384804, 751566683, 443583696, 684484554, 896837847, 298951735, 54707948, 847798050, 288509163, 816590641, 202827770, 578757094, 208967449, 317793761, 695271331, 746772865, 311804001, 773774554, 637538204, 434122453, 121219925, 542524819, 248926029, 767826034, 555709040, 234968250, 804167294, 276488440, 689895781, 814097156, 444802215, 726890272, 332722388, 19123845, 115815846, 876895703, 493205864, 494262919, 709310047, 400624948, 938233435, 155497650, 562509367, 1461572, 634174560, 735184559, 46470233, 698795142, 461644940, 656037566, 311130435, 221604598, 360080252, 590410947, 308000866, 486065064, 295918191, 883802920, 789132703, 350465839, 24908327, 153403751, 556788515, 999523424, 108487829, 134779178, 455532547, 573977707, 448850173, 510715491, 748225137, 377451957, 200773620, 632167366, 35379227, 455506088, 750024572, 668697539, 914117116, 739944414, 393797964, 209965197, 371881842, 22137422, 948176910, 622720156, 791132827, 278547386, 808604018, 486064378, 241561698, 21239543, 739232545, 10479438, 879032601, 56196217, 390312576, 837980803, 497176530, 143625211, 725022990, 587078997, 393005281, 588314020, 58899034, 836936902, 432902248, 498672682, 561726367, 655064614, 291574962, 364118515, 923986156, 289516779, 827357176, 141990184, 324306449, 696382793, 127497886, 922883316, 947236427, 346431497, 975899715, 452215494, 592567495, 292841275, 125449840, 930268747, 399781598, 40394032, 27544283, 607171017, 86875686, 187661142, 681045967, 605224919, 797002889, 505980848, 753798487, 72756672, 212868110, 277414754, 3693739, 660414404, 612407533, 671360415, 633282035, 982461245, 98218200, 89148420, 445201909, 471111518, 370273926, 455551816, 93968980, 595309582, 787377951, 454293358, 788630716, 425352431, 240021690, 838265307, 892164559, 661008023, 821628899, 517386232, 91031754, 338726761, 502813158, 557312095, 254689488, 858186260, 339381817, 654562188, 171218135, 179381869, 160251517, 455461131, 522074144, 729935464, 805281210, 914479559, 96435403, 122935305, 651155415, 417537165, 830985393, 458706960, 658229634, 62070772, 340898000, 123701558, 109663953, 394235899, 718922818, 591371176, 183030789, 170636738, 99773675, 71192080, 190745231, 746392160, 137957847, 141227472, 30653977, 320602268, 6222513, 550409102, 529730252, 536627031, 594186955, 709893981, 782196814, 366623684, 795328929, 757154304, 425600360, 968203805, 870941625, 630225792, 491606071, 217698044, 418683814, 672106986, 903158432, 946520326, 509267519, 348464113, 783071065, 899841768, 678389218, 168984435, 195892820, 346675866, 78569363, 323381108, 872220575, 451022013, 535072548, 705554089, 912536690, 168300538, 865670948, 891737028, 25950741, 540523528, 627045034, 793091081, 385058870, 818247139, 325765258, 763263239, 316759803, 454482340, 276408434, 943151618, 218559867, 85154652, 695724047, 503239690, 358666576, 241127239, 631175890, 78518960, 829900311, 780058670, 705864686, 993499045, 272802447, 718314575, 853749729, 924029665, 162424920, 726164579, 836859856, 669925686, 352388351, 571966761, 154786580, 248831908, 557433785, 53233304, 105041277, 904488773, 126789475, 518102703, 737435473, 807881598, 718043839, 46918072, 47266877, 649998637, 683208151, 219940430, 569166611, 41420415, 776120618, 392305711, 791228642, 280869797, 486542065, 71112132, 85181359, 437837219, 436307096, 679241171, 360888563, 636684358, 139134667, 215979761, 562456805, 444250484, 155361760, 568954882, 899714371, 972865929, 437039653, 816438671, 700932562, 192131145, 898676012, 803231316, 606849121, 683869380, 576541864, 118871526, 614914440, 967346128, 262348790, 593661100, 654370885, 575906415, 615960745, 224272426, 316001318, 718228192, 971954106, 364167524, 417229695, 493520149, 130527700, 76702723, 48810888, 964523391, 294561234, 620137940, 677459179, 621575280, 439388958, 425689941, 605279017, 846890262, 9788553, 859546664, 25030552, 28618493, 390101104, 687367422, 883672322, 604986488, 856660337, 20293246, 291980536, 783279413, 527669470, 794737045, 181909303, 675428716, 970173443, 442941434, 672753442, 800400212, 710690598, 34419229, 143701078, 156883230, 435242224, 761657952, 131902503, 867160609, 660897895, 779198379, 758952976, 6570505, 197818600, 560075397, 386259646, 618217453, 197777695, 555019939, 150705427, 796631978, 462746624, 659525567, 26390803, 656987799, 198440489, 105122543, 604449544, 261873887, 972574244, 714406919, 75645271, 568017258, 249697409, 390273206, 696113460, 266806641, 41558718, 344292120, 903386041, 988064511, 319739286, 866099853, 999198592, 620638374, 853795762, 134318284, 193741169, 312791962, 378287556, 629285190, 267216753, 805597187, 808733275, 88501236, 994486488, 161642406, 426384556, 252183622, 837847439, 504567268, 958811456, 218130168, 730782940, 188984932, 860683087, 816875491, 230248075, 630174158, 802424559, 163582557, 688918125, 139584498, 218181222, 86985573, 958472671, 563239193, 765956590, 942567218, 180322723, 32778255, 666855704, 68519606, 631167570, 404755521, 138570691, 243092306, 624262587, 873228113, 487209113, 492921023, 481824813, 887224458, 792078331, 213899476, 597633179, 765052586, 345765252, 635149723, 860157960, 471565466, 690766118, 16835762, 247859023, 23878246, 300078213, 352383213, 370500780, 573597516, 346106020, 161897750, 918346719, 310649181, 840059697, 218507084, 991111818, 451795204, 708705441, 463978022, 654388509, 122172073, 233081792, 7860419, 334296861, 694714234, 591184513, 1114194, 159689612, 349629874, 764899915, 110922812, 810945746, 699097336, 850902776, 574505236, 940682636, 493103712, 975837478, 998565418, 818399512, 418932723, 771195350, 31995375, 774275699, 472768147, 1485480, 235575239, 100484004, 33932947, 973913133, 690616990, 68608158, 117128835, 191591274, 966685707, 520128103, 773184568, 118389631, 454980587, 45140067, 358694666, 341849597, 913377571, 572044703, 159025417, 425259182, 244308685, 180821510, 221225523, 710071109, 253674258, 495723428, 500545025, 265214676, 858014911, 339791694, 550909332, 894206391, 496881146, 13785118, 268611292, 32140788, 692979668, 565014279, 992894313, 723013223, 826719230, 893415279, 762517209, 422819186, 678523024, 792132493, 549404046, 532548045, 33246969, 107952601, 99593862, 159739470, 635345614, 355596090, 736714639, 166943442, 773735266, 467242307, 237847704, 369452109, 940645333, 932811622, 383783266, 281706713, 713865352, 15560390, 518633635, 825310284, 682666300, 155273331, 925977356, 142910822, 950220576, 298910969, 826986059, 804588027, 308149728, 336015613, 332299893, 863144154, 927438996, 474791345, 482553305, 21470670, 59631562, 972903439, 993610910, 251664253, 835991678, 439067909, 602619457, 771594431, 117794853, 548486723, 416415657, 634609735, 948721223, 22761663, 351341496, 628726347, 724188335, 585284505, 687887851, 60329913, 572507661, 249974897, 725670249, 472203507, 131875644, 105219859, 222155734, 842683779, 826056346, 665575375, 158024782, 87174631, 51741299, 118498002, 362755622, 54866834, 298511852, 51153658, 402761917, 792363116, 353829597, 720164691, 828490068, 908728650, 673556332, 816005708, 121492699, 587702725, 944998207, 457103703, 594739756, 210490862, 132652470, 858689147, 583636226, 434104486, 240885494, 776971458, 886285414, 244412868, 795070807, 45788133, 274632488, 584508095, 451993221, 128615984, 590178956, 705268549, 274254749, 806195843, 448623249, 191839212, 416890113, 965477357, 51511408, 560804543, 448171337, 729662767, 380133801, 147600443, 643428773, 148983994, 651543948, 258551628, 942452252, 614875211, 857612929, 35384648, 342777180, 450208895, 768692073, 777086027, 609408343, 237892658, 152943349, 323526986, 831605933, 632169508, 431067806, 205961249, 610556273, 530066880, 106524022, 104158682, 900497460, 768708485, 337233892, 700458124, 665625544, 811393378, 595806919, 331717821, 608074577, 427578014, 389016205, 650005187, 543742369, 269130646, 714748887, 499089907, 949969964, 852580734, 429222411, 770997675, 42913085, 977266798, 514890061, 852773029, 964269846, 791305394, 353581663, 684686608, 817790658, 132158307, 280065223, 580216012, 813555007, 127192757, 162140938, 969777133, 280148439, 711731706, 331011769, 935704394, 898754979, 86644156, 194969285, 777861, 947327420, 96147595, 949475463, 50656148, 611077543, 663241541, 215350939, 67269255, 680352496, 383647460, 888889347, 598462032, 290488100, 383073494, 941383773, 316363638, 418682236, 225162995, 410231167, 195368800, 177475307, 21246785, 803490875, 355807460, 459198889, 12040051, 74209668, 472142255, 164835052, 149090477, 696156769, 496199142, 583483506, 855504932, 888503306, 892671040, 811185352, 78056623, 347517189, 10208184, 358765569, 930181689, 745384387, 717754016, 758038750, 932419590, 561398220, 229488199, 877411166, 641521158, 975315318, 999749137, 106314382, 685737228, 960590811, 16442415, 559098040, 881283839, 24981318, 718922401, 530642556, 576792698, 980205677, 2587044, 588266426, 911116414, 52185126, 233934502, 377360052, 595349302, 70507661, 398725068, 879162525, 315182158, 206007682, 996913306, 896553464, 442540037, 881712702, 921070191, 584774773, 213140171, 599986972, 274267591, 514641160, 193257788, 767935982, 795980042, 382370966, 301885987, 819348876, 483535625, 36718387, 2402418, 637467790, 775304244, 336709105, 448454912, 228098378, 129084140, 56062757, 317095395, 405884696, 452878665, 823228984, 817534261, 832796398, 925272496, 732321812, 274800780, 991938930, 472365996, 705065118, 400191240, 356618556, 228572106, 291635964, 481025330, 163812281, 615045918, 320784359, 748940604, 274036681, 321238830, 864325477, 35015678, 962391021, 779128182, 72086076, 539726954, 710068183, 343144362, 828115726, 26138066, 681426953, 484053854, 52340712, 72425118, 632509743, 970188311, 714518539, 55927409, 505033257, 374109931, 604858972, 201081999, 218997699, 517663076, 456935975, 635262561, 491605161, 930887993, 636422730, 197744465, 9213555, 606752386, 433822493, 905989040, 746546959, 265449868, 85899782, 856730142, 771892271, 754650457, 460804950, 34630481, 510563922, 302286881, 198267119, 372259830, 46104878, 361864566, 278021193, 792243304, 513155655, 63187444, 956872141, 303686655, 305736464, 230316062, 36057954, 444987280, 490275653, 210393215, 503615193, 582704536, 522023438, 365290047, 378625015, 800399197, 953003201, 762569181, 524881883, 571538617, 211482946, 720473859, 490545337, 960235164, 608156613, 681231270, 873606635, 415618466, 810244125, 66831911, 528662625, 974011442, 354818511, 843059874, 762172619, 664671363, 903605854, 157491764, 941617856, 632870834, 635768955, 811602483, 633519512, 988468803, 267292363, 740324836, 954324289, 258235023, 990434875, 741426387, 273938109, 671012268, 396766762, 589124313, 684163436, 55996323, 614353685, 776628649, 650938305, 833127547, 828232231, 559196117, 796565026, 21894980, 95890797, 824149167, 132964173, 768363574, 231390645, 130828913, 447640319, 678134570, 431091874, 981896101, 552954239, 887184199, 659105787, 7031737, 338916041, 683670933, 930327596, 139323796, 125681155, 908720309, 957555279, 572631555, 769849481, 318774509, 429039689, 463575282, 887276542, 943650112, 662490145, 464991834, 654635069, 206809942, 716914176, 755806734, 675142795, 338337656, 379675374, 463028037, 869525580, 303361853, 802380270, 754994246, 674084920, 153711406, 77741857, 858678385, 559134349, 15620384, 657484155, 444024243, 356664981, 101088985, 336123160, 143228481, 770240500, 648397039, 99389398, 778341317, 776036485, 61369827, 148653392, 972070796, 829855082, 158138108, 923273857, 85188217, 605504116, 250280759, 323418556, 189585253, 108614156, 819247635, 806753684, 490312342, 631550054, 836040753, 352178551, 650247910, 123223673, 371239473, 867483584, 765185420, 337257301, 393231064, 843436928, 38715183, 252973891, 121874363, 215779283, 674938741, 528738400, 775887649, 450930437, 266716754, 796874650, 855644844, 973433586, 689985533, 866189062, 595545293, 74435393, 71546080, 973062780, 80369383, 608917864, 59317263, 845249051, 166720237, 319393844, 841422131, 300808736, 629342084, 695713777, 93037206, 652788563, 251724929, 731720074, 695246763, 567346565, 981494632, 326830428, 845641584, 846088994, 548846505, 989879477, 897307453, 378251404, 138821836, 434356862, 306661116, 159145632, 916122603, 180349147, 787790623, 613081633, 523643258, 81593665, 754529969, 271069002, 945398178, 622129154, 885858340, 418970665, 75898083, 803258470, 868922458, 45951477, 917705508, 317913850, 29215551, 223727705, 959524208, 780618358, 179611121, 101436555, 184155626, 784077698, 518251150, 290361294, 414638476, 972958763, 270904577, 99849741, 779917768, 958619074, 383767516, 940775562, 213164699, 867015832, 134036088, 284210079, 528607625, 796471689, 671560216, 102758285, 996664716, 922145557, 219528848, 308112475, 563050697, 208666815, 216563564, 117861320, 137554334, 971876387, 383398913, 92892497, 4199732, 628830355, 668441803, 953800031, 260926175, 345326781, 416138043, 167783280, 272438101, 393168653, 760868373, 222786255, 360044798, 340351457, 518995213, 447514427, 490744617, 793128966, 804588310, 199269600, 495743413, 702524903, 331837133, 897355153, 493144723, 86314692, 598433963, 874967193, 378874010, 999489757, 343972386, 654001357, 278308955, 256357263, 691404484, 277174277, 886312364, 823890525, 192496684, 678002030, 114180514, 765779900, 232974246, 104929085, 464608851, 288364120, 620566141, 342115863, 5716678, 848959220, 624234236, 934643678, 564832393, 947612149, 556872337, 472762329, 389474568, 110322594, 677359458, 585719466, 175067851, 436208553, 775877036, 513679053, 659968617, 726918979, 389415362, 864854929, 322655883, 93413926, 496280975, 154980428, 651960479, 928955158, 493222106, 371205135, 467584354, 270119139, 31746202, 928408209, 933980725, 447533487, 307662249, 909806798, 988398996, 530828705, 975899203, 617250275, 57582382, 558514195, 416914727, 398865395, 836149490, 786268733, 49016365, 112918986, 610632479, 278142615, 755381157, 837052633, 909013662, 913140440, 53991085, 573447496, 357060583, 532371228, 494554519, 827396343, 720788242, 686575813, 168036646, 983933618, 608068110, 221699313, 898750384, 355415729, 890780196, 98046384, 927544209, 699620379, 42306207, 118411436, 939099132, 646444489, 547824376, 952714995, 496808497, 773614198, 717248308, 97972431, 798266189, 929571201, 644283946, 864143900, 832725271, 964973748, 422432470, 835244649, 127039682, 356828967, 894702521, 303714521, 192865856, 239651859, 120310547, 381541421, 923933228, 502404106, 876145843, 158500096, 854184799, 725792750, 168508045, 404166420, 530165846, 565333355, 940626465, 933439099, 568266997, 60865455, 323737287, 502276618, 456439235, 486671493, 617432513, 744909721, 553208143, 417762835, 461080992, 379754290, 109232177, 473587828, 870716402, 563525782, 696910285, 13829810, 74317325, 209267625, 478582623, 580968262, 796464420, 568884409, 853425127, 740367620, 285077829, 336939883, 315072498, 228369420, 756110572, 388059426, 93242317, 643837572, 812031756, 555354354, 944626484, 283301788, 829629665, 56225982, 26063510, 44050692, 428630898, 878731625, 129345830, 679098963, 961752902, 998004498, 503959258, 387884936, 310628658, 768905627, 416158007, 767197895, 276581580, 451041771, 443088143, 367945381, 303891112, 189015641, 539474327, 636513840, 360604389, 659352517, 797115132, 485676907, 958522116, 618179167, 966948165, 574891892, 464547520, 370522535, 438569025, 883030937, 353697348, 396020397, 685217056, 725736205, 767481196, 525011880, 894095872, 443409945, 540412960, 142358271, 724562210, 524408696, 264234070, 22695661, 864117761, 773627288, 735359106, 768449611, 242772084, 63491391, 298891557, 720592445, 144687363, 573473376, 354084736, 927066520, 152127378, 134803927, 95131159, 691421299, 808742959, 377442347, 48739417, 810333179, 962255631, 318207971, 321702226, 642418595, 896091951, 45147875, 598832289, 925401345, 116139837, 186612701, 354381990, 612290086, 441514238, 739501690, 172669048, 164366594, 736329897, 835822614, 29388569, 178716865, 526066231, 603149289, 63835286, 940775498, 620369327, 976362565, 664273680, 117270402, 525213212, 307493248, 722813866, 218349954, 355551916, 61265583, 821595624, 203846829, 680601274, 357715701, 273916571, 942872456, 560809192, 539718746, 947852210, 460823868, 699060379, 840269323, 709033096, 165278307, 279329758, 24756488, 717727827, 57235254, 67413383, 637370770, 419586733, 893467978, 105400687, 148657158, 375654764, 661600317, 311352639, 313520462, 231867554, 31588301, 794991482, 127861940, 569127628, 629852653, 95732901, 334995822, 437805602, 791770771, 43692432, 885865361, 316000859, 439685641, 267719075, 232070497, 67619052, 301845754, 523179142, 54417081, 680957680, 725602121, 778722723, 469039581, 207374621, 580863852, 899623467, 695526859, 885394922, 44849651, 492488364, 85259352, 634131916, 403803628, 671761050, 966525131, 207501060, 499871087, 950468982, 586413003, 989936719, 853404919, 77367975, 385300531, 816912538, 663952506, 108593078, 665786143, 947475229, 260261551, 424247259, 922764252, 7767466, 713213231, 42070337, 32638996, 746301801, 356270842, 953673489, 870948387, 23059177, 724477851, 167503377, 79305553, 870934068, 576455602, 710319473, 639980178, 189509691, 992957305, 350553774, 430672364, 353004875, 960963433, 537407866, 221322348, 366109804, 843203533, 995805208, 540561476, 789615433, 320146425, 870259156, 928453001, 987970894, 959182438, 528359477, 746944825, 211638902, 627619266, 499772305, 303389058, 640154245, 214716937, 246316721, 356696506, 524332155, 755167072, 291461674, 497324457, 875523693, 611191393, 367636846, 988074808, 567269450, 848830060, 743326428, 179266645, 923597039, 428013164, 305237801, 73250100, 605711069, 768379253, 857687422, 808901758, 26869828, 717276319, 857951086, 650760865, 89900844, 459844440, 170075505, 455855017, 263982564, 832155155, 327477353, 502400095, 562551256, 23130434, 702661943, 785683421, 856490881, 500828279, 724754735, 203296423, 762370471, 673992924, 553902506, 277849419, 163212792, 368689175, 616583287, 175540659, 236292196, 952133816, 364231568, 642860401, 134382425, 418474174, 744703953, 389586208, 287877209, 173108145, 596100096, 934131024, 169725322, 933782955, 666315391, 95309463, 530169972, 680540527, 455368509, 935095550, 476880960, 926758427, 894101604, 281287801, 252923820, 517809778, 610890755, 682640350, 159393673, 150651981, 815124049, 237938640, 729514684, 54930319, 122062954, 686221656, 780436448, 249819849, 406736246, 213133119, 655210978, 667186480, 108914685, 674045454, 425203772, 891315732, 290058820, 940937005, 908391696, 351798861, 192509687, 89269712, 530692936, 79198365, 432779947, 897371449, 267195370, 846454261, 899526520, 471974542, 494238850, 555226464, 185117696, 152969462, 836295771, 325238851, 873727167, 444099065, 111089447, 246625255, 436188621, 844615445, 442577445, 953213729, 385051058, 638944485, 938988002, 894332947, 841112382, 596491998, 65961201, 449249954, 158210400, 490983782, 926909759, 683842643, 60090926, 158414478, 142567768, 25420660, 949359789, 297513169, 160160705, 230171730, 307084855, 186663405, 730323988, 814310756, 26741114, 793506745, 862263006, 874507163, 205773954, 128011829, 766480120, 94411627, 899356610, 364334099, 720335605, 622367636, 788396196, 444905961, 37021687, 454032867, 903720667, 770462250, 92339406, 282247172, 47043382, 291012206, 652003955, 515969185, 770393119, 861929115, 904639239, 348393819, 135335943, 13155772, 592764566, 153354301, 702347972, 171372543, 807883276, 676372892, 52217198, 393716797, 210388031, 866527081, 707090474, 494489244, 223951618, 276929784, 806496961, 843466016, 891124362, 994978381, 209346609, 377717317, 888530852, 515669164, 597953069, 10456843, 878638907, 818381446, 628210272, 422752704, 3213068, 846690479, 778924140, 513966698, 309849943, 910963980, 415781411, 552381242, 823909129, 782801351, 739914290, 897326923, 96631849, 456010426, 194121902, 472167140, 219792384, 862617066, 163312123, 102693019, 374539722, 980713466, 879358531, 873853254, 701978288, 299666132, 863370496, 640910108, 928753395, 866438771, 556141927, 614105292, 837824517, 179430194, 110865753, 918313288, 611188036, 569609723, 100532832, 123965683, 797079434, 758404200, 314421935, 37502582, 677170294, 791305575, 541346841, 490404776, 796889460, 290794378, 154277807, 531307506, 889673845, 103957419, 595840517, 265079347, 374264240, 944076507, 994809795, 973359580, 441486482, 856352849, 689806031, 282533700, 677911274, 320255209, 912103142, 700697092, 245631957, 354631783, 167885257, 737311876, 855464718, 717946769, 980727095, 401052785, 56478191, 555773879, 327249806, 114809878, 625199494, 233785903, 115994351, 958789223, 444211364, 404131580, 978032377, 361214795, 224523160, 31966265, 863065592, 992637304, 441183667, 647341777, 790286565, 574644724, 77101287, 865076904, 700576358, 432952540, 439988750, 357921829, 492347174, 50278968, 382675718, 161701804, 279739922, 802715368, 110493214, 616667323, 362044775, 965940628, 141610558, 894618520, 961186749, 400502821, 937454554, 843582853, 223404497, 351754239, 666843670, 292111225, 174607203, 25511969, 561078624, 931555587, 984522551, 284405245, 497111094, 64469891, 353924515, 355048428, 320416458, 21676009, 828131633, 283141655, 730459586, 655170226, 6794002, 954648002, 992761019, 169701456, 847762064, 419685446, 467944676, 553283831, 642949755, 810977315, 829153347, 425780628, 924120313, 322692681, 524029204, 115910687, 234719583, 703068231, 859265766, 627881291, 710327127, 346171487, 948119047, 784656183, 289943950, 537628297, 127144945, 21838671, 234455189, 492555733, 309288783, 551179683, 844312027, 70375912, 6244513, 829724331, 765321613, 603912395, 565715655, 190567025, 431682273, 408231620, 448537252, 134144867, 994034446, 525349330, 231558816, 580901122, 249039018, 233986766, 906074863, 466984275, 432655346, 316055231, 397629968, 596552620, 506098376, 571714506, 145926963, 30079130, 203325892, 496983634, 786726574, 114202462, 145516256, 841666623, 335026450, 540464347, 876272526, 656101511, 262596735, 39813776, 389805205, 458945911, 65421445, 901128241, 512434224, 161961096, 322829763, 448467519, 895289513, 121334854, 674289665, 87051523, 930546810, 412371181, 338474658, 694610294, 404511562, 217978056, 363115905, 963219427, 847768663, 332668670, 229189914, 299323833, 924477546, 759157596, 627170718, 740640927, 46592530, 216780944, 442491137, 643520691, 381284491, 512363797, 982476569, 996466039, 223881765, 687672496, 88630752, 678197383, 880192603, 830331463, 848689214, 364991425, 824337237, 686250172, 609435164, 667059775, 666512465, 211323928, 743226889, 87979391, 121877667, 646364955, 856478807, 950914086, 240052955, 223197184, 581107451, 831660485, 367401917, 945127968, 49362950, 297293624, 718259236, 714395398, 196856694, 463465317, 543352871, 739245589, 252326181, 43422191, 439567283, 407701581, 759475238, 315315158, 145990304, 316811057, 605306135, 777613150, 525685079, 9893508, 296160324, 647500241, 880275027, 520603846, 374978112, 796754866, 338969751, 100817625, 647568545, 875383501, 577619838, 912551544, 128714015, 56994792, 396297126, 831619512, 421279611, 244761990, 663602449, 790239657, 715656355, 891578997, 797734844, 693808540, 193255770, 23180927, 888739114, 510542831, 763502241, 178891071, 778286696, 708740274, 155612656, 516929939, 913244689, 953766124, 150029102, 952058868, 100141135, 695175207, 95553001, 704855227, 660599480, 423649157, 653686045, 766652665, 401657931, 962986323, 345106704, 679777865, 517062829, 2873598, 496357461, 502668467, 9384174, 769712901, 197975777, 209365240, 978161290, 79238247, 7484150, 52693055, 557792869, 192337645, 565198695, 254331328, 192321972, 308960582, 279199929, 64534025, 446923569, 999276665, 918896874, 873110160, 454504683, 604637273, 108409529, 724483229, 921701046, 347336012, 465473878, 687340647, 368007525, 637537072, 942575796, 196130356, 649851867, 53946964, 609223495, 280639607, 512156924, 521275913, 417144120, 238871304, 659799594, 492837289, 591894810, 982305565, 615354163, 399148952, 969769457, 651286441, 665420601, 997479567, 633402051, 830904975, 842024705, 168593233, 522170186, 387896766, 156715480, 317512717, 218667934, 584220917, 783438229, 222143309, 992478578, 593923040, 691189454, 195536879, 169554375, 952654317, 260010652, 870563114, 696722123, 764275728, 8793451, 812604568, 552630206, 673379781, 303375952, 249992102, 185800743, 53904140, 986057055, 378578487, 783894474, 22027723, 40468640, 859085861, 982969275, 948465651, 856175339, 212073600, 460717052, 45555752, 49495710, 461086370, 833718284, 911694537, 695086104, 739803281, 346732709, 229556824, 745094342, 133312261, 822759842, 512080318, 397272253, 549354103, 93497961, 312272597, 287439153, 743793376, 576481723, 918102111, 538764174, 771479488, 613170552, 407349347, 470734444, 558733324, 77766933, 479039761, 664220766, 352375250, 202101415, 582642452, 504574762, 476420481, 813470092, 830557881, 69341190, 100469056, 738355544, 389877615, 213705517, 896417813, 826919488, 392805746, 565360275, 448321880, 540510038, 494958728, 489608989, 344615020, 387303165, 404560862, 406794022, 715078997, 804585935, 50486304, 772743706, 744731442, 296800130, 123761031, 209974909, 550335448, 6094629, 873419174, 227628664, 133630133, 347488253, 189210746, 337824567, 927781389, 277341621, 229354805, 933582174, 304798394, 273322742, 603691637, 288209919, 132310427, 105829905, 163759868, 44770570, 525712650, 464554752, 966357210, 631686061, 997898869, 857715111, 672209105, 423542399, 693882012, 713722700, 154587716, 508258616, 853671237, 142112768, 636536080, 714918409, 51565898, 222800152, 677223513, 321804157, 229542749, 94189010, 743070583, 808806491, 174391957, 399371398, 773091517, 633867349, 400751113, 715146686, 790774881, 281927994, 101730284, 778801554, 170779820, 997450165, 814431509, 867150618, 580824783, 756190158, 964778724, 667546600, 22044127, 27473009, 18599742, 312619111, 81440311, 555066197, 627061651, 902357185, 967223596, 540768535, 952215523, 884225733, 50209464, 631027124, 994377516, 755844317, 918602300, 124863395, 514226345, 614605773, 142687231, 487112651, 86762039, 614121285, 288693717, 867071858, 119137352, 332182596, 582098842, 905526341, 104191150, 221889911, 560390608, 525592232, 758915238, 822649574, 732006525, 405016074, 969839154, 575938258, 314403885, 768160785, 452594569, 192815473, 148255858, 475874065, 719620170, 565958234, 222155565, 492565702, 805807565, 625925724, 74688613, 274169017, 849077973, 494149209, 887325102, 622833354, 152169571, 831318111, 827149975, 871840418, 766183149, 315233386, 298709883, 269723175, 338050313, 317557125, 706443169, 171556144, 994869082, 629233443, 207953566, 443741017, 60872533, 833208486, 397761882, 329670357, 911144822, 797476615, 334374238, 731864620, 26983604, 240357608, 181876408, 283071810, 583088687, 590440994, 698896332, 277550444, 472208102, 135767373, 383539570, 82711489, 31534820, 937495321, 823835039, 648583567, 870054193, 839400565, 949202436, 156603339, 550993115, 79698194, 817116032, 446653868, 548205891, 991780597, 815983336, 814978385, 125624353, 861265648, 905530084, 557780549, 596357347, 58453273, 529366258, 756245319, 216150069, 419837005, 668370525, 984264364, 738910923, 466629732, 598459158, 426744648, 140933356, 94376044, 950212371, 123177449, 481981011, 610884050, 338146413, 128710541, 881238882, 185852687, 296486080, 654227207, 173521377, 391698224, 220792946, 783976167, 518455582, 286787826, 741220308, 824714484, 622267609, 612866351, 239886040, 553498846, 380628757, 239891710, 224747265, 241915106, 919279202, 588290885, 397651602, 368595844, 454572682, 289024733, 637735321, 332874336, 473685738, 583993809, 862162811, 447749721, 19184358, 379348277, 398702380, 206418343, 373562511, 892647814, 801587551, 355669809, 281374753, 513494887, 681830858, 544164010, 847126958, 223408795, 324023793, 953653103, 257204507, 643738262, 434101522, 857495736, 370776745, 96673640, 666261464, 284497999, 410876236, 696794269, 545433395, 574818685, 568799804, 28411241, 602399412, 533632646, 615594362, 388842305, 358155352, 989095561, 924710826, 884541912, 467566358, 599330624, 930432553, 158442323, 461812331, 895962729, 372825566, 612800927, 731029988, 701388444, 717453632, 987753198, 628923134, 745340222, 557156985, 173051600, 594256953, 317570207, 828282927, 705876158, 278665574, 342467379, 905144441, 177776046, 572326046, 845493321, 427605, 379118093, 590104478, 524655300, 933016162, 221865562, 798746958, 476718005, 905643637, 919180214, 205853681, 556121544, 481069833, 392627502, 387336537, 450794883, 135241171, 771860948, 247989748, 801825481, 162060393, 153257430, 53385529, 119990100, 245220697, 331053970, 424165063, 907395546, 489716685, 494150342, 799407923, 304667714, 679663189, 210132713, 181360467, 624796161, 954670595, 842553890, 231939141, 968016188, 207307407, 143236113, 215930327, 189208249, 986669283, 254154064, 614260094, 148385067, 886415370, 829379885, 657989344, 735560442, 121722559, 63997905, 111434452, 118351657, 680301343, 495163181, 441146440, 627937433, 928136474, 649419223, 198757858, 608067495, 612638533, 252526406, 684422871, 902927562, 463336109, 347407468, 341427476, 929333418, 817313049, 781830746, 162526615, 798838366, 571339809, 265367562, 931951039, 337236488, 370916902, 636931742, 854940168, 917472886, 559315450, 163766992, 474774956, 452449568, 111424043, 178500734, 931169606, 309743650, 625055171, 689366460, 89788305, 949085221, 385002680, 756461661, 714177012, 292588626, 81553530, 757150007, 941808490, 386742191, 464494049, 594807592, 488450755, 203358903, 290428088, 131717500, 537479868, 912411083, 368866425, 938393049, 228997277, 679173524, 374369972, 544929536, 184773813, 967377853, 688431733, 486762104, 488319573, 200319256, 356070709, 412509252, 715151187, 573274171, 159583992, 141752616, 824207171, 623718559, 122941317, 661151665, 716405888, 365484043, 523842110, 364506667, 63198342, 160947281, 165270601, 266726521, 513038318, 372825962, 914542159, 31597426, 576072991, 215314250, 655244732, 841322237, 349995219, 69413627, 307733756, 588910057, 382035655, 723452161, 647733980, 269729544, 604175601, 124548719, 315164945, 414790183, 193237154, 661289720, 698271021, 983592366, 341157382, 866327069, 429350209, 540967221, 205352501, 917547612, 697112945, 7022511, 544767449, 533559806, 971465961, 572358610, 336638532, 35754738, 908312442, 749786318, 981138010, 743893638, 884485846, 111653698, 425833311, 612287013, 15532030, 312504537, 490286524, 873471531, 907358557, 216381841, 138285669, 692399367, 510185036, 609519600, 528066135, 949811224, 285421964, 933524552, 668178451, 427627948, 501984979, 880458088, 745973296, 39482057, 413470107, 738508856, 999928707, 121733170, 368712179, 271783783, 372194373, 384967480, 467547048, 604553103, 269806488, 218037040, 569523377, 161258609, 853593298, 5793892, 44416420, 629693571, 946510489, 607946531, 534086328, 136713932, 868945491, 101358583, 269925298, 448896642, 125545005, 172897906, 923529263, 264198359, 468672381, 323451346, 471910771, 967083303, 370149487, 633948818, 21216927, 498259800, 240752255, 228897766, 184399075, 196597678, 562549131, 453122513, 56092995, 560382196, 249396610, 181786547, 852242804, 295606523, 79545717, 617588980, 696802417, 135068067, 161655463, 190028721, 277457200, 337903653, 237929215, 583866183, 703354508, 135641678, 851338403, 316167557, 393438841, 631547521, 45378952, 487234838, 177363729, 995139196, 763702732, 931237156, 710038565, 493733251, 414614324, 38778980, 982215177, 22097563, 922604525, 316187004, 522229347, 404032065, 216048417, 508071901, 193707383, 569467525, 157153206, 709476502, 13461052, 179169384, 302539562, 639505202, 761194957, 861372320, 422999793, 576562625, 573652940, 161085359, 828763933, 355120139, 205255957, 684080655, 36881654, 879709400, 404501103, 545380216, 436702511, 745766866, 700422113, 453945399, 11080504, 418509929, 57417582, 779692079, 199733003, 455277273, 7152522, 854048688, 442470810, 973511258, 983213203, 531555687, 377857882, 963685422, 352138437, 154950249, 42349433, 346323446, 553927172, 40164830, 528221872, 474018095, 248943273, 724481389, 773841843, 532728157, 927246413, 582077669, 315008496, 841469453, 233636383, 170433511, 366740182, 7845710, 932238249, 714625962, 479000359, 320919279, 483959627, 205542515, 958966152, 736785789, 702461322, 504748715, 885799215, 263538266, 922948535, 452825151, 792198472, 217602095, 380351548, 933595402, 254934967, 720460155, 975743359, 99440667, 774027802, 199263021, 483581570, 512096474, 982789082, 352045223, 937191037, 416355343, 50643515, 791554157, 226671755, 314988931, 786161764, 638305973, 653616941, 564011281, 623092786, 904117101, 547643556, 86132033, 120582640, 963481053, 108858205, 402927228, 10095031, 410340892, 752387616, 878524538, 830973362, 791743084, 11924896, 34411995, 529569761, 569599075, 346895556, 927541464, 266053058, 620814172, 439240890, 594008111, 738485824, 766664838, 717203349, 54367239, 349700118, 90122019, 881040974, 936997885, 201531889, 400168059, 129415244, 523184132, 149794766, 168801443, 916300845, 831924919, 425015792, 36790975, 118316015, 305768233, 886601245, 405221133, 898922648, 660830163, 696479336, 222831035, 25923431, 554096712, 842956293, 803912172, 291096490, 578114337, 249004020, 273812994, 713519460, 706302302, 411129556, 331857632, 176363368, 757072004, 726076272, 868658043, 322244669, 77982430, 879977033, 611055263, 555610787, 836491381, 858650858, 19188532, 38950163, 477995106, 932684166, 449074707, 813751491, 498334998, 182065895, 254207483, 62690788, 193595628, 19484233, 726455795, 648472306, 779386477, 999617006, 49018192, 971600797, 375417627, 295851766, 16350586, 467678085, 298750560, 508946995, 778031107, 619958240, 517843252, 931266987, 989306479, 105254190, 959707725, 225987551, 169397332, 691187133, 918923595, 43960741, 867882932, 506845086, 230773594, 285320415, 867145842, 328894363, 886604821, 752808437, 47645799, 521828393, 40561625, 509094256, 642790298, 239545804, 485293712, 727464790, 251617408, 115111361, 498164684, 740879795, 8484628, 907307801, 448923322, 177622414, 748831075, 825299396, 201782604, 583068950, 56892974, 910767423, 97970446, 5793098, 38138498, 294463666, 966603162, 97546946, 90712277, 473535868, 734190253, 33814813, 543415060, 877397004, 498216998, 93434034, 401343174, 974150884, 973154240, 582694946, 593168975, 427139781, 280992083, 961959066, 189708000, 933215909, 243064564, 550250431, 238762074, 672122159, 20565647, 921557779, 980010752, 818804739, 499864674, 38137316, 252548710, 467820211, 610696205, 246671684, 480226332, 537657647, 191809665, 575498895, 426914111, 278678261, 999152170, 350441750, 245660369, 932182233, 277084679, 645236239, 527899458, 619236059, 101631178, 984981337, 667036522, 727885510, 842425631, 514525017, 876916200, 972977517, 175109278, 579924400, 368637987, 783193335, 491931771, 561978373, 117331503, 278941330, 377501313, 719537204, 866642534, 950606445, 343021825, 215560755, 64299283, 211463580, 9147862, 388401325, 867537959, 827758265, 831717274, 594160000, 841731593, 242395685, 713414376, 866977697, 333065071, 961908245, 748422198, 291236523, 528328374, 229803534, 571895572, 712275165, 119704082, 617877850, 252931808, 418540809, 906933773, 773121257, 614209268, 990393176, 950027104, 359856565, 701098257, 251306053, 374913311, 680950907, 226363749, 796848193, 211199294, 647666116, 380230716, 330443390, 993278569, 258952593, 404912125, 877914494, 931629959, 847151880, 292737500, 816769971, 42175259, 125951085, 471598812, 284963914, 515861571, 8531353, 648543978, 225952027, 682577585, 77897458, 4149294, 784852569, 880296013, 346059226, 54684370, 690046289, 152582780, 652526155, 58976630, 748177538, 824182933, 494205115, 787217127, 907398583, 287632839, 219831936, 451697971, 896110857, 6994354, 893464857, 279848702, 293654927, 68885322, 364389632, 530066911, 756676731, 194792241, 7096568, 352731467, 442245374, 500541685, 527635719, 966962082, 999632300, 88709399, 895547583, 978652542, 401480896, 515346043, 186138506, 401954973, 499556108, 345047827, 900693777, 60723129, 126948358, 967247124, 356705195, 472161724, 203459717, 995738201, 55635778, 834060118, 124641512, 189643591, 34145876, 519242031, 459781121, 413767756, 110741278, 779902524, 615900455, 10094624, 894919279, 363985742, 894442081, 900320094, 114303424, 721526570, 999814184, 331376754, 840972073, 178714172, 991595226, 225460386, 344355958, 679171478, 943647077, 947981590, 778853856, 729868609, 262594648, 793864657, 422443946, 988529555, 514703836, 105262512, 20563892, 926627499, 952605552, 233246687, 484161269, 151125218, 466205016, 481315762, 624423064, 26576520, 859080448, 791127612, 901783614, 48876505, 774571882, 889917024, 827940644, 17060597, 432213713, 649426390, 330296468, 554206068, 132240169, 803011370, 313258570, 754914144, 901779361, 240608647, 979497828, 885716092, 226927663, 360808897, 988455278, 593555192, 467571409, 390936813, 568876574, 448509779, 297350097, 776021062, 937609121, 264648976, 245809426, 697677237, 789490994, 359653489, 78265752, 467167764, 258839017, 162288960, 574162259, 718069389, 652868174, 678159744, 614614897, 724920736, 211131315, 128638828, 697952742, 227381582, 106832026, 32136798, 723808210, 20190907, 177223939, 837004214, 71612831, 208477676, 777734552, 585885566, 359418382, 12244617, 493409661, 50479095, 292894105, 871449686, 551870109, 594273888, 5401116, 520495039, 463624343, 944945527, 949562114, 391282466, 937171530, 709698640, 529666571, 42468023, 164465500, 112665715, 776181207, 33275532, 748615378, 695033788, 998794840, 466917550, 464379929, 518177880, 225362828, 111992323, 617703278, 554135693, 275508642, 742828257, 904152715, 862655961, 174358899, 993333200, 659411248, 607330097, 590128810, 654320179, 36372039, 670132519, 742774434, 328328789, 412333830, 378274016, 376264959, 960861101, 794624538, 320258790, 629443570, 292000312, 836955102, 841597780, 520348125, 122675019, 654652648, 139403218, 265545160, 21746707, 357744819, 611954777, 583954090, 545829425, 286519280, 633701312, 133229163, 977178655, 246949935, 330896773, 164593366, 534014959, 375093947, 771995560, 690718866, 612638162, 424563385, 901016713, 313072714, 115866675, 620536319, 377669884, 11945920, 501414096, 590921709, 315348139, 83688272, 844410195, 683351892, 341660229, 889692609, 528139856, 891456018, 749921396, 616556928, 812502161, 385356439, 304394505, 267239991, 479349774, 888432936, 372735686, 565277664, 797163665, 181896914, 426766684, 527567511, 574923915, 237370701, 315275502, 54762044, 595871555, 162569042, 179906954, 886913169, 171569122, 422876386, 532435351, 36430843, 814306825, 883983817, 598319192, 130998188, 771671057, 712229867, 276471699, 237197537, 961714289, 236566042, 586219694, 98451928, 445211774, 961972850, 3670932, 302768128, 757245879, 831851880, 904208828, 256863532, 866515984, 435838334, 820394692, 704613056, 47698853, 165870737, 742848653, 875615869, 666399647, 456056318, 931257061, 870293431, 108393560, 180273511, 21376368, 372867996, 500133637, 862585946, 670826291, 864352248, 778544708, 598472145, 313206916, 692851646, 956758406, 651828143, 952711040, 877727023, 473472303, 615707725, 716785997, 733074881, 703823204, 278320077, 120278413, 287516086, 585174103, 375235538, 673165232, 717672459, 463615281, 38084954, 363496808, 969841295, 442168248, 178857799, 661917191, 433362143, 712586899, 865868680, 169191812, 757738923, 791599461, 681116949, 378192894, 145512242, 249802852, 265471556, 190034078, 279272064, 881024449, 988452097, 315615475, 640436872, 308341051, 401546402, 446665850, 622607940, 539593638, 133624247, 175583901, 386393920, 530981906, 221305272, 382939873, 654688377, 401878899, 608296159, 665951664, 950133871, 315512282, 408714327, 356204020, 101041719, 522989384, 165307509, 251083210, 779650264, 559880331, 644078810, 331601914, 593504544, 582039658, 950737064, 215746579, 299352802, 509858051, 723759699, 977262948, 336209807, 849336419, 588323193, 361996039, 330354620, 315289874, 320529407, 354824013, 943008454, 148329696, 591809823, 540170575, 621682128, 317212488, 948653522, 22540292, 506602162, 729543391, 386087448, 172004616, 18913512, 366748908, 298051987, 663251410, 518107375, 429300969, 849799228, 390454701, 604067421, 169854908, 330075136, 667681811, 143792787, 275918414, 897254730, 548832505, 631028133, 549679256, 266021762, 303529200, 313113847, 187340826, 181374591, 888367263, 293285857, 557412094, 891061712, 330640051, 478395663, 832308417, 867079873, 467173748, 849045108, 722325470, 831042594, 256588620, 844629677, 681884900, 211106233, 73262894, 654683672, 403284330, 638989695, 767353309, 844796418, 310890713, 560550271, 21939396, 327331125, 314951100, 229841203, 716789306, 746418348, 88607414, 282485149, 291655934, 919953487, 514984307, 319464392, 527464774, 973055694, 434273147, 875438422, 814290300, 614943141, 89007512, 247692275, 892176684, 991406590, 565617123, 84988407, 662815401, 937086421, 906158430, 514482056, 716108973, 416587972, 103688119, 140630388, 95789784, 134817124, 345057408, 540631234, 301150366, 576324630, 169179458, 970728976, 923658426, 128517625, 295164133, 378654616, 256256725, 290099514, 858692571, 57246224, 636197327, 209382979, 298225286, 600777287, 869199237, 387827914, 859457456, 312216806, 587071754, 599435256, 126359598, 514256081, 120059414, 903016913, 783509593, 566059142, 883447955, 90177635, 442143486, 364278681, 574221924, 168077969, 720210256, 941076249, 932154993, 50661358, 487181782, 468558508, 578853926, 118856091, 997409450, 82421513, 24791417, 88132836, 351667316, 528399085, 322661565, 503293983, 833873942, 869830759, 408361303, 549693150, 690194927, 397518009, 983181290, 62188551, 764147855, 803943782, 421026975, 615047456, 644540788, 360192101, 159461407, 934510161, 434963374, 232030877, 815914184, 527853379, 936093369, 782411431, 584210964, 270239325, 733405014, 188441739, 994318011, 305521675, 621566707, 483382671, 140625358, 571474852, 780560061, 532540092, 455360590, 80635905, 472237300, 526959513, 478212052, 910637881, 936178309, 612852113, 566374213, 597477448, 133444671, 661511170, 149937226, 622318462, 181750347, 383175787, 73464535, 793893111, 302684459, 405831950, 849299049, 15684101, 759697646, 134056620, 974438182, 496324717, 900306960, 622811426, 121268555, 697798971, 207896221, 839886736, 493272436, 583170483, 158892148, 643455408, 763057424, 764059598, 51411128, 607040733, 227686146, 594425892, 691115209, 88688564, 204307975, 925450764, 568285663, 590336099, 313659400, 547964772, 275615440, 312518995, 230163524, 952733487, 71534876, 475138155, 495743433, 57845584, 238805964, 742763783, 679749988, 661900740, 317257403, 197082480, 62696911, 137513927, 209442215, 665717136, 973059555, 977477124, 508435148, 25710709, 456184124, 822346944, 913205086, 912746684, 386088495, 378583746, 29177337, 306026379, 443104636, 218658370, 158061571, 644094566, 117388560, 199698764, 779802923, 59616184, 351175358, 556031675, 752232102, 77553474, 705041579, 286242488, 461613903, 410396139, 92358784, 50961757, 651079919, 875774766, 605207271, 30004229, 813386407, 112214445, 983181356, 741970318, 46541924, 408626795, 547079765, 359765502, 678772713, 662353672, 290824805, 663629319, 329398241, 465722474, 42296165, 471995565, 686714386, 276995662, 107655030, 286965589, 566406646, 487454898, 792584086, 654929287, 967035045, 890083265, 129623311, 57986849, 865828697, 305629794, 106052563, 365565667, 279523844, 712139972, 656192147, 168931911, 709597953, 968437702, 768822254, 897942493, 140197083, 81973139, 404556060, 337995110, 201954399, 330114025, 456454906, 144684771, 793974952, 986173130, 221082234, 988051192, 258662454, 325643266, 997122312, 488506868, 976701685, 968367152, 790830548, 877099370, 436674446, 485088552, 199500608, 686609472, 455362091, 168038057, 725981994, 849171364, 99598230, 859592147, 159918240, 530437786, 744205958, 140689140, 939182645, 859339875, 73056790, 520511433, 185566562, 37254045, 715122494, 595211252, 333546765, 989673391, 984931250, 353858813, 595032089, 959089291, 280483253, 787817459, 655142426, 944395172, 9836918, 726244202, 555721101, 547229289, 858059378, 415271896, 243473503, 255924181, 146230546, 890025229, 467923403, 840780272, 810910398, 344858569, 662204664, 497404720, 195022393, 912587351, 761900297, 552851626, 537371075, 839097835, 865244703, 895220679, 414688853, 357567294, 519235598, 889274395, 33081337, 969746078, 186583433, 410513721, 834706087, 766434476, 906201, 399485314, 180477840, 59792303, 213105348, 636854787, 8608845, 590736846, 332246084, 395359442, 662869817, 167976229, 116363641, 939203345, 167353132, 404593615, 962731474, 667627184, 34389280, 751183355, 225520788, 720678576, 386943808, 534997439, 500018659, 933372441, 187774944, 709644276, 364424424, 358294910, 132289907, 503629379, 902446966, 830696398, 968815113, 232699163, 27609989, 53147624, 143626820, 628474575, 860397687, 882650640, 696490802, 493529412, 961153124, 972329602, 195016616, 265871438, 896074477, 402257168, 416968703, 705508070, 614217386, 470665115, 955891933, 912712804, 969821126, 119016957, 193655003, 167122456, 344381088, 305307245, 483780483, 94477322, 592489035, 34515891, 181529705, 791160819, 34243430, 73553044, 343208289, 922368467, 363158433, 369922111, 864021586, 875770528, 286472978, 812524051, 844541474, 224036112, 869647410, 893773194, 46340690, 3597972, 966704657, 933153459, 540171429, 612883066, 398307559, 139832799, 609954305, 454820959, 494022427, 401855467, 201565229, 201730621, 963446562, 549659848, 336164722, 140294383, 89354348, 911399163, 827268053, 849736958, 100977405, 461563017, 159754338, 820698900, 113269844, 730936685, 659550403, 624653376, 945181403, 750147756, 519168317, 316129600, 331711325, 268906324, 893566474, 774090140, 996215570, 11906910, 298486851, 609349153, 49230258, 205211281, 712050210, 692696942, 520346773, 353881272, 251114755, 775244362, 717655102, 102691251, 722510777, 645317480, 915929553, 494753438, 593926915, 522710340, 209881842, 615635658, 115836799, 6773251, 356043700, 430800270, 340301905, 680218362, 90223850, 532723486, 869453033, 74674658, 560956167, 440840352, 947193015, 897379167, 541050378, 628660900, 173890197, 814304772, 218758442, 326822108, 270553007, 901856460, 585561467, 510366023, 506035376, 18611471, 13171593, 712784390, 239925553, 21773841, 209656995, 595960255, 733978548, 370235838, 233753856, 849301291, 3175796, 276612462, 365408856, 234131284, 113832252, 538471388, 816324669, 693969815, 325738854, 388387517, 303529844, 924183333, 80531755, 684122624, 136008858, 732349295, 20515867, 704490959, 311552022, 647706760, 984652386, 760284181, 259552471, 196936653, 532144351, 98201023, 590115741, 943956849, 473584784, 146141096, 229662311, 958139849, 478418356, 340294770, 384001068, 770107546, 201059861, 14588705, 187218258, 228726252, 471741878, 242078363, 546963358, 240457192, 922701879, 619089666, 528349529, 226623335, 583986269, 501996308, 818144052, 487361766, 516717386, 286681264, 193579880, 902139131, 981564006, 856417804, 660754167, 260690140, 76605439, 294214876, 372208023, 932583494, 910017103, 882994378, 26446602, 12830432, 189472811, 953350588, 290685096, 904056856, 226123117, 247568785, 821364400, 461583488, 10521016, 774051362, 2680800, 582139508, 827964428, 214301473, 769747993, 31700592, 234679837, 498757253, 253618426, 532654843, 934548302, 298167183, 658581130, 725198886, 861592723, 451100184, 394115867, 581266854, 450210283, 225833408, 1728344, 356116930, 270015909, 983352851, 844892538, 24776360, 777313954, 501324725, 904809304, 508952448, 574329531, 773859362, 774505688, 662507192, 402076566, 644328153, 412511162, 599901636, 810092071, 195624151, 343588332, 296940613, 536892788, 815812253, 992734590, 996030593, 672226881, 373564387, 908757946, 515636565, 963358684, 483606109, 47323815, 678299371, 2318900, 472259657, 799532329, 298983874, 357571174, 565867982, 901460755, 594659460, 780830712, 197882785, 621076116, 140578820, 799419700, 220502222, 60509905, 766374101, 170714092, 820536781, 140208957, 210637530, 6793789, 339522904, 897609643, 576376690, 971260103, 456491792, 425851019, 479607539, 764541615, 17234194, 71447870, 811908282, 214598011, 155773172, 617539115, 252884482, 386842148, 676662897, 144802995, 402343228, 272766080, 51776609, 814470273, 214097945, 100018713, 628184197, 100425670, 973770395, 653081916, 388708780, 784391509, 430234823, 694750349, 464047930, 546344397, 375178176, 893218592, 136236612, 232696701, 152839071, 486248742, 117133929, 480424004, 107855484, 89364412, 750623663, 161956596, 218241280, 750609527, 526812902, 648311019, 677494591, 560106745, 177837061, 81970383, 563673550, 478370851, 825545731, 263505826, 146340879, 384150163, 50363514, 716191720, 580390632, 38005939, 958272765, 228642564, 749472694, 280882122, 956743202, 104784363, 55645498, 245643553, 137870714, 964046751, 55054758, 137933310, 887826366, 88950549, 270096417, 760922410, 837644461, 791065729, 820650016, 86751996, 28545561, 383898592, 346635111, 124984644, 76691142, 595501571, 165220000, 420804280, 310364244, 526116965, 472577057, 756380641, 212416009, 813140340, 243935284, 484441557, 192668341, 400933859, 737744063, 557817145, 240472386, 202485954, 311223996, 913810037, 766889656, 184974536, 659148283, 308023997, 832483551, 101987116, 68522332, 853428062, 903041638, 497060534, 613494053, 132644316, 503663500, 713139737, 483335446, 752338486, 112938569, 498327343, 819534436, 907735528, 95149333, 268324590, 130906766, 949992472, 391127555, 250297349, 697926065, 392718864, 136287964, 75729798, 943030899, 436281654, 316909931, 476586682, 332220443, 336302037, 935366237, 507959061, 699586988, 484230109, 726903227, 497647979, 786406345, 893304563, 167523248, 497162928, 928059567, 696278349, 391060802, 676062702, 613426727, 246009920, 664625445, 404403754, 95135891, 624042136, 702005837, 136571757, 914192033, 500446039, 242303774, 676401963, 20192367, 649329561, 416627772, 201961589, 247108607, 897606486, 704402646, 218323920, 24261330, 61312658, 417431702, 587834270, 982584796, 494984979, 288050539, 989862587, 325600547, 177381566, 279574358, 187769207, 422240951, 864511176, 957651922, 748214476, 76769229, 989826, 33813810, 515616601, 660099748, 680267899, 126423646, 638370178, 880689052, 754666801, 367207702, 694322907, 829630116, 981165312, 816286732, 897821277, 851018667, 245554382, 213890209, 699964314, 878133100, 929985077, 689466087, 618328865, 271632438, 800545059, 796974147, 903427998, 269890977, 71102758, 504062371, 416149468, 591966835, 828821263, 25449039, 96723276, 888278365, 342296510, 591842165, 307142622, 584660924, 585726982, 947534179, 245585458, 396865899, 242741609, 660431210, 285726728, 573051152, 862450389, 686897248, 978739790, 36914479, 787286011, 475072247, 763710703, 24269009, 138770354, 672933305, 278451721, 752976229, 180769579, 431275957, 966493724, 945960823, 317455238, 727280541, 159879830, 628766053, 601000744, 173316762, 44592275, 974763035, 215563633, 525954685, 992038286, 757809920, 952655595, 804965161, 370032236, 735066298, 454583545, 191969987, 958819612, 718671, 644860843, 398853747, 170345787, 716102861, 111288717, 465917288, 72768670, 196986407, 777487425, 915995703, 272601229, 973380098, 509846906, 713044594, 257692230, 240184458, 697739898, 96945043, 517652476, 461768798, 906739676, 299960367, 389040142, 395709943, 412345911, 142866769, 783095026, 14312104, 217672948, 255991836, 613201411, 159848609, 94768436, 505279866, 676997205, 593164458, 359789015, 513925554, 696603737, 939722136, 393575429, 373412592, 172982502, 172113976, 278747471, 844162902, 225648457, 874519062, 625787103, 770369535, 507694152, 494533405, 238715372, 408527588, 751745664, 508658499, 978316012, 228809664, 779162850, 398934715, 43514282, 154204795, 498755208, 504318730, 615399869, 619627191, 764655415, 113918964, 569228517, 578720470, 94905361, 417793572, 82663149, 847618646, 223019740, 330203690, 585278457, 556014155, 81299578, 953374390, 98028608, 164009900, 431524828, 522095287, 198264317, 764786128, 737293333, 530679854, 306627132, 805529682, 683776470, 193918829, 634345162, 137621062, 841193930, 526306031, 458950120, 835115609, 989201369, 552989746, 177905846, 749623704, 395885600, 311080580, 953656282, 500381520, 996601663, 807930919, 600817272, 231862573, 406159362, 749088166, 243506905, 222624418, 84808800, 5265479, 793443040, 968058124, 770480295, 702787960, 324992474, 313837927, 397023924, 358044514, 816701949, 770974690, 124160572, 242191524, 269781840, 76677855, 728967954, 525053489, 620731022, 483118121, 6602526, 850314901, 449561821, 159985328, 411263698, 581638594, 206018301, 887453963, 440796068, 704955627, 873228766, 149055782, 255257731, 841398687, 858875494, 340144466, 698725219, 900997646, 365299576, 77751172, 57716861, 346490198, 714444817, 33751120, 686206418, 903538353, 924219631, 35468011, 539770247, 192513401, 675951692, 798218379, 352851028, 68071082, 369015731, 437557489, 281446774, 379551117, 923434906, 70066059, 259488964, 407281330, 961094245, 976481754, 150631296, 310963393, 579636681, 673147166, 419271733, 263589495, 399490000, 731458987, 338477976, 471440494, 876423486, 265595544, 373019305, 665845998, 240802516, 252356960, 802191692, 232250364, 166506999, 942953825, 55940047, 967731379, 107183865, 72636271, 497776063, 631805425, 981955085, 954035044, 232915931, 813874377, 615939444, 514523862, 70037552, 649483895, 570682734, 447144008, 53325173, 945281151, 919654947, 795570125, 461888626, 814070318, 933490999, 172326747, 735855585, 73708120, 949028030, 250584222, 378563391, 900179082, 484119553, 848099969, 783906956, 900799420, 837979888, 902707285, 602782950, 859676132, 501359836, 780926444, 92918980, 380797650, 944792546, 199949234, 508303965, 172435942, 791739698, 350821631, 797018125, 403637765, 869921420, 979089145, 545461141, 39401423, 536414948, 173459068, 317770843, 447380816, 402821376, 545148034, 188168193, 851675741, 874891091, 893882793, 545532951, 930698259, 495195907, 614243015, 9785495, 702697383, 639618156, 901305908, 669443484, 639982627, 678368349, 170801141, 214886461, 859291999, 89950311, 620591407, 329024060, 698708695, 136671491, 183619493, 477570478, 506662247, 723670085, 380203516, 41154594, 979444308, 859383286, 32658637, 413070046, 233177574, 504059694, 887849550, 909151005, 416101676, 717542924, 676480936, 834930885, 128823935, 544325194, 501423772, 135768458, 552991609, 523883435, 922331974, 296463317, 155898682, 720195511, 757828437, 308329343, 949623318, 621251810, 880851350, 667079537, 874183869, 128405201, 32397513, 408075926, 664775882, 751724164, 820040402, 877972300, 277767730, 235036681, 580045255, 400176891, 375787671, 954336808, 407844404, 827928060, 452916115, 467945059, 720648050, 385844715, 558415463, 710941313, 699695289, 597037948, 141523852, 545530159, 541484131, 2503515, 179091216, 517622863, 645119381, 552053097, 387939367, 911262392, 834737175, 707615793, 757103553, 316403862, 305420977, 314570042, 837547051, 776723044, 858296165, 640902937, 112863592, 709331155, 714881286, 563746196, 877413598, 389886143, 517807147, 779860317, 206224838, 594997210, 565635126, 141614553, 181054850, 87775816, 892263955, 999094180, 160826254, 616869098, 447126984, 253770636, 411007012, 918479667, 192009273, 604906735, 294901615, 7182764, 23124086, 390082336, 34683612, 111496602, 459558797, 91004097, 603314379, 514195228, 150344492, 385920347, 706406338, 800401153, 177481091, 215210287, 876758280, 917881645, 373230399, 781723262, 835499654, 721595947, 221298343, 674826916, 687319230, 487341488, 651701697, 898329158, 37840460, 230123467, 407470517, 320426787, 263309068, 689193680, 363884581, 184522875, 982681461, 859722477, 577587012, 526824687, 724994131, 460529204, 249926492, 877100896, 652346947, 754357851, 86624265, 689146540, 477754036, 916444005, 803300544, 540000009, 345626693, 140875054, 490163049, 964336516, 884665299, 700297473, 742429328, 627980177, 763016345, 280116538, 166318714, 379270995, 199121790, 190914749, 383623829, 300864563, 313565633, 760551477, 863549573, 176771159, 120680742, 48963065, 385417538, 746477476, 591977828, 171656399, 853102310, 421191335, 260460719, 766909044, 952853669, 300843476, 265913765, 99774765, 686283724, 724495582, 354389572, 68530426, 50753152, 449485118, 507581754, 890702849, 71527815, 77520227, 85213283, 696274319, 421249544, 374565336, 195042452, 672629286, 69507670, 333641153, 464573022, 988899600, 809025312, 79108105, 662118233, 708788179, 98626296, 419444172, 155336812, 789314352, 889069910, 473174136, 535050873, 557001038, 815100189, 675181759, 342281458, 971444619, 45067218, 911805546, 29455336, 386352918, 650639404, 678372461, 286842277, 635698763, 261797378, 58810999, 510280869, 892160557, 74807805, 660455754, 779450081, 298484006, 173315376, 136810848, 309289707, 235603281, 343503727, 570786283, 484000772, 70619551, 337321204, 330724969, 86075885, 688925001, 554803015, 463989855, 876307141, 723918764, 891909274, 701028095, 823609996, 743518066, 670961498, 593573718, 275696077, 802195863, 843863499, 396515876, 310621680, 81374919, 672351897, 992103064, 925980201, 748596267, 301725305, 887515949, 36157086, 652990248, 717510270, 284949312, 167961913, 548288685, 903127088, 463339522, 897818305, 339518319, 300342274, 377829680, 288894413, 206562965, 700788543, 381630511, 838947523, 250138597, 351392232, 757935771, 155201708, 6475801, 277524248, 482561004, 769067520, 669404965, 504759495, 180972740, 740410609, 8896405, 896017410, 969299130, 310192177, 595921333, 588753658, 310531647, 51698400, 932192543, 170730302, 629379938, 69277149, 988464029, 520708206, 460938936, 892932067, 129269427, 999016805, 935071823, 509406092, 324422017, 121103310, 383241779, 870691303, 91942981, 879422190, 637620466, 225204475, 92880021, 849684835, 310287883, 708339761, 662023952, 87003333, 921274370, 220834861, 653078792, 383031139, 605923864, 955477884, 984550478, 175535020, 606428136, 44336621, 730403097, 107718740, 547701384, 646891757, 241112100, 290174602, 394433411, 165690036, 415190011, 178353650, 329481501, 999454670, 51113671, 959205217, 642043218, 331647694, 441382474, 830536177, 245578354, 893104813, 140200551, 381422930, 123206213, 421006645, 61276912, 138093110, 131549065, 858600477, 428680689, 310051347, 851192383, 604223157, 35442465, 869721579, 253174040, 314993387, 795279311, 632482812, 252097198, 586212523, 649565043, 674030637, 746539328, 545616819, 489860825, 431694199, 224030771, 638053561, 601522713, 691742476, 740851983, 229816541, 843945553, 225816835, 695495575, 168641145, 603335014, 856535235, 234752766, 345177232, 891541990, 866368459, 452504698, 758804951, 830477055, 901386856, 16163612, 680301965, 160642380, 906541229, 432679026, 523979002, 376154026, 523952577, 269734387, 913127137, 189404988, 369402481, 569728578, 164169892, 209572954, 102103106, 903544027, 357892589, 72715721, 648440979, 423070612, 47167917, 771311538, 950142257, 883306006, 223563906, 811902518, 680075153, 425152364, 641847315, 343800447, 557263277, 93451275, 378502082, 7158452, 52361726, 204181556, 423243482, 38748758, 160536651, 334430216, 676978285, 126822005, 25182228, 108212731, 58676326, 796859697, 976709661, 58295582, 994148825, 675862818, 897918905, 993612352, 432497925, 784058598, 218001619, 914009633, 520878195, 275675529, 368363269, 233061225, 465953124, 775365425, 906910010, 717593531, 492126381, 847832640, 735334592, 369870075, 486357161, 332679688, 710114030, 985763718, 729440191, 687965239, 603521377, 263696350, 782946464, 762195393, 58709916, 27268961, 801948577, 272491357, 237346983, 791077838, 307337251, 496640724, 634415448, 815122438, 949649453, 14001760, 204061787, 593799709, 21824208, 306646863, 393913998, 95095285, 62436752, 623838102, 76793029, 102240533, 305057613, 495556460, 863636851, 137061314, 163749864, 280960060, 33712969, 696507473, 65801837, 931153255, 807782640, 623957005, 817539076, 776885378, 433061634, 484164391, 167916171, 24045487, 950437254, 65708264, 946642370, 993550130, 854531765, 779943617, 417185909, 36552389, 977830142, 823268783, 908443475, 260360557, 80846355, 870734566, 28812671, 179306088, 514774431, 793258687, 33293976, 499414141, 693557335, 21145475, 429018128, 433795543, 363190120, 238242537, 738543771, 526592189, 288762402, 242211728, 257752866, 731650536, 169079496, 277473077, 497521844, 117244326, 242993713, 859109574, 771298705, 152204214, 36641528, 203473318, 351526969, 328735101, 199371877, 140043457, 956957435, 496237611, 506803765, 821874706, 788211381, 374269552, 491794966, 212324602, 832882788, 693255002, 532557173, 108766369, 328095637, 885769785, 164717126, 169552433, 144788252, 694316725, 1515266, 940076211, 725434742, 439516937, 872394988, 696599092, 441972507, 465233702, 375206059, 570306471, 447583088, 43726322, 542635245, 499452122, 65447575, 876562450, 409498666, 793600574, 110512556, 908572979, 869093037, 227848026, 372430155, 564414613, 374926399, 241704033, 383401437, 769926567, 543782075, 817125280, 148227146, 636009870, 438648747, 563138595, 641159204, 291573478, 465636935, 592153750, 529143790, 747991152, 306219658, 405943803, 797398469, 811962920, 429482687, 229251049, 186228988, 180994144, 673992286, 158309840, 16292125, 938907036, 174695551, 343954768, 656099750, 110645312, 687226610, 18845389, 160463206, 650679660, 946779635, 218283845, 163578792, 325480386, 571446856, 180663493, 475487667, 343746430, 992419520, 617514544, 658843441, 776084591, 760037023, 744948498, 469724425, 518641539, 657219349, 328668555, 760460943, 832313589, 949179293, 721353605, 479670452, 68444430, 346102484, 128766352, 217417277, 11518830, 72712141, 803961976, 885527737, 170294876, 11811629, 84144309, 713276199, 277844116, 272906081, 297913849, 977116053, 990987152, 736390624, 369645614, 996571154, 719220899, 119656427, 936729912, 715559781, 281237288, 927420090, 813038272, 430029758, 829303068, 525940777, 682268196, 722360138, 354276700, 236639568, 267246164, 470611409, 564277240, 363670660, 909429314, 472455240, 616543630, 397044034, 33393004, 412144854, 20076603, 954502594, 379515579, 238036190, 898006917, 658207151, 171934140, 700266546, 155648514, 80167481, 201982706, 690100716, 435876778, 808257083, 35915988, 212801013, 558551173, 563317755, 668288844, 482193042, 628550775, 402174836, 480818761, 162729240, 623581605, 508706340, 196242476, 53287309, 594500000, 903360036, 220409674, 569312833, 622272942, 303087563, 980146173, 780533977, 19834387, 237504622, 803455556, 918054465, 307923469, 948041189, 355839647, 19763282, 509184155, 656527791, 942976583, 705443301, 922184048, 929540987, 586144852, 600499898, 755035858, 997378951, 596296883, 600246157, 676148824, 28959395, 165781632, 163563319, 652191378, 500096792, 381425090, 909551791, 513877448, 278785399, 803499013, 267236189, 678834919, 519782242, 770450308, 616414146, 439915764, 73497513, 824968206, 809688470, 35155884, 244372621, 861711827, 690107587, 593260457, 498719092, 55954687, 928550979, 74733143, 501175194, 653267611, 907926724, 205480618, 964475805, 944601581, 949020986, 350262728, 88557017, 244422053, 745395216, 594254943, 705484304, 642110266, 660207309, 260942370, 875600140, 491130673, 601534441, 298845526, 596150045, 749862500, 328851820, 750651535, 406647882, 112331034, 976776057, 540456609, 348203204, 208153650, 985483227, 445622092, 93057131, 86823109, 276413391, 134924649, 143517765, 716683257, 636146010, 717460658, 362240474, 175020992, 429935562, 73601466, 761565766, 168033554, 86583162, 914715733, 324463825, 704355287, 521965845, 291136255, 517300413, 545623979, 186191297, 336831173, 754844325, 625879649, 452020918, 729352301, 610362205, 238399947, 605134297, 79114483, 568372901, 193946152, 389140619, 977758791, 978860350, 391964113, 838643484, 446576206, 491490121, 470492698, 94527435, 823298241, 421576419, 219356055, 175455534, 131354357, 432237903, 238427697, 242487566, 753503949, 292945625, 717686471, 760782495, 372006363, 503031185, 711291027, 816901716, 896703591, 363516844, 436225252, 332672514, 261746707, 592170388, 11233218, 399885486, 367649503, 586614961, 540090679, 841824302, 178367143, 950615970, 288437612, 521551972, 374169257, 52413407, 381603408, 975320926, 901153466, 481494022, 95347814, 777000546, 749532979, 645867806, 686230947, 851930182, 951493128, 69682706, 55702722, 802870891, 599602149, 988487737, 628951512, 248682061, 631397498, 389562968, 717349344, 199361127, 856669713, 985945491, 793268060, 898693371, 90058827, 96049879, 598870182, 646188076, 73229191, 339940558, 505141634, 341358221, 764971187, 936688133, 902765918, 28216023, 284167727, 36391151, 610608797, 84111807, 360980513, 120087479, 164841760, 669619453, 624425231, 83197632, 800160511, 929757920, 937844346, 443922697, 192443073, 75154700, 883029476, 724977034, 732785699, 451350129, 603075833, 733179132, 145658876, 133741243, 688891610, 143062674, 738838231, 265615048, 743300471, 1927792, 73441960, 119751918, 177275697, 886354221, 933633101, 404734041, 521019732, 377513309, 43846469, 321192957, 911966802, 89408590, 179711368, 121577318, 45210095, 600800527, 973812126, 816899516, 542807873, 279987825, 465319560, 876622155, 601773719, 448718082, 79527333, 553386054, 130217267, 149801708, 328685682, 293324456, 613174020, 218872364, 174281325, 37067392, 391193919, 315799265, 848850496, 202722079, 384252303, 453655953, 415372588, 474068240, 791599182, 551606135, 955657640, 222965720, 170171863, 851865725, 37887296, 828897818, 328892790, 802726921, 309822563, 450759185, 254009544, 267349066, 334435092, 141384578, 819251416, 217384043, 545096041, 662780325, 597037094, 239001046, 613228334, 760074104, 442655078, 825591405, 974308715, 49317641, 853617856, 351821397, 889974086, 497596845, 497402170, 329122733, 876058474, 974777315, 99665399, 190189635, 515147160, 763903564, 70965535, 970193316, 26909465, 333243580, 727200529, 278518761, 323015066, 3079743, 946182859, 685528757, 106646991, 496928379, 712972469, 573026588, 166899619, 747846340, 230117054, 640400003, 782364063, 819233191, 499300742, 803021324, 684444934, 311991209, 950389963, 532088557, 887634538, 953806270, 889071596, 246841416, 25152773, 967907185, 332274469, 236930156, 880380627, 783758674, 721920683, 650113364, 484371724, 451443025, 607453637, 382749486, 492586584, 928909597, 517774502, 362021407, 618685143, 2810027, 361211789, 385113732, 465679502, 258963145, 118616371, 44391876, 637812743, 876013710, 352142124, 291484373, 677048088, 664914869, 873383167, 869434160, 709445897, 179527963, 78264373, 548562323, 245847364, 287286441, 338246554, 453634054, 214996951, 98448652, 882926633, 152939409, 969373557, 248716992, 482619376, 241796246, 140374866, 76513166, 673480593, 961772672, 625389244, 652077243, 420871603, 510538749, 963700989, 701192889, 445522384, 820135427, 54718245, 748686595, 668858097, 434736119, 752743959, 907963692, 152721119, 870012858, 444476562, 50061023, 628793399, 989590770, 325841438, 485822764, 40706267, 303275492, 672680295, 854542068, 699062857, 738422781, 175518319, 231833681, 702771168, 361083230, 829405830, 609982754, 204736299, 632579508, 757071898, 62766629, 881210867, 216248225, 184174093, 167020043, 870143376, 894596942, 709599599, 287177452, 131834980, 574710670, 926125427, 268079686, 724853986, 515427580, 231172673, 253480468, 629440237, 711368276, 319651265, 579119563, 656859160, 368036444, 498055482, 727662111, 428341627, 356597855, 399292323, 664739933, 908414167, 145128666, 135552934, 877999535, 43792823, 60996738, 204297927, 941415966, 556789122, 42197267, 757386588, 380628676, 487404727, 559260462, 227114760, 22868555, 959309733, 749968556, 637978288, 941165760, 291362874, 24084601, 741994750, 161082941, 215213297, 3858844, 317923686, 230632166, 307823246, 978498758, 731199397, 208092495, 855746292, 667590819, 283018332, 964068655, 615882293, 455291560, 845417325, 723811174, 840694760, 594121433, 282223568, 653806122, 572096343, 361145206, 378442864, 318755636, 489788771, 852069561, 47309608, 982739878, 756989366, 283315108, 115636368, 151146264, 933980924, 640289375, 830318217, 41541158, 832469039, 300365644, 465644499, 679522503, 223147712, 188605125, 275765477, 595047006, 379246188, 347579523, 146716689, 764062976, 156282910, 763920958, 345544155, 66490631, 571721333, 167773132, 685468144, 358445992, 76055301, 445459839, 59590637, 62632701, 71351032, 870390761, 758404954, 178169391, 824482994, 593681482, 634055277, 890402756, 211827200, 945600843, 523372076, 45217636, 198572887, 193308406, 235810128, 760819797, 147195496, 681001565, 451586061, 627800256, 100098271, 168221359, 76747918, 977350606, 826945315, 477571126, 585490606, 213171914, 663699487, 675795352, 567023011, 954375179, 531059784, 183318491, 967232294, 154514945, 159336789, 440871798, 572701747, 753086312, 722411262, 505426418, 510427372, 774014634, 947776982, 304203673, 246795253, 129701969, 206957563, 645644820, 407898373, 989416341, 312180766, 76010805, 116045275, 298889653, 51609100, 108233523, 658816298, 796983058, 398000785, 774894939, 874877980, 492361599, 714352339, 202248648, 406415097, 267819764, 745607467, 314717665, 174635399, 397703341, 593970833, 567155020, 509511010, 359516872, 750131164, 857445097, 94587121, 899880476, 725226739, 695701879, 926090476, 563928130, 86711635, 660607114, 548373164, 170145631, 152216223, 476882968, 417463833, 699013057, 612151534, 22953347, 780723295, 696164961, 505711272, 565067033, 454652676, 729028373, 799510020, 302855811, 465456270, 426197410, 203152977, 616507667, 194321828, 715804756, 978978628, 329801628, 66909177, 863651269, 141078903, 554541051, 572925419, 89289873, 515942079, 949361115, 754837977, 931037313, 821076242, 725290184, 298058290, 536487910, 793163657, 664106227, 14074197, 202900914, 195737926, 103638844, 722866331, 110178568, 815024590, 916769441, 736537305, 750082632, 229122836, 971328677, 40210391, 634776499, 491940622, 252950205, 382394785, 746283421, 518474049, 159098581, 723390264, 323477096, 566176527, 382451555, 997419857, 942373366, 366431220, 938199899, 845519670, 678799111, 272164001, 491425434, 450914945, 287536945, 739946510, 96877918, 624830119, 333755083, 111658997, 845458910, 558288500, 804344323, 993239194, 181771731, 136490501, 232667188, 753540252, 288243849, 319824800, 804234011, 170592913, 571562205, 853447266, 169531724, 351088025, 872622752, 707003354, 714687182, 934154481, 512335812, 750870107, 288293289, 285703067, 133544700, 589131752, 997325327, 663102334, 899558563, 258222191, 358624594, 644295644, 421671826, 674514949, 622199557, 469175398, 450617892, 869848889, 192105909, 82585707, 549917833, 58978740, 10708568, 212711836, 721356209, 97109161, 608053344, 461118705, 741938996, 400588690, 242220195, 595293074, 62339032, 998412638, 937551537, 799483795, 61367798, 949482997, 540490129, 341371409, 707368983, 739467675, 609985732, 837254723, 309940262, 220394598, 43541565, 182436396, 859142497, 309481535, 266177084, 78944428, 775469551, 822561795, 738773686, 319880591, 740702364, 516142862, 405502989, 535018802, 63852217, 448622838, 184470170, 102891426, 885621543, 992351517, 807049180, 409944442, 238206835, 732906041, 895031506, 218746075, 849534588, 788519037, 661402413, 757502884, 230377407, 639837591, 364402642, 922209979, 351848214, 706864033, 705738954, 576477813, 555991801, 551882531, 402688646, 539018412, 693060837, 40710765, 167640454, 223663940, 859397358, 236682155, 931208159, 516756557, 423179766, 886401070, 947556778, 655854969, 453871985, 10798695, 683083320, 368457423, 403076643, 758762167, 864180657, 664432028, 267190164, 125178433, 11761797, 532808893, 8592772, 372293684, 805965731, 251370399, 95680663, 43620729, 320183343, 139173956, 767061054, 710599855, 95881300, 408774849, 279566041, 611170255, 320263409, 941982846, 582829328, 593135605, 953424236, 543334336, 582131751, 239937781, 964366148, 124890291, 505867346, 339697952, 778174588, 129077537, 712328180, 543089106, 799818033, 179026904, 360905285, 927009672, 59129499, 42183974, 327582197, 124139136, 773573596, 307457657, 478269652, 340272253, 317147939, 711484406, 58891244, 3979007, 362463548, 721741492, 447118876, 184952841, 392857350, 887599786, 594765580, 303664003, 320629687, 50188228, 754816850, 88689595, 29443280, 655576245, 646182415, 229151835, 424295113, 836533867, 137188373, 475786648, 369473212, 853280294, 107767611, 639891659, 469813912, 955244943, 543430166, 208367995, 34206574, 959026582, 375459198, 468512700, 790723730, 103421731, 972943333, 48726861, 583664433, 728190399, 997343858, 413378359, 534819078, 493712174, 871128183, 543980342, 224972321, 935675606, 226617997, 46300715, 348387139, 435182746, 524173253, 301872786, 184701397, 277151532, 59729666, 229180618, 600705649, 625379156, 469305961, 49071902, 30862449, 496324947, 403048166, 841793381, 23193375, 490597348, 199963070, 894621845, 871390214, 883888475, 319226788, 725959706, 31197561, 911909420, 630078057, 555878728, 50799327, 52359006, 522127116, 937837512, 493978858, 623375394, 856756042, 746794828, 378455617, 139814158, 351938343, 949321027, 603680541, 665710966, 142023061, 763518750, 457993921, 128503186, 993440586, 954576995, 119676705, 488713419, 374784718, 574013261, 349530117, 847888265, 342099183, 874668434, 801338497, 303134288, 597944206, 380836396, 942998656, 308268814, 71157705, 521544899, 9659337, 687744980, 147558734, 777491442, 869846, 600069504, 672098480, 801381599, 643523774, 204418699, 96783101, 670489857, 644714631, 425148613, 959711518, 718882032, 906779460, 660655171, 949770214, 931181064, 136637297, 697945379, 137518451, 127431043, 764462339, 192029256, 345252867, 282097147, 36758853, 298240631, 661093481, 672408093, 136519356, 209669851, 336129292, 618414961, 405588293, 601062736, 30176839, 284907791, 547022074, 587583388, 58811065, 139111519, 931470348, 271703712, 308243678, 174083041, 683443559, 183299425, 943965822, 699697375, 683540955, 451157721, 361987582, 212432986, 12740171, 185097157, 184789974, 769401474, 926280434, 678421505, 89794975, 285127193, 369653388, 347697825, 340224522, 883812553, 924273722, 944343435, 372867434, 892820726, 222375881, 273696852, 442855521, 320288622, 841290846, 754026939, 101200961, 477021584, 97180234, 289931547, 9569134, 949626342, 682390906, 523821200, 764743346, 810236015, 93359041, 2397224, 264566032, 1881404, 704162748, 387215139, 996992538, 578241145, 241907534, 603523279, 823849865, 492918817, 237886653, 79331079, 706502619, 386981237, 638543023, 573041828, 69018841, 111112565, 671147257, 468418150, 538489181, 861569880, 289282554, 257053143, 506474901, 725723036, 651032880, 492836011, 377707517, 77019527, 943599848, 511225911, 270913219, 794080045, 946018829, 278882975, 31014026, 736616286, 983499116, 205759895, 833783880, 472430554, 136683670, 725702060, 301453231, 514787369, 964412901, 260397320, 348282519, 363224588, 363703143, 112018919, 445047965, 21400546, 184167581, 899808843, 682558440, 341313135, 238609404, 556975082, 741049783, 748446562, 81368892, 529325599, 294409220, 961116280, 500637607, 109507512, 152463671, 807292004, 572635329, 16618312, 825064675, 108820237, 296303797, 97045802, 171790894, 603582145, 272271526, 682211093, 44183774, 215065869, 746028869, 208057243, 220289297, 465800163, 664896702, 654070120, 33341186, 578934780, 800180799, 480491053, 259468921, 856691038, 684873928, 121557039, 927242705, 179886473, 968751616, 539385293, 745494278, 282371330, 571642206, 302016745, 849840179, 555441410, 78597311, 590791279, 679719967, 863308378, 122080813, 277014228, 364154005, 115696326, 435440029, 128192530, 904030770, 405973493, 509644533, 887316579, 266081579, 540437124, 110613028, 416293033, 732735428, 987507934, 65307753, 641686312, 578541119, 418957358, 444504487, 858715538, 459525782, 436943919, 450119190, 932611196, 855871364, 998193274, 60501842, 151169659, 650317493, 174865438, 903743654, 338535052, 929613342, 688069303, 198741161, 919662653, 16559281, 620295466, 31648305, 934844882, 576179287, 775009313, 969127612, 650842721, 755595734, 60355777, 454432908, 403187777, 735745533, 858244892, 468511987, 331701854, 57542500, 383124512, 877828177, 899327299, 706339217, 816142727, 940334092, 952732054, 539624668, 549059733, 385533545, 134833024, 169959175, 841509122, 956958820, 592908340, 232713019, 532707634, 719601572, 891466643, 919995943, 924640788, 751962062, 546468282, 862856279, 93611782, 853272970, 410804925, 333147529, 906212962, 329152925, 31133108, 814478446, 969188731, 751930361, 582803181, 350580682, 426398148, 645386054, 826768698, 773514665, 297402141, 263103046, 120683384, 354581067, 103322615, 32263743, 48478484, 273019626, 456101454, 837404513, 970787680, 320097560, 249135855, 114531813, 282443293, 928873805, 442939412, 185392427, 615748276, 554841774, 716177598, 100117702, 680069669, 17226645, 735801260, 587595064, 59927554, 331624774, 403352079, 615677999, 161108459, 911029706, 146648184, 681533718, 451449553, 161066388, 666702462, 856392431, 359333054, 216617376, 284811158, 207677249, 418388327, 16328199, 701007791, 834981909, 939514378, 226351939, 896282691, 34726271, 385903658, 729078310, 160500689, 338211449, 810547369, 463621225, 136056645, 487423302, 691600224, 848944401, 649443569, 9516831, 8973653, 793502684, 867568657, 677184277, 79752447, 536129004, 496726357, 25599813, 154426443, 710738154, 871459855, 806684116, 22432590, 739654858, 860698951, 259329078, 361488252, 521931950, 469398623, 11541231, 509218706, 864745557, 408264053, 442299695, 831011416, 369256126, 683386809, 864750142, 766361556, 42154100, 104801426, 759393065, 471256450, 173786221, 913507653, 911521392, 213111575, 288856593, 709805328, 32226326, 800841871, 631925199, 428786167, 686674190, 965821472, 357287386, 887959908, 218849117, 253417708, 714325305, 843312638, 41007054, 547289928, 354690701, 164946557, 439177775, 626970380, 547733510, 205698586, 647343447, 406512293, 240898428, 281579838, 694958881, 505155495, 747515967, 999279147, 493719219, 242988800, 941087980, 465322820, 622519719, 307863496, 140361508, 538966414, 363403933, 349888719, 622079532, 546589896, 304305124, 497047311, 545522477, 195883882, 341840, 848403410, 532077205, 624994207, 325408567, 63492943, 716741451, 246420186, 822669260, 808162246, 913339214, 365483898, 831131973, 459296161, 146684424, 980556650, 298930566, 720453548, 844861187, 906218922, 977040257, 422480074, 296397937, 486198580, 960438387, 566849452, 940360213, 377541120, 3624824, 379856312, 242216747, 333745249, 11773874, 623071861, 514174324, 129591107, 690994374, 780225333, 83979917, 288892889, 874534477, 575606054, 362731259, 455837708, 571159381, 731585261, 683053309, 340436925, 529393116, 453070379, 390568223, 827114117, 392007788, 465268901, 462150827, 296371460, 250814403, 777244504, 453739725, 453838951, 628221316, 195310111, 843518755, 209805816, 725636254, 883837583, 861503174, 828940922, 88671515, 23257758, 834623027, 850074270, 497476793, 430408008, 132486275, 380988568, 633363423, 8778234, 771258199, 252557803, 517814468, 427930623, 358779910, 261229984, 987402740, 10012547, 17577412, 548725971, 144180375, 267003467, 452401614, 314788924, 160082247, 49292900, 493143361, 292604956, 609337086, 339394351, 505942231, 944036078, 553794770, 248651301, 9958396, 537483462, 630919802, 699835682, 451591915, 297360562, 610907299, 457077014, 96664205, 595971736, 70168438, 450630161, 959009690, 999380713, 594448176, 557855205, 992210681, 128446614, 736434410, 368503198, 165927681, 561106884, 994034478, 111100455, 999770115, 96639318, 317119135, 144269313, 889533216, 164305830, 661164932, 153856316, 536455929, 281403292, 707348671, 517626450, 358016940, 407405677, 424682620, 277471291, 602935827, 553910941, 532128750, 798376692, 205243222, 365656619, 586085619, 599831877, 747730100, 659328151, 578499940, 679199590, 35688625, 336623664, 773183532, 93382170, 291745415, 72735171, 861661025, 112734584, 993502571, 215736608, 842203652, 223526939, 97569849, 985350075, 829287017, 280473217, 267391981, 817893801, 253949253, 858929403, 910870417, 870339948, 245009382, 978146658, 13605044, 203107966, 955307126, 12109552, 535120358, 490118151, 282176239, 323786785, 261620138, 785700654, 178113478, 662993455, 431542023, 7145872, 378116581, 334289980, 668425793, 884260928, 719784637, 195202773, 453453626, 163913949, 360048428, 164143589, 871401557, 938172114, 173957118, 897144889, 411453247, 222814576, 997864604, 549796278, 402223521, 747413438, 296849600, 727931295, 262744479, 830266312, 134234293, 12251197, 483342698, 668901617, 125743924, 369621239, 910407460, 177497324, 838530106, 925320562, 52511267, 369501417, 572490866, 988884816, 754453601, 437311273, 227954679, 793880462, 194046649, 308656971, 690796877, 631085913, 482294590, 167844705, 613385025, 400711325, 248436867, 126463983, 117421811, 382090980, 325459079, 196892508, 840171506, 510624044, 995793524, 963187089, 633540193, 920021445, 785187505, 808919279, 91600614, 577923833, 243660906, 95418328, 369537994, 133317878, 573851699, 949904260, 124883286, 492276307, 403292828, 956254969, 33589465, 674910178, 296454235, 27625971, 231075041, 4710635, 630728958, 165913494, 417115417, 596524238, 566215450, 768601735, 774885191, 149957391, 471972910, 43324039, 456670699, 570247582, 161239647, 991040941, 582715930, 82642169, 837915070, 521110745, 227543895, 165811497, 740325490, 503518123, 705494379, 239740263, 520205869, 608655650, 217404035, 799532495, 429091363, 689669336, 523689195, 739124744, 31488496, 686518964, 724071199, 739971781, 207355689, 574048997, 925822115, 337171001, 895844909, 316544715, 539944956, 799978449, 350113710, 394028005, 68253811, 10633375, 370934519, 553730398, 286411532, 320898435, 657389393, 133117695, 445843728, 194047313, 392515499, 922680999, 368275489, 561571559, 104898698, 924206621, 460837401, 29719740, 680206571, 317306027, 203466208, 815831198, 827394967, 787273873, 216925376, 269093140, 272928708, 85797632, 208280681, 189845021, 102196249, 164296826, 972305350, 148023523, 312200345, 334844542, 32987067, 426821863, 319693040, 245378515, 842845725, 189845681, 957121072, 729498524, 536708313, 39344052, 137670592, 214533593, 170551574, 991027263, 241115600, 854135477, 238669768, 784007336, 218646563, 274138621, 295660997, 624849331, 901686655, 817907972, 347705625, 827064492, 72738228, 76890770, 996322944, 900323178, 80442796, 424713608, 815910910, 905674643, 152506252, 440897778, 138325771, 683287244, 344890575, 662736276, 586135627, 807700905, 415668465, 161256151, 925822704, 33555005, 965609612, 578220531, 250019986, 897463890, 490557167, 450443588, 348673100, 123754327, 652557474, 434815149, 463353623, 991232678, 144076541, 13080224, 897377716, 518500846, 479498304, 65035737, 583455733, 518646103, 519732359, 760982386, 237924135, 487496900, 70593770, 747998349, 280343452, 799870890, 815589488, 877866435, 191836498, 632337379, 712609521, 467641950, 298561807, 953191798, 171224217, 919390761, 760397295, 200019085, 222053001, 416586621, 431177859, 684976256, 595296030, 969884073, 218422521, 96751211, 468759014, 187032300, 928580368, 409742941, 520954692, 159079534, 596481832, 794859948, 983930068, 629954919, 741665503, 711510963, 185552971, 132386648, 69671331, 811964093, 165995313, 145515663, 741877830, 705951656, 493956981, 897035466, 445614697, 36306839, 277977881, 998896503, 570153874, 620653365, 125838819, 191280419, 24564877, 390635926, 920622288, 318037658, 918934743, 885785164, 398952161, 125596286, 751527749, 30235003, 315520859, 645407754, 784830312, 301518847, 113042339, 30522391, 257387528, 786444656, 191829863, 709395639, 508222438, 418160415, 900490105, 619338721, 962945428, 443001173, 193886711, 181969082, 642307235, 265956466, 988882909, 263959598, 304599187, 84347421, 266967400, 684927092, 397630221, 974020423, 595809176, 95248500, 709975967, 769556802, 208547719, 936801241, 469772497, 330537709, 894998783, 539003309, 559925769, 474254364, 896292718, 481848342, 472306682, 974765723, 41243439, 464364723, 931917016, 253933589, 728970837, 631944666, 54365343, 163416981, 765877622, 107887674, 601759376, 432920945, 489128387, 760532216, 136447501, 925557127, 514766034, 424862957, 362403516, 21975996, 393956259, 64232274, 295240257, 801747660, 557593461, 214478926, 999821468, 259742802, 981600339, 116842574, 870993990, 397560863, 640379174, 3762168, 261660514, 596836860, 118911463, 938271934, 689002210, 137332972, 392030741, 76352443, 89529764, 223208307, 592371943, 986877794, 193291490, 71483986, 384023486, 214035676, 490248323, 681454663, 636114037, 452781904, 453258964, 900457819, 869783332, 835465703, 490575061, 816901695, 73412542, 272716382, 261165005, 24844599, 963238335, 781593997, 769429655, 507734544, 170056316, 777282745, 566960301, 909191102, 695257755, 655274351, 546454165, 313946009, 603867112, 614365659, 368029689, 937946244, 336214466, 373371719, 661040901, 979010969, 832690361, 888114759, 494820495, 186616078, 394465133, 97757300, 460801045, 153641201, 345717973, 138803575, 167765327, 806707254, 610445799, 503125778, 123154114, 497742702, 164532424, 985647610, 393609022, 514273103, 451571615, 944783951, 983126089, 292331413, 551644009, 218952027, 219604645, 286465620, 209840458, 969776829, 343630462, 338103250, 213064025, 821253131, 705571036, 604318535, 373458810, 767121217, 25086732, 710805343, 690508666, 225691470, 822368286, 132224786, 503509582, 952155181, 515361126, 912403580, 603386238, 866331927, 1267468, 195458570, 291861875, 904171622, 366279114, 389441205, 110500688, 127149233, 335704419, 611538409, 364172048, 841267696, 192379559, 390699681, 931963738, 890203452, 985206380, 344481592, 765067479, 737365985, 838759613, 346876156, 862164733, 350579648, 493235739, 270655196, 986141986, 914662565, 599050917, 415895928, 562876732, 94283165, 577520325, 485425564, 27632010, 951930207, 105974296, 307523975, 431357845, 679456122, 534603119, 853612840, 722811536, 452808402, 547551646, 680794031, 281594816, 392650533, 969969981, 512868126, 903262785, 338627612, 819192856, 836808792, 133217112, 919147841, 204933341, 704684902, 572305542, 584746297, 22282380, 655331746, 215578753, 373283119, 121321259, 526358322, 357961880, 681288663, 686954163, 182730604, 472731431, 843606931, 489451361, 462852840, 435839237, 395273702, 553431032, 913301432, 552659904, 845461405, 376807966, 464854654, 439583536, 758191730, 630498867, 827826072, 829379189, 976555007, 172054857, 928231073, 809769173, 118760371, 722313038, 110731822, 424042490, 731296008, 65509174, 641167899, 380088448, 239399366, 338730011, 554975111, 556964588, 436360561, 724856607, 713914990, 690651009, 501821065, 197943986, 948542928, 295462454, 663833868, 861609223, 827170014, 600546566, 452037802, 871809379, 244810690, 436767487, 871596344, 35830941, 416726002, 260208855, 161111671, 426018696, 690947634, 193809138, 670388282, 88917312, 917309694, 777194008, 181455687, 727079297, 561232563, 376550102, 763130940, 429474894, 298752382, 345065615, 335821582, 84143422, 75907328, 858267060, 787774882, 804221413, 217918561, 428843248, 274781230, 968745212, 897279680, 229503246, 18679453, 752210195, 847326689, 670199119, 96739694, 132232311, 584280344, 18394119, 421603754, 855686041, 400341492, 671816451, 407179216, 19691607, 640766289, 67364838, 415276954, 328766075, 68649942, 560326373, 496984420, 828343584, 687686861, 551836106, 333801018, 116225867, 303805276, 567322749, 828735623, 977316699, 345308971, 532436021, 367939508, 507544590, 225934253, 17175362, 763933807, 107081804, 701893457, 630746709, 951156355, 795757851, 999990405, 344447807, 184167849, 126550385, 68312456, 921194101, 75459619, 515764555, 7741123, 362422639, 325016768, 835652600, 448270011, 37699124, 967478166, 114818745, 307346285, 935649441, 235571012, 608451327, 202412138, 457687073, 90736920, 623621124, 441262642, 266486948, 150570511, 192773132, 58722721, 709623617, 732409925, 496963722, 551340084, 537204508, 724440309, 665222532, 358978551, 960923690, 851891941, 904838502, 827283195, 139300395, 926332622, 534106618, 177633911, 792973205, 404878017, 618642199, 29498775, 775976836, 458305808, 110685373, 203901632, 516668659, 33359373, 771855374, 902878852, 187600651, 39919088, 228886260, 529354211, 506701294, 684762321, 999651657, 49340335, 643720822, 208821887, 191277397, 591291459, 303803007, 54874391, 143415744, 622790922, 689607400, 907633073, 847289940, 610573859, 252676623, 819402896, 818223028, 804241779, 596133113, 723571101, 332453466, 503305104, 143507406, 325577560, 808341210, 645152795, 304536916, 667460252, 180986628, 885509130, 316772377, 281080572, 949546776, 486626683, 681870083, 790261249, 368294395, 11379903, 97354249, 698133057, 340161148, 265683365, 269825008, 32401494, 999759617, 869759644, 51579883, 512143286, 194802591, 928625740, 288034746, 41399862, 978170358, 122914765, 658558519, 443174030, 699366364, 911419826, 812912804, 564194513, 645367010, 415012249, 582797365, 440201259, 322234085, 492664798, 789505234, 895564413, 530532258, 5149352, 964033066, 239277297, 329376629, 541978077, 664309209, 178024251, 798005233, 738410687, 551357638, 8150904, 613700311, 774123721, 602856744, 38091396, 479292342, 650995870, 761220975, 938174312, 421988522, 62484261, 764075690, 631646904, 979939967, 551450753, 414996267, 185072656, 605343725, 678689133, 267221901, 805037281, 727144720, 207229267, 542959368, 327801118, 207956288, 442420821, 734892979, 822466400, 816525820, 624378393, 684805517, 331226077, 973752697, 135863074, 701522079, 200412149, 948790713, 261677330, 345554540, 512837298, 330778595, 55335104, 301202509, 748380053, 817572795, 451467959, 777291407, 817527863, 917987009, 494563805, 549977138, 511207727, 759177149, 578887732, 798509406, 730988718, 945858318, 612850962, 966752698, 634239912, 510309099, 45648217, 639985650, 99686512, 488467344, 84168420, 471045664, 705896162, 46784140, 518757123, 245461131, 252458900, 77119747, 872779965, 725940784, 329273353, 500691947, 183675649, 5502827, 411578451, 706799104, 419615405, 75313784, 963111050, 12396708, 456169655, 395392022, 87216707, 2295036, 343602386, 571619413, 619865681, 343613363, 507331509, 832504836, 226983244, 267979538, 450263570, 789112212, 181655431, 75581342, 837535661, 674988794, 883690543, 229707272, 489236416, 389369881, 368655534, 654685916, 52155691, 232840470, 358181863, 682435256, 559067565, 813732753, 181622018, 480038381, 661171226, 734982849, 537661387, 411859310, 750444854, 474856488, 412189364, 573990817, 804596188, 319844715, 995341897, 592887003, 634816501, 141950838, 250072923, 982135742, 288634591, 55474402, 656027986, 530476130, 739705536, 913214705, 946711158, 321905570, 27464037, 635286216, 604510569, 250345983, 626049372, 17195661, 157935553, 466724481, 411607462, 117549821, 592945432, 796028911, 105841808, 343314551, 566786343, 312453480, 546861550, 267715903, 649424182, 828985806, 427132734, 618418050, 469335617, 533121538, 776485268, 27561065, 578101046, 187218886, 764988541, 994914462, 170582561, 335255157, 914282460, 100503105, 805652050, 756148086, 239160008, 246141469, 306489031, 865102962, 700106537, 752254175, 3036499, 721080456, 647369590, 599628622, 829725473, 401633217, 214501028, 133332487, 218974685, 268278281, 691032691, 565790211, 473082434, 400434346, 738951321, 789143573, 547643128, 957240878, 807193681, 71526531, 19700225, 32112197, 192107324, 133120211, 665051035, 48393746, 506930556, 258006799, 231410430, 967765760, 694472578, 499046116, 961948975, 258689062, 576279884, 871088709, 168623132, 736613241, 975407456, 356058543, 619502388, 177536162, 564526129, 108985736, 448248619, 407388495, 880488077, 353790142, 876287387, 877738897, 661850742, 768229746, 35360648, 639684633, 495252809, 972697159, 159580073, 114616642, 852116516, 441770413, 321691383, 214547205, 675647116, 9700460, 848187143, 939831494, 993762769, 970473565, 634469806, 137978051, 403325370, 369019923, 942193665, 633014369, 263821338, 814571785, 400586046, 21734779, 228896007, 333740152, 159346796, 378484826, 375054874, 922423252, 430847950, 138238368, 342433535, 340818556, 285415247, 851532449, 297789405, 703844978, 87219929, 327663598, 498460592, 823066273, 878339843, 964024886, 639254857, 256264809, 604856697, 640087762, 26471058, 98008299, 500597897, 154732164, 696581869, 143238324, 609706903, 188275587, 201599940, 405936241, 262929379, 745118820, 863298043, 416372780, 990537675, 644385530, 159821604, 970319949, 439831828, 268192186, 281146157, 563325475, 420094008, 154436369, 813992924, 797325756, 987064285, 437960127, 329308598, 591933182, 993851577, 199299628, 996202913, 495482077, 934003878, 908765972, 626092645, 171498433, 771712281, 470118180, 682450829, 575305713, 46353784, 126922659, 166745247, 803190182, 137435201, 664626044, 938994569, 169844302, 332488609, 667507249, 850992691, 110269709, 243022550, 217733144, 916806143, 365228413, 366742696, 910782671, 471944207, 676166345, 934978925, 750520880, 601532456, 362094684, 221405647, 666502733, 320650295, 334107005, 421801387, 374749443, 239706020, 309598295, 637537589, 960156003, 47085604, 979766780, 322953988, 543507326, 243861411, 672018787, 690411302, 334334145, 47603214, 863855234, 912857576, 190100017, 42663645, 163599672, 962794052, 923133842, 598230223, 615936358, 483325323, 430999814, 174448299, 555099641, 479643480, 525490485, 716037399, 671901723, 224027163, 752386544, 542564855, 544016895, 316947779, 322575912, 330556972, 283292825, 41819070, 976089189, 476185514, 116490786, 588921121, 217307075, 868241948, 119834393, 484914885, 591929300, 633241406, 661034679, 1572848, 549449885, 466922634, 803834167, 239845799, 322881591, 783729994, 367532099, 290588233, 722618750, 358175001, 498537872, 470041832, 968071721, 469711188, 724785067, 753194529, 973193184, 183076864, 674920576, 113699691, 862217699, 379968995, 419858592, 476805817, 571298967, 994669572, 195870076, 960508753, 636773565, 780374495, 912127792, 63757993, 300014862, 618966155, 342529965, 170305462, 522237165, 828454789, 129530266, 467591144, 990185812, 923343247, 133688631, 103562026, 154685433, 706395367, 884861864, 993025907, 287730625, 67299660, 625512444, 961953381, 912096873, 694395334, 523736386, 34872365, 150394345, 603409095, 823435879, 288083399, 365250532, 966407897, 821982505, 445847268, 236348832, 518331427, 390809628, 924641383, 214615588, 602297781, 596286505, 18323060, 480322866, 631542928, 822952868, 20952087, 93587037, 901141274, 566746422, 236054911, 455546161, 11077756, 835587990, 545297274, 838215492, 632100236, 10799595, 202707352, 906546978, 830742061, 926249670, 279348808, 598486656, 587589366, 727918844, 94009133, 697460957, 83889312, 327293291, 452452228, 115585200, 755934845, 894731408, 810053704, 843685435, 688272689, 400983690, 595300717, 184364027, 12307054, 433494963, 761404169, 300495668, 295671436, 167847254, 721779283, 437171327, 876571359, 128692531, 181309917, 169781877, 620548330, 268106143, 819997939, 801975062, 457902198, 590481640, 799534974, 716299327, 34717551, 132170590, 368569265, 902215263, 133733724, 825922477, 644705404, 886089206, 127534607, 992094981, 351478999, 584693282, 33567577, 521361985, 145795482, 724668856, 22171194, 567994237, 920926486, 616718726, 144592642, 940405207, 624703154, 801017064, 497895749, 855984920, 192406847, 239171608, 663900273, 624180680, 98856322, 819205998, 843072148, 5874837, 633326155, 405453270, 493763415, 84105181, 340392301, 319118158, 539699648, 741404271, 284768313, 962286071, 397831237, 255920105, 358109470, 68462110, 455756252, 599125728, 663361351, 786874944, 914310244, 624632940, 736089770, 519347130, 422062656, 962630738, 45278960, 730269648, 304709137, 949222274, 495990611, 694935668, 805494522, 248277700, 583018900, 589993850, 809453427, 189726488, 115365663, 502333486, 428160813, 856636302, 642366547, 832809821, 166965199, 416276047, 351281668, 229334525, 984448737, 261114272, 832470195, 222440992, 975580893, 197731224, 525496851, 11973660, 97424231, 542265768, 378748, 81260717, 45365031, 400163442, 425898587, 457810060, 738070434, 172953377, 175394742, 217956821, 424845984, 858279883, 322893107, 737188697, 33721452, 834245934, 523417120, 415417848, 294563234, 124089831, 313252072, 249759110, 880574235, 883338215, 69564150, 32633264, 571574001, 61361309, 236854737, 406066818, 521483248, 90884298, 725328004, 676613012, 20852642, 794864527, 991887284, 295075666, 821460865, 153820328, 958812847, 622183559, 919980910, 565403051, 918502339, 655561356, 424307847, 547341498, 997989713, 868446011, 722020358, 839707685, 306057359, 100797330, 834256154, 150329749, 753700614, 472556265, 735371193, 561931422, 330441357, 834169449, 239422160, 288108717, 810424395, 117922562, 890767391, 780899846, 203185434, 335226293, 819138377, 67733660, 251289420, 80145469, 685949973, 418034037, 967557448, 331068486, 773177447, 623398926, 408163186, 154937038, 268295673, 637265378, 826675020, 163922997, 157912790, 610243216, 894722211, 438153565, 32898904, 350964570, 190198135, 232176202, 188115193, 433556232, 679464598, 809504333, 365456483, 723533035, 601632132, 555291207, 420826595, 470956342, 103104264, 561685986, 538542822, 123628577, 260595168, 558886142, 460583906, 189808564, 734423269, 35432871, 60566505, 296349064, 493256808, 623178004, 537621486, 487016412, 33125054, 232339091, 543273395, 494219647, 638515338, 86532073, 724987678, 441705218, 965110466, 919053760, 109854548, 318596682, 905125952, 144365648, 415835460, 858595415, 116905747, 799543905, 669662687, 898954889, 947209822, 366200462, 228600389, 588039094, 326739951, 352661576, 129659948, 46863340, 270035219, 372174906, 5452704, 12736580, 731297857, 194194875, 751285671, 91859556, 226326246, 930192089, 219969144, 521999841, 327350799, 235314076, 123542122, 592500421, 526535811, 158375718, 65984985, 514541061, 392960607, 715740004, 667054681, 238747967, 243525689, 839445525, 459215147, 415014429, 844466036, 526904520, 568548733, 804192999, 657925399, 829606209, 787916737, 822621136, 185673733, 822208089, 262663220, 71034334, 116411115, 882016508, 87376218, 758551232, 495994760, 4268784, 487171326, 194983098, 76399165, 248162968, 199433962, 942454653, 494058084, 455110436, 398455384, 969186863, 494775398, 847032666, 41092696, 594414036, 605834100, 65105685, 259571814, 7837306, 29510581, 337494734, 475145457, 866072379, 679423294, 907435404, 182900218, 701159018, 43326807, 42749038, 840018414, 825625882, 325942552, 881102092, 667576608, 968344486, 849414147, 892314933, 228339344, 60759007, 495441223, 847187330, 785311185, 100413061, 588227336, 442740780, 143556027, 393738076, 479221454, 953134130, 9128634, 423885440, 916137720, 401486140, 647059315, 822650753, 604166100, 499917808, 350554019, 252901855, 343183172, 602461645, 745472002, 79894204, 466011322, 472636019, 724104788, 125338164, 738982519, 337046933, 374447701, 978745003, 319772308, 114328451, 627706325, 903828160, 979672977, 740584680, 984139515, 14528332, 685619633, 21813106, 82166332, 501280473, 2066863, 664017758, 675880837, 564072170, 761700231, 229359302, 183236343, 74381204, 831818928, 712075940, 391843509, 22735833, 783807457, 177528599, 826812032, 656116300, 696011332, 236361332, 867508559, 139087423, 549853408, 521390893, 473594423, 847217425, 105283155, 775827284, 78178612, 469428912, 149632860, 964309229, 590142694, 961841611, 184875048, 499498626, 42679829, 48847749, 580734934, 302892814, 407032422, 321369203, 259584426, 296801710, 239032819, 218156691, 696892618, 300549573, 236365917, 736104391, 841819603, 71006641, 594939454, 966977471, 94131116, 43062605, 600048485, 129410331, 455556988, 546884644, 422956214, 233521577, 112015195, 435661239, 792132234, 593169042, 967021637, 687466932, 621189955, 835981281, 11673956, 421462349, 746278558, 73872419, 721809256, 337818697, 806708740, 543419331, 73887830, 722252119, 707621071, 758937666, 316766196, 790042960, 155753018, 980939641, 421899003, 896834177, 21204040, 574785768, 462864446, 697356264, 491499291, 217250816, 45999307, 888517458, 553355291, 948852981, 11489267, 755206684, 616606302, 416937591, 90379134, 362435323, 231986397, 297334146, 321337291, 175738618, 7386302, 228578259, 56193164, 79997359, 958385101, 434065962, 334228997, 809708390, 894040269, 479542418, 809981748, 656188179, 480539497, 116122194, 152369556, 421755143, 298959805, 974971812, 170297122, 984556870, 895971902, 41343408, 210032276, 438432463, 197236526, 727232687, 180848345, 178811187, 827822952, 178927266, 554382834, 744845165, 214600148, 501226311, 343735502, 502251291, 551513715, 792125177, 858256884, 354165019, 393233316, 109028455, 740932892, 404288658, 857506328, 315580429, 148003805, 259986286, 747500017, 264181605, 555687970, 161176818, 180664784, 505764338, 733327978, 13425365, 974177709, 223962290, 488048069, 916410026, 426160995, 562855365, 469672240, 691892817, 128444240, 143848242, 508018082, 293468627, 462131331, 699275889, 556702126, 95821293, 599818317, 307556688, 358468521, 552067126, 627830573, 258470828, 238215551, 477514982, 464248488, 819922973, 86229473, 858745871, 784077226, 838521694, 168114243, 603201001, 996479601, 860355089, 25919165, 424247629, 607501071, 887517950, 574907197, 742627550, 753207828, 922729421, 560084414, 612925008, 266826413, 879584022, 686952916, 30574104, 822798700, 39237947, 384875992, 893025996, 340703684, 635413721, 6781205, 227414472, 428810831, 844960729, 800060312, 566923869, 69107724, 381489672, 928652480, 255676119, 155071376, 217674966, 254391924, 440563555, 903303645, 829133480, 510167181, 277297974, 42856590, 87232516, 11186559, 338469900, 785865723, 375442524, 916131009, 162064902, 376790466, 658231252, 595044434, 927017623, 975269209, 392788667, 269265535, 46078614, 548795537, 578432983, 180263594, 973205666, 139582368, 576306219, 174441544, 993601439, 47661205, 970488898, 809046356, 9747740, 106547921, 652302122, 812229539, 38881388, 502670591, 418734509, 843074867, 727191058, 238798988, 548827181, 526204998, 33960916, 540196216, 869643858, 863650513, 706405983, 518228866, 889831054, 728018818, 487658768, 619378664, 533455588, 894012337, 567329163, 159212749, 252269878, 807924145, 63221340, 546022454, 536222553, 608110909, 933082598, 27137277, 601924518, 142626951, 190392569, 259543207, 550785847, 347544737, 322425113, 332176682, 308200048, 79905303, 214846786, 995332976, 117467357, 406362114, 328709788, 881305210, 554258835, 217893863, 191556055, 36356904, 54945232, 254635826, 480755647, 661167295, 813054114, 903960713, 547130793, 922806403, 119442141, 255106119, 913437526, 781933186, 915780658, 238025557, 529055211, 23187365, 468772418, 759012815, 366454769, 878064090, 468828684, 520748016, 132542237, 158918115, 828084397, 293352021, 840469763, 213536174, 37492532, 376832341, 824967181, 48283892, 675765937, 111688990, 524458914, 627170741, 527389772, 601248900, 646276818, 691387309, 268995937, 644993260, 535795251, 776193713, 57778523, 722837085, 675354533, 987771068, 56515861, 216472005, 872933099, 250568133, 872366158, 449854190, 61612337, 526126412, 173430835, 520155513, 562349257, 863418730, 156317789, 171486036, 350815927, 568753867, 314873388, 882453001, 217858842, 398319613, 650092353, 400947503, 738841685, 697633099, 986348675, 969875236, 682109, 574083720, 703103011, 704869076, 902333742, 784811902, 242863986, 388083745, 984551092, 416440156, 698456842, 345229439, 582521532, 543950202, 926809628, 876943502, 231943190, 72638326, 976973577, 925699210, 180291482, 394402627, 626188628, 256271506, 279005005, 546127708, 371119292, 73176035, 812444836, 288908539, 590437854, 210644619, 107592817, 975402247, 167970436, 495421276, 474031903, 700089959, 150681700, 577505682, 151867970, 25238164, 850844552, 923480511, 267812595, 24572804, 446573481, 148295725, 636480880, 402677286, 501949282, 476686648, 860999709, 336688888, 690712405, 405682447, 271095202, 461774335, 663697732, 872834597, 565870870, 37975870, 900242069, 329486856, 12881807, 691900662, 404084194, 951345418, 957644297, 519528271, 990914433, 793330899, 693003435, 644119125, 631152974, 496015723, 553675103, 391097033, 386380349, 477047143, 67627657, 373351045, 93679522, 364559134, 76206519, 53812329, 198247435, 289957530, 357844654, 868387359, 308857915, 166925916, 190797158, 607009289, 924408591, 457522639, 191251203, 680090151, 714776085, 459926219, 875756945, 505903824, 579318420, 116255044, 789556783, 781958442, 859600730, 377006137, 3167671, 231104879, 882731492, 319566506, 908910096, 821248729, 93604915, 520857595, 749289914, 246418124, 188429784, 309245299, 100006236, 565364117, 619390577, 108906909, 3408089, 471918267, 116241490, 580050902, 883613081, 584254725, 166436430, 962008914, 684393969, 60559868, 812312037, 115026006, 653961314, 777880569, 419998723, 308156738, 934818940, 119409264, 573105505, 42752453, 159815462, 978196931, 141191360, 355913466, 44267988, 458777554, 103494609, 984349880, 637267672, 175735939, 412644733, 237381192, 528600854, 959606498, 537667860, 914741235, 87171335, 706027889, 350211359, 175930292, 176546739, 383761061, 308362258, 802073480, 44457144, 747439494, 637230891, 237826145, 186725605, 274336141, 432348332, 90494435, 401004214, 947294115, 770490821, 31745205, 260502454, 724469216, 545794554, 838228219, 708159562, 503532429, 615687598, 677202532, 380928515, 754253863, 742158214, 243341883, 199043483, 433631120, 159049276, 538425623, 997420938, 628942339, 172538757, 45572807, 937773299, 285556546, 689646673, 533002617, 691167697, 369665874, 450657548, 306500332, 146806852, 255056867, 964390995, 301010509, 279542827, 941961120, 339454281, 249630831, 312689641, 90599883, 395224565, 494179398, 79547639, 51345622, 81986952, 350862277, 503473918, 644871822, 872166976, 19240343, 731876159, 158946547, 348406337, 856578256, 958062654, 874764260, 202648111, 930719895, 615852295, 679907603, 962007740, 789354899, 440371821, 331131732, 407655765, 719540160, 988788730, 573326006, 718791854, 971591616, 764461129, 99199988, 770326441, 556881782, 53837750, 399374764, 182997705, 455739376, 388120576, 40367843, 71191955, 177962399, 998747332, 921999965, 449487865, 484544734, 534221035, 855622604, 721585520, 925504353, 26960431, 596158016, 676073137, 777588559, 256254221, 479141207, 255324226, 176411563, 181343132, 671148014, 660966695, 986675942, 830927181, 819598582, 381094890, 381926555, 313110852, 553172325, 536982080, 719569578, 281541947, 46857034, 208659541, 130227267, 781423885, 942994981, 196949611, 294401224, 255763035, 306818691, 497873191, 362259769, 420287595, 750850702, 943925699, 961920873, 816364743, 696571696, 814812988, 96326171, 312288174, 222298436, 517722812, 4259197, 797292188, 199393138, 436127027, 589972941, 854615015, 645965313, 312933840, 946871837, 251525761, 16641590, 58768814, 796742523, 260166458, 165844015, 730017110, 221167089, 791798775, 823790405, 359441721, 824253210, 228248391, 786849451, 297332951, 549942297, 602812754, 796311247, 92861995, 997521857, 650582425, 286426939, 36833001, 7907466, 487850125, 698244792, 876393365, 916250365, 694171288, 635842805, 193946634, 152491570, 228391945, 951854756, 527457350, 687712757, 4883192, 870346566, 722923556, 724779929, 654632031, 351202252, 686574544, 44858861, 151019006, 435288948, 940622580, 441160245, 595100062, 671258950, 475826276, 84184953, 823577446, 416777212, 77106715, 793393472, 742340611, 19196839, 739133359, 314768074, 933487159, 112723733, 504275546, 421886693, 120559194, 571056588, 252022405, 438162884, 689002574, 801728183, 848445763, 798953458, 919945806, 522369504, 983944281, 868189194, 425901988, 380338679, 411963186, 491382652, 19109287, 205505712, 913691310, 391402565, 801158324, 157653169, 284035929, 68728551, 539251504, 971234550, 877309167, 368311145, 727541544, 17436720, 551265458, 292672919, 802039596, 929836531, 794296459, 110055512, 459964876, 148907159, 489858645, 243774301, 967918344, 862379811, 729792836, 917789455, 86684990, 829824866, 776692955, 373280313, 780721983, 669706528, 39724663, 311325724, 925450249, 677012656, 564606633, 733350645, 166044429, 404918230, 652432758, 782816683, 138859726, 139742268, 415449408, 620296579, 215865682, 435928394, 507069345, 687685674, 222324211, 836587187, 193448646, 711107245, 642254758, 366856891, 905019047, 393539664, 353641663, 588317606, 722874147, 709015958, 346565083, 85341476, 466714708, 634976055, 693647761, 215626595, 147450106, 690528195, 46560812, 474928090, 647449204, 598155532, 97580281, 281639791, 848069169, 864638981, 896184196, 434317442, 981290239, 329630134, 533942346, 693485490, 211443204, 221792029, 944086061, 578725513, 955361506, 335842587, 834512545, 15369189, 567478824, 979049572, 153765045, 914869663, 117166087, 117619777, 450862088, 626534219, 808066790, 11094863, 107185092, 334328310, 457662523, 335761831, 132620353, 416050820, 186927132, 36683379, 494735523, 270752985, 386636551, 176944457, 802416470, 228830899, 647250746, 327749325, 12000912, 925297786, 450625316, 878421528, 421040459, 945747491, 639759836, 196327849, 596871935, 649241435, 180533648, 195187405, 825705585, 336087076, 736764825, 384749495, 255588210, 791852105, 961696324, 15479612, 670401642, 901677490, 636352036, 480945762, 742411354, 443345037, 616424696, 64382718, 528406752, 138280599, 612525100, 16057590, 369715279, 362736057, 122614828, 245263089, 880739756, 598302919, 461535527, 402355335, 415628702, 291083641, 117530535, 26449651, 563376565, 727680968, 976369404, 265286819, 524553082, 23596058, 293094868, 947488582, 371364226, 122089837, 393597566, 258211248, 601603568, 770154151, 7211504, 328633170, 209816881, 620505250, 267971416, 886488448, 26221944, 403067685, 656989154, 367226556, 950547537, 226128327, 297153143, 579245242, 563579008, 183744141, 846953134, 939264451, 673881369, 855319691, 461226225, 612031695, 633005239, 52617295, 393994223, 852777121, 309761670, 20235930, 419204618, 192478775, 80794641, 333522630, 998262592, 117786944, 882487112, 432876522, 774845215, 932436763, 874666664, 712373875, 385725643, 87891179, 239513910, 255245836, 658818684, 158751784, 43627255, 576445612, 475342976, 585257601, 32485899, 20995826, 222347725, 783618441, 507823733, 470549125, 419351540, 363254069, 722758705, 584091924, 854619865, 578979093, 251730676, 277004315, 332482812, 530820413, 749269325, 610676721, 499786797, 518963849, 290320060, 647334387, 209345816, 41517870, 490123081, 935088872, 568938951, 427849518, 822897816, 667665869, 724474930, 863608063, 214036123, 349245832, 528868982, 800644811, 630677802, 26816835, 831164853, 96461178, 141250593, 279991926, 364411437, 328411337, 604214163, 187192269, 364090186, 723048027, 38805161, 432714159, 826168897, 877045510, 327198372, 690055639, 688048761, 106373680, 303413984, 351195518, 371614519, 391682636, 308205200, 573531111, 253267562, 870293437, 469538749, 8249721, 977600205, 297537469, 919263645, 480900559, 745455376, 127440222, 416263796, 741040646, 721705959, 217576466, 16061816, 36350538, 409188186, 796990532, 734374228, 307819385, 87697710, 394143420, 985154966, 274023661, 490964143, 918437100, 47008744, 111192289, 931287764, 916680165, 238924575, 913321633, 472466418, 617736571, 195315606, 733577183, 33028100, 926034834, 397937084, 940622244, 501345099, 291007864, 161195931, 576359387, 477095807, 143747093, 549868145, 695547438, 743168375, 705319519, 201938203, 168929347, 75553381, 89293400, 87943605, 305165300, 333934997, 362287737, 583081436, 103717724, 418252718, 816359297, 352645640, 255364298, 724555644, 507098714, 283732462, 474310610, 408257047, 80604439, 209096284, 172144464, 363121232, 903352916, 515651291, 967068942, 778200906, 508779848, 711674080, 506661204, 329012537, 884842676, 71994136, 731823978, 962258686, 674903558, 721993390, 167998434, 286731984, 39539821, 573196333, 36040098, 370710543, 8698122, 721120067, 677733200, 436672399, 804262416, 698121483, 362571638, 430291321, 752901677, 552441912, 315159227, 578062104, 590107054, 120452182, 857216798, 21819135, 391903653, 456159317, 459053744, 824692714, 244761830, 414032453, 735250559, 769866783, 350403225, 81719812, 245375662, 537259990, 489669089, 887221183, 721387137, 387780475, 692239609, 189721787, 12855866, 674942673, 371016781, 118680802, 414839213, 584044484, 400821146, 169890028, 243498674, 683783938, 215294705, 270848743, 839353197, 142139224, 181262790, 358096682, 825881087, 85291493, 600459302, 523174283, 29315230, 423381123, 583184119, 637173385, 67197789, 868227495, 349924287, 426806336, 899639082, 927611470, 227276915, 915426961, 661761756, 697519975, 515365108, 406511293, 880010274, 8260912, 989852079, 508930342, 160001582, 266172591, 621421652, 600665114, 337345610, 356481198, 983580551, 417574883, 894299591, 598489304, 850872655, 332547112, 828701444, 664902778, 635017716, 67794829, 744255308, 656241565, 655560048, 901370950, 917033932, 246232378, 43504387, 707115485, 982069991, 477785188, 301752670, 792548856, 662335529, 873328784, 812844831, 579730061, 562886784, 305026456, 333883205, 281802924, 728472865, 695560647, 667023588, 115466742, 377908798, 445024761, 230034989, 389173737, 866708997, 242989663, 375477961, 624421493, 785955355, 444082877, 970506160, 969601683, 206955075, 194647951, 569022462, 171219007, 890140609, 213010365, 139366137, 240707737, 644593295, 920911688, 611553872, 426382416, 822362116, 120765654, 1520342, 483287895, 465853135, 711469273, 112896307, 456502672, 587164374, 167481301, 344942128, 454259259, 779221491, 894392732, 900399059, 602176123, 22185078, 619646697, 12990503, 456809557, 208016426, 270195813, 976991034, 723221650, 544409728, 18851391, 476701828, 573542137, 648615732, 144735751, 779541686, 972324510, 568812912, 212977558, 568966977, 181496872, 797331132, 951397782, 753426613, 982903579, 624792921, 545164334, 370221192, 52390852, 712130509, 146462672, 254796266, 940966664, 507834883, 326580228, 720102983, 438997633, 641351016, 196392823, 505716329, 576695809, 966214422, 710753025, 668265523, 497366630, 493298944, 937398664, 257956775, 434278095, 716848983, 486486458, 361732417, 395605038, 173251163, 878083435, 890187270, 856848167, 806553687, 734673679, 597814982, 662534078, 63910768, 36050051, 912699701, 413416939, 944500860, 596643194, 934552308, 211237362, 985834463, 936381382, 500139855, 871540885, 957065657, 108109991, 669493245, 965246409, 734520383, 335267387, 842055009, 383894352, 299261785, 139114278, 56404030, 629645475, 213843793, 510088561, 571293602, 927591379, 464613447, 713728766, 13710572, 360459373, 246165197, 817926394, 231028356, 930477637, 350201455, 739869709, 394121474, 413989346, 682973227, 254122473, 42027504, 343622748, 256030625, 717772386, 86446022, 792933137, 73167735, 172279208, 856508931, 24772830, 559984014, 10398255, 915707661, 477199736, 492139453, 90117527, 944918147, 657904053, 378266226, 770350623, 672284297, 538636598, 288576795, 905175003, 709277644, 245108367, 908812479, 310925539, 581926367, 425079022, 986190636, 629387238, 216704307, 320265069, 979568042, 71841229, 556119398, 718296769, 840465920, 728234264, 39920266, 892964551, 795736800, 573902680, 119182670, 558465492, 877171244, 846091646, 959078313, 127632616, 758147411, 844602729, 914503900, 797632120, 844790203, 168819153, 829602666, 569797336, 475789918, 364001408, 75142536, 357455985, 638479617, 419087947, 377930827, 263908236, 635459228, 32022638, 287299224, 871547992, 443979356, 500016237, 972924175, 154383439, 448690820, 715196585, 453191213, 800872636, 872325376, 436903253, 311045028, 233621965, 3996962, 846371570, 201428977, 314152948, 696894008, 583988870, 331809013, 842999065, 471791273, 204099844, 589332670, 592914002, 583649951, 933527137, 103536464, 778092079, 439026121, 9840492, 686677851, 119517817, 297757556, 908317170, 654916341, 305185537, 650111410, 798949681, 275904921, 910538172, 431229237, 555179074, 481624921, 863417898, 334000807, 475775095, 213769896, 987084407, 846919001, 474308669, 470976598, 169170088, 481741539, 557544624, 762125797, 210388766, 192297779, 956687566, 825555263, 378669152, 877141626, 232105382, 603038886, 398718705, 304596397, 145905591, 371679074, 852855769, 681704926, 843197432, 428848020, 668721648, 270693207, 233763087, 151298040, 628710931, 5783116, 586995319, 739133589, 597338437, 151867889, 251702836, 676487851, 407828501, 809893165, 312857470, 378806782, 234982892, 664594217, 2521151, 407420067, 10289094, 792113328, 761393218, 874744768, 3197609, 157355703, 903783830, 267773789, 793680700, 797347249, 137232722, 442841116, 228254441, 223505826, 878279398, 138697523, 808588768, 768357654, 408968014, 433522353, 348966174, 961731295, 79043908, 88684258, 43696953, 844000102, 386514865, 4719126, 869515767, 490774970, 761092077, 526622429, 79515692, 508353966, 78896059, 377930146, 464813495, 416066502, 784966801, 577356218, 697661381, 561725274, 610850762, 748860445, 53762715, 353955051, 122550175, 451309510, 498046403, 517328939, 131863239, 888067484, 267912423, 943591891, 678525556, 615881977, 143776212, 647710845, 428143653, 786021282, 396421793, 923613511, 776474743, 177438234, 478381450, 157581273, 647531415, 42225835, 247093639, 784245916, 1860601, 39346198, 51464002, 639855661, 258892243, 749400920, 816266620, 3814127, 454934718, 597461093, 247925918, 745932418, 900286370, 271502559, 786956037, 229416307, 433760599, 99879478, 409318541, 313612968, 741509667, 134268881, 129375863, 555306800, 611277704, 131455500, 29859488, 85284161, 528118786, 779165941, 835362396, 933810452, 300454654, 767418450, 828045706, 970314007, 917851892, 332178495, 506698915, 118791120, 977922493, 793389282, 562925268, 799347944, 27125545, 646169927, 389311161, 167747901, 865752181, 347961150, 285839209, 918427791, 421041217, 897688481, 130441564, 379655274, 737933284, 394140915, 753463528, 42346004, 958107526, 740383007, 911666065, 388771612, 179990359, 387226753, 977749741, 313770056, 251103948, 70039827, 650567745, 311824492, 421697268, 968095748, 797312726, 796873710, 629718853, 813341598, 232181856, 420364164, 8158169, 459692009, 949782585, 29533759, 745821823, 801315336, 221412276, 379867799, 456733963, 76781689, 405004400, 39955427, 570347258, 75777432, 253032509, 453959305, 844904510, 280448333, 995337330, 436277478, 738601644, 576699386, 277531677, 251735337, 659402639, 382414112, 359037035, 278679239, 434233853, 306303970, 188703145, 920134676, 947403402, 108063425, 251688462, 458153493, 314546418, 756150441, 191189599, 103156504, 922825765, 551967941, 596121952, 368084154, 839108971, 988835728, 439323370, 87895055, 934942309, 486543241, 776702642, 742163018, 726092458, 477676815, 964018581, 882523047, 431828288, 913257890, 921708712, 116769330, 858812157, 671056605, 771124880, 493793263, 841851954, 724521840, 958650193, 373649037, 421854548, 288952141, 827537699, 40950589, 408951466, 188590046, 580275460, 580398551, 306671039, 914795697, 196805954, 248912019, 218708654, 206282105, 840224709, 495138600, 24245102, 250969455, 260114776, 817788535, 722932247, 845127242, 183903474, 469457244, 859371247, 375490218, 575264399, 232140134, 467043044, 825515219, 882551823, 834430733, 397246608, 488378116, 598230501, 782055371, 769980911, 374087312, 636519546, 401467638, 358367051, 252001450, 554970759, 579861393, 694480200, 670545544, 843900521, 813632263, 649763481, 545580972, 574970842, 876967356, 346354838, 51032463, 630161223, 255056702, 592194207, 328443232, 211260628, 710757496, 420978357, 501271092, 856788789, 340083721, 552600537, 424293603, 620749271, 139610264, 286179243, 162778182, 744511618, 85596784, 47318766, 572985593, 236785712, 69790847, 659051442, 580968044, 112606405, 977710329, 422860079, 784656862, 463245422, 407562088, 422374421, 803926818, 153464081, 756349020, 721534700, 130788034, 339493985, 420008270, 296538797, 84960979, 141273213, 39353341, 362745879, 152361043, 969335119, 158175389, 333934701, 782875569, 646556162, 898111233, 497913850, 883557171, 939425938, 537401120, 733778457, 1120149, 469150206, 743988830, 178182356, 731494201, 431548258, 697471018, 934119408, 63614917, 473679163, 957870596, 383463480, 445426902, 215867226, 621943637, 948532252, 876899736, 61803313, 184331325, 507812251, 341117906, 111548820, 592683464, 368276721, 812303705, 311339016, 831417711, 666501537, 249857290, 374156173, 970621920, 975147827, 72675443, 412168384, 539500209, 512976749, 485652670, 281101664, 77451782, 764185800, 377218909, 182296666, 59204519, 758116685, 106162238, 654744270, 37033033, 743023673, 717338893, 51037616, 964927256, 851384023, 72386559, 770957279, 254427691, 80644216, 696534290, 552440710, 876406416, 795796950, 626121646, 876244592, 862652557, 165557415, 942429307, 833999263, 331682672, 390913955, 251726390, 184140901, 387990956, 899250397, 733039067, 329091084, 260899683, 855352911, 131606551, 833300533, 436503721, 229015135, 954921460, 8973230, 206496280, 852343997, 508851146, 836540542, 387062180, 6076542, 33058802, 185743623, 978547256, 742016936, 931714983, 788578203, 412797534, 979099332, 321920461, 42255252, 957579168, 466744387, 836381672, 47302508, 913721712, 306093649, 35210442, 770383994, 808044599, 533454944, 311130595, 868482134, 286061663, 739001905, 893112751, 46591349, 628079999, 901173156, 625278365, 393519455, 709447236, 443977041, 116927420, 42894320, 105395866, 752611725, 868985646, 326512437, 190974873, 701827241, 339247038, 867318368, 823713538, 380762233, 191419322, 943943578, 994484242, 17174518, 210615657, 75029391, 549160429, 70860146, 979379219, 203272188, 681802189, 454456064, 981636414, 892634166, 838925200, 814712317, 95079474, 447704073, 150457028, 636701275, 149821985, 249426938, 532697456, 256728703, 555768474, 809597950, 717523266, 772948425, 370683612, 613290452, 915585261, 353941331, 482948274, 454016576, 150267082, 18771541, 489221891, 627935874, 893065149, 993191392, 95491839, 960336676, 167642977, 828040712, 179761661, 377182232, 24348447, 652434734, 521649694, 343332570, 860640384, 810008066, 373859223, 463953873, 114950673, 481485428, 792776386, 703989341, 254548618, 859549038, 34300555, 389152366, 284455369, 375022, 166079358, 291066755, 879088206, 327796580, 244738188, 171701691, 406850132, 499131523, 166492060, 168286263, 483628245, 299191923, 424874808, 348365049, 983700844, 165334654, 99572598, 829357264, 932313384, 208274639, 462262995, 399109648, 449260888, 89230016, 865273031, 970253014, 906617852, 815370690, 997989466, 310619341, 529652067, 644952099, 955495247, 258369727, 420785475, 300698330, 313847853, 321720575, 883506052, 700670154, 347287313, 575554162, 372639878, 158352056, 563267181, 470408456, 701222531, 447968227, 174331961, 247528172, 957177449, 838086652, 18641406, 479289164, 514081261, 462437201, 702722815, 645411849, 651683044, 197160429, 374624599, 967036652, 319563517, 745563019, 54561467, 682025109, 570543084, 156099487, 11187454, 858282046, 973679902, 259566146, 892539837, 60704157, 228240498, 415046522, 725245119, 213182923, 129180991, 873527342, 513413206, 590175695, 253782766, 327763930, 353250636, 998172418, 409508954, 883041821, 744300367, 166431082, 688158653, 958298847, 214181094, 203334583, 566209948, 357419952, 198199953, 962394272, 132267570, 782348503, 852931320, 199529, 596121602, 52901039, 100008196, 727344675, 252760491, 230799838, 876007909, 533690941, 182565788, 41420096, 590156851, 492543418, 44159266, 489786694, 780470962, 305198254, 231101376, 533795176, 702970926, 257716401, 94018335, 487449941, 60100272, 417009021, 557688836, 237936927, 991468604, 498794539, 590785529, 554456908, 411398207, 120994417, 536343738, 208283283, 55712312, 12929310, 555273634, 123393164, 244174978, 806395856, 369992504, 156067778, 151226717, 942085832, 550836345, 967186712, 664875019, 881552976, 54604667, 695982643, 438424643, 619364241, 425725236, 865867960, 675503030, 555139212, 899068438, 449066383, 754635353, 952830442, 740307098, 147703794, 414693692, 276770473, 760643664, 61188648, 223890992, 961837146, 608608933, 789061015, 462238221, 249980785, 450583703, 465140646, 90635294, 980029277, 756640539, 249691769, 976825378, 282840979, 693751387, 774157254, 657792854, 169439525, 717341820, 407688288, 629635141, 229782348, 928138672, 238717665, 699866000, 769772401, 896454601, 319860520, 793275592, 733172225, 657657263, 714876497, 901342097, 211234194, 609154225, 76543203, 312947841, 105192085, 810468072, 933622704, 307797172, 130988640, 346082434, 498875621, 646670226, 394455198, 242369250, 401586547, 219999560, 953748144, 204546083, 434430636, 12419995, 844282436, 399180980, 511380807, 150145819, 790598800, 136778401, 718470269, 689714990, 443365985, 271734052, 955551157, 570263534, 173857232, 343307974, 650327208, 353976572, 845396793, 362590792, 437321564, 389977313, 131794008, 674449449, 768291566, 490767186, 649426980, 507879785, 475518285, 47933321, 339652233, 6397180, 175554886, 790116747, 438510471, 780554598, 582305124, 770432710, 294496495, 493168663, 5485880, 325980922, 723378238, 603237465, 723790820, 279848869, 58237647, 841613605, 662516137, 702155304, 349912060, 21266024, 461856205, 267769009, 645966852, 468410548, 306148903, 825203728, 182899057, 619815674, 327708301, 220168450, 510711770, 29908491, 751305003, 162134741, 684448648, 648646750, 560707497, 224946955, 127395490, 614271266, 283769960, 798853728, 529786777, 546469680, 287402505, 426216829, 694771845, 286163744, 421633130, 908056106, 912884928, 709366410, 213503147, 403473922, 6404107, 699498841, 71750368, 432499603, 834748399, 826011980, 388253149, 996981336, 875084686, 89206033, 816440384, 774372560, 122893428, 531521899, 937615659, 86664494, 733854636, 103594048, 490158399, 809426465, 709677916, 987013363, 18465258, 326273789, 670086280, 412821378, 856417292, 922230835, 484547066, 994638321, 57389182, 603638324, 61839672, 393133626, 663103311, 788054290, 280042284, 970885498, 427136991, 318107845, 4990492, 631764138, 550639892, 267397499, 654820406, 67738157, 233138638, 519365185, 110845684, 324701011, 192687671, 761316254, 726214708, 733718747, 337255301, 213203235, 529400202, 736353738, 344675324, 498567187, 770815741, 450006050, 320018771, 538808879, 269708685, 518626511, 446667357 ], 30976 ], "output": 11903895632265 }, { "input": [ [ 931457869, 528982343, 832811983, 219264374, 690235836, 763477395, 358566536, 946427686, 362529971, 81872163, 677866425, 136275099, 767144081, 978873749, 572081491, 939149948, 851809628, 218875647, 738071500, 119140532, 407942670, 929601131, 132055306, 513344845, 259815277, 972166427, 169916467, 656986862, 357517094, 345827795, 864399062, 294997391, 874438634, 120264223, 919940436, 43934781, 866577830, 22675686, 381939749, 308980696, 190991862, 658665743, 916083252, 843987301, 97720500, 999607957, 278238147, 952422390, 467045098, 845653106, 789614443, 235341122, 954149468, 9306793, 10452505, 468108938, 948524815, 997358381, 609934339, 681551005, 169727226, 879351432, 898833266, 984702055, 533905310, 444584927, 520666283, 152566832, 572863671, 952692904, 66957329, 717364755, 777800494, 771760545, 268879201, 971126705, 114685297, 958949441, 260096430, 264394448, 552003960, 615793940, 774925572, 804974392, 628600895, 662321433, 398438343, 20490843, 613816334, 495659629, 743427879, 649890211, 129351522, 662353848, 975532404, 707331954, 414811331, 794026317, 705876301, 300401114, 132390025, 261915946, 140554222, 316303762, 465494144, 998630634, 145885971, 800203585, 265699700, 803316295, 467159478, 609456387, 838777984, 884649113, 41118298, 73290920, 844926109, 869720945, 723944769, 481080712, 462181258, 906108987, 626563049, 339794855, 140838857, 374242072, 529354298, 18023409, 25014082, 261696193, 962145438, 951279170, 227186804, 840597299, 434463903, 548017435, 452319216, 590750317, 402990247, 698637414, 886198447, 296669807, 73888672, 917404362, 218038994, 338459843, 515435202, 246693880, 909848461, 975605306, 694852624, 816572690, 689529070, 755213979, 34668067, 975873413, 64121974, 166501700, 941596641, 699270385, 40033789, 696407197, 841822557, 784156783, 64089699, 575509875, 450735940, 534701247, 582399402, 252199490, 412843502, 639124339, 706242060, 117677544, 690617996, 571837042, 475706080, 314068006, 665492665, 239593144, 373386651, 124875898, 884192380, 828356050, 352944675, 362915875, 379456887, 53049838, 202431673, 655966705, 404037893, 727994413, 166961855, 737959464, 824703635, 301803127, 675129358, 70022019, 822752297, 441479916, 418242963, 47861527, 92302510, 822853310, 929328891, 959807978, 490248314, 236707257, 414127099, 21536018, 118076199, 820304680, 589586860, 367826850, 146904103, 48729311, 902402768, 293017295, 413973721, 333069228, 816547711, 423453005, 443577303, 521018691, 80266497, 186106230, 172754871, 43201811, 304656469, 808406285, 515397519, 657580374, 751713116, 735629263, 566908133, 175139874, 681745182, 809958277, 823337502, 408056419, 34508168, 43095892, 938450408, 181475948, 904504489, 38991885, 694982637, 773022636, 247634154, 683807462, 509924960, 658943415, 814948349, 887864212, 752769317, 891504123, 294411318, 596584410, 359059262, 127036498, 288854851, 750676396, 508170076, 852780707, 864917277, 951729340, 347193114, 214233694, 146334282, 100333652, 977295454, 403576591, 958431909, 85626949, 795240994, 146045495, 188423121, 410659808, 792203387, 370095648, 429893224, 212171997, 534926415, 663616359, 373011728, 788633891, 557932294, 964426273, 406179876, 307786781, 808470210, 836384437, 694942993, 759614115, 779093709, 997273350, 631574706, 222281974, 606114143, 297052090, 704041585, 590854745, 505363512, 404587869, 249926952, 983879293, 456375543, 274902080, 400878707, 273359685, 258885260, 916078636, 827768480, 519193058, 555422962, 568789286, 470891055, 838415416, 940536879, 567803138, 680036051, 876192041, 821509776, 125127676, 817506577, 872023831, 692411348, 426908902, 409346089, 955058558, 748549280, 487022918, 796293193, 605440363, 194954651, 259941817, 681648009, 863498809, 53797460, 209638604, 55513542, 596980498, 384726124, 494120075, 21919731, 995032385, 991203544, 307006773, 533643923, 653840992, 214571773, 336088595, 102254055, 75958648, 65989513, 336567970, 52971913, 207528648, 303549931, 733104361, 861471933, 399212298, 6804213, 818815046, 197456149, 865416748, 887393481, 382647466, 707071469, 615332870, 340359364, 777898291, 83278881, 275086997, 776992775, 504693950, 889323767, 561595414, 245781786, 944214968, 747190893, 968525408, 938965471, 777181042, 484027584, 796874941, 146275425, 232158196, 508272944, 463170259, 822471568, 972825143, 385055193, 746545594, 828905811, 413706916, 113685572, 83249757, 745059901, 949489534, 897286131, 828954537, 357648954, 389241551, 879557034, 79206423, 500436444, 350936380, 280384366, 898019759, 174635683, 891610193, 656628495, 131214325, 77772469, 113659065, 199202612, 781377498, 996195104, 226294542, 648184703, 312324101, 904906512, 390718409, 66147679, 507507434, 439983671, 633247632, 600043781, 757325844, 188233271, 569239527, 220554772, 569909133, 123414841, 99626172, 868137523, 521111691, 114945496, 961494897, 639137142, 372299273, 765353302, 513624008, 840461889, 914403470, 580460545, 108589979, 451497702, 231977439, 290566538, 759483159, 872481628, 993567032, 219974692, 424306225, 545247983, 410281507, 796157927, 853544719, 877171410, 17895708, 711556779, 645295114, 696980435, 877245254, 561370769, 951128297, 272162382, 932326370, 827374946, 168439447, 936407781, 703547364, 885737469, 262534022, 592076541, 703909339, 702051526, 353504619, 920685354, 604255625, 37861791, 225803045, 713687081, 821707839, 912777206, 342325665, 306794202, 488998858, 369283589, 269515719, 26007070, 670396422, 749601095, 70139086, 744906776, 518845636, 595860329, 274986073, 109633509, 584297159, 684157160, 868489476, 743837136, 505286986, 747690699, 502632152, 663832315, 936078475, 502076293, 316759171, 767748230, 592180629, 123007979, 27117857, 358456816, 6193271, 297825112, 496051575, 130551282, 644386657, 499035948, 651427247, 744629287, 644770019, 937372814, 2300654, 577530767, 860312217, 483327689, 69197731, 34127520, 462019896, 800839981, 44348505, 157621899, 618141291, 828547235, 176897259, 876245114, 604902324, 491646940, 1283506, 787931404, 136546834, 593409407, 387393751, 666053407, 643910914, 307032515, 115450640, 130614952, 25382006, 526045684, 927260205, 992371791, 380335449, 148846370, 270444648, 965748336, 856075995, 914194134, 46623088, 778008844, 840162392, 616174000, 67533885, 979154879, 581682640, 642539455, 612559599, 381481115, 180004487, 494330968, 322933761, 109440448, 503187109, 23578587, 183011649, 864428459, 630357258, 987853082, 995052224, 725838415, 734810840, 254484379, 529827755, 757589955, 518695413, 547410570, 867271782, 674506562, 184616, 8266459, 728100376, 563300265, 547210076, 248953545, 675657953, 508229841, 381408544, 713872158, 871329826, 732225050, 819609569, 519134282, 614085759, 782117411, 635865649, 906384716, 563169012, 50458633, 438703583, 627419343, 762181837, 682526186, 295336698, 309960867, 819738866, 944112518, 653676144, 377249905, 635287400, 292009829, 628975823, 49109627, 931932911, 125435921, 573930577, 140108008, 190054250, 454280537, 758740240, 939462136, 903026537, 44211776, 188190693, 935402531, 843121759, 698765108, 860852926, 926878460, 836453538, 127069855, 478264711, 369467740, 851779387, 893069054, 401801714, 635092202, 319256808, 432729663, 564542435, 798185314, 229517261, 400523483, 561522797, 379803567, 450775101, 908819325, 183650702, 452921845, 695194911, 970577965, 517074669, 110166009, 23693208, 553976789, 899011957, 521440674, 984348948, 815174605, 202967033, 590130232, 35886142, 802667407, 429064819, 748007983, 237254647, 529471153, 316975385, 142417534, 319996198, 593463641, 77503800, 571025181, 224920506, 501825737, 985086808, 455212316, 118769854, 519741568, 171105405, 426909920, 231551180, 83510933, 980019824, 753079792, 78278563, 98529200, 733991671, 886454893, 194852987, 237973807, 646246674, 92816934, 32258955, 15118767, 688135990, 879696664, 562746687, 431638492, 399171, 998593357, 61333919, 764928194, 72556409, 51312228, 954448058, 62952284, 525802420, 880530732, 783046402, 568713751, 114868441, 971491098, 828659021, 752867186, 337193955, 515875867, 924293488, 590387701, 29881966, 995384866, 292785669, 324417511, 63092186, 39525440, 294487901, 575399746, 773505302, 792799628, 539635995, 898306152, 383490660, 909586801, 907240976, 984750054, 687394672, 8965099, 828072258, 671834870, 83584031, 917466438, 678157758, 226067470, 99580693, 879089061, 851863156, 788059334, 418246617, 562046440, 126529608, 628354607, 1900840, 985834183, 242332397, 702236852, 597402203, 750914847, 62770363, 658619816, 504654508, 51204449, 348403863, 712076504, 629068559, 189216976, 710283800, 888659107, 736701106, 489406685, 610280709, 857848760, 828952347, 991215862, 768659759, 707437854, 601999703, 815862912, 210332221, 915888700, 643793576, 856007502, 529977709, 632855638, 161574738, 441554503, 38890648, 401472207, 93976220, 253929009, 893672489, 340916481, 231696836, 854869455, 111991813, 728829323, 452217637, 120698116, 804427706, 767522907, 376964894, 965289182, 439575172, 774046534, 194488499, 108602954, 130063517, 983491460, 529987711, 999305311, 641639123, 542284092, 272929583, 15057437, 458196065, 589758973, 472181099, 104127957, 957250796, 553698909, 655100192, 199264943, 921130739, 719302030, 511946333, 891368314, 647991914, 422664947, 67198540, 546604286, 501546450, 329063138, 326835342, 961051648, 721916811, 983432533, 944194543, 277179644, 510358771, 149155310, 986826883, 49183493, 895675384, 617204978, 162316306, 408269658, 718135068, 598081680, 775143995, 152160960, 230349162, 837046627, 125477512, 98496231, 338839964, 316440538, 642750567, 704267148, 841196920, 511735492, 420487833, 385045355, 266083591, 750096140, 50791663, 168710312, 238504193, 423307006, 758050736, 470531620, 594660854, 86032120, 13541695, 819083157, 707447455, 717714554, 791051797, 988633707, 729749797, 756348466, 700910341, 416395561, 856115522, 569033473, 267039966, 124063038, 474149822, 375290973, 545761910, 227184999, 87068257, 248459079, 623521825, 792691303, 189076249, 350659225, 811857235, 32863245, 448740741, 312171537, 796652030, 256168826, 121946083, 780336726, 483655245, 777926536, 820739688, 801658919, 54223417, 483574361, 696966164, 734218478, 419914188, 409710112, 389704436, 785667948, 331604391, 293848204, 388937418, 269460809, 38117720, 709690084, 365176941, 37465482, 454531871, 965284519, 700063724, 210395423, 756664095, 374524704, 166443541, 652228993, 544399590, 180604147, 528476244, 348492423, 586236033, 654678433, 763408541, 667081289, 942087046, 21807013, 17532087, 608331111, 917486083, 951889021, 696379848, 957560221, 8637184, 422992924, 823205762, 182217218, 646065271, 352040288, 204041954, 280451124, 211830189, 639101268, 939183772, 620059621, 569199884, 987303462, 30097459, 734053074, 393388335, 532439034, 281806912, 882618137, 948000686, 820773830, 365686777, 20731656, 758142549, 368528413, 229418868, 51414277, 690275274, 441160176, 553048116, 967414737, 553249709, 770935921, 72046419, 254679334, 472103351, 388266413, 176420465, 275650512, 576520625, 770802874, 463544298, 37270495, 670915119, 601038225, 224052092, 522270156, 702717371, 297218765, 422063832, 419804946, 465140843, 533725084, 227823948, 242019910, 661501696, 844727480, 150011253, 834352744, 588292608, 702137602, 546219000, 951348888, 418195917, 298748095, 267559961, 37154729, 523732808, 938901705, 318045767, 900988277, 766567104, 252028318, 218129755, 784389160, 406658270, 373422537, 439267434, 550257683, 984545093, 251104827, 426971561, 294978959, 580131748, 527325503, 549295617, 964321671, 249316479, 841891246, 58170137, 244505606, 18591260, 166031858, 237142101, 264622223, 848542897, 337167740, 448426535, 872332135, 257452318, 279393246, 861262323, 602853872, 229357803, 854867051, 33249359, 832924753, 641316168, 643451367, 423060160, 483345938, 572221190, 66269087, 225226003, 102853604, 978163697, 358995863, 477631714, 475693455, 758799954, 748178783, 646035504, 675096750, 814762419, 950822011, 811432932, 467213843, 278338839, 364214608, 687983996, 191107249, 470652656, 175926935, 68696055, 439816910, 730474024, 898099270, 558082662, 842076014, 745405602, 531201217, 832090687, 608410956, 531203550, 587763601, 863785554, 321102186, 886895267, 509891568, 32064524, 734895930, 718957427, 825314694, 291471988, 133538110, 117859676, 589997177, 973620982, 918651550, 607845728, 177935127, 455805882, 148325718, 482262785, 460864442, 660195050, 855285034, 52659772, 238749716, 120098206, 897907678, 587750187, 12605399, 542270615, 282730640, 572975091, 406976900, 913593619, 146743803, 580746040, 126587532, 163326862, 385327148, 970760642, 279878854, 347060613, 219579806, 823821338, 767438612, 361138934, 230200833, 339796783, 452811723, 590736141, 199046848, 20883725, 728260806, 425496528, 372761434, 788134107, 453846738, 831851684, 829849167, 217155570, 605934827, 609191364, 870279157, 37336700, 903932891, 866441708, 881300644, 267277137, 51200249, 58356381, 819159823, 310589786, 88517587, 524507220, 376348945, 905062100, 537433389, 135059610, 483316719, 841578509, 198378188, 712613525, 10278121, 990168801, 804209126, 961834670, 201597475, 324036886, 744706346, 162923490, 317657094, 80701568, 475452626, 901785348, 229864492, 285222183, 199025794, 307613468, 457839768, 354160368, 470685406, 712614434, 134272959, 878628037, 600533697, 428159265, 931794599, 756285519, 389618175, 986442710, 582972546, 612693297, 653113881, 48216347, 122124953, 559562401, 297011793, 597079106, 584939716, 666944771, 853426939, 591674743, 746138003, 73543435, 298645328, 348676254, 412176393, 150398061, 206084867, 823408590, 345730203, 52474219, 112562106, 380640806, 802659545, 204883142, 226743897, 728396999, 165293714, 869274697, 77184424, 774681882, 926811702, 210658991, 360157796, 508778974, 295467786, 30307743, 853341567, 779843304, 388415353, 790578263, 220167456, 449672306, 915566915, 440201723, 6905630, 885253364, 545536918, 332186277, 572239664, 363216983, 554245663, 390294435, 219139747, 631542213, 48128229, 496631615, 671355902, 770706182, 730461631, 688047882, 184302461, 479968678, 814852431, 198401630, 841449923, 511938138, 11709347, 471677335, 438484755, 720601916, 518606687, 742080633, 100732601, 514831345, 852378874, 517514538, 963096399, 817028746, 156972064, 737455151, 201181455, 86482608, 152008580, 891593625, 671683099, 581001829, 682856398, 975960080, 218452382, 933682616, 454843152, 779908164, 214426999, 215286158, 132989832, 277891554, 582568495, 849728214, 526700535, 148846407, 835543134, 130023785, 410941657, 919114059, 396193262, 857326161, 842478322, 634953256, 269980673, 407593328, 154641072, 808521612, 584601280, 902122313, 210620482, 678866560, 710693909, 785924715, 177463622, 774235142, 144189124, 287527325, 755625768, 701511732, 560400751, 636136841, 291954599, 125050743, 313843906, 471727520, 543467530, 547867778, 333749829, 854945075, 55557465, 569694349, 563017513, 267665109, 169688713, 141379370, 863342296, 225994762, 474162468, 260959119, 131238464, 855711577, 725337537, 407401459, 403388794, 773000132, 200841262, 15179963, 237037168, 779871253, 324916734, 962017419, 577638361, 552459183, 103724036, 558829281, 593907294, 376527009, 227315070, 285729175, 202881439, 225755887, 66539229, 692076374, 998623856, 680949633, 406889659, 632821261, 212825347, 559093643, 124478158, 195146299, 578683830, 893210969, 559582391, 806702400, 879110574, 23983315, 33036372, 215854802, 30642724, 227965945, 904282151, 78991787, 652110589, 485738144, 803609588, 532840188, 605626535, 419530330, 497733476, 128106435, 507984716, 380022554, 96747056, 155152482, 132559668, 522468287, 350265675, 684359138, 27702660, 673687042, 882160321, 673100117, 936424543, 419322085, 317380893, 812842206, 517285940, 169798582, 550064747, 536413295, 220080400, 845000655, 779756212, 679496440, 893434162, 41944569, 918509317, 168042250, 884824129, 835887562, 650678896, 895768254, 60919245, 540203053, 701518596, 877303465, 195227665, 59412540, 53612761, 99777400, 564185812, 10758717, 602682184, 444147081, 683951733, 351565996, 794989070, 151202847, 630127794, 685690198, 249362228, 458780728, 793454611, 958388555, 66365157, 738291847, 785505941, 871683119, 366562963, 938809263, 804474354, 64987075, 631251982, 76614873, 706724470, 676978250, 593717762, 909554913, 185737601, 86868733, 953627012, 836588917, 945629867, 895326761, 372937962, 458692949, 373695373, 890067131, 661506768, 317123787, 703308667, 392431829, 280815004, 903389436, 416054079, 438232865, 354794820, 310541962, 877389186, 702953113, 697568617, 284522260, 155853217, 942349677, 385268064, 864696890, 545559103, 488962591, 741666385, 112537663, 855026294, 52293206, 677181424, 424563186, 883929176, 362712415, 989684019, 825856253, 366528782, 762416024, 242955557, 411782493, 329051482, 693849195, 549913313, 675731613, 908596481, 793086451, 906142734, 690533786, 209222305, 275599333, 840043116, 291346667, 698458227, 824196036, 839575818, 751473255, 708431121, 98811385, 771436662, 94058146, 712471236, 259067341, 685458573, 67044516, 58563635, 531276717, 759373519, 688320438, 544224604, 232748437, 114103024, 444727954, 364956748, 119638250, 810324112, 711743316, 982897794, 289626257, 619307141, 102420280, 293257828, 6383524, 150293359, 958470336, 258760166, 653655392, 464652200, 67434968, 65227937, 573799137, 27884040, 503145181, 921806388, 236134574, 205596671, 601797080, 132742166, 484241530, 486061756, 361499092, 177228299, 337241854, 486887050, 984347902, 205469711, 182436453, 442033276, 288464467, 475064897, 864035055, 205102583, 660374018, 812380945, 8423537, 894174267, 331909581, 650152813, 921837943, 109887205, 68806701, 435342392, 431048531, 706158242, 219428414, 839318156, 986575750, 3836355, 583286030, 171443180, 234449174, 765435928, 990114503, 354598369, 904289376, 617343630, 685516972, 204295484, 230821297, 617916439, 48139231, 990497453, 409396414, 611959873, 22498853, 576226847, 486708367, 694217297, 757320212, 992568335, 893166691, 518050593, 176579154, 129331194, 652376908, 1811686, 309517785, 834043884, 360563391, 201525370, 826573861, 292387234, 475677086, 960070719, 744316451, 145707633, 261259882, 853350064, 668881229, 568862065, 815425673, 28684226, 586294205, 599209800, 378101807, 467959505, 98415742, 442453515, 96922891, 227999291, 811406061, 590629550, 121305219, 494579454, 42424169, 761782678, 805665999, 948371659, 78552635, 329228952, 474014386, 365667397, 241604890, 647137765, 552472350, 338137337, 377407336, 957188335, 956506311, 532068029, 30466363, 711572006, 558391662, 885348335, 903538461, 824767704, 670059356, 261272723, 13699728, 929509359, 620908095, 372219620, 58645051, 309464619, 275873056, 281115045, 956571282, 296272221, 937815510, 960225372, 241370078, 932895976, 920788070, 539373209, 725269875, 474495756, 292901162, 119628765, 908284900, 517123286, 195136672, 219502595, 564102742, 289456239, 437135762, 620593969, 930054857, 852798275, 964304288, 470750190, 996401297, 302210318, 557288100, 259414205, 401964441, 31171874, 616511817, 134008026, 206860293, 476638531, 606978626, 657652822, 120212232, 406613886, 486354926, 184018677, 484034074, 648422004, 673704677, 368791179, 428841403, 302764268, 318143728, 621740047, 596403692, 586260419, 467453787, 392441531, 286192554, 36855151, 476682538, 374383238, 812806956, 232469189, 106545762, 664538237, 8139629, 472550057, 46688367, 663693202, 673859611, 945869031, 330564266, 574570940, 418491320, 242583416, 230159223, 393181032, 666480818, 3055659, 667004566, 205273714, 546158963, 646140479, 553727484, 884237990, 542503233, 458157509, 555413040, 761798610, 152757811, 62408830, 514272195, 135268649, 141876545, 76979770, 496089937, 721404137, 320015348, 193515615, 420533849, 68363579, 546703386, 366780834, 348157541, 59901758, 670894050, 113183784, 33262303, 302603174, 948735017, 285127366, 655598013, 278844464, 978744758, 727158512, 411443773, 885339070, 721605629, 798889044, 61102114, 923155801, 761383449, 638950326, 799361194, 775459871, 604096113, 589325718, 870494934, 880126163, 794404961, 13127153, 532590250, 464198321, 987865653, 730781252, 849601945, 135439595, 71271212, 501290284, 784870040, 92743312, 742939545, 890450999, 188013957, 551019830, 50444835, 140428111, 923276969, 669200565, 861651721, 545817946, 934544550, 197603325, 106914497, 476432964, 150120386, 764443174, 770576165, 804646866, 686319807, 302706055, 271326461, 787946546, 647568717, 210789099, 905818577, 38517086, 486542369, 150242869, 208827157, 342465856, 59542125, 925293832, 185710341, 476202733, 984926846, 156247401, 191927503, 561413648, 565387117, 991543023, 925508417, 820156220, 874361145, 148822073, 989563758, 107050205, 852779732, 961961930, 343408497, 459899826, 867806668, 680484918, 127118619, 591453273, 593332121, 153903574, 457007890, 714132006, 389199607, 559638804, 874295081, 5963496, 786520703, 846798535, 607892497, 531477978, 814020068, 184834391, 318589104, 563972137, 596695317, 871848438, 912941382, 142691079, 590234272, 271727117, 36362220, 351979424, 415369181, 363691003, 874579581, 209351544, 82143860, 142109845, 697777978, 180977103, 636747847, 608350807, 441448433, 206080648, 92784563, 542636123, 806399239, 834698839, 584919138, 465547313, 854262212, 650651583, 362509201, 595775159, 209699541, 89242367, 295951415, 946605067, 113728274, 569545828, 501583575, 808812433, 854964442, 304655880, 244731709, 559429444, 238500102, 147858525, 146973006, 606145393, 589238045, 296632420, 365884833, 341648802, 66340490, 854248385, 597934923, 572456056, 564473858, 589584521, 72697851, 952089734, 704657300, 550448359, 235505807, 786371350, 111756174, 886478937, 47194094, 901658041, 708269754, 638063434, 356630418, 196034054, 457355678, 976532451, 489005662, 954146923, 91477975, 742751022, 593089102, 355882199, 655210496, 99415556, 790983921, 665568410, 830029571, 112147592, 845298135, 536678804, 695877478, 904364146, 501653006, 4752854, 504266760, 763065487, 189473956, 806661498, 184723032, 957054090, 363010768, 453798205, 989624124, 501310192, 702187637, 615041387, 508628981, 137236400, 882857421, 43327547, 528335887, 622308190, 628043934, 434564895, 937457765, 77855151, 600754258, 237532131, 173777969, 376275409, 198706229, 45413038, 110375743, 623334693, 576751276, 561558378, 455188737, 137694855, 274043278, 816499441, 535818825, 897767055, 252449243, 914620506, 349088707, 131697970, 889688323, 536952648, 337499772, 757226037, 508370659, 370656543, 290445675, 574746324, 647627104, 453360033, 464036483, 145242717, 586694502, 43019601, 661970058, 416337949, 680352082, 214733728, 720569886, 926349388, 150471068, 38849005, 896469316, 160629820, 214117698, 536203082, 492476981, 739330130, 7118046, 451384981, 998423845, 856552721, 287402487, 803518694, 454559758, 962331337, 199259467, 402267975, 703486893, 888540117, 995947527, 295767924, 560456687, 92477501, 384864841, 543948780, 604546315, 931829037, 179368887, 709363134, 643119735, 254374336, 939468095, 347712866, 447901550, 694043883, 219638822, 637906403, 204857423, 757395431, 829692702, 254295548, 953066074, 60094278, 105596883, 635856347, 268338351, 534854940, 17735445, 325222727, 832303535, 215659724, 973107766, 467656467, 533614479, 968303034, 105122653, 853137321, 354676594, 262518744, 882315881, 304329654, 579377798, 315917592, 382170321, 513613565, 15839738, 130226841, 159416213, 320941099, 317940365, 571851665, 791933041, 936685763, 566457009, 12098928, 890161141, 584072617, 573725644, 735317914, 420869309, 604122222, 315037976, 902078520, 129052884, 448255949, 225422439, 626948241, 640295458, 221245716, 471506468, 118250641, 754155909, 877472315, 354880210, 426987013, 165445004, 88571753, 458799519, 289495388, 235290365, 377744670, 960237451, 775930310, 52635497, 730656330, 799110171, 96137336, 257708662, 639183426, 405711768, 286855592, 55236709, 847570693, 764669739, 386759008, 392888884, 448669518, 769129449, 12852069, 135606107, 668932366, 448130449, 643577738, 206922087, 376682789, 998854140, 409983904, 191988473, 516928192, 958955456, 658917686, 1858649, 474718723, 751843789, 680772816, 243034957, 384887350, 606265814, 126238134, 406703394, 558656811, 982451180, 594293027, 600027790, 938986331, 201308154, 971084874, 391704095, 688499865, 36301204, 106215603, 321596013, 95484760, 584340116, 956977726, 507697291, 150632164, 650763808, 56206276, 442307249, 747132815, 458835110, 433510568, 598883818, 593255554, 226076136, 887819707, 267013938, 847999181, 442640030, 131788516, 795337180, 918162148, 958191633, 100525348, 965024952, 69501402, 265319126, 117383261, 930789000, 172327629, 721869439, 492875743, 581259456, 844145864, 598067924, 689467677, 477334555, 646389813, 240969734, 183098345, 165376525, 483243359, 614459885, 355554083, 485261166, 626159641, 501121284, 847723710, 617920283, 335611481, 563732383, 157772131, 446132661, 233030721, 864686828, 851673179, 739641971, 997608433, 931927904, 13030658, 198336872, 385937562, 351607047, 815076820, 966151830, 150281959, 479246777, 845117553, 131699647, 154510323, 410198363, 797954619, 814626601, 824343042, 950884037, 620853533, 189085291, 699495900, 368430868, 777713243, 989012130, 131805800, 463791784, 946564272, 59461303, 432182693, 522796054, 345550327, 534667445, 180711640, 790676940, 900818730, 699379058, 199584710, 706809051, 757643296, 718114544, 804638764, 739564795, 91626437, 714983485, 66800629, 377479309, 77767615, 420146134, 270147099, 387850641, 581369795, 802846848, 328939837, 287889852, 977245143, 393064617, 200899287, 749507971, 755100006, 700455947, 478735054, 452980704, 846540620, 959179725, 770692574, 133210087, 991017934, 576533836, 27645148, 925829006, 18859300, 162564548, 350388451, 432762240, 379346097, 566404885, 53730317, 829838251, 452645057, 43581710, 127289957, 137804905, 464581681, 756354874, 509419846, 575562912, 861307757, 696655538, 679907783, 632162221, 912603624, 16152465, 785363407, 495127582, 741720838, 35430665, 48080798, 615446942, 737328527, 542988375, 234189117, 934473551, 924461960, 943227278, 125919321, 131790538, 501858831, 397438232, 295090456, 270310754, 161250715, 2194886, 581624075, 742673958, 886975455, 113432893, 118943278, 737903472, 685616828, 515590734, 932225570, 660028514, 373842916, 316052747, 910237356, 172117063, 717679727, 556771483, 521022846, 547683840, 48961874, 566831207, 22784296, 547299723, 90931896, 858890837, 141159395, 852936978, 253677570, 543255920, 993527225, 448104549, 534657662, 196493797, 91494253, 962559440, 14873529, 496563359, 144604816, 661221402, 385569965, 695389599, 327947136, 174520733, 48514486, 170050326, 439409473, 949406518, 113786174, 66357897, 266833459, 309357412, 409456815, 982795146, 736386740, 446970786, 646989572, 950472956, 667980054, 260427022, 191073792, 791992983, 761692674, 982691029, 330017166, 892038249, 134452038, 136765877, 118594497, 536773000, 227258842, 735324576, 350145735, 13687643, 993523204, 206017763, 231505292, 545964928, 962330717, 597620341, 617752848, 844865615, 213580192, 801271944, 407189037, 272767004, 53852617, 384443090, 611385459, 488313494, 290335897, 356275220, 24336774, 13903034, 787032051, 408596039, 728655041, 960803363, 60668588, 145990787, 146258170, 359420865, 472384731, 828914248, 12364641, 675162392, 427714620, 419344070, 318490522, 897489194, 697257658, 945270778, 869389093, 255545736, 466485958, 661332352, 679638765, 702162356, 291358410, 77773478, 127002649, 481769828, 411969073, 669160281, 671343432, 876004614, 166661255, 896181526, 601217569, 448578026, 989393114, 428926378, 169226997, 338105177, 622935471, 735462366, 279152758, 377626400, 98528724, 242511766, 964598112, 706496204, 621343534, 457232225, 836433573, 348929988, 397208677, 416928321, 257401403, 959302897, 279427548, 606234044, 194942470, 892586822, 959225989, 932191256, 142688907, 565461156, 58189895, 327416882, 118975941, 165176029, 762790939, 488145692, 865414762, 474150784, 745678547, 894812496, 948916129, 265086210, 773430867, 562977281, 684012467, 513496505, 123534331, 205945665, 688533201, 515167518, 362000047, 811599941, 617375867, 424867936, 106850157, 113330081, 520423999, 108230977, 983426980, 620802253, 269646432, 590247921, 949520562, 485917533, 722954220, 495161788, 139051966, 525553968, 785384325, 751918955, 61318169, 801083773, 217556983, 597842001, 194287193, 32728503, 419428817, 802208377, 217722582, 424106873, 763314567, 787656346, 65539880, 357033133, 272034416, 396512172, 221775867, 166662718, 202786468, 972093293, 727681945, 605445670, 589938750, 753332300, 474397835, 60637632, 669329961, 755598271, 263759742, 543752428, 410652335, 118291037, 893756989, 463713327, 100131289, 60024189, 814921336, 835870642, 722051282, 314456061, 300674435, 737654503, 107016152, 853426329, 147844780, 443131218, 384631906, 287729552, 903227266, 322597080, 484268683, 617697793, 803316036, 42720800, 550067953, 679775688, 772609301, 538328750, 605723283, 739786852, 932904272, 994619969, 489699044, 33551073, 412549028, 709904350, 131720113, 283224116, 490746675, 516946645, 29455873, 966109625, 130135250, 33165624, 241528693, 140311349, 557704357, 148775911, 690152630, 25792421, 95467217, 494897194, 811443862, 291711366, 535754638, 908837563, 114560666, 394640844, 621210293, 874606153, 401715624, 650858707, 159622085, 934063168, 444455444, 849041539, 525441690, 316061606, 315038621, 493157237, 177237147, 837868010, 857656195, 150482161, 44668729, 76412268, 703502179, 806342267, 645987957, 519876599, 754434384, 632543659, 486663392, 169924550, 514725088, 130106882, 35270018, 985176069, 453123051, 162310268, 476576193, 143360199, 741373904, 59737078, 448445788, 75528200, 567055686, 188061378, 520551130, 930067382, 854220226, 905261610, 630607401, 853875587, 771378295, 976067875, 932456009, 748622354, 613109659, 947400109, 701946687, 378578832, 33210317, 169717272, 300476260, 366215632, 479358694, 601198236, 779961805, 427356169, 787047435, 895237107, 576434614, 717318039, 896402200, 338789825, 261571237, 411527755, 539179706, 412643346, 11989940, 623590508, 853267673, 492746332, 158120814, 949538957, 646882310, 126050964, 7937458, 38955148, 587423131, 264088305, 171833501, 393206212, 422731135, 770886446, 186614942, 913836099, 935553603, 435427998, 906179215, 75028161, 873060060, 366303644, 474139910, 104257183, 498593155, 494481741, 72411093, 3706625, 364829784, 853344341, 567253868, 927442731, 323542950, 292294282, 355391819, 819142852, 850606610, 680810033, 964132515, 882967755, 138554106, 812622931, 108076524, 109185999, 13517247, 908490503, 282877149, 72909092, 571334934, 32275576, 554733248, 136650663, 691035849, 332707938, 587802406, 441376967, 315874169, 459159730, 267896246, 927338351, 387889938, 693798282, 762242888, 267585525, 703925561, 630198434, 31369800, 188746626, 919613918, 33157962, 67357398, 739819466, 752478943, 811094255, 904300087, 159412965, 250315952, 159880299, 863208297, 182463343, 136151952, 391314053, 165176653, 723260965, 365018577, 982779434, 718616456, 668903064, 222880671, 131426265, 545814922, 896498453, 786823071, 607752695, 124416966, 677411416, 675217403, 820263096, 474684596, 807989348, 535186590, 651760894, 331526803, 437639052, 37090423, 949343646, 349217098, 921053479, 318085608, 598526569, 8535178, 348137978, 530821606, 49662938, 815039837, 590558427, 281063572, 97930233, 297944957, 645077121, 187185057, 811947120, 455374489, 764415689, 157683404, 30570444, 648589470, 896768709, 652067907, 653585472, 521042548, 817032757, 16937796, 341543085, 228352068, 637474599, 835642848, 681063756, 506098622, 339036742, 133176734, 943163393, 352082382, 630204855, 885175246, 702418134, 302323355, 311144712, 436424886, 312599005, 513551029, 45707784, 580031335, 624773428, 351291223, 250187828, 523622978, 573497255, 856207149, 428091104, 463049861, 343182642, 846277249, 28414843, 465796825, 246510458, 263511660, 687687512, 205393614, 208792493, 494408720, 650095603, 69949058, 212158393, 733406256, 574528513, 952423809, 356079734, 804641597, 202452833, 840712607, 657786938, 13907374, 803194380, 880886134, 970282614, 314871334, 233689862, 707655675, 464295619, 365998759, 230815092, 457420806, 136121198, 856999146, 347135422, 805406708, 68418724, 626558879, 758489942, 124978392, 367606761, 364481556, 825986948, 638807334, 751914419, 885203802, 864054674, 264898214, 289108722, 263648197, 614929911, 764118257, 486567772, 395695123, 323361543, 107238714, 162758665, 637717027, 538965438, 766600233, 305368167, 108272355, 4752772, 165572563, 324567448, 30909127, 194881262, 89771826, 925571419, 890851168, 354693617, 874558403, 935867525, 25389211, 940476024, 94900776, 649726983, 956128264, 142065226, 853069161, 897161000, 658948309, 769930108, 36230644, 235262164, 866274846, 658241250, 185742539, 57287810, 615391529, 630919916, 136439613, 800948866, 830090538, 431214570, 223295010, 173881872, 374672496, 885921843, 25943929, 279100508, 36369516, 717563472, 33244799, 321232024, 93765932, 487912736, 491519060, 346677223, 638971162, 923770989, 92969646, 622041359, 866517782, 490391770, 662068245, 211427978, 112733278, 893760674, 514105859, 523884904, 139758109, 864291151, 970734228, 351227647, 389017700, 441667209, 265726060, 650141981, 737189726, 420136304, 917187967, 541307101, 483874825, 183346546, 367977351, 820261292, 409895458, 664648511, 574568238, 674373733, 65660068, 741296596, 946049259, 520467683, 629488988, 911128321, 550965085, 353577149, 811963325, 280735840, 735033579, 579674018, 145588728, 133752796, 851211900, 665009660, 416715349, 944372919, 889639578, 721568946, 707447985, 404124602, 926280934, 237339930, 821300862, 372835613, 212354137, 90001310, 135580984, 3906216, 358055322, 639468439, 260087869, 290492356, 346628403, 149771785, 39642207, 624925073, 572720182, 350427581, 674133703, 795797027, 860606867, 726259885, 413457432, 777895893, 368614132, 772468476, 519015117, 158030860, 956413018, 647259062, 772478535, 422615030, 318318570, 120460131, 557030160, 899117574, 922046930, 767387021, 935833531, 883165635, 870233240, 727719506, 747247888, 560679906, 769195022, 985312337, 366624549, 2426127, 228040701, 581988174, 437466771, 300782892, 868078432, 391715232, 929699182, 452617161, 499357826, 410054910, 486612990, 124826391, 252448114, 938832111, 995837525, 662292192, 538267592, 781598455, 942327971, 339067906, 157615917, 236758739, 484140071, 532909838, 683794308, 987009179, 74282455, 153365380, 642524288, 2318334, 993621931, 80168767, 918453640, 62345483, 798211866, 746990419, 900560478, 449695698, 393709079, 589303957, 122270761, 625671409, 453945299, 319124670, 429386746, 849297837, 661509394, 841196515, 778158478, 6818346, 406656083, 420747457, 129716878, 356888501, 127728154, 412311910, 282505604, 881998081, 983968434, 503898996, 127819699, 374887341, 831312397, 38900902, 316436760, 551669336, 825371762, 102017769, 256262714, 155224881, 910898928, 26650187, 791525959, 344748490, 940438714, 300794322, 247799649, 654541909, 804519051, 718815126, 600393061, 328717711, 368481719, 284692051, 852178428, 916308819, 269010590, 205293661, 212827294, 124664157, 397437668, 381171377, 82262667, 186919375, 114315818, 37708772, 853516597, 865339456, 110808541, 187770362, 970165000, 617226165, 261829707, 994355903, 180828262, 221444882, 191953576, 641245199, 786036323, 627501388, 178833544, 575897755, 33176436, 942772429, 496311829, 986544737, 275276037, 791614545, 426609242, 637588713, 214776401, 67085395, 611701763, 943686212, 973681490, 112227384, 899101714, 150912527, 125418445, 211666071, 761628039, 354490891, 334159489, 399228256, 363703568, 492479367, 233174359, 9174917, 501980478, 932393830, 423753323, 740683007, 951188183, 985649810, 146689331, 139315045, 674939149, 29683843, 334815271, 168672975, 756968813, 307590715, 973461020, 186335701, 868199495, 48754283, 731282076, 209157749, 863144937, 360173507, 497855440, 885674913, 588206606, 698241110, 720071706, 577287857, 572734003, 618150464, 373193845, 200385570, 511182815, 131846129, 319431826, 739538779, 989571594, 288528588, 894524148, 700588611, 131675770, 508823382, 141745541, 396728567, 844537959, 787713743, 279135508, 554605371, 250618830, 382277687, 533696059, 961359426, 473225080, 825468221, 465939068, 14731263, 18806894, 9999603, 678263271, 973060905, 825849501, 617541769, 795771262, 737476845, 6162390, 950255682, 978119562, 778902455, 697935031, 511292776, 248353601, 335025871, 959525791, 695332251, 229103622, 658726748, 605974015, 159128005, 112789642, 551306316, 219588394, 403517854, 325587592, 866094788, 707308792, 126350237, 637776506, 804435986, 743576112, 750488603, 792847465, 848509913, 891151186, 183051898, 71753248, 812200075, 524959066, 522959564, 112669615, 309636888, 896715083, 159691507, 299864218, 197581530, 708141305, 30024214, 735652555, 957781361, 669185163, 905844583, 68739513, 761761218, 224361891, 623663171, 738949112, 739449186, 977765343, 325890175, 937227695, 955124106, 709025428, 500067271, 133061942, 607492402, 275904774, 655089602, 974620187, 162987721, 633315378, 871789345, 598692099, 597270707, 257245811, 900979470, 782438257, 164071853, 324944367, 527311540, 438860244, 908661117, 936013415, 846137243, 12728553, 526421784, 274628136, 931990351, 659452882, 425245813, 740723592, 161421793, 948287466, 476203956, 337051006, 210916759, 565443708, 742468547, 307491378, 814396473, 73602943, 122240070, 121181816, 205350718, 23504227, 154848589, 443486391, 482536260, 626598972, 68986436, 298636576, 643217664, 189503829, 89214638, 165585750, 463187928, 744397199, 762979231, 832375872, 637816989, 435230363, 354674891, 530944890, 619521193, 746017054, 610559605, 274809680, 755594149, 989872198, 630458219, 299466740, 81233488, 18963355, 71310361, 559275212, 138164518, 873682215, 426065872, 529611527, 555257360, 261485006, 453248350, 382553743, 897669578, 176321972, 907860533, 980772410, 695409889, 364527563, 504784648, 19591915, 981206453, 429799163, 545103362, 810166680, 82873435, 661884937, 108245564, 589254524, 639901935, 371750291, 389847601, 239312767, 443425485, 407793650, 418868611, 821559130, 533223822, 540933705, 183161363, 164935148, 150049352, 287338635, 582942793, 214766232, 767444400, 889251516, 89053685, 22717957, 126506156, 736658760, 779578552, 320644897, 444652297, 708821704, 349127894, 679907447, 262782335, 291281384, 581748844, 359026530, 704212799, 876038387, 586591542, 717832341, 272759192, 244664009, 785418875, 27924484, 458830394, 326407626, 571638334, 984815981, 440866259, 523030956, 514011214, 533936395, 339287955, 521208828, 904167477, 978817808, 602339168, 592861730, 940298440, 693323816, 97196091, 635273567, 42589652, 495967117, 152116591, 474232192, 316480082, 102247126, 224016685, 311662586, 467274065, 159695307, 991206993, 918213643, 830332190, 854538490, 984010893, 59630080, 874036730, 229688336, 874168508, 772385426, 250948350, 145531615, 838828465, 35234224, 485204479, 765643367, 629061641, 579889493, 825008410, 841499603, 292559017, 700850583, 839610174, 833381309, 359940011, 83161280, 269980120, 41532280, 528788543, 885839424, 533754490, 256711286, 927965310, 176284003, 793621449, 326884263, 465614315, 608216841, 297109566, 679570233, 246755460, 780203804, 27980343, 106200303, 658694945, 742944693, 407439850, 215089238, 193729148, 498107873, 508395934, 304954790, 35175882, 499355044, 4871219, 552804133, 275396103, 647204488, 879241474, 808224164, 899315979, 953418134, 498789071, 782866709, 17653923, 948212614, 319648593, 605172827, 379332183, 856466461, 760072187, 655126898, 363286504, 385337240, 317249315, 702619515, 897933076, 105978948, 145416348, 911154989, 912264130, 883543900, 599491598, 453253784, 667147657, 838885967, 392888017, 324534700, 518730649, 111692904, 980765028, 533195309, 925942973, 29099555, 567092912, 98305456, 574712735, 382016690, 529809963, 464627240, 451553961, 502816692, 724737648, 265537034, 607437258, 47799934, 759518448, 823750885, 330243075, 154437926, 168565369, 697847887, 366190987, 724073737, 96540098, 219803972, 332877005, 394133357, 137773351, 318599418, 256499009, 534041271, 940670483, 863307696, 940333213, 227574637, 532517912, 752378024, 362917932, 190586978, 677012057, 103524651, 863955166, 372586736, 755963180, 595134166, 373061910, 592842915, 4029657, 162466744, 443032996, 234239891, 96230288, 789356934, 425825063, 327653521, 231980011, 540512932, 270541846, 6413304, 501408122, 246744531, 289391134, 431672840, 767286297, 72129265, 451483122, 22858392, 534415696, 506521206, 70112581, 833451560, 854682443, 558585793, 317125510, 126989327, 374668285, 661680782, 27831407, 940205697, 160978104, 406557863, 203212900, 599533493, 947192573, 799111871, 350836242, 397183692, 923089037, 747625793, 940319077, 698836916, 179490245, 275803565, 714666630, 419345518, 320657363, 889859126, 603729709, 655997758, 391151428, 832428803, 318638436, 141785547, 997604791, 505860831, 103205765, 86446455, 332273960, 184837662, 772352695, 175805381, 540394016, 695005517, 737261117, 823359834, 221514360, 304288631, 534709348, 913253600, 427753196, 675826997, 519405861, 865523416, 279032800, 773954693, 952535706, 392880084, 445670245, 876618436, 365027294, 417558363, 160131727, 651885088, 308868366, 745980044, 19556216, 746874025, 733559951, 119293235, 739550031, 431097617, 903505233, 67195754, 100017755, 821077441, 34652224, 51690017, 940267008, 244634540, 422167385, 521963695, 969507987, 136346930, 786466367, 740350976, 944901336, 111694122, 908033908, 143191785, 242261205, 908518313, 484901472, 960386161, 981902895, 71173683, 503979014, 449648461, 191462735, 531787650, 718019003, 175577551, 104390706, 224761651, 554903662, 746278707, 799850174, 105446256, 673259939, 950753245, 51823557, 390476754, 643289499, 307178195, 404822606, 666890272, 505883816, 701044569, 370470110, 749545996, 685809073, 416737521, 826840435, 102692280, 666240209, 13977079, 795123945, 15761328, 841799291, 114187637, 275853843, 950814668, 322804864, 929487599, 442975949, 715253950, 898569284, 701016078, 182468111, 296149285, 636911381, 399563342, 385910398, 451252219, 456902438, 640538193, 470774196, 239334912, 984764408, 811753010, 840131950, 804987672, 992104630, 653196160, 188384035, 329171589, 801801597, 945487830, 135763460, 545915987, 951883236, 938398156, 926319611, 891291669, 3391437, 914460894, 274094049, 361871082, 295676653, 542338200, 294498636, 537262747, 195312593, 745387775, 752235594, 279007505, 453424194, 371945477, 308700154, 411038171, 589944838, 267889520, 525928892, 304393448, 126575192, 463026841, 133812482, 923815058, 294953658, 334138742, 528228700, 313281046, 993406711, 867899411, 61641320, 376255969, 156862317, 137413994, 357560027, 804887117, 413117989, 202442346, 384989203, 750039935, 171331087, 52603630, 924554761, 759739737, 511889654, 288866909, 505545417, 207100585, 508267104, 587897335, 169002624, 528453223, 239328335, 295906952, 904933002, 691112421, 234638667, 776487277, 190191550, 82079411, 267167831, 296449579, 772421089, 428097821, 320838324, 688838915, 202530883, 16765994, 506715099, 431649793, 909160916, 29299342, 615074213, 408273062, 485825481, 63425338, 825276628, 179126421, 797398603, 720892297, 107723119, 756349535, 664417233, 110972868, 99596787, 674880377, 522597730, 855685625, 961921106, 348151665, 932958306, 23224130, 346503118, 121146712, 792946152, 403514006, 157155653, 337390465, 434468749, 45089741, 897749879, 870991726, 826021724, 612200514, 927709515, 240693443, 234655474, 797057685, 331892682, 295961297, 386147379, 500423010, 476896711, 288717439, 50702889, 959415908, 567274787, 747363586, 204136611, 418976448, 666384758, 177757540, 218317988, 828637672, 177217619, 84975228, 351705160, 778197748, 571721588, 81383404, 617754701, 998784264, 85309000, 438383659, 174533959, 43042625, 418719653, 461115784, 401098293, 180224970, 974212531, 402033915, 813761019, 125920766, 578255051, 207778726, 927694111, 348940218, 109449859, 243766533, 358632924, 593187191, 355434862, 461602156, 377401948, 105842422, 311735110, 813006078, 288155282, 615248478, 76219771, 860905193, 76390817, 163270090, 159488316, 877234253, 275817307, 335595214, 959975035, 637795430, 182910003, 453420118, 237697820, 767732784, 955903167, 134763256, 248902239, 424273391, 838129891, 617407654, 526487421, 772564815, 234748394, 102448201, 574003619, 603048375, 303718086, 393873253, 405177994, 643391451, 557617342, 457596112, 167642354, 281301051, 250728827, 719301415, 436902538, 591816744, 873673747, 980696653, 137412092, 347507776, 876424933, 930902986, 991193844, 415206448, 170068987, 896924316, 519375281, 696609285, 578708110, 652522539, 13372325, 622036783, 93401290, 49645764, 534647564, 800275490, 803428593, 251073927, 478640348, 770358591, 265723521, 998301760, 483578339, 24995587, 473988035, 920614770, 796074123, 509325047, 770137592, 327496305, 788598582, 995647978, 318265602, 720499710, 294689848, 400061350, 682691534, 901458787, 106234345, 35688519, 745295450, 488585936, 597594677, 685792898, 544905016, 273462880, 104072962, 457885313, 111277264, 523169241, 911274817, 731124410, 59487555, 284966912, 54260220, 94661898, 394543511, 479062198, 167837962, 465217909, 118917174, 918491420, 909303989, 759299571, 232295904, 133043848, 932698049, 877459015, 457153266, 651349699, 156196637, 990737869, 708287545, 589457330, 775375516, 153437505, 219827702, 465540940, 786518599, 531922816, 990535544, 355377859, 733371304, 746811412, 756761005, 337015703, 32554962, 589240811, 402330639, 934940670, 144857777, 654479653, 618206238, 648031460, 487384678, 727288500, 93839474, 395969905, 64471412, 700153105, 964609796, 722540724, 573290441, 338993794, 849356662, 682643960, 319789595, 692209083, 444532302, 761295251, 106509992, 611199854, 942774110, 66662860, 578195516, 809513746, 662778258, 204320030, 405314857, 300901070, 479605672, 357039894, 413736756, 489609810, 838962972, 65488548, 722701947, 495915309, 838398898, 753883066, 50408212, 457656325, 764536901, 378149438, 441252398, 268621027, 274458363, 390761646, 997488524, 860524775, 289259856, 402298590, 890262368, 325010069, 491092479, 230395971, 164713748, 517838739, 119941729, 29959817, 371975143, 971598017, 904345345, 986351074, 121524433, 750389374, 828375988, 436723491, 265817844, 704248453, 2248732, 198235664, 716978923, 15024409, 387705355, 274330291, 368135174, 848286970, 971213527, 438393621, 356320337, 712880026, 141334617, 609905116, 436998940, 402302611, 840332258, 548627555, 766450524, 449931224, 901579154, 829256576, 55056640, 269931930, 804486441, 870944347, 939250003, 813038297, 832984815, 496392888, 828116177, 324124360, 9424652, 366595302, 60739915, 549732021, 18276357, 632363898, 441446358, 332573795, 214714471, 457069957, 822268577, 694614347, 773028356, 641033203, 426792788, 744538715, 85931004, 495620853, 436518588, 830074706, 690024859, 846832539, 413531756, 59464974, 132466399, 996104023, 861066995, 778311266, 914926951, 797691085, 406610977, 442312674, 275272245, 222035036, 641119065, 109786669, 921606110, 358430091, 208545779, 430593934, 733312368, 239620341, 965815913, 9008666, 415840235, 206599969, 267600323, 855568123, 657035458, 675220778, 971145281, 6800230, 142712657, 701476840, 710506074, 908148077, 80160828, 622126221, 665007743, 47463982, 228012237, 941510800, 51648548, 135200102, 715196875, 809569960, 517711870, 484897868, 313340679, 441064041, 130215722, 680365080, 68652363, 448771169, 986955289, 210489804, 208717455, 870770867, 973386032, 815750758, 64635676, 954006428, 392391490, 416992561, 881601411, 708388697, 832101133, 55135627, 562981347, 176669792, 422017725, 537932685, 754353745, 91725108, 130064923, 814577210, 663761956, 969231639, 483056957, 661063471, 507695953, 170084362, 935730789, 274788065, 618918231, 251795241, 218222684, 127679803, 978209780, 102588063, 452545813, 351406707, 581369481, 347913447, 35379253, 809448777, 616437511, 933606672, 890511781, 469525391, 60640798, 411010961, 987546683, 493335907, 160704500, 187488110, 244802939, 586927470, 469935366, 491767233, 232452640, 313435351, 784502239, 199480752, 313356907, 834437801, 563853503, 566664306, 586649396, 412165305, 118840107, 711228973, 238753491, 949213482, 494346197, 961895857, 693073037, 659831923, 766910468, 336441671, 798842314, 635555574, 445452022, 141755941, 519116832, 136730679, 551210773, 663157042, 680297029, 423194864, 793874424, 654538408, 23819000, 602614168, 176228677, 937406941, 651134394, 537168110, 420211422, 357324185, 667566597, 679050576, 768362647, 953870748, 14580000, 462310111, 666172210, 853171335, 622130014, 659496415, 221685619, 442959853, 644761136, 925198245, 536243403, 536796625, 964526515, 14602873, 430017055, 792701260, 121674065, 540511237, 648424076, 803639468, 203413374, 914834841, 924602151, 742872368, 174850436, 374789884, 808713395, 836550168, 997196458, 158315796, 780537879, 571068509, 432346471, 407729023, 263736230, 851663875, 487819007, 363514468, 799481468, 296255311, 790301488, 498265895, 169141106, 164904716, 696498011, 458677865, 70501470, 352056265, 902429464, 929760286, 728929907, 681643234, 780482551, 239167393, 164261123, 972470117, 601908229, 550449828, 9155175, 216844235, 64686654, 643078188, 825006875, 474714074, 634245903, 511774209, 549156950, 810251295, 567639958, 451858341, 107303050, 344267128, 991394964, 455564439, 579109477, 56268359, 623234222, 188751152, 260176893, 26307157, 667179443, 721520040, 53752991, 870249056, 205874166, 98114290, 178461717, 788553023, 298058214, 168406570, 915005344, 577306300, 55351090, 660875203, 629251603, 558612759, 507157225, 737607154, 1585978, 955341985, 674519939, 778609233, 532565638, 307207706, 167015203, 866405241, 413650175, 553448743, 542295871, 204689673, 103694124, 230195865, 2891069, 792391134, 207525581, 165148857, 670623875, 774007928, 411781841, 266767782, 732626027, 485834562, 569369820, 296086511, 27850319, 858986294, 3778311, 474808850, 671329802, 173160934, 450394756, 863993231, 749698857, 303795363, 479866732, 344774971, 61292518, 804697496, 236819355, 968145834, 881670178, 546907837, 721804956, 328148628, 273794655, 468742847, 584757759, 793041412, 341601947, 375195274, 504088196, 268312116, 395438973, 408212349, 741038191, 830945466, 191929178, 841302013, 964033523, 336967706, 847722845, 705347596, 363982566, 420027798, 503732465, 586439139, 486660097, 682517455, 914657825, 810783513, 961487492, 677253646, 855179184, 482087265, 307513348, 177039264, 825972519, 881360730, 755161269, 307589988, 862291400, 894868331, 146654096, 818398488, 334827734, 895440550, 700102512, 537078438, 130417157, 764320850, 412397272, 279406610, 479339202, 587986800, 923951253, 509770732, 139748612, 56992852, 226770679, 733805117, 540608293, 898251652, 189481910, 608623470, 872810363, 523503718, 895364581, 4675797, 839610759, 594287625, 827732043, 695585016, 862671229, 419455205, 720536825, 334122597, 172212746, 918658380, 338116725, 533903241, 240364524, 947212682, 663173076, 130479403, 243903027, 539545372, 165034984, 769559112, 384159829, 135748276, 302586097, 185038636, 678458970, 217597967, 379117260, 286821748, 369088359, 905458033, 41849481, 875189832, 503683746, 471470365, 515817199, 946095261, 373595592, 543904347, 828799290, 493251496, 970955290, 776749623, 771711489, 443058844, 342184515, 748418159, 820895648, 590261619, 483871504, 529423095, 89240363, 339535491, 528211449, 277397957, 403888686, 750107291, 119418224, 783494789, 223550320, 963391740, 164091996, 924392410, 197060724, 482983420, 410416235, 973726102, 368515337, 153875574, 384782756, 404731716, 712738944, 358120928, 346683776, 938162062, 456179233, 881442000, 781258759, 749908571, 630308658, 587088584, 710440094, 190959645, 441538875, 817559255, 230542009, 647541877, 200649018, 250806411, 467208024, 637077599, 572543971, 76955234, 479840252, 995002389, 562330237, 682608030, 944167223, 118415483, 289742819, 738876213, 713845376, 952961287, 459612504, 483951720, 959194235, 982255169, 795932774, 498879780, 686404060, 551110985, 573648390, 699134526, 592931222, 963143174, 161157035, 901595831, 683678527, 162674628, 141205851, 753059072, 807186026, 152604078, 838176849, 814965749, 627571690, 731680459, 994176715, 71186261, 344314792, 739115295, 566058121, 410127445, 805047793, 992277371, 744112873, 293275768, 761617238, 549571895, 868270855, 651564803, 385675488, 455512601, 443524238, 986624593, 185058615, 251307174, 842237025, 860160593, 119907930, 379896208, 853231042, 651513108, 804019500, 722450404, 897296581, 536973138, 535432999, 741804427, 275545874, 782207294, 709077199, 49791280, 930155729, 940451421, 287135563, 950706114, 345774415, 633753968, 976133780, 824858236, 275366930, 960336441, 57388364, 402460671, 234582904, 586771932, 648942345, 518747337, 49296961, 243135969, 774899902, 936364981, 537323145, 148028857, 962472557, 766791762, 587207407, 506288884, 684438679, 387870599, 638836357, 990358283, 888139003, 410219342, 979977932, 56797871, 845562496, 441034996, 359746107, 211230190, 846757890, 614087264, 828591033, 380444840, 118472258, 647432925, 992336109, 910614660, 130001056, 959877229, 962926936, 542954109, 823711505, 956224506, 416378751, 144941610, 18805107, 439259454, 48192329, 627953935, 623696083, 471613404, 943372597, 114999604, 962460510, 821335042, 985294334, 571574584, 294536523, 656858640, 657135914, 473514241, 316894228, 321837213, 717018207, 437862078, 827314013, 714187368, 18988616, 511577836, 906068806, 917019967, 758487325, 774509943, 521483830, 369333866, 113500837, 121799156, 850190250, 247209257, 259243765, 728128200, 434834297, 666787305, 255203919, 851341476, 933772935, 466859837, 886798520, 325367723, 740274101, 132989404, 446949191, 459621282, 33416832, 954490573, 307708869, 177811494, 746157280, 678671632, 532284036, 743652027, 659878711, 836969717, 811964083, 523397423, 664098704, 961895025, 129275292, 826992547, 62017912, 963938499, 846387610, 66758643, 655288709, 787613787, 927863059, 780604851, 666002456, 467631312, 34547741, 70516682, 990723336, 976921314, 304735315, 464286583, 693383068, 509685382, 249610626, 799811180, 927294128, 75764778, 59642791, 750044256, 311343856, 491664943, 39328469, 538562528, 296305880, 336879134, 669186363, 768967466, 828679323, 323858228, 815428034, 735823921, 559226846, 482298174, 607367870, 3951268, 735325794, 156485790, 663581711, 561198733, 798391769, 738164060, 868325310, 422204576, 947871393, 714766750, 405753594, 925884665, 816421576, 945378933, 39212874, 72767138, 469694334, 311975990, 557533728, 798400992, 824605398, 14382125, 109718096, 446522420, 886540157, 220319972, 400506449, 746404420, 948396568, 322615854, 453558037, 349516678, 96066745, 478685449, 57209753, 271375554, 17742268, 580072076, 428645325, 620528125, 287517066, 250913097, 66587788, 401683309, 818982343, 931512653, 567692034, 41380011, 754405261, 618958074, 260489233, 262018040, 292183735, 826834981, 531483922, 526627724, 907758984, 972834543, 139008022, 746940220, 784500440, 844137296, 662790930, 856359810, 747853439, 18766180, 341679323, 171040143, 418788088, 317512426, 930510690, 606308962, 972526846, 858777176, 144906397, 677948089, 606806388, 367169771, 413901302, 969980622, 310814689, 191143702, 29322170, 492659240, 645918292, 233951157, 288970908, 174773946, 161210602, 677222346, 721896608, 488437876, 419846882, 58625179, 607081544, 921311587, 933345373, 562514719, 317906761, 496373565, 439047489, 894454854, 700565758, 42901408, 18591341, 631934361, 43950727, 748441967, 967590736, 431840483, 402620566, 960536572, 192147787, 646310303, 328958909, 562599891, 619775782, 6641941, 78313788, 517185761, 11494460, 970170802, 787782418, 835107448, 642283886, 216614593, 846128618, 816290054, 451565960, 939235128, 249056860, 323476795, 900495521, 262372714, 940369655, 946438107, 516312674, 609713853, 665557510, 864138197, 929677691, 962011212, 724782445, 676515376, 254137816, 148445188, 696860019, 1222006, 244475730, 17122316, 876556062, 920667758, 704934110, 696411183, 811168558, 672855258, 736046881, 111220233, 524036023, 901528076, 909067113, 690455943, 580523277, 83682802, 907108376, 863077610, 826203440, 529915503, 904641232, 118717384, 298713850, 385875891, 872279822, 138519028, 600780455, 509665001, 563813986, 626865155, 408556936, 721571680, 848703739, 628748776, 400997667, 484323355, 593512519, 134132747, 24124102, 527385111, 949380254, 212693574, 562094614, 946222896, 28008276, 301569545, 434423567, 586513436, 413194296, 691685392, 348046345, 915563716, 998905417, 138493103, 498446652, 463605568, 26300522, 550381687, 908450490, 51282760, 54277907, 657934036, 676817500, 131450797, 361477410, 414280363, 603343205, 336191360, 456758042, 941993795, 152577796, 411766764, 304283901, 477336870, 616996290, 576449821, 708606039, 154893986, 651735289, 195601568, 240933882, 501064950, 954903312, 434567261, 602803661, 202063198, 902269511, 651624075, 709026003, 798743540, 668507643, 982008685, 835728657, 683082230, 663420953, 481986415, 162272842, 410397056, 357350515, 542723584, 236320329, 848424696, 597093266, 717918905, 913917550, 657336492, 640441697, 457452732, 976469497, 901958577, 542074342, 403153729, 755080822, 747375987, 194435341, 661953364, 719092163, 616683496, 952730585, 368797456, 567811915, 791549, 949324336, 363523704, 714764848, 230241994, 397154600, 562417803, 235949512, 756121166, 499168024, 952205035, 482812675, 935173894, 905563717, 444651985, 130874425, 254296500, 153191149, 32504884, 246114424, 50295367, 327697247, 876605233, 31826392, 277752586, 246573207, 475243075, 30861321, 596306911, 230153942, 408944300, 366994533, 690799205, 337396949, 558027033, 985764314, 965367895, 907594183, 313892470, 353018669, 865627588, 487653593, 868605801, 94127908, 353559796, 635368065, 114577415, 657259416, 688359209, 978255245, 624350341, 772385573, 325530468, 764890489, 277884119, 346906778, 656991923, 959779818, 969509681, 678849017, 68028612, 363399455, 342571925, 233940536, 583128532, 378759415, 381332722, 465002508, 490369663, 777400071, 433929618, 500239436, 368128758, 265866635, 214506180, 624697499, 856513941, 533605911, 374950013, 367481219, 837330997, 875259270, 499428190, 316487599, 439809790, 829914976, 438001114, 528665895, 898684029, 436928061, 333686675, 923783362, 694385335, 335646916, 632789649, 952751677, 885257519, 211486218, 392783730, 681374114, 160146434, 363156214, 177314016, 161439396, 470015869, 737962108, 28075532, 544608984, 719573126, 107446109, 242514598, 796846723, 233143722, 280397051, 754837095, 289977876, 896939152, 339025032, 651309471, 586711980, 166975884, 154139317, 29511995, 710535302, 905329512, 818664143, 445701131, 102758256, 362752665, 974620960, 823102651, 356218705, 796928679, 874284191, 711183143, 771660211, 358422010, 781252794, 929509489, 39750890, 404579882, 995592465, 225255102, 390868766, 306659286, 717701603, 29120502, 159343418, 563423861, 751256765, 685090962, 999561883, 970030524, 769652720, 573717799, 692170061, 198930271, 561936009, 305363367, 430699356, 691722622, 514445417, 761109431, 267783604, 20579855, 652169900, 804157617, 51703683, 810928169, 180196856, 647851608, 491744462, 295686975, 845244957, 901905995, 720616789, 227301942, 935642516, 326340295, 883781072, 275538057, 78046283, 290577366, 589606114, 825058809, 167771710, 10375061, 36127196, 450769859, 82773519, 100981390, 995641942, 976790999, 257495447, 953056796, 607835416, 265982664, 399291299, 493556370, 776659167, 217187203, 363599740, 902001678, 327360081, 748932710, 554207420, 768676527, 678031017, 435667717, 903173498, 49425086, 717316721, 840873364, 873255716, 673765355, 334585921, 293227210, 259374030, 190293600, 583637060, 525315431, 571891554, 46131437, 808560937, 72540388, 455666324, 309813803, 275142386, 545656020, 531508235, 670272470, 158139180, 982006686, 249751428, 778849625, 134705000, 911756363, 386674207, 886041312, 93612012, 168534503, 604697904, 602225058, 225403164, 766345340, 515872361, 771884619, 324688055, 816253367, 118029315, 47643612, 340234327, 228001889, 462938704, 982793155, 502430416, 686925267, 379396480, 951603390, 925169894, 4675154, 789851867, 582764857, 338435356, 446504667, 232357737, 803797914, 46430469, 824477858, 909153125, 828811554, 415390693, 928152817, 655753089, 732317873, 319655458, 498104442, 324943154, 949631716, 759882869, 416968580, 161631996, 5815273, 842602674, 294670183, 964011853, 540327006, 763260570, 560053597, 273655398, 142608947, 333722438, 37485084, 766748588, 655872022, 185881634, 925785393, 351486784, 759695363, 394338362, 759288768, 656634479, 279994226, 213378172, 281699811, 367089894, 565223067, 270688664, 57568096, 120833667, 46128110, 616368592, 26981864, 705812140, 746509005, 754870769, 336949322, 650601183, 582536637, 498709561, 432290381, 348896207, 528185190, 828725722, 387871588, 375581049, 712846541, 102712705, 924229450, 702737359, 77700003, 823518100, 281478714, 895646466, 902300879, 172454889, 144061919, 755334749, 623542597, 524298372, 498868027, 296915853, 482586587, 419608895, 356302932, 777523236, 525244174, 108503794, 103862868, 743723184, 214710658, 95815293, 978654042, 982887075, 40824047, 211471733, 313725968, 536610695, 668561315, 355244971, 267346906, 728273564, 459128162, 33928809, 622285794, 867129235, 444985141, 745061968, 897503020, 283401608, 679512833, 937209587, 811430598, 621795383, 185385586, 995519409, 366443775, 796254306, 510363582, 290592519, 775370922, 470495259, 887422607, 177142312, 358437064, 75104127, 451920857, 42261379, 639236942, 36630970, 495871675, 256947306, 654007956, 119246505, 341038579, 400942679, 570355015, 537364418, 207840637, 173055703, 611892150, 397821634, 971987766, 175357466, 811182984, 875760554, 253946324, 624739026, 131461090, 916616153, 544341605, 21978632, 635474837, 75329316, 789371766, 883105007, 309275206, 464915344, 427934364, 913312577, 352722919, 833031982, 912527852, 352798414, 118557227, 159147118, 569357249, 520373528, 746688457, 125012698, 491107430, 411388546, 818571913, 621059351, 297718362, 939946559, 107257107, 40017449, 239623892, 595442822, 722871653, 985453623, 386119887, 969723820, 796681909, 351154459, 614396824, 277874910, 936438521, 647201425, 413206885, 214961916, 549944618, 706789804, 68483534, 398779308, 103145739, 210614282, 845918899, 862376524, 368836768, 648092810, 893129267, 85521151, 861540940, 541792416, 978735143, 836156147, 172107241, 89619587, 979858325, 554540811, 333358562, 905100253, 245043283, 736357118, 601925155, 435059769, 583211123, 922194179, 957105012, 934919756, 310577778, 963077260, 88001500, 549133381, 355327779, 143113761, 241470219, 121070494, 193021795, 637269893, 926220043, 506763519, 242080903, 220172545, 834268303, 248744996, 851759783, 191831926, 894093734, 692044936, 400432104, 343052277, 204887554, 419572618, 804132273, 533642718, 180929090, 688990232, 368584311, 348743065, 132719724, 882119665, 463530829, 7187250, 470728209, 556937154, 970742355, 394934544, 34427165, 337856368, 824968232, 54958163, 47241126, 547160735, 554190474, 889973097, 453354669, 323273527, 439605348, 498013632, 976335572, 768665164, 505063008, 401242627, 789321554, 208606929, 850610556, 385194774, 829944473, 327461425, 572636422, 981566908, 474506338, 420690463, 580231521, 369245395, 386896066, 47482083, 321171040, 543522040, 660001059, 673736515, 580663933, 636725334, 596661707, 161068721, 174359220, 583210537, 779259648, 217443090, 900979744, 391886538, 204310765, 789254479, 172690888, 315557425, 857473736, 201050455, 965921304, 899193413, 661394755, 782865771, 92062571, 954157917, 779192854, 921634155, 631352879, 418850146, 637702755, 329250210, 5157749, 992734680, 48433072, 216727803, 763550414, 768453370, 372437564, 955182779, 258687763, 342209484, 204160116, 817173537, 953183403, 446242432, 718538971, 785138427, 231443939, 136411466, 513481155, 238192041, 363713644, 258669736, 883685244, 12661447, 948081335, 566953019, 790487813, 927437510, 913837216, 29204170, 488175327, 981991567, 980488426, 837387356, 580875117, 346039321, 655367673, 632668276, 914279643, 303968648, 457569628, 568162364, 312638876, 252254422, 895082637, 692506388, 180335956, 616914400, 905553427, 522811621, 740234575, 21420492, 166308907, 432645400, 66060083, 597927952, 612228878, 968802619, 777696264, 290560834, 474325775, 531888251, 715877319, 600544592, 408383189, 34006715, 656688601, 35831116, 209616701, 773041066, 566275877, 829581349, 803594509, 298660663, 634895136, 761334210, 727339838, 755562043, 668094838, 869540648, 380041932, 224078708, 757284225, 173097661, 937842519, 972681107, 604062990, 77272939, 429164316, 643262574, 543545820, 256219938, 301730741, 591364367, 58292328, 782093003, 579155980, 643131266, 910285787, 111873091, 807096029, 285253766, 654839928, 876418598, 94529126, 154009216, 730012580, 508989532, 610230522, 548298114, 322846735, 243896927, 195593599, 571099803, 833729571, 334260167, 585033239, 899636620, 220238935, 260300387, 354693831, 447830242, 13594576, 932222644, 73098711, 927683376, 318448060, 114922285, 881523056, 92809756, 329707087, 600559843, 325437272, 602390066, 247737786, 945196650, 492412299, 700389356, 839642312, 197157882, 961749370, 415171160, 616201901, 560586086, 801147213, 342581422, 157449419, 513987082, 930592281, 707897731, 840518260, 495679224, 791528424, 642733635, 360589091, 549633113, 649528286, 408049207, 490088959, 677644345, 737893142, 161199351, 963757362, 504125628, 285032832, 341544, 864223003, 161441958, 240860776, 242901504, 786275868, 646794729, 872008015, 761620288, 592314873, 533469514, 946315717, 453744167, 651491237, 260805362, 211462824, 637947740, 154722379, 335935822, 500447433, 719607057, 148714256, 893343901, 853965140, 320998102, 367409060, 57276975, 876651557, 506129994, 715481660, 491337661, 987767123, 753304921, 994044609, 902799018, 308453242, 328849171, 123673448, 179721267, 198544388, 444173144, 843391008, 843667407, 382048012, 378500400, 501703907, 583683517, 977841812, 441110579, 314077508, 457706369, 971340539, 673005296, 928420789, 877981828, 962157200, 341448502, 296797237, 721122, 699486116, 347361328, 830429830, 630508048, 618330426, 96756518, 264378279, 363475628, 571488567, 752877132, 154890611, 278835500, 947345415, 930679437, 338673244, 454942753, 726176669, 595086296, 844323412, 836352306, 749862508, 176884355, 170606836, 554719379, 275699869, 216188547, 875316619, 823666696, 63924774, 965709464, 93431933, 445171448, 985070243, 567268199, 634592158, 629306515, 759194134, 925526534, 209185176, 163508673, 192024913, 677927958, 97915054, 625871459, 425308298, 893591528, 445036947, 190243431, 552874244, 85152155, 382684975, 131241578, 190661888, 637682234, 444548046, 109789115, 853504838, 768094120, 877774922, 745121198, 274869139, 572148888, 974068041, 347578221, 31989674, 685449728, 572361637, 76833485, 218431849, 953765808, 274071008, 989088261, 287880379, 293607920, 514895771, 233264538, 77321001, 964265387, 957107122, 279306521, 284793699, 385847742, 817930554, 317548751, 517727699, 701321079, 473814833, 700388605, 233351346, 320367645, 833412098, 755038097, 433401722, 784986816, 432029066, 456812912, 306028857, 971962157, 276701563, 58257753, 292159686, 657878573, 936255624, 990064045, 957884947, 72746216, 559050685, 268508088, 705388362, 30758194, 224766819, 614761354, 115106925, 171739300, 842490560, 45537383, 151792285, 201703928, 576562673, 727206986, 701363426, 746976137, 911571907, 49103630, 841438124, 170286148, 946128094, 522697118, 42417748, 306439877, 665828038, 591833384, 833972114, 990006562, 449875306, 194027276, 99403784, 550594526, 965432568, 365964299, 923780316, 90156758, 959700772, 645162793, 69757800, 538833152, 389373096, 985200305, 421414087, 858356970, 990606433, 247526825, 193834472, 778801925, 728815917, 971296459, 464026301, 757210508, 63397324, 46499601, 702773035, 506610237, 84659197, 264529371, 528591772, 363655718, 190812234, 435874324, 766013110, 23457927, 89865588, 273935116, 536196623, 570754495, 699361599, 759798009, 19432170, 580769311, 706306781, 542467340, 396403590, 467056746, 454774854, 331033188, 469161181, 741562061, 251080421, 998406786, 373971249, 469322602, 841251667, 216190021, 196969543, 576546446, 28154057, 135475317, 284078033, 390819277, 816351483, 644717314, 727629460, 46525148, 450741131, 689716884, 784542661, 208630651, 891055414, 231619443, 195379715, 186496056, 456850119, 771142251, 691996063, 542297008, 530760102, 101827162, 201155098, 878207636, 233630452, 935570354, 650857252, 680814784, 669101999, 677601771, 96989224, 142420256, 782192174, 453316721, 253748546, 481451336, 559477184, 743115115, 599172826, 265951315, 21500913, 420848792, 807162164, 745649634, 425418464, 42769078, 390005159, 411581525, 230982655, 726210808, 71925136, 29956742, 12966392, 296363909, 528216950, 226216352, 619887373, 722447442, 447975010, 313709090, 705352760, 449908811, 153515207, 697901109, 341309001, 179244018, 464036770, 847605318, 44954231, 418567289, 175822202, 745165063, 39014500, 897556393, 59782585, 719706303, 444864602, 684315786, 874386370, 46215544, 141179055, 272238787, 668511164, 166169634, 19030728, 252327448, 265357708, 196425769, 234075585, 273928203, 47674630, 339100909, 160592972, 549443098, 271419384, 542865855, 795389463, 270150918, 600650331, 287425151, 342306959, 67455624, 520810675, 262348422, 979202064, 103048925, 284404574, 174775941, 975421428, 849287427, 966302602, 260776846, 317287016, 766365282, 129356589, 808984499, 714304399, 164623769, 306806796, 780864784, 466344681, 87661629, 31927140, 613178422, 861293670, 165809272, 669405004, 272692137, 437199801, 431728322, 604660124, 741004548, 307668703, 512384929, 878609896, 633178252, 917916793, 158661513, 52143300, 800767023, 964329269, 459622197, 853495503, 381760609, 758387330, 898074561, 220161588, 8049909, 69742670, 369250342, 718503863, 64044616, 57985635, 78212157, 713253087, 636757055, 953551362, 452745879, 804450030, 74591168, 617382638, 151616106, 941582740, 421310627, 401563275, 452370555, 853957021, 425661288, 159444622, 756375194, 187080224, 221152418, 999214636, 925490304, 951510393, 106648620, 456348828, 738816085, 434309297, 832724549, 773223341, 963862566, 973869422, 170446249, 789956337, 119103555, 147962241, 148980023, 16118613, 352901730, 958771875, 736679732, 582943155, 666347009, 613402194, 534376073, 121360507, 467711038, 560221882, 55001232, 884021876, 475151080, 879305520, 166949202, 373791937, 801976249, 430705416, 940046405, 4519978, 647531061, 809645055, 43001913, 735902321, 894831507, 744881559, 42861169, 54735451, 364659868, 859389523, 428785472, 645377827, 361698249, 227764701, 804543442, 613626629, 620986789, 833659914, 54698276, 551403740, 366714048, 730864756, 486870769, 146856001, 189756877, 211577229, 869978589, 696051469, 603246930, 562262722, 947826930, 803482180, 834954348, 796658377, 410533260, 881410361, 995358314, 119428298, 91075643, 709098179, 259828250, 124238640, 173426568, 895816058, 261556435, 540645308, 686020122, 282400421, 867111157, 546706783, 634073948, 514751068, 301084845, 378213447, 126384415, 15097373, 598707607, 68639192, 907620740, 795005649, 925226697, 773908093, 544450131, 287574943, 56402240, 438708023, 26354270, 806308940, 621557093, 890408287, 161026711, 746214047, 536681803, 58401120, 756025318, 184696327, 656019810, 667027453, 584149557, 536262097, 773808074, 968516553, 848588888, 461012834, 936128933, 419016886, 799878205, 508392248, 627250766, 325211339, 27850659, 896353394, 893462527, 599593825, 513603195, 835941153, 883895656, 808855126, 695933609, 59433870, 213023363, 232983246, 226833149, 97421214, 174744509, 3999392, 516966495, 822831536, 176221854, 694769810, 354861876, 906365836, 750284084, 911582071, 122448281, 952440030, 615234213, 52696811, 426303626, 849297180, 563961255, 460933604, 510878007, 935884638, 786537495, 482059999, 979878209, 51596146, 360899733, 658547754, 216162503, 435477198, 410751321, 27204851, 615157899, 514613995, 65543496, 172709918, 5002610, 28534203, 260201131, 278831175, 450521600, 64310340, 331122736, 969903280, 227800404, 500423586, 223273029, 938709189, 165232444, 30227132, 464316633, 246476639, 257171755, 531321260, 178669983, 757830231, 947220790, 194943560, 787890066, 878979029, 593074283, 803665562, 651296950, 664710442, 107572477, 731992368, 716354222, 278412854, 125847149, 780147156, 298608875, 684769417, 275114773, 717388135, 541435833, 581173829, 74807748, 578724704, 809144344, 325658788, 209359134, 343314066, 625387806, 322025273, 571398283, 657193486, 542211402, 242131188, 225744371, 830938874, 773363075, 670082777, 756443293, 41509685, 153754927, 130918956, 493401650, 341946442, 834640801, 425358386, 132041297, 117425120, 274455409, 310515281, 350375905, 240576987, 234237247, 685177704, 184736455, 253832978, 664913083, 196653068, 629413462, 476542082, 267920595, 947875131, 22864686, 209619916, 305761412, 406479930, 604612770, 952464502, 275098554, 589194145, 682398907, 101224662, 252303168, 606230116, 244177451, 362638254, 354242313, 742883335, 856982545, 776583244, 62822916, 420244328, 909245139, 96580131, 101335047, 303808619, 217557542, 808571158, 441355566, 600031186, 207694708, 162158024, 606576041, 186508996, 711651965, 458183417, 506880090, 97374595, 836822211, 965269994, 717926811, 2675766, 406487682, 462083683, 955582151, 185598392, 579293867, 79323775, 165122523, 465629594, 721781724, 865596350, 792410485, 51338803, 282632091, 569315888, 619300270, 772657374, 316993188, 192107185, 348495686, 90660820, 500811162, 972624156, 680464454, 646450639, 974294754, 625690441, 760720289, 288889103, 14172395, 527567476, 197819792, 560750266, 92189639, 558057435, 436304377, 555008694, 364293482, 761437172, 629105972, 157749518, 567120337, 600075553, 800157036, 817384555, 192293364, 726843606, 57203909, 52324486, 276436882, 523728379, 2610803, 491656193, 975211669, 901776315, 884859723, 823996452, 443614966, 343253260, 532882183, 584276320, 211474157, 70147555, 723356923, 87685631, 773387264, 251881181, 824642459, 454020415, 847271725, 563456185, 747641484, 860315792, 991193318, 708027597, 121720949, 23321907, 271566443, 426093594, 597323159, 422698196, 103035848, 288932809, 235182379, 363177175, 279285403, 651647856, 41071691, 597755943, 588870666, 914671439, 923363203, 983259134, 449853899, 793166667, 211038138, 969815703, 936159264, 811541719, 109425516, 981034496, 97827138, 464629219, 565746659, 581652474, 958502338, 634811046, 966721436, 928165903, 611994438, 993096302, 130252608, 857903015, 810244318, 471777035, 804990012, 605558320, 903365434, 623138337, 771429776, 365745766, 445959990, 624106644, 565102689, 782289167, 784338114, 268715170, 683252947, 916254158, 794544651, 96174514, 651540424, 724259760, 433529957, 365434565, 580935550, 789614287, 261686221, 109816479, 17252576, 162815722, 202616998, 15826546, 860665503, 799092631, 708127401, 266521139, 909390974, 250918778, 475030646, 712167022, 286462555, 67750767, 937000730, 672280177, 722331869, 549569173, 513159205, 376705432, 702112872, 832502138, 524757930, 602099582, 764092759, 927686177, 940799602, 895486986, 678576449, 412232939, 506424972, 386099875, 480225166, 407982751, 595708048, 403935461, 600326996, 303722505, 709752467, 272224953, 217019897, 168863989, 93455096, 366926177, 621561819, 555078519, 140224573, 204335328, 641682250, 382340869, 521435032, 906462684, 143976524, 906278451, 92512073, 979244392, 213428236, 12938313, 622928859, 930783875, 189439074, 881647453, 619275741, 515869057, 477367753, 351939965, 198218724, 25184586, 720276005, 339202111, 841349728, 972924452, 243217544, 359256136, 103955380, 74008714, 944936903, 371458668, 876075310, 434622401, 993171010, 953233932, 532656757, 743817369, 640447139, 391829770, 247371574, 817134096, 229180612, 161639551, 932767967, 479622525, 688908374, 401996904, 305122341, 443384092, 561954917, 268250340, 676317344, 655711469, 621559213, 34678318, 159143485, 125104591, 360783378, 815529873, 987207947, 705595842, 925242971, 640022998, 106121422, 880033780, 940511797, 648345387, 787780655, 177199660, 959820577, 106189124, 780629014, 61268757, 500049821, 324099993, 843838542, 694390732, 553541085, 193835980, 859996992, 206885890, 298007493, 338711363, 991212326, 588670935, 59833678, 240119451, 788507200, 842730108, 361548785, 541661807, 307917502, 342798760, 192819858, 901895768, 115422482, 816785610, 514428254, 329656106, 112823309, 784110695, 849395253, 341187631, 602862336, 518182369, 673214361, 11407767, 237846075, 160031077, 182207135, 170320104, 351321089, 46408853, 781440268, 573327485, 602476424, 306008338, 602706037, 971000551, 703063812, 492237935, 8739850, 259281062, 535798733, 962681198, 174254540, 638318469, 26418246, 3526479, 567414207, 407758717, 765596979, 415353548, 448549810, 885026106, 873920235, 851425162, 128611735, 163706807, 140693605, 27946623, 510441190, 976100614, 268817376, 988327338, 239414008, 858556435, 443465150, 410945682, 458797853, 961633258, 347780623, 898338370, 405134804, 813309373, 228343653, 376353785, 610685043, 310506899, 73785083, 101591115, 293141230, 944071767, 281330210, 257082726, 475547743, 231559826, 110696438, 82809224, 749791023, 677918425, 298808320, 42559636, 431166096, 15542468, 424697242, 7894860, 639054436, 825333170, 506261311, 399270200, 83393464, 196534153, 829140529, 75277259, 34068452, 509093012, 365285806, 702925894, 864601295, 473420079, 955591622, 445904089, 984480036, 115529632, 851020766, 787015847, 132148091, 624539041, 596504935, 226153938, 127972341, 69123724, 385067758, 6546019, 792866194, 510224640, 31702209, 349412117, 973023300, 961402056, 847391075, 840645290, 164771602, 86879747, 239051403, 901206682, 381364352, 892186074, 623582712, 823374199, 640565136, 441847661, 688682982, 967077876, 506311058, 813323738, 861884305, 154504085, 837766145, 128989709, 17333917, 156648257, 453767454, 641363252, 910344323, 285959355, 49601317, 898135488, 287764143, 230163700, 667142502, 358311865, 790408416, 684108285, 468295585, 679956284, 289568695, 784825480, 643438475, 614857777, 344394714, 295899178, 595729188, 883496490, 127541538, 436564892, 367785214, 551336676, 856577768, 641114443, 754487599, 190006790, 839253764, 953794686, 879254156, 704013898, 157300519, 606022229, 911938978, 266085094, 130065206, 543654536, 811210641, 946873429, 642466749, 260005487, 105968302, 543904929, 321163834, 588051480, 693475904, 789794021, 326835510, 632066814, 644863930, 740813230, 651028090, 65730137, 495508660, 986797896, 261208776, 388378824, 738003152, 105321392, 426683054, 41656732, 451199277, 865767248, 167964657, 748242085, 968451935, 619418264, 883650386, 864918613, 142187143, 948502653, 549237225, 455032074, 375191881, 97595225, 572132180, 236744436, 815877592, 102821130, 891301074, 725872809, 721819862, 270144918, 584524429, 891778015, 538401452, 558800733, 192494914, 503536483, 925245243, 763649482, 234833141, 109234400, 219512124, 345802599, 136213853, 689605837, 907851073, 936729401, 256360290, 147570021, 195448122, 115806880, 173305781, 115847290, 307991589, 592643614, 779006418, 452076230, 642949623, 692728432, 631985198, 242617084, 193343974, 312050054, 310804879, 294117564, 995915410, 310260079, 23513804, 470451214, 475990426, 466421587, 979910238, 971271526, 158907332, 666608080, 563852641, 427574141, 108381760, 353900771, 306795630, 697298553, 922801564, 363281030, 592161608, 840097427, 5444888, 962246259, 754102327, 887143424, 565589804, 49603059, 906185437, 437521146, 252960585, 339510852, 85076740, 484891470, 45284641, 215707000, 407012051, 326580483, 103875018, 972080386, 722813775, 165716545, 948419883, 578039846, 245657179, 228135344, 551678499, 896211774, 148585068, 149488968, 302242150, 299907067, 22377822, 95482566, 657677119, 574873554, 453598908, 945231978, 612641697, 123463269, 884307970, 377425170, 640946573, 243456565, 406919079, 139404194, 358489278, 183636737, 974300476, 269290014, 979775915, 581677969, 580699208, 668959048, 127146152, 632004170, 505725622, 31321491, 995083253, 866985882, 992972371, 475376010, 459109941, 586195500, 326254614, 873486831, 189220119, 824992571, 731841859, 853322078, 112647283, 858910796, 387723184, 107258962, 402027076, 281919195, 608223186, 236775503, 614323812, 310961214, 115275904, 680270898, 382001788, 923929610, 53189062, 752389057, 47296309, 936329426, 57926517, 959163709, 831103638, 273006392, 492697572, 59059359, 267210356, 962311837, 436239528, 154513985, 285978925, 254145494, 144791276, 114733909, 210100036, 514739170, 156894271, 830680606, 42100026, 45360637, 69776973, 943723318, 687940701, 238680342, 301266268, 515512133, 270924635, 862444689, 292591929, 158517786, 605026334, 596596956, 815271480, 136890084, 448214460, 236517865, 690492990, 547436290, 292611826, 807377121, 194209427, 279787578, 990110246, 493037880, 247326657, 52820557, 118875382, 55163827, 813997438, 544894545, 944594384, 192589968, 194794495, 802280276, 846587813, 98089719, 689957313, 537394963, 653622900, 761917117, 929569137, 995982911, 842400411, 757316781, 748242071, 606438529, 272094604, 765760207, 776835442, 351704024, 227136145, 527604503, 293610014, 585124916, 50092192, 340920791, 704270560, 706212550, 993416100, 316088477, 542817550, 657074101, 158964367, 392921865, 345575030, 433242617, 438355798, 274773291, 108616657, 672136872, 136606631, 236094935, 132908813, 834517827, 901770952, 77312442, 172048051, 917172533, 729388424, 18780153, 975638284, 492229149, 447168917, 606577499, 592914539, 862825564, 142287384, 789735441, 87343537, 827953520, 222842567, 528416542, 341693660, 998541759, 935412124, 325677873, 615640112, 40065475, 7712455, 909557612, 637312955, 875751262, 815947364, 605287324, 165332029, 352790069, 179665893, 859705061, 789853499, 209629480, 648900766, 247509167, 386549762, 452528434, 81203807, 494427412, 723699345, 902339098, 865817036, 533733515, 511606928, 857044067, 470755840, 103214522, 594423885, 335038269, 774791096, 763978090, 553607706, 731063734, 564061619, 221508187, 788120857, 855432883, 779398315, 721805938, 237479269, 109835174, 855877239, 318228630, 200268336, 865314307, 882854708, 2239737, 147641784, 623444152, 276527858, 990015552, 696380361, 643439113, 317106007, 141282360, 169262846, 326674149, 432758329, 475331056, 1482959, 450127046, 251862500, 615384468, 209010564, 298590225, 397596436, 948445709, 468703150, 480036529, 915293638, 594415852, 558171223, 571847833, 276104097, 617459020, 699084184, 406823494, 306604949, 926061090, 748641101, 573557371, 227287213, 159151026, 980888512, 612626376, 620767012, 75969179, 5798216, 518461579, 661859775, 759697375, 134056377, 623359182, 382124907, 481217470, 541750128, 216797471, 636125166, 799966769, 955363128, 808940956, 135243790, 621383559, 320863259, 992419575, 701567421, 156168184, 624800403, 766159069, 614505572, 610156057, 825382437, 78360753, 400113352, 758589410, 969941793, 804285309, 717186663, 738599983, 487685001, 177754126, 291507631, 974163085, 68459128, 146736529, 14635449, 161840161, 535120889, 665826438, 191147802, 134412232, 386599125, 639363105, 475474381, 137804525, 455521979, 163939029, 959740812, 163394179, 468758944, 304206720, 864752973, 740362993, 413253022, 688398400, 780130189, 290765543, 850865430, 6676878, 169341566, 486145157, 560788501, 962477794, 126441162, 782904143, 745145447, 459702612, 862529224, 69913402, 932287554, 545452152, 940289665, 982111414, 362833109, 220005390, 983599775, 278398618, 519262003, 587218839, 28878334, 4610723, 88876482, 577277504, 722278748, 116657985, 975346656, 780599075, 218065622, 291022862, 102731502, 98072683, 911810224, 675439187, 682197184, 762284536, 249404362, 404449251, 751155307, 288544389, 893714543, 178004948, 530058018, 621431478, 147464403, 502672657, 146195114, 691510438, 783822597, 285235161, 457590950, 270743996, 987339215, 251994732, 562761646, 320598568, 876556139, 346488438, 393822895, 627988767, 113905158, 660776745, 213559744, 925562791, 816455852, 430447815, 754439907, 636493609, 214157900, 295086347, 584621985, 557756256, 297587861, 893648221, 388936582, 890246396, 284803298, 143007670, 400471358, 447326789, 769124488, 463419503, 437473604, 946661896, 928947019, 579032135, 957021395, 489743804, 796873838, 166753590, 199099821, 578112508, 40449814, 149671478, 217647870, 26093299, 499685373, 618005968, 221687960, 623316893, 706966865, 979782020, 402622996, 928458352, 26192673, 219756399, 173188807, 676938810, 686121488, 615690862, 545912277, 901232172, 854553588, 808241085, 49712262, 667954806, 9656085, 537085304, 181503383, 521443878, 203627966, 484799048, 691678058, 606469333, 600851401, 28677359, 753454875, 786518078, 195609360, 465088314, 199204226, 907765912, 848094751, 223025511, 151473268, 550326715, 589670995, 119618353, 273636665, 185235855, 408690583, 922206364, 412504022, 527894633, 455983805, 664987327, 387039251, 973355706, 698401409, 693973175, 327140755, 251859247, 496234885, 35418905, 300380928, 805663791, 839960896, 9513547, 297283013, 152983459, 381478292, 76432903, 858221671, 32602590, 406437288, 10907060, 871856043, 175200867, 144043455, 751685465, 192731645, 679088491, 408669561, 948960437, 785817761, 963627885, 877851058, 25921262, 292901201, 253879568, 231627844, 996351061, 700227872, 946856783, 93511056, 729639315, 56614176, 540513372, 966263342, 63509005, 661670221, 939145418, 565307922, 542268121, 966345603, 730430646, 432583043, 361606213, 866459846, 330613101, 834564336, 956523265, 610725061, 518380003, 44040686, 624858216, 715687588, 216524015, 778271068, 128265375, 910407496, 697743941, 517887596, 264096339, 303728492, 467004489, 886148645, 357653651, 792546567, 859783826, 620868198, 651476923, 801938219, 945875408, 701766412, 780680858, 158789314, 696358909, 94249220, 777088202, 729696052, 92745067, 762859698, 818199426, 661553674, 381412040, 474841280, 907787859, 22896758, 60946088, 9193382, 338381821, 336724417, 564054806, 875454871, 982303901, 145465970, 319319756, 722507649, 910945849, 164394252, 671148145, 235122506, 592070844, 61632899, 358549158, 343501452, 898849011, 88176901, 491722284, 398383691, 566330712, 771041186, 753134234, 305354235, 997330462, 798760043, 143787028, 735607554, 149091551, 869019734, 74847497, 883845975, 416097545, 773666272, 762190465, 843720686, 179533806, 19927942, 548665087, 960030505, 954855509, 683063693, 765601025, 855959680, 385629372, 696675375, 365606659, 253509941, 497334258, 147042218, 927558487, 231542192, 375859406, 759039148, 742056576, 590531556, 941663919, 49821492, 947996919, 280182911, 824966441, 339634247, 238111812, 409454008, 970673716, 29223579, 126543054, 74923312, 94879799, 75399733, 419682722, 587720026, 631496040, 919360974, 699020378, 8646850, 967590743, 447444105, 333460841, 304576926, 549190890, 267769488, 845003353, 297873642, 612467324, 653023865, 477081131, 361004052, 397677548, 921903969, 4822890, 479379937, 923266646, 96159252, 920608406, 105229856, 777012070, 592821352, 793831881, 551479015, 602881406, 746935107, 687700815, 782545499, 55041966, 797608087, 275430523, 453921408, 341547464, 856490013, 744505137, 233343465, 188569025, 894901958, 798181383, 460691104, 505946541, 107952886, 237211459, 829843066, 181036343, 251332944, 91122694, 861919836, 399293916, 760677168, 670569546, 883880229, 665652805, 668607438, 695254414, 362273393, 196871993, 173063314, 831779170, 361325916, 301045160, 891465595, 646557078, 722318829, 115967882, 27005564, 39238627, 691000847, 673267289, 915779101, 219267031, 10579697, 246509991, 889437656, 537071612, 794098469, 202511652, 513328385, 612702093, 728010928, 310152754, 988859212, 86663844, 713107282, 190616399, 11847167, 775936107, 614532625, 112610341, 748837578, 792022702, 141454438, 876732429, 179933365, 171946225, 230176500, 3537217, 979544888, 304765919, 954204033, 83048516, 897967794, 726346002, 244832496, 332381654, 277449034, 938116053, 6079060, 526026039, 38330127, 239737505, 312540167, 997112680, 258509546, 744243512, 844297826, 284631216, 698563145, 428722194, 48787817, 692006989, 115677127, 801491500, 539379394, 699684427, 821142329, 856097725, 827838935, 484804805, 195576867, 662576086, 642361079, 342029152, 780309819, 436356792, 369253695, 712539166, 380279321, 10749549, 507530845, 641853163, 61685123, 678314597, 613435455, 683233672, 558724753, 45109555, 944295784, 813906771, 447732583, 13922273, 478741779, 177966881, 594470740, 519235395, 554504297, 378105913, 469294159, 633768106, 13188713, 955001634, 342897193, 578305268, 189183523, 691182337, 63801533, 958427549, 111452386, 881109421, 170322301, 452596308, 249638160, 571175779, 747318627, 552118170, 603290942, 854494324, 186736106, 296421319, 18773988, 374885373, 42388733, 606980028, 955405697, 857000079, 289142704, 783442876, 853838, 782225638, 36803647, 555008060, 695118, 708960600, 858570765, 690336320, 868457860, 810406620, 369329746, 671504809, 505122329, 818935457, 46726355, 796443097, 457807189, 48117062, 358780792, 481387257, 20186629, 109003096, 393045397, 289195684, 936402702, 703719826, 284574288, 965114364, 21571663, 794835726, 516855002, 387223161, 152438895, 195826594, 804852377, 391321705, 985064772, 628723540, 574091229, 501595354, 735599565, 62276101, 783116066, 560372002, 356644206, 555742351, 78084047, 7089856, 359108798, 424070275, 954949929, 676419268, 225970033, 27740358, 320244025, 431034808, 536661602, 170949787, 886189241, 681431663, 635028820, 850201094, 158944287, 446442836, 920800013, 661242280, 398784893, 995452827, 328953483, 433564437, 199089717, 782855699, 667742747, 100846611, 299962479, 999462397, 210643067, 412225733, 857166701, 861595369, 766669820, 127356160, 116739456, 391277931, 855000142, 937947453, 814596666, 759227979, 113376379, 398199115, 492505738, 761552175, 554949383, 93431042, 112356657, 217354061, 305115619, 130802419, 901841655, 134240823, 826725515, 748387087, 711864344, 512071150, 829869190, 900464926, 101791988, 527762546, 154058822, 561110464, 999866418, 526637698, 948756988, 261837791, 126143954, 854022596, 586093908, 896928632, 213456216, 984752965, 723391859, 631009785, 462269145, 155210889, 316375011, 170717890, 834794773, 657548826, 114210838, 522567032, 821753757, 614472752, 255732936, 245667694, 453530985, 713435377, 745683465, 686023232, 873293343, 706688881, 73923747, 61477458, 275322068, 242409117, 7184383, 936964442, 5566497, 960290608, 456675508, 680125788, 476249838, 600872707, 252725599, 916532874, 942489894, 221653993, 989826551, 660216675, 343227566, 249318331, 37485596, 235756800, 695167103, 768033071, 945109236, 13474229, 691583819, 346653, 718662510, 71723829, 295891800, 750630330, 188046608, 252157363, 787310999, 403181741, 195661785, 805320500, 643831910, 772896434, 548566929, 169234689, 984710518, 517991177, 268388789, 55531396, 857119637, 545094375, 788728655, 953782714, 868184255, 745958479, 30688244, 256342134, 839110040, 127202942, 767496379, 543208225, 562280477, 230522165, 487138159, 484549450, 479672261, 319034772, 982630351, 884057845, 698962798, 586972290, 523168957, 847495691, 943685291, 721804653, 38268014, 631398916, 881138153, 80837825, 471717670, 942704928, 394103874, 46101409, 355202870, 655134570, 978239138, 776718679, 601489410, 367053395, 2463498, 763051992, 930327562, 377107050, 648571514, 187439704, 625682621, 970724694, 647710139, 527109830, 753188429, 814576204, 737230181, 273348969, 28081013, 420550769, 415883484, 915786562, 837856628, 853165428, 9467985, 332621056, 821445482, 808811415, 424208220, 434216243, 588530236, 668370090, 798601390, 395052607, 111692680, 167998125, 115825963, 487023078, 15306711, 10083223, 409266475, 337338867, 295779946, 972924365, 6139307, 142439540, 46589670, 905593077, 181033874, 24170785, 775462394, 518711133, 771987488, 785306289, 155540068, 82429943, 361838481, 16929832, 955384103, 89130462, 666684592, 788085622, 562695205, 13455800, 882667683, 164509259, 398949590, 545233147, 817061593, 841497741, 689108276, 323713512, 667177410, 456526711, 464932914, 794404075, 935989775, 653521722, 584165780, 428445404, 48183781, 972073585, 902119401, 537009143, 97153395, 252809696, 148219103, 423520992, 730150248, 301710925, 422580913, 821980374, 295719992, 344877119, 939415691, 921228849, 534511114, 739197819, 655138833, 276412985, 214287146, 786074088, 461000351, 778473023, 65667611, 750854735, 707507423, 179649844, 725712497, 710035061, 903842230, 606942293, 412961395, 485885220, 236706690, 895620707, 934418103, 585378782, 758461346, 413189190, 868088772, 883796893, 898017437, 816903510, 171937561, 792126276, 6411261, 183856914, 230211101, 570884221, 479964379, 750741094, 86996968, 282496381, 645355914, 13836355, 162237355, 146007980, 888288300, 170889711, 337452920, 69117631, 434828387, 775622167, 314171584, 391926440, 801939709, 941156048, 97049145, 360704374, 21829596, 377180459, 547665455, 148682901, 197293781, 504926074, 16544026, 767284927, 432814314, 498626820, 351180397, 701488455, 79328062, 487377561, 969202320, 575345689, 611420545, 945119524, 357248897, 359723813, 180769559, 850654986, 50205321, 860541309, 783327310, 3150229, 608419889, 155158064, 415545553, 672755115, 989977999, 845325016, 148785444, 524619110, 383978417, 493466435, 690996974, 880347020, 204274606, 202421920, 621596233, 903985023, 144968442, 768723377, 285307262, 195293190, 814838479, 723105011, 8760351, 159816141, 449563393, 670953613, 707998217, 318202222, 612166919, 52879761, 672672148, 229523878, 565389859, 740104127, 330871404, 335155808, 125911128, 950490929, 169319560, 493012975, 73943768, 350443992, 773977210, 711348841, 252887594, 162913013, 38955502, 345124874, 662583050, 886377017, 440642903, 352375606, 67909116, 63302390, 854588112, 177552619, 52399112, 39258263, 36969867, 991866520, 178882758, 559605332, 507957989, 847777457, 764127340, 305074634, 988566506, 694576429, 198940437, 170040415, 140973450, 628203437, 833993050, 862966572, 38904322, 87941595, 509859633, 181964247, 394395660, 826301470, 559048243, 233615608, 383980618, 461452853, 781637594, 447011401, 25663216, 923284363, 982573743, 993621016, 172646913, 875199734, 210174344, 266764022, 905908706, 387500292, 935092383, 718636613, 315902940, 905652698, 129221806, 961855464, 621923712, 545431653, 632977750, 373972944, 129938413, 915582782, 237404952, 598799869, 527082092, 531777528, 315458416, 667519087, 56258683, 786095695, 175402898, 183518386, 144033394, 342251258, 122361506, 977896135, 154603335, 856802793, 784166875, 304522758, 437343855, 234100209, 498145698, 320129964, 874486064, 972175246, 613651857, 918646407, 22293455, 903432306, 152698054, 409903995, 599669218, 571317917, 955389669, 545842244, 828009428, 338630299, 384340936, 105951421, 909915978, 465565501, 527833644, 434253318, 690562018, 619311029, 416003916, 831260585, 82345883, 476504312, 474346497, 315573301, 288167166, 658512590, 580777676, 498024722, 732319339, 362755924, 150143113, 419307493, 637471258, 768161551, 700046236, 82858184, 405691664, 370260548, 149206491, 602428990, 108369967, 826649796, 338171831, 522795519, 159476897, 883867319, 469075027, 364734880, 45628978, 701799423, 938466315, 289265287, 503328625, 145910143, 422921547, 591350076, 60943624, 662656218, 23705335, 331125369, 790005349, 483714750, 942099748, 947736711, 433665676, 363701361, 562835333, 399308411, 960679581, 965998035, 453724879, 678017275, 754319261, 963321380, 594733431, 633884758, 900486982, 245446561, 429907292, 859254915, 450666610, 439528010, 497038306, 78956436, 641516358, 700311101, 778041500, 575314755, 83728458, 912073120, 882511598, 399619158, 674110591, 310018490, 271050618, 984764955, 307079789, 806861492, 52148440, 119688424, 845193671, 810836974, 56661839, 169584219, 446113696, 467190762, 518359168, 804783848, 594743090, 111580265, 60690458, 596369338, 908273170, 679919917, 669845057, 726373264, 162558874, 774827292, 479398217, 752690251, 366154764, 967152979, 751809745, 926964291, 87556830, 152051429, 365074750, 356827924, 756952862, 758100939, 449354063, 184787308, 280603296, 15402251, 603503719, 927705844, 436630204, 41364739, 921135924, 389700028, 486411222, 767443746, 288379199, 188771892, 135502142, 956401200, 93053223, 130554871, 795996158, 971345445, 503797311, 45614991, 814826883, 797115938, 582129254, 391068467, 720550246, 395509644, 784197862, 341868906, 838602051, 639543934, 953452046, 606060998, 723742774, 944506840, 457472343, 539588837, 514392373, 474384249, 849962277, 307815446, 225512816, 581597468, 843810890, 972423838, 362798415, 134007035, 663835502, 424077825, 625173111, 552247518, 756862430, 907002491, 215607928, 177079248, 126937423, 357427718, 687537991, 171395351, 188827320, 72103971, 791953695, 898236413, 258934856, 241086027, 187371244, 49112578, 693014771, 420116057, 274014435, 768166031, 2884043, 894764112, 908933010, 959270293, 753543923, 256698068, 109619340, 905510557, 908451206, 734579430, 372080984, 648174569, 681244676, 405445589, 750324238, 648100066, 728257093, 416990875, 97570887, 419529541, 731004153, 84035252, 359713637, 970407705, 298808193, 80815656, 508994712, 496328383, 704353116, 728393524, 310934726, 103780987, 702092749, 54510412, 732697455, 929502755, 236352501, 813727, 961016074, 428325459, 876469718, 939523726, 909751607, 806629819, 102572458, 975801376, 434949249, 672956274, 984215268, 606502266, 402296948, 136922416, 472078958, 103547423, 217072052, 153792700, 916942409, 695765372, 706679167, 671038351, 483079891, 982997894, 981349953, 370589992, 216570356, 180018039, 655226287, 298334191, 884817858, 435923067, 246149878, 129061591, 41738485, 270473613, 249221718, 875881538, 299554245, 783932314, 939589369, 607110881, 865809320, 452942593, 646914844, 548746443, 277092132, 378304945, 843729745, 258105214, 356481024, 670181914, 798284282, 852277152, 184019278, 452587003, 720849724, 673113179, 971089387, 721325153, 755612359, 688775805, 874255544, 36668336, 564540840, 372080959, 282402504, 339362297, 561168642, 648836747, 374008106, 698561469, 644030716, 330841123, 97775833, 102445334, 346203340, 123643448, 782418437, 972023693, 178240436, 891777367, 738896840, 280186013, 713072879, 7981678, 119343300, 202300128, 172908824, 107872000, 976398289, 925317351, 214738747, 696129175, 211321779, 508969733, 995886561, 745504571, 242434929, 208020183, 402674001, 888924269, 820424092, 205900613, 750956052, 216299747, 572373097, 359009712, 811006875, 923341893, 572725526, 144375838, 10953523, 464009116, 442034861, 854193079, 518587105, 144380261, 208639824, 733642439, 582692849, 484132733, 356351265, 199047840, 625249801, 550997068, 716204689, 28262911, 315425560, 15121777, 15753826, 158569994, 892703400, 437030201, 405034940, 535888845, 776191245, 517169405, 880561316, 490669250, 446520480, 629768543, 664067368, 150078843, 92957550, 655500558, 474372175, 936607400, 877384288, 465963482, 547448481, 949157903, 122099958, 380977616, 963616814, 867097000, 527353865, 547908913, 48386585, 314880881, 157181857, 34405193, 573333614, 869720256, 833904554, 874655183, 873387491, 303684016, 41864166, 623274370, 373635183, 619215921, 435507168, 837255493, 878069558, 307069218, 38084828, 497805470, 797007613, 358780781, 144871263, 412244755, 593082153, 509784998, 758630620, 646276776, 89493804, 275716698, 602254700, 310871976, 420035496, 227876793, 817695015, 43009984, 434101788, 513735588, 990769224, 45514248, 807388697, 980075580, 3844099, 533418185, 927131066, 262373426, 997295750, 277148091, 525589010, 257530717, 134286369, 474734118, 932603018, 488307553, 798047378, 232458519, 264458166, 861338978, 97719654, 656870458, 641179414, 491628413, 820537201, 83730292, 448060075, 117043616, 779030410, 571252131, 200841904, 707754636, 914707519, 689035653, 816956714, 519734967, 134732960, 835358972, 645462369, 26804992, 361971142, 683402876, 133661259, 526082683, 105899318, 514613733, 869796137, 777331123, 820922612, 108479138, 299552614, 616491665, 24240337, 264965356, 429496099, 21829430, 320254024, 472536527, 45308122, 215182756, 650485390, 140152641, 802968558, 262042553, 246859040, 228997591, 18173093, 445940166, 734307858, 769629849, 528289595, 230514282, 241925591, 296307055, 559868236, 75045937, 332991199, 358197730, 419883477, 873369167, 373249767, 943592882, 812183456, 909312342, 14284968, 40990993, 663697319, 477846358, 203404721, 260703267, 191924873, 548331598, 893621392, 333006538, 699984605, 719207026, 548855383, 449338032, 777243548, 78325372, 279128294, 208951677, 689976777, 796778175, 865994459, 350913516, 819643720, 339647150, 635680960, 934751542, 534244165, 967677893, 210706959, 302846864, 533046763, 136372293, 624644684, 233530866, 162421400, 728347361, 738533393, 570737807, 677535232, 941556449, 876805167, 970198628, 313609541, 801485353, 396083195, 118899803, 401420370, 921375606, 445014528, 729165196, 939769293, 642594879, 890419052, 313612937, 867929219, 133027283, 280801240, 690203255, 678861961, 577330370, 615083109, 247682654, 713694447, 528351024, 244760528, 509683494, 373882101, 850852164, 50385281, 714557576, 961046776, 653696562, 182899579, 101913565, 263347340, 280459686, 393593343, 912210478, 201555112, 413883771, 508827135, 872375763, 39092778, 398934729, 743813728, 461962396, 295286703, 185945101, 762395703, 430501155, 850268194, 405025877, 527736075, 182646255, 988077471, 355410596, 812167105, 479935056, 321184953, 320211668, 953264367, 263823748, 972608225, 355702974, 6676279, 870536223, 494416039, 339259366, 71872547, 179474323, 272758928, 362882840, 615645420, 575041185, 381406524, 876662073, 339044359, 685988985, 692188035, 535293164, 235834129, 587254488, 451729262, 197127539, 277892021, 505252422, 723127464, 275420770, 125602319, 248654272, 425758075, 858596982, 137260502, 289085239, 220828600, 639876836, 769218220, 139775607, 811345745, 318359733, 844818846, 901492056, 652263994, 53664195, 347553254, 726111030, 563562520, 741318293, 580928598, 202307715, 694079581, 142500452, 604294972, 977989323, 502187586, 393833172, 795516498, 410599918, 214232468, 229764665, 735296387, 863192762, 865114498, 427757001, 972135093, 803055333, 222477387, 666582038, 882510534, 436168166, 656223108, 42851176, 169003950, 32307139, 798927750, 720808600, 852944205, 251900116, 806943036, 433762140, 654073796, 319000219, 367890047, 154053391, 558111053, 345697833, 49470709, 972771768, 856223849, 128123959, 275713310, 229332971, 729340184, 886062245, 985342195, 735733968, 994333347, 652964392, 187598295, 625876882, 292592916, 519522857, 43161154, 216254280, 522141347, 632487262, 553543739, 771140216, 107812978, 121141404, 574318703, 940964906, 421015095, 454170477, 813943723, 947986860, 389426029, 760495887, 275437914, 235927284, 534002915, 951415570, 435727231, 492166519, 956548664, 451714450, 19161626, 569477624, 588078185, 262693017, 141808318, 646515519, 494889083, 802440424, 169615655, 479197426, 361900037, 129736035, 740544361, 632694782, 194483959, 682247894, 646165167, 669136999, 657722363, 418725197, 9866911, 641583596, 903818480, 506397107, 508755765, 453623957, 187861788, 104448038, 475169542, 892962795, 87698183, 788671474, 311440219, 73051358, 141320105, 939567509, 395561968, 229455527, 719922683, 628866748, 499936282, 19817955, 135819768, 416707430, 676778195, 306309258, 443205466, 388130199, 783155541, 240176355, 567566899, 476800936, 542202951, 998480483, 809295765, 21341056, 140683084, 89387362, 301432598, 227590334, 971547521, 858689830, 64597643, 825484267, 183319016, 331105058, 457341510, 742882563, 308880194, 547684772, 305092763, 571709094, 510898953, 186527155, 396879295, 129331407, 935914964, 435907104, 893768269, 627414445, 455443113, 395732875, 881999424, 162666255, 330211474, 242904394, 354469524, 635825395, 419515838, 672608100, 342583663, 921835358, 693580106, 585819737, 357607791, 883274410, 276148562, 473340383, 523965188, 534274566, 211786026, 486865506, 817584660, 467911240, 947343802, 388824588, 245007278, 3593735, 273273290, 482242339, 320886373, 169622517, 916899390, 63377439, 718215615, 245590714, 864917853, 940044767, 650246779, 402485027, 340784185, 467987741, 122954706, 939442977, 290806000, 124699969, 423467360, 440827858, 126393778, 766536402, 56656681, 260260715, 396764551, 59751580, 601437911, 655338375, 404290499, 612361174, 748160884, 250996091, 601577885, 354400417, 360703306, 327532751, 744536784, 429943686, 311109890, 592723004, 702323347, 257053352, 903158328, 700772766, 325963540, 223376591, 405775906, 281643180, 927490492, 26941145, 544240082, 447041655, 860376158, 267058612, 914779111, 367881406, 580427543, 217696964, 925708663, 332185198, 846639108, 172710103, 34847953, 9863899, 383273302, 521741288, 320857571, 601194025, 906330435, 599513950, 387850634, 915931117, 239603715, 566435678, 228379280, 513561503, 775995369, 148480362, 379074083, 279271406, 74548815, 113780397, 976175141, 864564598, 543641171, 772699052, 466420592, 678876140, 337900239, 292202953, 315919258, 272587890, 66957031, 11820130, 221583871, 463846204, 550210285, 146286505, 298051340, 871721718, 771413044, 436189625, 943139064, 971178700, 138095865, 194792560, 570321640, 810734510, 27912800, 956531013, 920395172, 943232904, 501173942, 106992954, 870958274, 18202301, 390698301, 203259843, 959358948, 63770974, 569401031, 276874501, 477870066, 254983448, 219740838, 889391733, 452318973, 237777294, 678973706, 664554221, 509048376, 235582899, 497618818, 676555789, 549072320, 440970502, 244129014, 988580982, 572171770, 856862645, 388484778, 9064553, 94321881, 625004250, 330927165, 886443784, 84953928, 701044637, 911331843, 735146976, 752043990, 854224255, 232485402, 495705774, 228841301, 208547161, 864960916, 202070534, 704289238, 841657150, 438459559, 27280730, 374902159, 309791206, 604001603, 857967338, 790282434, 669533439, 32843927, 514828267, 41120540, 635182344, 136250684, 645608396, 857189319, 406688675, 700399703, 437481550, 588287713, 40697758, 152997806, 448747744, 238628052, 832944508, 381413199, 326572200, 260996058, 909986519, 994723500, 216661810, 409289473, 230058557, 161551534, 84565282, 883205320, 653954263, 202840064, 301446555, 600584151, 967829958, 917667147, 58177207, 964083729, 38809747, 941463060, 681304878, 871042125, 639148318, 336898559, 124270593, 386498315, 828057932, 831738609, 655343578, 121218900, 811279765, 633257818, 575718631, 62328484, 407734664, 776283762, 572979250, 503202625, 833373795, 77958086, 589514266, 511487034, 176651884, 269598467, 399063682, 850315801, 968524154, 511024517, 919014391, 180664958, 866011890, 5438357, 489823348, 617106679, 826202504, 526434253, 60961311, 211730283, 747002417, 258075386, 57662208, 870393568, 505204243, 229460940, 339913330, 835789728, 846985781, 149434129, 435228750, 947959236, 893211308, 26982524, 890844421, 899061036, 371099965, 67173018, 114771829, 747824868, 38526726, 506183996, 733324140, 630330436, 196730349, 471280302, 302138107, 706222240, 776581531, 232234316, 910510217, 321772855, 497685182, 783227093, 953261815, 337743816, 95945249, 244690302, 733967520, 355142123, 534273080, 481884285, 594499806, 718116659, 402560538, 441597747, 900735442, 860751610, 392637039, 320425100, 270472470, 213066412, 706218877, 161624003, 198420098, 506621894, 10313340, 693610382, 164239465, 144891780, 689427616, 876808588, 721106066, 577418415, 992980272, 476418216, 555280156, 888901555, 301000599, 409598071, 538725843, 187428087, 517459686, 781567806, 225136244, 98445914, 725909306, 334564967, 906701871, 875410054, 670547914, 445688106, 396932639, 299431835, 485005497, 445834852, 658232037, 137819823, 189137322, 818981802, 852036553, 903207124, 172599217, 937357098, 783416703, 275482152, 847072014, 564749807, 586596657, 525749954, 553714083, 39911903, 698752190, 282356686, 98695666, 748854764, 855831321, 228752630, 219540001, 270170087, 425630830, 902593242, 878533470, 982001286, 192683687, 90909686, 80478594, 77050000, 819839369, 226486815, 781746481, 231142340, 508270979, 235195868, 680916293, 844725317, 280794001, 852536985, 725625400, 172485896, 17877987, 784994974, 368824237, 148356784, 830662553, 421028549, 864579123, 152907491, 445776674, 533898206, 855836244, 173535376, 906837133, 81635869, 248852576, 216584076, 480004700, 107228872, 24471507, 412082487, 403950587, 894200209, 879261549, 923997044, 96194452, 917155893, 185567554, 145864773, 923897616, 483010831, 661563216, 117890158, 497577107, 727360454, 92102893, 546092512, 84265521, 468562593, 244554541, 852620565, 585549312, 274595125, 562774977, 723342961, 308523358, 587594320, 422889356, 103224048, 913334958, 826794481, 6995003, 196872412, 323071295, 11301557, 39733010, 503238352, 85082309, 186156728, 171812378, 88968304, 907949566, 947835386, 19984994, 573839536, 871723004, 397298050, 487898942, 987973624, 838595286, 310385376, 677420847, 112088051, 422620129, 323328018, 897098543, 465009594, 349562502, 884158761, 557277231, 230988039, 713898038, 456363341, 430634876, 436168763, 692462864, 634641638, 151674721, 598810106, 321421770, 488729855, 356175142, 361481953, 914670460, 514388150, 551482402, 654205346, 437416688, 457857290, 231875288, 788367346, 441928447, 504753374, 334672970, 212414370, 393015991, 835633397, 948351739, 846975685, 313296808, 785520368, 432680723, 362668099, 284872011, 931627660, 730924629, 146822842, 200031423, 868609969, 618803433, 628514456, 907865388, 765479605, 927015522, 726240156, 193153918, 158283120, 558917801, 578123098, 381965163, 770615388, 789140953, 801656619, 83327623, 964876222, 867952867, 998791270, 243899404, 49488003, 812780142, 146447766, 633129539, 260184755, 316192588, 201177115, 319883871, 660466919, 403683095, 756958091, 100380796, 857560415, 257376458, 250697979, 154854555, 136086642, 753731296, 918347600, 967583301, 891140786, 403338293, 12967490, 248639904, 517589641, 357179621, 348322650, 503877419, 587602469, 451611339, 360330008, 546461818, 715959449, 700031041, 868140728, 368229518, 861125317, 802320955, 417174526, 404196314, 56289570, 110076178, 989617085, 144648817, 191918623, 173233354, 254879912, 852211190, 318537576, 354981934, 389073215, 908557447, 759372762, 147839218, 552580751, 510723760, 24459439, 847703968, 265703820, 140334617, 524067229, 297098387, 277898799, 461558766, 479703442, 718685835, 379184353, 383609276, 551270319, 667839674, 872762754, 604477043, 326100712, 885700218, 553766035, 80893266, 813772759, 177296314, 185584372, 619445225, 784570171, 965826303, 529893346, 792414934, 687395973, 646897544, 77292924, 447056191, 725312539, 608041591, 507896036, 329808370, 289800455, 313245959, 863702992, 647817719, 743067392, 99545875, 9630072, 462601462, 460989779, 463919133, 961742170, 281112256, 650479317, 43748710, 704496475, 371840347, 449816925, 227664953, 712115737, 955483094, 695869785, 641613636, 537578932, 887207091, 673619730, 463975185, 292784480, 528338363, 596315953, 1513927, 290770093, 904096607, 807286885, 129917446, 798967527, 858365596, 766330222, 233614607, 790854327, 788149632, 199142152, 909374675, 591920599, 27091333, 180663263, 926257797, 277839729, 846877208, 983636009, 268056028, 193404420, 937519766, 729871576, 288678364, 783623566, 131766074, 528289378, 423562606, 959813683, 209128587, 840580850, 399044186, 262512687, 590069673, 299174815, 662906130, 941606266, 128612807, 257763219, 987984906, 7717034, 351230513, 407668893, 479550644, 420189696, 105807421, 573422800, 694148709, 506377558, 278294665, 884083252, 353019618, 991823705, 403900720, 607465232, 887477052, 879851648, 302486267, 875373052, 595023856, 421056914, 456411157, 804822590, 574382122, 750215923, 429862960, 897609468, 579190897, 555548198, 105352771, 272236706, 893474582, 904627534, 714631654, 461268100, 971301067, 444370878, 2453399, 702921133, 170679821, 85671969, 950991037, 8024493, 406875397, 758497871, 400447578, 111990374, 997079253, 536338892, 399919493, 149299524, 841091481, 10670119, 813298770, 980948384, 666920038, 683760745, 975895883, 649182492, 595494035, 613260720, 423103834, 148836325, 771646787, 690257599, 558349269, 606472578, 971891922, 218227474, 29660399, 974057942, 263074712, 900200449, 258798545, 819066252, 39646476, 15434588, 584103531, 753586686, 332214484, 388736663, 447774750, 452836191, 234937306, 374690053, 960936102, 433958735, 106070766, 671301220, 511799260, 240378700, 751986533, 882814659, 325505011, 599183185, 888768984, 63330746, 926320437, 250350806, 919709593, 839814870, 115201566, 352532102, 90253276, 715314404, 931075200, 784982474, 203351360, 638431742, 223393680, 48849982, 66313252, 897342746, 192392821, 22882666, 410729095, 19053421, 705109351, 492342097, 889662547, 784641202, 499245627, 108531054, 418464815, 670508021, 741426598, 393253787, 583892028, 576471263, 307163213, 976116635, 461366790, 628975967, 659983787, 485876108, 70878678, 330150027, 247979874, 175200239, 859040541, 431796668, 439431194, 409230339, 872388024, 271336593, 242189198, 647039780, 28120588, 708838466, 374718314, 991981837, 288824232, 914251697, 171252369, 735853910, 91890077, 855535206, 589094908, 939710399, 441882960, 114750768, 116490448, 769471911, 116553650, 825851092, 642772908, 185880608, 686232071, 33348223, 178692572, 645836488, 647827000, 153253493, 812949692, 549405909, 293052912, 938320919, 62925104, 839704653, 561180887, 94097977, 283612691, 261378786, 903856425, 66209165, 624896547, 871437886, 299742683, 999170514, 570087544, 225692992, 898772627, 30033327, 677044815, 635874806, 157083126, 69905300, 630081088, 833428233, 614460323, 103356592, 315856950, 895548004, 808374815, 793783087, 630624899, 319393575, 706296518, 297667357, 566161564, 494370688, 264285775, 725694644, 572486031, 121307978, 745497508, 38476099, 400722115, 159123055, 156697185, 312461566, 466627200, 581021545, 635345136, 119502819, 679869874, 894453203, 838720785, 357959576, 777404722, 72790189, 405768149, 575151826, 860375491, 636258546, 977497765, 912263137, 859238813, 245704829, 173114109, 840111861, 374345413, 92201888, 106351100, 79723068, 73680276, 149149607, 26950658, 567322829, 531972716, 701288454, 490616618, 28977681, 389394389, 628410060, 479330884, 117429251, 452417264, 334259359, 593983224, 317716922, 974096054, 309555846, 693100219, 702786590, 255418958, 989073402, 581057567, 458599086, 326720495, 468553574, 644610495, 808134365, 655162314, 305342144, 23803773, 410256168, 962490357, 603239477, 741448542, 562164145, 919911210, 114943041, 23908883, 722194755, 306591468, 951834050, 337725029, 800362745, 461893895, 180201286, 862264957, 672416767, 722488148, 22132305, 775265249, 65748626, 571288704, 638273860, 757450454, 861253972, 328475327, 510301266, 66023294, 903186202, 27539175, 722320877, 486937991, 661638674, 807282094, 664716949, 96063027, 763520014, 69133973, 94737573, 71422078, 229108964, 210750687, 860622074, 367021103, 593770302, 278978509, 760715696, 990197581, 445866822, 648709011, 590474729, 816015016, 450448728, 844684187, 885781940, 220427193, 877342396, 155717882, 74670392, 521867524, 729695820, 51462255, 311240868, 183653376, 924730816, 145529564, 13838762, 702862631, 474948067, 978429811, 977340441, 64105305, 989854586, 718589512, 341019787, 545284174, 359479466, 837075281, 643006928, 299117048, 55798268, 302759560, 449195066, 395677717, 357223028, 733598611, 654194901, 82154701, 484499623, 774568370, 799129916, 283816012, 831035366, 989031808, 964994245, 307584307, 413953959, 695699410, 894670423, 562716187, 396134672, 441220678, 308967081, 837515240, 679775669, 487096568, 815958106, 945970192, 374766345, 530727969, 830344519, 851985610, 612231742, 673064723, 157191008, 814954903, 360085392, 352304742, 620470310, 553225609, 344014038, 701495015, 521428991, 277075022, 266988016, 304226255, 244240160, 679293423, 130867407, 249792445, 364426672, 887800241, 640846910, 168373295, 213266300, 844558549, 818618624, 395240243, 251590826, 673082961, 135510283, 331367899, 57199627, 115690807, 683448459, 964232948, 385983804, 124936536, 164176227, 802649010, 433080170, 681968154, 81959581, 735439712, 964503781, 814809536, 547799753, 479622895, 662172437, 474976938, 211427941, 315441291, 872282903, 768744477, 713548253, 747744010, 175434515, 944904623, 608543829, 338189916, 674152328, 546905933, 93492294, 440029371, 454745664, 582579485, 412369758, 218076324, 839702279, 715246837, 797202914, 970598446, 868937127, 810364328, 3517179, 211589262, 267569924, 451947455, 990284321, 196730902, 6432028, 842694386, 202497953, 248066634, 303653307, 957790985, 52720942, 3893993, 587182832, 521003306, 295046013, 819164902, 155456224, 45740701, 889936795, 538196337, 592286121, 947597338, 465390036, 205620622, 637002653, 305570296, 686811168, 641489918, 175997401, 860205383, 647651937, 693774727, 487734075, 479864887, 544813077, 382726012, 679078672, 882597666, 453910490, 878623955, 819723426, 465002283, 656884422, 272641981, 885708042, 43892487, 748595096, 260399089, 467201215, 269166713, 477345229, 545547454, 906733342, 432209125, 946389705, 778478893, 675195635, 554676030, 93498268, 717478674, 197153598, 730056832, 561910661, 688287354, 42027042, 816451985, 453531052, 530761465, 736816853, 746327615, 711070927, 975914165, 513037831, 757833356, 699939836, 548755647, 189566564, 117806237, 772034758, 840811586, 71073194, 970191408, 744915721, 86623455, 130129812, 458557014, 6965747, 765601884, 672779051, 173157199, 805986911, 968903033, 28853421, 42141017, 337669776, 229879625, 564147086, 13953730, 548741856, 899654924, 150077849, 2151754, 326967135, 181741778, 902051714, 218064017, 73164250, 459690245, 648372699, 242798244, 720500352, 395686589, 64624428, 423004405, 87281213, 214357666, 964735589, 123308741, 993813679, 236936203, 88521690, 913845876, 477580819, 302183242, 349062730, 842732171, 687523313, 665919007, 109774503, 815997623, 851774819, 719663858, 808188457, 853393615, 624247580, 478233224, 32911222, 210564755, 434724031, 682715722, 476248943, 399833193, 409960147, 474892465, 380868761, 917858409, 695067127, 213808317, 695386973, 450252935, 692903934, 286758696, 637165923, 672384492, 977416000, 119466875, 836212203, 858431188, 396575987, 99954210, 632745444, 86871805, 208022656, 1050917, 225041313, 78533742, 41099982, 958103546, 887917508, 271800311, 345765919, 625703141, 938817041, 159464416, 950600737, 459165928, 511242364, 490274974, 689060757, 14435915, 374239342, 829461387, 189277317, 478339411, 60735284, 143989223, 729134500, 162424842, 158591667, 284206811, 636855554, 962384211, 41278702, 840614067, 187864236, 582487927, 168477003, 390834179, 451164965, 217252667, 220562723, 398835742, 81653006, 325319249, 709641465, 440012067, 282298070, 17430563, 522991856, 54766938, 353834724, 105311039, 182804623, 743654060, 234030887, 999942175, 891841599, 303469358, 972611096, 358692038, 698766577, 460809334, 930054599, 316532289, 151767469, 188425076, 710384082, 141878018, 170742163, 670854964, 775561923, 597643352, 631014807, 241383981, 791992528, 832558394, 409968294, 594097241, 222971271, 42000156, 773193367, 737310705, 678928002, 120458191, 44845375, 129765702, 129773124, 722329043, 543205877, 803154309, 110949854, 77477662, 691443895, 886946134, 193170616, 617699482, 766004257, 501074918, 309839425, 681265890, 802587241, 467113009, 877983353, 703286660, 743742749, 527995678, 67679777, 538520249, 188822877, 682118111, 242032854, 891668767, 446243251, 923793618, 12618249, 124641490, 111932310, 146337121, 896246441, 461639409, 634089181, 823183752, 64186538, 539065907, 774004410, 721089516, 343787655, 263299508, 317161991, 729562116, 131391847, 479152891, 348152322, 674461589, 893159262, 649881723, 736597750, 131972028, 970403065, 245506684, 532978726, 255996266, 2258190, 247881177, 631426897, 500928664, 348789800, 493702136, 392014049, 927262867, 793529908, 88834735, 738174084, 119769591, 119261226, 286916427, 164849851, 952322249, 59157671, 225031883, 186980670, 616729664, 207384839, 530800661, 734188383, 383988582, 488514399, 687446250, 296699615, 629869470, 618035036, 179370601, 981505925, 631327773, 212130929, 485181430, 771703503, 663402014, 361460521, 678420503, 870342270, 841929883, 355241650, 928651878, 679542770, 563414758, 886845167, 267842416, 592557536, 178028342, 740586085, 779382382, 235770581, 143353578, 630733267, 216569018, 903301334, 882570759, 992778680, 17431971, 178313856, 746087470, 213182783, 216120829, 2740333, 862424008, 388900974, 659552905, 356741246, 354232825, 616531396, 739329433, 141602165, 206156343, 446441838, 372025469, 312360805, 446654580, 880776833, 636326558, 369634929, 926761717, 706098441, 912965949, 261487323, 523696599, 773648082, 503247188, 628703264, 96321093, 899092898, 595428004, 634061052, 516426515, 604211826, 675558003, 296018321, 465817786, 939365776, 226089611, 46989416, 297725321, 456231627, 693574606, 240424085, 714052458, 527234610, 9940687, 678933005, 330419267, 739113910, 877060245, 567120332, 576404246, 476441360, 322159232, 250440378, 683379443, 264502756, 903231434, 855703902, 637549003, 933762886, 533573505, 173478736, 714240507, 484270296, 457486027, 65660294, 283764230, 45369709, 554833397, 316197128, 602424775, 372321698, 690250051, 504513720, 191920049, 403793753, 581266895, 145908241, 615931479, 727243397, 48535981, 854100239, 570485630, 531919418, 705752462, 994208796, 717394259, 477260435, 757433318, 93938294, 391710732, 736404602, 596158999, 206674674, 473639928, 201194390, 835538325, 933195124, 760652750, 55986467, 844634944, 185092770, 152675873, 999218632, 950078135, 96110950, 218374965, 742925364, 550473905, 956771505, 341305203, 162513437, 843118850, 398721246, 184088192, 581263542, 798815963, 554495623, 111265071, 141310527, 247786119, 183189669, 713304934, 459778826, 634466737, 909915989, 762470219, 972709208, 670184092, 8251319, 407470592, 224335618, 418073924, 176493960, 685868607, 440764582, 117838439, 468864024, 778062095, 502256806, 308795901, 686125650, 160265226, 840634741, 650323213, 282140180, 583760057, 565937530, 982893312, 593360414, 457777593, 563382868, 561267458, 500975563, 962535786, 607449369, 128104400, 757093682, 740665685, 770478595, 687534624, 652955150, 313511788, 986749928, 116345793, 421444397, 272111084, 62393688, 900225684, 992873235, 946007253, 388008967, 112471016, 715048227, 862910454, 188057795, 668062892, 403760778, 282828417, 466099119, 219951662, 756576761, 698626290, 750793915, 760306239, 103364004, 553884118, 983412672, 920454665, 680602951, 426453806, 13592689, 202707836, 898311579, 138796378, 885305217, 789733913, 386487480, 53799595, 479124297, 714451296, 492139809, 568408690, 349420936, 613408096, 509202226, 107878735, 620633122, 779631918, 934317346, 550125556, 513617840, 728298799, 761020744, 306830415, 590042463, 201404271, 391619969, 791753961, 837587637, 391609011, 282401026, 892378900, 375134920, 241578700, 638761901, 551914676, 698769997, 771657984, 191839004, 271975233, 633992173, 614111743, 224663765, 681836745, 428512424, 872415848, 703870826, 565333920, 462998232, 414123050, 513268152, 873556730, 389830088, 453800650, 157973847, 575906656, 302151501, 193641440, 79635880, 952124102, 990774427, 850060512, 812070181, 540807495, 284377290, 99092071, 449060949, 393196689, 28254017, 32827665, 120163348, 779114036, 966993877, 82779512, 653770056, 489288819, 44528549, 166735625, 97372596, 55753877, 401607507, 214080433, 457311780, 218338399, 497308169, 138911239, 300483846, 936450629, 385400716, 876541467, 863776997, 774935572, 483340594, 672212591, 740010264, 498138084, 652675869, 803552864, 407849012, 190222544, 187249613, 706275691, 200884314, 568373871, 326146846, 993358566, 522324451, 914853603, 448491307, 15787987, 213506205, 497390426, 140035450, 847838998, 522589011, 344469825, 277488786, 493667918, 604844225, 91625222, 546791959, 213622425, 229952834, 279511550, 76695066, 154444539, 776987441, 571018476, 56986045, 582969311, 732884111, 78560615, 343703562, 914676921, 917106840, 55997923, 934028363, 560969166, 106416352, 477568757, 330656983, 21639621, 628276019, 294188721, 497976133, 695874255, 864187904, 882767047, 660798693, 664100685, 768783182, 567012244, 189164637, 712371915, 855399980, 905852719, 20773467, 952851796, 293736250, 880454123, 766137223, 372892764, 640771944, 153872284, 272158359, 398773194, 955456068, 345277094, 414683, 516373117, 891669381, 565663225, 513894248, 427056010, 787611222, 849288144, 469881907, 113808340, 497199398, 8747024, 662601748, 913027739, 298105831, 37956021, 552088770, 154778313, 469696203, 24602245, 819695460, 640366590, 869658869, 347452578, 425893488, 51124210, 712028213, 321706777, 218251221, 571028118, 222918477, 405034927, 936918999, 548081313, 393700958, 252876426, 539516253, 381625344, 957150155, 677467159, 623236094, 462910365, 556071596, 762748425, 784966158, 867527141, 771575771, 251646127, 52938762, 985799653, 273440405, 162545964, 927996769, 648321153, 195259981, 410239306, 636121483, 265503074, 615898193, 79460382, 591310526, 386583677, 251578554, 777696093, 949200563, 733318111, 843836967, 86212540, 294328955, 681217853, 447467551, 26344961, 551972240, 873420355, 161080779, 106160414, 438624795, 31020, 868238263, 23610230, 17326451, 49783737, 676236520, 437187515, 39224321, 573699360, 859860223, 449862528, 42229802, 423178750, 719086520, 394055568, 934489632, 400627915, 977515945, 40075674, 999213925, 392886603, 897529367, 752779147, 108083957, 808550820, 852979609, 149505761, 384394807, 636625257, 611617564, 172192977, 952639212, 990746978, 407091210, 829939805, 602655520, 326577856, 776067089, 343084856, 830630471, 395983225, 29132678, 193890419, 417650012, 553481229, 532254282, 234400625, 20051655, 912305476, 572283259, 388431160, 708274313, 533804073, 824531148, 908779280, 292789934, 550103628, 453165753, 740871773, 986338991, 151299399, 339710591, 970908618, 987871371, 234601173, 811550557, 598795810, 514017210, 118882850, 439581240, 14230541, 682328286, 812753220, 856250844, 199100607, 350897642, 373572365, 111184898, 220728898, 372043460, 562252354, 416146752, 631934534, 550073159, 476544414, 930566159, 801056234, 470728974, 849623978, 136656001, 819865295, 496247312, 305134132, 812518122, 211408989, 564740098, 589683530, 528783838, 996071240, 371700775, 193672063, 615815070, 646223029, 912732395, 105938706, 401809768, 160606012, 728277466, 283020906, 677788099, 321909073, 48474514, 291822345, 585627957, 380185316, 956643137, 173755560, 579917560, 216236404, 532311530, 232246281, 917224027, 472422051, 501703007, 95222027, 197370639, 737070399, 594036327, 731390546, 937511045, 990968194, 588813738, 877000229, 680405877, 704639992, 185931167, 276194742, 785388721, 662686402, 828670453, 404049329, 11977609, 865528450, 508877822, 156613083, 217144678, 541616496, 525016422, 253921103, 599833304, 335588821, 226085733, 360870691, 722648970, 684544458, 616324310, 905591707, 12157807, 105674685, 700998468, 592211480, 48916744, 630211064, 151408130, 278637442, 483443848, 537872894, 862596461, 908617004, 14624500, 668262332, 490185581, 677344145, 105566334, 602278682, 697961910, 221876455, 662886568, 208692221, 805335122, 868115842, 567347659, 275766098, 758505006, 5997966, 928741570, 974974069, 88940993, 596943103, 576199524, 461535592, 618688141, 436903278, 93002304, 364501815, 609124488, 922036465, 619704619, 969707307, 376297536, 404128909, 800181174, 185493502, 935827182, 207821868, 195007224, 108313960, 228296640, 986614785, 631823715, 927800106, 630895310, 267781028, 573563359, 503796609, 44110522, 501749556, 621620454, 163888891, 25093766, 790166626, 972756906, 232167149, 342711147, 169670169, 782983817, 313849849, 674325863, 572441165, 498284442, 951977266, 350086868, 252516853, 371399035, 537592584, 669561994, 717686713, 98440091, 39407001, 668425693, 212394590, 272389242, 160587206, 432389121, 963736324, 520904558, 659736975, 333012047, 354730421, 892867217, 957667397, 21846982, 672849604, 566783190, 932304210, 651664001, 789935722, 413642498, 605610148, 429308196, 449190136, 266098145, 272826080, 697279587, 853692273, 375706746, 823910780, 397758992, 278717407, 283501363, 60028014, 582464807, 859139530, 855875070, 551394573, 499136387, 605761443, 862298622, 706039399, 993922356, 943355829, 717225629, 173137924, 550770066, 76405522, 431286624, 949323637, 20094103, 269203381, 762234194, 872391276, 891625725, 305051029, 99339845, 199918836, 514941040, 738778069, 73866849, 132130031, 361102668, 384092664, 268034353, 266688381, 848021855, 268030364, 728711250, 626994199, 698670259, 921143555, 205208809, 349815293, 669630014, 898979669, 659145787, 204052976, 721171029, 630661049, 460882862, 675380646, 81813925, 254367558, 869482131, 222742650, 608270378, 557010500, 804834618, 512115915, 900484275, 842908507, 322038302, 428830244, 580050626, 40499094, 795172239, 196857452, 208127153, 816102258, 475533441, 67490156, 703098222, 576461191, 255155475, 483746357, 200948754, 721637985, 776267653, 461844930, 910268308, 471512097, 894146489, 796363278, 728324863, 800550420, 325114872, 766266508, 253446531, 70220085, 515595221, 859348602, 92845383, 146357482, 273185793, 183941337, 644223617, 73642477, 221928662, 601067071, 233566866, 736973136, 823083323, 757690818, 641492385, 19644142, 402737027, 371925700, 16960362, 2864913, 704735563, 67233266, 348444967, 797846179, 425048507, 249487941, 205059328, 690083233, 517809865, 396869814, 892740401, 205778799, 557301263, 981733481, 315375833, 621872315, 457910519, 733945849, 134868929, 136755811, 492680203, 806863963, 2108099, 956824377, 271192393, 676751107, 202239039, 205328093, 142710352, 673667956, 274570467, 555814548, 705639649, 639761705, 425595330, 125332233, 139198822, 414211224, 164976291, 119731315, 318264856, 757399240, 711695714, 160031582, 261267535, 483318298, 81604218, 77604721, 545027410, 219903383, 506451482, 930906328, 542440873, 999828942, 464933892, 414614014, 994971350, 130427323, 994210260, 659373644, 697552274, 641158546, 276871921, 851892065, 457932821, 161128500, 160990250, 319148632, 257720842, 546468425, 336362380, 405421583, 217601981, 548028697, 205477466, 63012225, 410530112, 815322560, 355469965, 732465042, 753328495, 68489938, 157999917, 55358454, 927841232, 331347016, 603148478, 113966722, 680957152, 292143365, 705993946, 529173709, 364476838, 129178267, 512492317, 171522886, 518700365, 239740940, 720289899, 288970235, 171309822, 886477695, 949119119, 838928732, 93632437, 331754163, 53316279, 644648131, 35808992, 45035222, 821714728, 641840286, 748048822, 439070272, 452363922, 939537200, 133932658, 167974147, 727361076, 715571257, 340791359, 794371735, 940249445, 475580829, 251596683, 473742725, 170409701, 365604705, 537174931, 434190781, 534312077, 417437393, 132632641, 58389895, 175654891, 602317520, 567801905, 743031363, 376852926, 906233544, 265378670, 654078843, 172661702, 787443590, 679683627, 833651040, 191499110, 254224198, 538221717, 919603037, 402246447, 625245480, 472971660, 192754498, 464921041, 459501376, 369118655, 565669850, 897803628, 260171988, 46592150, 702146136, 748246168, 218318040, 639937460, 756363287, 922345417, 514535596, 361889928, 492192478, 418456602, 792600073, 779175099, 206815761, 8407492, 503007137, 32071149, 618300682, 459298566, 406798167, 561827785, 591789030, 297704423, 825787317, 91893696, 883239966, 719297929, 683468988, 637145773, 973410603, 389829848, 203303525, 146617660, 216260577, 553269889, 934845246, 650112745, 551931100, 827160035, 513821076, 647049287, 881043595, 732848601, 153118979, 159568052, 340550252, 404928810, 854791930, 567820763, 171390422, 108564283, 477331421, 751895024, 333472336, 853481839, 635277514, 888186613, 566022666, 388351909, 303733016, 858409374, 401494608, 500356302, 756171664, 846048579, 842355871, 351237357, 225445008, 183794584, 757736869, 656049325, 668163891, 775096945, 116590472, 774274341, 845988326, 883691202, 590649108, 559635801, 363760765, 886690081, 319022326, 209560533, 364081121, 435875615, 434063558, 151082134, 699950238, 671194042, 123303231, 734411558, 685190785, 314965990, 512182302, 495777241, 941744783, 723013412, 353594678, 318099613, 116002777, 328138178, 246170211, 72311734, 830538576, 112417362, 640388083, 78218792, 679756230, 846601136, 332788975, 185551832, 41576359, 165729316, 882809330, 499275243, 471699646, 979054823, 602739498, 140667876, 972770523, 570946538, 148573680, 485185801, 937349259, 607272692, 38649681, 825970698, 208196125, 652476631, 138503717, 61605823, 303036549, 986545086, 501764111, 476799108, 487604744, 871226136, 589677854, 787362563, 283170734, 150962940, 109885314, 668396674, 334224505, 723617188, 72136219, 700496921, 278127033, 879889829, 280171640, 848666484, 293874131, 435465954, 422462837, 617411095, 58206701, 166810850, 306832004, 718198670, 750272038, 943630710, 102789418, 859892987, 185875569, 73190368, 590630834, 790331402, 266481368, 660217762, 192124713, 3915099, 726695568, 119445742, 506192683, 917342171, 891581645, 593318930, 24841027, 819857704, 705026211, 876045723, 155937375, 895753998, 810181795, 888739243, 208647758, 496478466, 870862045, 548487820, 677935121, 31866671, 135280859, 263124871, 171470799, 939627629, 169931974, 622501238, 865544640, 749382759, 717501605, 510705229, 423109529, 20378592, 713640917, 38637053, 271901479, 277645290, 318357016, 697044684, 508870403, 602581498, 567226295, 362207520, 573373736, 45982671, 836074161, 327019916, 464508963, 519137526, 588247370, 285386510, 285560040, 944258687, 390754309, 335225828, 630885555, 276474381, 831689611, 851636315, 402306453, 413374869, 939610210, 254305895, 355887365, 159570579, 448253114, 638467942, 679721915, 556260773, 717890841, 515211762, 639906754, 590213207, 205179934, 599550334, 757465349, 222959684, 242399564, 78803722, 214639511, 466551690, 162982412, 98700993, 868516788, 851776845, 547542991, 905406760, 812414634, 7647048, 270617614, 833331999, 26713907, 899267700, 563077631, 968260733, 50160676, 84074357, 777637414, 850410753, 511678982, 434385826, 640167342, 11094437, 122712183, 161132046, 281076352, 136358957, 884733292, 504782462, 168250536, 752375334, 654669793, 36931464, 381816793, 912035488, 681255552, 796275674, 165528508, 321662995, 717392467, 839242774, 959069378, 219279716, 319651010, 445481634, 742851683, 846121566, 391281066, 299736478, 40632086, 747825399, 602570748, 744724880, 710246742, 489881234, 434438957, 323575222, 487477379, 654330845, 301231435, 117978031, 972677285, 712115625, 649686033, 169782389, 492554944, 427790413, 119734322, 311245999, 316147375, 439262127, 681050206, 898371940, 190581270, 686925651, 568262101, 167089501, 612501328, 35353699, 288611975, 817372390, 15606865, 89212304, 318080135, 341901296, 709849262, 639064381, 980839449, 708796061, 844751723, 377954950, 541734109, 715706323, 363791761, 714948967, 520167078, 972102424, 194378575, 32982527, 507373517, 493149513, 441720277, 142754254, 181296524, 882660333, 407041521, 883222598, 820844263, 71613897, 763379837, 196275008, 949377560, 657511014, 69532662, 668673347, 229555203, 929091323, 390826011, 402223734, 384366607, 57245574, 366426807, 49982869, 739391644, 285116994, 182146694, 86170779, 265773625, 471562120, 803126870, 464718633, 107100655, 331280174, 660070024, 12340602, 319978973, 346767372, 111429764, 522406685, 11606150, 154138043, 686879211, 692024523, 894138742, 841188291, 372487034, 8027211, 281001570, 703832696, 304026250, 602980400, 492723759, 882688465, 832698946, 196504352, 437231498, 851846378, 909452963, 610714137, 865533150, 304970032, 34530722, 148034377, 730721447, 611232668, 823915570, 624522477, 773086020, 802033480, 380671073, 532917853, 105331651, 839866957, 767312039, 382529707, 55104859, 217168194, 949047659, 421160468, 613632282, 660178604, 669310837, 155023869, 929702922, 557070055, 451291103, 425161420, 712143538, 496467255, 452490057, 697486333, 221805269, 493094609, 361245381, 855029784, 264268188, 670598412, 618053550, 817670764, 189689969, 605950945, 804444858, 326497818, 492680362, 409871511, 226561881, 488961160, 226954842, 861515063, 266449564, 969667310, 236559295, 10803013, 31874322, 712310698, 59469555, 327046428, 596729074, 812293742, 502170252, 500649556, 112399840, 630037640, 271950021, 902574549, 959477505, 444911879, 327563819, 420398543, 706514717, 799429048, 949331636, 871409226, 111461357, 147416207, 81095973, 638485177, 603560253, 26571582, 721170748, 901518577, 53391173, 385779624, 759863979, 411225300, 693165, 332322498, 301789088, 948893386, 41643141, 90321601, 648295523, 103075825, 89390544, 976210320, 855384759, 97798787, 457926342, 224586211, 987860338, 644173332, 394878068, 335552788, 1137359, 493443722, 748461502, 624868736, 21597593, 623432100, 172913341, 491615259, 789458276, 41222173, 107087508, 572620729, 291555856, 358980763, 573772510, 150232612, 733536039, 847973708, 86283103, 611613861, 401084213, 234656240, 747640150, 434095597, 88541558, 995298717, 139505642, 823086897, 234022952, 236270882, 795633703, 768333960, 511023575, 493908637, 760559073, 450518864, 763020947, 162612378, 660789003, 229300051, 323805314, 184286289, 393967069, 652135769, 698309796, 367916211, 965617637, 841226161, 58044619, 470314796, 785816082, 944378444, 765083409, 321293458, 451023068, 738053309, 218550837, 842972018, 774273357, 182751817, 630481100, 519789261, 767570426, 311689266, 183546250, 233549480, 670164294, 994470401, 965165379, 178315011, 431301238, 864802806, 74233628, 595729078, 390095047, 586059707, 409873799, 677039473, 161111596, 294159395, 398781515, 350278809, 74825384, 331105655, 27626812, 533912381, 659421231, 926771080, 477647687, 510586561, 862392164, 257844611, 329379489, 38342866, 908354782, 571702228, 669955680, 582961626, 524653839, 850586105, 725964889, 998164116, 514809368, 550884607, 796737354, 588532240, 199788790, 422977529, 325322032, 232342995, 961327716, 768308290, 197781455, 215688101, 113342349, 653015005, 344537778, 977964820, 386568753, 958131138, 133367793, 368370555, 384633582, 811820166, 628350149, 241225470, 6678588, 427934498, 980065805, 992700178, 792271503, 324134175, 601112746, 186665884, 161234106, 904479359, 462056106, 834975011, 51060313, 347645875, 83175455, 841272539, 393715549, 60208135, 817452288, 262439174, 120126068, 888954818, 838218142, 38910108, 318965166, 71386850, 196944643, 997776963, 696703238, 746716210, 821540665, 7936061, 248184835, 596125329, 334005477, 241964102, 113700496, 301266920, 532784754, 340055767, 601555600, 406062133, 845527361, 970183519, 825242918, 236751454, 1775445, 899379417, 96888230, 724010075, 587219784, 820299267, 817200057, 496476853, 825637758, 737691095, 242828346, 21274751, 641808422, 852982971, 285065780, 717741903, 775499101, 840112270, 806608268, 612671447, 341006447, 512778714, 358840834, 858132518, 227656471, 549810135, 632161579, 449863318, 267455266, 386856211, 862806813, 923550600, 623807564, 631400129, 227105086, 527839995, 160491364, 790998270, 802953126, 546455320, 771351601, 188834278, 884957493, 612625158, 187164276, 914187410, 516402446, 439306613, 483871777, 127276866, 510994413, 543037537, 849863706, 63357887, 763929135, 689325594, 252627608, 572456555, 216128046, 732559671, 850017650, 227471198, 167608792, 335355506, 714257948, 757732332, 370986252, 263205170, 940759776, 369737520, 46313108, 275791265, 83409782, 675246745, 138839978, 290083040, 420475812, 631892002, 604626571, 56140551, 793142379, 811924140, 17364947, 276323399, 202297517, 884725950, 599157713, 981331728, 659916809, 51961884, 209279483, 807831787, 237898311, 340217163, 607028959, 896668262, 856893303, 378773005, 200122640, 630320684, 817926293, 235319166, 632442947, 282796527, 500124421, 656116467, 317879054, 736049701, 878146802, 956477228, 527220119, 763086623, 37850709, 55779853, 718352391, 646031386, 203595064, 288041367, 371903182, 218718743, 795111447, 731622411, 383566074, 78422010, 997791675, 835598583, 733455113, 459673371, 223992142, 993408606, 434569540, 47959267, 891344070, 648166477, 948561243, 594111997, 274902459, 963756713, 18928609, 142941316, 378040613, 992636577, 825414188, 638527472, 951308312, 627196844, 596520613, 256543642, 231171418, 507315592, 647768647, 925988298, 981182038, 418051077, 694231802, 155072574, 173324621, 366531554, 173322141, 375823821, 936227507, 1459753, 355368423, 890849345, 133196312, 576524129, 350089026, 372942428, 480996649, 453412801, 616226019, 246404624, 682141712, 163142508, 607554257, 889798786, 161383968, 503532920, 46464845, 866264353, 359633668, 293485906, 197785859, 704255185, 555057953, 135539475, 898262608, 128150585, 640465398, 693528545, 174396458, 261686350, 104040317, 460019737, 684706344, 351213543, 91253786, 898793867, 820261304, 521513931, 839957251, 84508787, 680001039, 413739276, 745879286, 251710453, 881199858, 81631076, 652301383, 838055066, 363802212, 567889719, 665543625, 264487491, 134573117, 329637917, 202907919, 291954632, 224613178, 779238359, 760295782, 319520618, 156686594, 357708488, 592810851, 217924991, 504299825, 195520291, 50326615, 669891878, 196693607, 519208574, 513639013, 96267162, 139321174, 806868344, 924721335, 779142509, 182813959, 669566540, 205473685, 30189345, 705689346, 701669764, 707498952, 586543072, 595016725, 305773903, 194874734, 444273813, 825544399, 52020845, 169326342, 688250597, 15781630, 665521054, 274408574, 514473564, 419796821, 120865803, 257177381, 431162770, 213777914, 876210104, 843590225, 557304420, 451900141, 641674881, 233366039, 80817424, 775975855, 240470884, 904793434, 517058706, 314248681, 791679178, 111649959, 390630741, 372281211, 58358946, 379083434, 898850872, 911746842, 591332941, 659469582, 83972382, 195483866, 420110992, 832385475, 414031062, 843792252, 739144494, 234397024, 458037579, 508775681, 316499367, 226838901, 378677642, 234067390, 28655575, 886491991, 457801119, 128837437, 119512717, 534817506, 647084351, 368970796, 404517261, 473880341, 999776513, 402354208, 789409136, 854212814, 654734076, 619244560, 613244141, 459423850, 406734261, 864806707, 119439739, 316929455, 113710352, 371570431, 467161400, 459827853, 328987564, 786899845, 443286533, 624987972, 125888581, 797631148, 948942805, 803603570, 662945169, 436871081, 900639637, 560673888, 499676886, 518656818, 270635662, 299893225, 541789707, 889062526, 105092011, 147456394, 339390663, 107598120, 241269036, 118028453, 810003003, 541962175, 896318402, 848419897, 83631775, 273421250, 215912367, 940633305, 336376322, 990834619, 779649131, 930918454, 190548171, 10387848, 655360925, 553828874, 733115834, 351653521, 971730521, 750996910, 568532228, 899131727, 248036330, 910147712, 306270639, 793600346, 803209620, 433078845, 644185977, 187131409, 781435433, 736703171, 621158011, 351417762, 188105993, 234755130, 571860286, 565902769, 332851764, 213710912, 857323270, 816944602, 417200894, 821763351, 520876508, 390393365, 58749145, 231879160, 693089738, 959679285, 519365035, 597318199, 407366185, 152426236, 936570731, 868312991, 567948077, 872861963, 614806419, 972029353, 658710095, 725156371, 855872601, 362692141, 867342625, 717459165, 979081077, 147685689, 872199232, 775431065, 777905403, 372422594, 682702056, 880507028, 831127873, 42446925, 614117621, 102728061, 457267458, 463961787, 745480500, 631430632, 862756514, 703894002, 548465482, 499248978, 793458446, 53201238, 958826607, 987226135, 762057932, 596037652, 105174611, 368709881, 94909625, 2043525, 889580134, 146574492, 292886419, 744575156, 499125194, 79335278, 747509749, 107044019, 886495904, 30790597, 780103276, 110470435, 192861233, 915285019, 454211226, 404661909, 807278993, 317009964, 641457575, 137931336, 846101063, 286416956, 91730854, 120957372, 596706798, 445801401, 857327265, 14429625, 230743651, 216683339, 768414660, 501389594, 985389827, 305565880, 116538970, 800465876, 4553291, 554802661, 657332834, 390122621, 271244897, 37006720, 703053689, 527730526, 443442198, 547305857, 535993130, 175007269, 154767100, 299938468, 381504243, 718244526, 667908209, 78470489, 205264918, 787671692, 979650477, 621541316, 992838279, 560342864, 994495156, 816946426, 324955086, 427807086, 53601518, 659105943, 537435405, 196711786, 295880811, 375423293, 495568966, 663760375, 252194364, 345587833, 786023877, 642028122, 579472373, 445946471, 850651094, 634697831, 863731086, 792509526, 933975259, 49098768, 969793707, 671714861, 746762209, 640116055, 397941074, 901185124, 759093761, 575531750, 51175823, 719315588, 616064664, 466145246, 52807243, 781103860, 917706392, 185837890, 735374471, 801032661, 903459144, 419501084, 36831615, 974726547, 307527768, 410371274, 108857786, 783841704, 915522726, 510570130, 589582326, 988569319, 675415021, 599185566, 499852600, 97986935, 103230694, 551676873, 82706638, 306452865, 827314831, 472710649, 475547746, 296372435, 182857062, 489512469, 870333779, 902245199, 357218315, 970765809, 919150036, 537741032, 180405, 721192495, 14431371, 943180633, 535257465, 189282674, 142483393, 267997680, 377504730, 847606606, 11938479, 85584612, 418788795, 571294062, 304766799, 426243410, 194868162, 841278514, 253890840, 831102434, 359601595, 718403346, 885141521, 233872343, 395792435, 20394742, 433555715, 600491288, 843700794, 256106037, 210694700, 990179055, 925617006, 605461874, 465832217, 872237952, 73848878, 163053967, 512347172, 343074512, 950617124, 702007444, 30996696, 78913188, 555662610, 355453427, 74347129, 336329304, 64450374, 936500136, 277757728, 431404111, 380773702, 840935536, 101701020, 440206734, 429732857, 575392686, 93446761, 81441435, 17811827, 741669142, 240720595, 860482657, 726372031, 515048306, 589825332, 179345579, 904674782, 707074283, 278396197, 413353536, 811578718, 893993606, 333213862, 885981260, 528947133, 248543961, 650885323, 516728238, 79670032, 420578220, 409803639, 984534080, 997586506, 668277573, 78089151, 900727600, 749817624, 78502656, 958712954, 318995674, 701144688, 937882822, 19105373, 208313289, 101419277, 941701016, 32771754, 763787715, 461470328, 911042183, 223923579, 120785197, 222173499, 849275379, 325201733, 941868129, 748686776, 805643124, 544828205, 884149761, 538221553, 473817404, 921860836, 799244090, 411253470, 560535725, 819805668, 976831036, 65578224, 327729942, 96659550, 256564167, 396925053, 464280047, 524515122, 710246413, 380341054, 693888973, 504532240, 533855555, 75060765, 535458030, 537838818, 847196879, 554393271, 257518248, 800762747, 409746656, 755667579, 164787555, 397680097, 692942831, 980481707, 368364105, 762126263, 504840704, 996473962, 816226258, 255357936, 720477443, 21184298, 310165960, 265832217, 241235108, 256430833, 292032140, 65437286, 499139575, 562357979, 941865221, 129145164, 16796743, 389636883, 798480314, 385805644, 544598833, 761276822, 864309777, 908242025, 619215342, 454384610, 632664867, 216054041, 180885038, 411348910, 275724441, 18946065, 982859799, 65921374, 607306650, 727121014, 400780512, 162251663, 333819551, 248925165, 177702302, 379465495, 449823229, 143301930, 298075053, 653957881, 787663015, 84633319, 734945830, 989297648, 781360416, 157088155, 891897207, 842075116, 929288587, 108714148, 884076308, 200244097, 852883573, 404172045, 452463882, 95429477, 105552242, 945486606, 356831277, 797284083, 6827964, 569393205, 648395621, 323360504, 305217695, 267125566, 985176298, 416196671, 914065831, 557757567, 919903255, 656191498, 309058315, 51592468, 523079417, 394829717, 935212851, 155282020, 643612826, 330071180, 413566837, 266747874, 451053290, 695568847, 643772841, 605172035, 376433703, 993184366, 217944630, 607089662, 951185067, 722750689, 743651027, 415778017, 408759676, 339039919, 786242165, 405685759, 223181345, 772404524, 180782712, 88921530, 26443962, 807182355, 303596938, 951802101, 752627899, 977586305, 853058066, 593125072, 807868268, 316988571, 885979783, 25375795, 432673739, 664825950, 907420150, 690036676, 156745354, 775433055, 928839311, 595864003, 912747060, 682701611, 167330077, 662241415, 228214083, 543205112, 418639371, 173201503, 698643019, 530732034, 614576674, 593672593, 30281174, 368477962, 609605373, 159548982, 522875646, 871535391, 990580789, 937833488, 369962327, 716938701, 752143653, 922541892, 65253053, 9662658, 88472747, 872239605, 360777299, 832988792, 723520258, 127711187, 863351189, 952191866, 182549195, 229672802, 754769917, 514914836, 307895669, 167672467, 751637950, 128327485, 959249311, 375396949, 238478049, 249434783, 306728162, 407726509, 887189401, 713356165, 3470073, 253894076, 356497541, 635077071, 715899647, 670115846, 914915123, 434367848, 730409309, 337221037, 547665664, 12307121, 649795578, 885017659, 820565246, 100693870, 748015700, 960031129, 768204486, 694145491, 495420649, 431139886, 721136752, 665830373, 67423900, 566921831, 537393676, 403230143, 895069030, 901195154, 242873442, 370190559, 28899673, 606490156, 832019094, 6349622, 532009574, 48638025, 455992598, 665713925, 674632858, 884304747, 193262157, 706189346, 115181605, 537021213, 613988209, 335180230, 248398946, 562981009, 962759849, 238759941, 226331846, 516938786, 438537786, 986620609, 402244608, 438793153, 520143450, 854937746, 91340727, 554427407, 836400146, 811711652, 585845712, 665835950, 611915358, 504898895, 671676658, 880645720, 741548337, 783340737, 201425615, 612888137, 995823090, 449763950, 476638947, 644022603, 718161088, 754442944, 441863433, 637553978, 926635403, 687777784, 134464345, 439663675, 566964862, 786816049, 403531661, 152105909, 632656208, 991572867, 767466657, 418812679, 99300613, 101775794, 960093829, 162711945, 306369543, 10919867, 567866315, 497278599, 74885113, 984551981, 549543789, 800222565, 558419306, 455045490, 686053248, 36315822, 846490528, 105719333, 672283719, 417308822, 74070797, 441753933, 67341249, 444764704, 15297991, 560377929, 601317327, 853155876, 324085268, 491577788, 732793790, 663690996, 877160417, 140061985, 411752441, 584326524, 982993123, 585542250, 444214981, 720642800, 311802045, 403954330, 420498948, 904921149, 825535737, 431092658, 89248445, 750402370, 163663707, 639944375, 293649721, 640395588, 908251363, 759997124, 554492902, 720477485, 886522803, 829333593, 610253573, 212537647, 228185767, 619235879, 646406188, 710017397, 367423095, 221096546, 356299708, 729432344, 409309555, 141729512, 151546642, 90972613, 486535083, 716082111, 936000911, 689691863, 774804308, 226893445, 830370208, 343452831, 147682243, 919903388, 6010227, 226604206, 118350448, 290520609, 787151905, 948919323, 429400788, 154893483, 332615906, 794481972, 400438280, 49039621, 307827923, 136862749, 810676183, 399041848, 21675744, 8643670, 406924656, 847240020, 81635920, 102341218, 174288436, 557094364, 385741268, 347689018, 511918321, 404999093, 676574207, 470263470, 319620700, 144329647, 833444213, 360065580, 535504931, 822964594, 114207194, 374519006, 725849284, 299875443, 735948971, 512012158, 138302981, 176172370, 822058597, 166703611, 729535058, 574029676, 766493982, 567788207, 1591212, 530194328, 123539824, 134218890, 461260589, 519839887, 293662841, 582658338, 469194860, 903625711, 577143788, 957010040, 417964526, 423156800, 332345710, 170016255, 238840075, 501067502, 434769611, 92362710, 926880607, 102885304, 405742902, 255032387, 211619536, 218043805, 700713445, 6862579, 390716528, 343641764, 748899390, 464641761, 442226049, 563497808, 420320433, 844240442, 446504212, 766733285, 485364081, 689041676, 258183920, 64406005, 890450426, 567492740, 618213519, 219367892, 451251371, 159462444, 207761808, 274213269, 70230461, 665821145, 87288245, 909561196, 975282755, 880739895, 871246934, 489454877, 962242314, 712126803, 6801688, 706683286, 968894935, 811824251, 697798955, 328459765, 123259813, 611112081, 292293714, 146579563, 806795982, 897686867, 952185554, 755295747, 51100219, 88273599, 213035915, 763668095, 415243951, 742599897, 990699509, 804340177, 698557034, 81876755, 586970269, 621027730, 552081108, 490653058, 2527977, 640016599, 167880713, 627573905, 366340946, 937856763, 797235215, 736858252, 881405726, 408119161, 13699500, 641181013, 490668925, 487364052, 247568782, 717126179, 977461980, 367209549, 313166350, 487738643, 392939191, 618211767, 909137227, 431048721, 935229535, 271171931, 881808772, 705865, 73543082, 944926932, 93846107, 813868108, 773707960, 33275339, 782259440, 529710080, 456902509, 310263921, 231093298, 590201610, 582222702, 236426569, 137329841, 204549090, 20418624, 669904231, 798834209, 83582270, 830604551, 704904486, 245572075, 626545518, 637458371, 779913593, 324931288, 449126289, 851130002, 378286917, 962257046, 989571755, 398104726, 706382287, 89262580, 820277974, 802859086, 794230852, 58201338, 849580622, 173981380, 678600690, 829668705, 619104474, 312386739, 701709180, 661313319, 2936941, 391146752, 29003542, 881262251, 388557857, 552675122, 358725907, 117622082, 724204585, 792795870, 728430202, 793792811, 642313766, 254466546, 494606154, 817124751, 322833690, 520624715, 939056974, 393276443, 861599745, 219643081, 155731094, 788656029, 353195376, 903761090, 489164690, 874140763, 651537796, 336125234, 457878056, 791706080, 719989655, 316605289, 765211603, 474876393, 210034646, 442416319, 612693928, 392785209, 603739550, 35827006, 515747355, 183388568, 38659146, 376309009, 916240824, 166799822, 166963736, 608991798, 341434646, 24678337, 510653592, 596383103, 738152768, 343909141, 863112751, 816323445, 729403942, 942431869, 544309486, 261860848, 202574955, 83035214, 106119530, 953239467, 269033592, 102015160, 654118001, 616835550, 920998239, 175891347, 354410804, 406858870, 195286746, 310034612, 455941219, 811514935, 580768093, 441836150, 447355732, 325237931, 388296678, 346682141, 845349244, 181380447, 367396922, 693182174, 702463731, 833491846, 352940455, 371155934, 82112000, 720960841, 654262332, 62791567, 33910404, 480442828, 896137066, 986680470, 396238615, 410446498, 152761504, 251196854, 260448375, 77765385, 355801586, 172139420, 811974894, 485152667, 522872418, 158436843, 593379974, 45484496, 163588923, 378740882, 512355898, 271282884, 579616540, 475077612, 793661530, 225931636, 754175237, 220624540, 210412643, 903466373, 291406719, 98252430, 198812720, 796989894, 299385425, 134274745, 140547245, 46922851, 421969636, 58118976, 291761731, 740951241, 249176134, 625102002, 793102496, 552038612, 711548761, 842201051, 177925240, 401182994, 15047203, 500832979, 315429498, 687283854, 252568109, 562510523, 231893760, 168117527, 986728302, 957911224, 85458574, 447083405, 427346942, 332845728, 778638449, 970773435, 482245594, 893529743, 208722096, 353613050, 59743455, 944162534, 752909799, 628591514, 871026840, 711534828, 108630027, 783325495, 372091179, 3799596, 192412476, 754328699, 932057877, 36811375, 511672436, 971090408, 456942981, 839643102, 253939784, 40248483, 340878787, 544897150, 890845130, 119419045, 988129345, 205615743, 130762332, 128951208, 415283778, 16542456, 712781337, 182025931, 808159717, 147207301, 118098098, 403103824, 166287558, 945450731, 704889077, 565128479, 60045027, 972620696, 767283127, 97559622, 459278293, 39642273, 241630523, 320563554, 292849730, 834074199, 653217350, 747612393, 186114766, 641856402, 762997776, 462452781, 449312310, 115376677, 933793636, 767303577, 927247478, 447842210, 272536719, 667884389, 91937156, 775974051, 123045330, 26656695, 131373068, 835567968, 667548650, 451749375, 305323378, 553525865, 210143138, 405867555, 259659871, 281348513, 382417824, 753821623, 482497415, 972424524, 405458499, 209273566, 281013050, 32772857, 506154813, 677580589, 698709653, 842751354, 906777634, 8058608, 843603985, 379352338, 847119884, 883578865, 983101147, 77623931, 984048481, 334305369, 11633460, 120862704, 613199225, 129180970, 636438372, 231265143, 977933205, 536915617, 129262056, 300211499, 111615422, 828269003, 777328845, 716118590, 907430540, 828483219, 937505596, 32643185, 636619001, 750782956, 730756546, 315430037, 132491552, 47695076, 960137432, 201578160, 565782028, 293399210, 414296119, 383396187, 409309460, 63479178, 632317196, 78750432, 24766892, 555870188, 267339162, 1469610, 529133848, 842739130, 523654731, 932834855, 160996970, 125507880, 87410199, 970973760, 374899049, 500525511, 698720154, 48963967, 556403007, 933242471, 322171859, 938364220, 867900337, 37400874, 411355154, 716475231, 508571069, 66833419, 154814588, 629897712, 539919842, 988130703, 190117433, 215004524, 199184065, 114187177, 715863885, 250109668, 384394762, 292511340, 182923420, 827155941, 343966783, 193711290, 117304654, 936401736, 534377239, 742168414, 136319568, 531150018, 831435095, 104511319, 275344536, 479705677, 562444612, 375263766, 21630941, 259827500, 943703567, 452578950, 567078300, 602470871, 41789601, 491333662, 490597900, 980020610, 604886197, 802168775, 293186748, 766034074, 799973245, 553297598, 827862150, 7928623, 260417033, 441082502, 426732004, 395752047, 848678672, 358861311, 107903773, 214643996, 608850443, 917411221, 105075181, 540958776, 967673189, 366899166, 205022770, 404494513, 587451232, 599892724, 452180643, 489530551, 177728495, 517909116, 373953152, 262055866, 237303663, 47020234, 378625025, 253429918, 949813619, 602132762, 564005061, 911035179, 370286663, 122757384, 324728955, 777940313, 484522635, 345336103, 420165341, 271289957, 959150742, 537661250, 359614882, 538230604, 352659097, 711869884, 950457817, 940257268, 73681839, 219343199, 757135269, 826893678, 66748461, 438845013, 156466338, 220917310, 177724346, 87119926, 902691238, 898515219, 572158760, 704531050, 6300054, 709061734, 411222977, 770848579, 782649698, 493039200, 681173310, 353919870, 545895835, 941458322, 529726761, 982390873, 421696755, 460441071, 325282431, 127028160, 720549658, 472195201, 193203705, 627430654, 720193591, 831685054, 28920630, 591066314, 240002940, 378198045, 377160027, 315402815, 765990755, 979287981, 259178818, 647308023, 416371542, 498901469, 703523035, 702540512, 3584418, 392058795, 276791660, 242841050, 418945604, 356149324, 907934589, 436536697, 714573136, 3382477, 934231534, 181897104, 18893643, 75066370, 508424064, 592021739, 832633486, 317545154, 78755866, 525995973, 10227165, 388798376, 123869679, 409955583, 76582377, 525930520, 225167106, 234850761, 642255650, 548446779, 524294387, 522075666, 375234381, 529849897, 458635998, 382836882, 187262446, 955903954, 354862496, 648670505, 828912189, 805122413, 550264960, 556766401, 856805501, 906727097, 418289068, 636252667, 922018204, 434992058, 29571449, 681310914, 120613445, 941524022, 7760770, 533325375, 598716010, 861361226, 294104672, 299352066, 654334391, 16164469, 584976836, 796845142, 354286651, 84314634, 269889843, 782450258, 527581309, 138731646, 544847097, 448423519, 850322218, 426225886, 361068026, 858507291, 7786395, 204219586, 437408705, 29639951, 211676364, 32469777, 737840595, 529051111, 726569215, 581971511, 485237818, 14859751, 402170995, 582550784, 687628827, 321056141, 852063157, 898833188, 744307162, 58642430, 95883800, 914762954, 287903952, 445410005, 545762038, 495662680, 916121323, 16958560, 816424565, 768214206, 83162711, 17523857, 280513748, 913041661, 985765692, 671194593, 959860812, 665624181, 300683784, 562952180, 289260148, 482050531, 513088334, 910532389, 345748552, 168430219, 21765223, 777979381, 494971396, 128839254, 822378257, 884630742, 192891908, 167072084, 295160126, 527943494, 255829860, 394167753, 822888868, 836295401, 924229781, 110451500, 71043712, 383443976, 80710782, 703840594, 763768734, 941634524, 870992671, 37410319, 945793977, 516663951, 213874694, 261390607, 111323277, 327229497, 233229202, 790103354, 121708005, 256675041, 705705620, 437349831, 931763779, 6916675, 126654832, 425833275, 243592405, 282792366, 233680699, 89287691, 315704753, 200651651, 658379997, 681197305, 852181696, 996531848, 247039187, 784305114, 363510281, 288893785, 553864062, 36454101, 779530948, 174990803, 193765016, 598457030, 243661102, 912596818, 886636514, 320728668, 416898835, 1795835, 227924137, 80103487, 853002028, 714954470, 857614398, 757587548, 22058030, 761572072, 987348538, 183910816, 107933359, 589383094, 841207666, 363375341, 118065763, 608527184, 575135434, 177787827, 582979087, 165901756, 566324401, 211764920, 840686936, 422379477, 314705369, 286842670, 285858873, 821345700, 135646349, 988115325, 560949271, 467375167, 946099840, 285275136, 709033532, 922037450, 81458540, 762416610, 138160913, 486665144, 262088325, 792682025, 39462138, 557556321, 72526208, 313751959, 515878258, 84458333, 530181215, 194886171, 259471750, 573567575, 670688187, 665171145, 489928534, 577894924, 701306341, 687743262, 110430120, 697264584, 395749249, 172368827, 530168449, 605565550, 413081678, 478465649, 564122904, 976618809, 25066372, 796975157, 859475740, 621380288, 385251716, 553370706, 985777836, 290497158, 447991274, 248000115, 12017522, 9879766, 85417248, 803844429, 787216001, 114909770, 6650872, 390985951, 308256047, 400266248, 40834549, 668139163, 51668522, 678284790, 571498869, 202312865, 923559762, 199201354, 356028285, 785944377, 980854709, 885286604, 35144042, 528416771, 379695357, 517892205, 609847217, 560893271, 31874659, 621839928, 791173199, 833539394, 711902104, 23884813, 631887146, 360558252, 565889791, 760836052, 870217242, 900906344, 357355350, 664401775, 638850070, 397419058, 376718203, 624829768, 447165323, 215089369, 38721703, 110551088, 270366323, 153075713, 208750116, 825780179, 947408577, 454922975, 738516837, 899565031, 565599196, 112425204, 489402367, 873060761, 145854355, 87098066, 834398832, 671540408, 666427462, 721816263, 514003285, 269728140, 809046916, 401868562, 638300751, 62418112, 11509601, 666122243, 710537603, 225620054, 280559224, 897363184, 942625565, 159907056, 681227567, 825372770, 495080290, 812495564, 950303053, 838002924, 283150058, 50904132, 658592401, 301818713, 130021542, 416352313, 589866315, 619830738, 614882294, 420310625, 250823838, 774229365, 854346919, 302379355, 924178653, 850685751, 265532598, 830592115, 851533632, 458193833, 216869613, 700667481, 689147300, 28641686, 668737948, 254320790, 995865728, 861592523, 252844731, 153944294, 11036444, 110445980, 200832836, 189356501, 867994009, 722460799, 110610835, 513687623, 853076485, 240863457, 198539354, 683858194, 422579729, 753792642, 545854233, 395302252, 80239648, 287478800, 834515399, 812935321, 676047250, 206249689, 128545109, 437303438, 993950489, 602811870, 934487395, 620539981, 234299876, 763343031, 293912461, 89617338, 657132641, 956654036, 855417094, 793623671, 53365347, 332351846, 975269917, 639020155, 864723118, 245148164, 745110231, 699891098, 779181570, 895316128, 778975248, 20328672, 378066858, 759186453, 909361004, 492078838, 285637209, 836419369, 505867440, 665479750, 807147569, 97026476, 962760417, 127201738, 378929649, 759902137, 949697617, 419410447, 444735785, 376634665, 285036046, 936950744, 203921456, 76089034, 940161559, 167215849, 235716644, 758319954, 935812705, 804694448, 544151773, 119622727, 54489464, 156766054, 922186216, 779445429, 825875044, 513581633, 563103117, 993895539, 262961315, 366315832, 960844540, 240358343, 57737847, 418526301, 180984224, 690768297, 46294901, 894582325, 749395340, 658740509, 713281263, 697151619, 927276693, 366885936, 538192314, 673051329, 882665913, 795413441, 576782759, 364563844, 565066279, 125231808, 294498626, 766290650, 427766309, 724735021, 651894202, 464469506, 75121972, 960725920, 426401144, 242846095, 92958963, 799264488, 843579564, 218354700, 832702786, 790278749, 587780396, 56417643, 898301399, 738077221, 193335464, 654163357, 980258695, 317186225, 761077896, 392732534, 238466124, 377323838, 741010222, 695616520, 938165496, 920001794, 142071927, 235497116, 513300282, 253095104, 684457484, 687109320, 504267577, 503824614, 635517303, 177532257, 758781054, 347616423, 909387882, 394441492, 842134208, 683737309, 798318009, 325751503, 366004737, 851749444, 836337931, 154718635, 546487684, 836003831, 634160855, 329973356, 279445393, 763478319, 324808414, 542894487, 243617057, 597212284, 267827156, 298773604, 465395932, 296928267, 337591389, 928607891, 972029659, 710058543, 278895869, 940872697, 252817301, 57073865, 230929241, 362782507, 194417589, 619418396, 237737717, 161559551, 998255436, 536560608, 938884755, 821103349, 540459363, 243455125, 212185729, 596387727, 638335439, 85112106, 574689049, 213007041, 714630820, 86910067, 297248051, 587467680, 568340997, 210662712, 13531839, 144827018, 678096851, 669427909, 428154160, 359120028, 232966533, 780740761, 561441498, 19164578, 46295078, 556197873, 125548681, 686234792, 624789305, 548120245, 552223182, 102570679, 850858269, 3902761, 45869595, 108641741, 598636388, 57149701, 587538160, 627192001, 298198868, 302929135, 895342521, 642463443, 173504803, 682716066, 129447430, 100953684, 351515242, 310423243, 906288188, 417543149, 771167864, 73454091, 308140817, 55972559, 547264516, 97511260, 878142046, 689841859, 655097634, 113957640, 746112913, 158928872, 974740970, 143764921, 657739472, 84467327, 928141596, 789638978, 581119747, 140231290, 671336315, 251777157, 840015910, 288185208, 86722098, 555689864, 815818144, 669332542, 11266387, 962167566, 563359410, 880997844, 806210383, 444830693, 554234852, 402501201, 501900213, 694065440, 555728405, 605578163, 399510248, 762276091, 452095502, 685392128, 47892671, 38588995, 564200109, 316625389, 232672895, 996220052, 842603647, 19580569, 677945353, 668462586, 453120464, 450942859, 81698372, 573389769, 275672177, 567637787, 558318235, 891675737, 133841403, 772295432, 37336365, 449463766, 747334314, 938490150, 241932277, 441803617, 902726846, 738998409, 323885939, 301839802, 306807529, 80904103, 33622053, 998153496, 870286567, 564510009, 679696743, 10270249, 842061125, 688779241, 591584778, 608394470, 722216081, 502401477, 533620432, 211083813, 868272914, 253520961, 748312773, 694655868, 654538768, 859579039, 762928755, 58728993, 386193567, 42540046, 73307600, 179565120, 962846792, 238845566, 593203685, 465795345, 588568615, 335501448, 407402981, 492923979, 835998133, 690937818, 543182000, 739476507, 997130466, 731789941, 681504498, 103097051, 841544550, 177002869, 987022527, 387396100, 460225748, 501660967, 870320307, 869461424, 278315930, 836127026, 437130690, 537269950, 319898413, 473970874, 653611910, 570401571, 331899887, 269010821, 538963509, 817032284, 353740262, 156079414, 963328334, 979345176, 515130709, 591856127, 486727816, 125433287, 988242005, 66573845, 100898606, 447392148, 141800692, 866815471, 570361804, 265015182, 1791732, 293994922, 657350232, 152799857, 481171547, 291741582, 827783894, 667991729, 658119875, 337739364, 178295969, 721292102, 270708044, 927288955, 970673264, 651121034, 655167165, 648923937, 336283531, 152989533, 288277758, 475291493, 929411115, 383131517, 590022856, 456928005, 153004469, 575288158, 892245738, 308061938, 107942971, 710106726, 58743977, 248897224, 407358681, 414717460, 209644092, 43873524, 624680483, 812339130, 470274480, 976514961, 992929447, 184811209, 411048667, 548853763, 178223056, 330861806, 353059877, 194531789, 496618730, 292969288, 133675347, 265316629, 526679214, 159326740, 187964831, 221231506, 38222027, 449719265, 689786371, 588636326, 226682896, 896782174, 438754013, 874969386, 823193367, 556075725, 624463409, 868952932, 258947484, 717370753, 266901911, 465549663, 312975402, 948632036, 862762432, 635513622, 166995383, 107707875, 420675965, 570109561, 48134473, 760010807, 66014378, 780889090, 261700551, 594959348, 693024426, 898380268, 339030279, 874137349, 930701875, 394858275, 613208572, 123587474, 97423784, 357104664, 621481625, 96138727, 947337024, 235853571, 628301138, 883157212, 299704894, 823246272, 208180173, 487800365, 208235911, 351540019, 520162556, 666305055, 443288362, 859117285, 660282185, 616773032, 126399373, 618835469, 418536932, 93421120, 524762699, 471239110, 110309108, 995083188, 595665541, 614288388, 415527660, 798537398, 697663329, 474685355, 750966727, 938284714, 186014240, 383445818, 524891591, 155695608, 645723476, 771085397, 657870719, 788921978, 916565195, 408394900, 146754793, 91977246, 40911841, 681857070, 351415107, 267766486, 373395186, 390889835, 95187293, 766226467, 825180116, 793740530, 890287194, 607299837, 994000949, 382262839, 69896886, 738895548, 953035926, 512032274, 251694656, 110313545, 674165880, 770562103, 468611813, 311185941, 378499510, 774272465, 575982210, 313443479, 513639100, 188490198, 102571327, 596157070, 785653016, 713860912, 966913668, 340147970, 975032060, 255080114, 848024559, 129037113, 260394991, 525836914, 869282433, 279333898, 931215837, 95112710, 197909594, 742971051, 674828661, 775703624, 704826821, 147498742, 284014657, 226686201, 979314993, 269650882, 226990085, 510477257, 241038711, 907770013, 808959908, 755629434, 462575551, 252810685, 320791546, 643558370, 309093875, 804759265, 915164203, 302306848, 893223034, 178314066, 125443321, 689056048, 920520140, 411906450, 508714392, 353793367, 400865817, 364628000, 706400973, 590961205, 946684546, 877519491, 658667236, 67806094, 57993807, 512405833, 166655441, 177515492, 90163368, 288016177, 502940196, 783220198, 889209662, 485293221, 408331265, 634253, 990292282, 408267651, 698550303, 66399908, 88854212, 116005186, 818907349, 842930541, 976655243, 332541898, 63565814, 854223705, 739539053, 157358567, 591571716, 259110190, 727955008, 440229383, 673163852, 685959715, 747879572, 383467579, 61564501, 801976373, 709101324, 172297095, 888532042, 322030197, 733595906, 887543725, 40929054, 566442232, 731626741, 267896983, 671168775, 443622044, 840411256, 276526948, 51248240, 318874665, 339532289, 15443959, 189513408, 490029098, 985732980, 360478907, 538481587, 580067013, 884970409, 719749504, 74981323, 321870514, 191874197, 388672938, 508553849, 450773078, 858807051, 478618027, 611446967, 898039689, 73596335, 558692461, 678330069, 206497455, 394729929, 751679524, 511406133, 775921003, 782193107, 497154192, 79594215, 572605045, 772603588, 669645422, 935460402, 613291988, 431283778, 748183545, 123223353, 584073560, 931410367, 406086200, 578265823, 930066350, 300676839, 415265073, 348685341, 642842315, 224306158, 384805214, 558228591, 878769499, 738915507, 164261799, 181162411, 846495259, 500689676, 387756618, 832653962, 260663088, 507868981, 676877251, 334644434, 36841948, 594844990, 624682149, 807021688, 684907510, 487390782, 512937364, 633085676, 181367364, 137974753, 151598519, 125613154, 452237346, 973345256, 816674857, 797593816, 423846350, 43627334, 939833117, 707685320, 804707170, 94144386, 729392956, 83731904, 352436890, 468844760, 376902634, 345700411, 930071822, 687487338, 98132144, 744846595, 574090506, 350794130, 620605943, 52879451, 647397800, 815892200, 777800091, 296483064, 808640229, 319442104, 905718000, 988838884, 304950042, 931964497, 944321056, 466055556, 647145757, 443819024, 247150392, 45039263, 93959960, 516275625, 682834297, 26579428, 654003369, 835517089, 291445576, 835266808, 225310473, 966608331, 533392126, 771519901, 523255752, 992041254, 714491770, 623499930, 489730328, 135862891, 149129816, 943282703, 830366678, 95147573, 628186178, 26221993, 926390066, 482894000, 549104888, 597893083, 331536549, 601574134, 96900030, 745254117, 600630551, 868488641, 307129536, 785500152, 27641501, 263919226, 665547729, 684489689, 460581501, 707228974, 849394472, 72079739, 864401053, 371322242, 622912320, 996987531, 962265591, 79551361, 906431331, 183175336, 229279443, 377598372, 337500880, 782017002, 942941501, 350889808, 976687894, 578797117, 342471076, 894385538, 276740143, 757676138, 661773322, 905760168, 178128315, 479604752, 134368363, 958097134, 785107122, 923391414, 265430262, 251639071, 477507969, 231202617, 151497250, 498132014, 364415905, 208327461, 934421685, 870005054, 103437144, 301463199, 213968433, 446892264, 991190210, 191103719, 254723516, 671457666, 258791685, 566800351, 759675425, 238709284, 979271190, 407890191, 956357984, 595284198, 231920573, 1827831, 451059345, 172665453, 610581120, 400599977, 402556186, 964616112, 759677414, 876597769, 610601567, 940208901, 876070465, 140915138, 708108760, 92430510, 411926365, 40955052, 657311801, 363863900, 339488574, 967619374, 48911342, 355473868, 847771784, 171635104, 390138768, 94552524, 390520996, 310719529, 384416509, 529116125, 894213377, 723519044, 173874953, 291998784, 995733458, 718435867, 126275146, 438662745, 982359269, 885804980, 306457641, 993310331, 252756297, 436232790, 976603421, 76016969, 378346980, 230969961, 666540294, 25567341, 399118143, 981716157, 344243961, 41282837, 281701128, 79218336, 671585738, 834194973, 204588829, 888387106, 834205705, 197518417, 215491527, 697981946, 765248478, 844884841, 690521399, 616916166, 294305152, 174326309, 893425046, 805980911, 919289960, 73588387, 93234735, 387531050, 294488060, 849426966, 562155939, 133753615, 121541935, 383099172, 212884778, 756021262, 2271933, 710740004, 588418080, 393758884, 724272790, 144955598, 690281397, 585461707, 785145475, 989009232, 582137679, 37587927, 995011813, 796821735, 807998217, 63690492, 209068254, 909782943, 819298875, 999125800, 843717580, 892862337, 651112707, 945052928, 34489330, 758323008, 887060513, 471200170, 94155675, 507072704, 275085725, 22099589, 322359678, 448320564, 470430264, 348579872, 19499442, 77572983, 168023447, 613003770, 798426705, 623262772, 376521373, 843766463, 878993267, 172403382, 717455414, 515509990, 55379993, 12135282, 478726971, 671582336, 623856279, 137081900, 549589554, 624893634, 840427582, 828862575, 421767409, 536466563, 877493980, 947663801, 468058685, 785244031, 651516191, 450351456, 730542941, 742968210, 58913456, 236338980, 828916984, 217196320, 316368333, 137498294, 143779751, 774823689, 610622967, 308175899, 770587096, 796098171, 535588896, 598854845, 675695580, 987455135, 891942019, 261998245, 905391605, 742260564, 224462553, 946957254, 393456549, 939073338, 311735206, 342523206, 360379136, 360459050, 589902718, 851839229, 416265098, 630552168, 16506700, 298396694, 969727849, 25735080, 31442788, 273217223, 513773235, 391581928, 698145379, 301941198, 205257915, 512455669, 383671579, 657585531, 361668027, 643996434, 360147774, 333459817, 936047824, 844819205, 817682182, 776922226, 435369447, 947292847, 82005478, 862146907, 369520901, 907367994, 853261642, 682497950, 686221156, 422687021, 513184732, 697339637, 480422164, 856159321, 325782867, 889519185, 784690163, 759081788, 902284939, 769433958, 23220612, 421295366, 505891001, 572106263, 138785269, 924706831, 488993607, 477384411, 953030545, 90803817, 753270166, 171474688, 202321931, 572407884, 333717014, 428153447, 480018346, 20099301, 558157610, 72471489, 301090396, 260444556, 2251218, 4156128, 776777499, 702098673, 441301099, 43911849, 932410881, 818533487, 572905448, 737012788, 929789970, 918201672, 344122450, 175974527, 605428659, 404742375, 228403357, 759460319, 5629176, 121483960, 882470746, 162360100, 659395494, 781202168, 737092783, 403001372, 236250773, 23577265, 157943148, 978152442, 851909230, 306016243, 683312698, 79606187, 48274192, 771055739, 923535733, 378021461, 113000192, 969929691, 55478472, 722074304, 330448829, 204490261, 918304123, 595420550, 237569710, 3717747, 899177254, 616534666, 621559528, 474225329, 47977021, 344746182, 324237626, 833280573, 29792735, 57445722, 220363552, 106653335, 462546002, 726071705, 227503329, 998668343, 740591953, 727965614, 548036573, 156496826, 804253685, 246948038, 117014208, 657376578, 73047531, 47303466, 912962845, 943453964, 965778495, 537425424, 734997724, 997696384, 211483549, 613102837, 105505428, 403632361, 389530984, 155621983, 567945927, 307798939, 617024696, 813097827, 395353911, 341494, 282232419, 292534599, 721936587, 799637941, 912174664, 649342175, 32018904, 522335583, 753735587, 739747524, 293991434, 52500751, 602320504, 234691862, 119423488, 490862252, 573424503, 327331539, 831048934, 920665492, 918396399, 136315508, 305180106, 200911941, 99036164, 472679740, 734992059, 646036270, 737436756, 44756694, 622388907, 823310304, 872179241, 651610533, 433185596, 537728553, 346310179, 286300179, 517876874, 476693274, 268012746, 305140869, 464164656, 651601057, 475698810, 234177802, 318304570, 929513426, 778741781, 458711793, 651354335, 388147614, 919158085, 253204464, 260632505, 453688994, 759567946, 615636321, 69021458, 694253890, 236244301, 66360595, 317766856, 435957370, 178189901, 239826498, 724745131, 238537023, 286779679, 249968768, 201829258, 802630041, 456494818, 93832974, 352789205, 793638656, 648730562, 697437338, 46328782, 328926728, 609049003, 573002060, 353942876, 281201049, 271319374, 884884074, 836570585, 123856949, 182995961, 188991301, 190612136, 313151532, 423395551, 275040307, 666910682, 338368138, 441502646, 965996938, 576613441, 773189237, 317567468, 92753676, 962214992, 76943376, 604530372, 838362688, 764835225, 556640345, 481993008, 749274528, 780108343, 685896605, 206607344, 773489220, 313632763, 765280257, 296168816, 988959935, 414281521, 38497635, 93464486, 226212321, 410147436, 673339064, 9784903, 49709086, 989223658, 283392238, 206471173, 531720703, 676871015, 863894726, 450410272, 567202951, 591120210, 224099032, 797934407, 339611636, 426359177, 98607861, 586560301, 81232, 310250227, 144577845, 205815376, 302225426, 549686152, 501870677, 269544469, 968802323, 937192350, 885170898, 800705381, 161943273, 121503120, 986884116, 33348329, 132237297, 216345024, 267101214, 804618072, 83426688, 287914116, 919064290, 848516401, 795321339, 780804530, 409661594, 368871901, 871375569, 354154631, 118024022, 201907708, 404827739, 431662552, 804461749, 526856192, 150294531, 557246491, 182090152, 152803963, 325799980, 465739937, 496849549, 86077536, 933649622, 648396065, 685216760, 960281423, 1277547, 268723675, 679350802, 179416134, 481295034, 388162731, 109629759, 523995460, 533241786, 61377138, 660828765, 691277368, 478444966, 305720073, 27584819, 887017778, 590940454, 379460386, 598984448, 329939828, 54698817, 990815665, 631626588, 560971763, 876193155, 467912153, 916010625, 909307522, 154430637, 547404980, 827136921, 679347536, 68109590, 381873252, 105855566, 350762121, 147426432, 784920607, 288058341, 898143865, 38261448, 695527529, 328163697, 225305627, 574481755, 526707249, 236997281, 693063498, 612814709, 920253953, 996648418, 575747290, 988278226, 664117748, 262735609, 886532513, 930012182, 637635386, 899040766, 127652713, 515290082, 343137785, 655764650, 949054299, 955642682, 689756655, 546450809, 321911030, 247363253, 154118021, 705054455, 555451411, 497659000, 312167049, 713531497, 802070494, 121109983, 56725650, 278981506, 559567663, 413445202, 835628268, 667901053, 85145609, 993651287, 628872702, 110158543, 375184928, 849221153, 907970551, 625743166, 504886796, 466991289, 350232251, 93399132, 358576549, 567055980, 117263529, 613834445, 150972541, 472908805, 531360292, 763874947, 242423169, 465803567, 452904632, 974908211, 39179051, 476293330, 666046514, 363884782, 273646902, 934077469, 972135328, 652278968, 113800928, 764733867, 655807845, 229840184, 276058257, 899938315, 474169502, 136583031, 511190948, 92979840, 41058945, 983781364, 859347587, 33388838, 369432597, 196220081, 572838934, 893674627, 248802064, 324157776, 235352505, 790240623, 340144363, 759893159, 602684547, 340660594, 258234314, 742471263, 217438287, 793854471, 665954329, 799286048, 294326878, 512462998, 985894915, 388960579, 268051617, 937072918, 264870177, 571705313, 919250507, 393837185, 287476625, 460573251, 225627929, 53098908, 170209455, 863934729, 666218705, 10622077, 503125606, 572456674, 65048148, 703968112, 299542919, 841241256, 719622328, 400893254, 248272507, 438629631, 645072764, 403254758, 222124888, 41217491, 735417024, 223157050, 505474637, 788965792, 932885204, 223555095, 177431331, 499099532, 734274045, 541984252, 57288808, 36917295, 580351817, 817285487, 108366072, 475102309, 227206304, 128059864, 640371605, 627340002, 590327482, 197182938, 44253963, 198983396, 889454521, 390650489, 763424547, 168983573, 633771994, 714969546, 987107620, 548000320, 573162808, 956313612, 411124285, 94196119, 258945519, 297056890, 49299141, 89339177, 24986113, 981211942, 217131478, 174941986, 179595480, 591985567, 544576830, 523890815, 285324262, 688928960, 747979055, 749879805, 831819654, 130633712, 207642896, 331897573, 38050945, 567696362, 1311129, 415929686, 947921474, 742898310, 795524195, 439925554, 325043849, 315999406, 996205335, 871850493, 161915443, 910742481, 561582807, 549202430, 919820700, 245806114, 256209560, 784903015, 853791846, 958791356, 445549762, 333118587, 761850007, 720759609, 238426407, 398670825, 892476598, 538276877, 291264999, 534272823, 73946289, 135660143, 500517920, 127814420, 690541812, 210457609, 448772351, 358437101, 559550744, 840758738, 65987459, 459345888, 913708655, 224745437, 587444402, 69629758, 287245738, 116334967, 589452385, 335175139, 79626746, 417348792, 191420850, 973546200, 680194880, 558277386, 881616711, 146169096, 51783002, 543118699, 296854571, 552852668, 484564536, 994149408, 963553365, 883307114, 787561843, 587760560, 580047534, 610806037, 532955827, 817536602, 156975678, 326539436, 279286822, 320761145, 277913543, 860327949, 593591514, 859589739, 788533279, 55269731, 29675221, 350174286, 503474898, 247348650, 317090462, 270131638, 324060503, 195540179, 499170627, 609693499, 929351166, 791877600, 946267897, 205318844, 718355046, 584803093, 535091958, 427734039, 608997494, 757639376, 447457869, 549043674, 583191371, 612824115, 768160369, 16445677, 430623234, 667329494, 825591087, 434655497, 868200028, 784025623, 976711800, 825287148, 629596105, 643403664, 425388207, 44364158, 666064518, 823291029, 76358043, 790979808, 281876688, 942911347, 890397899, 594707635, 908528744, 457047447, 176175796, 657973159, 84225353, 887807115, 268705439, 374986039, 21868813, 982629851, 739615525, 758014821, 242094899, 815217108, 644020278, 112917560, 165551896, 321778088, 304271742, 778832432, 909983607, 584227989, 404882514, 129916793, 496524745, 672754970, 608722037, 327418197, 960057198, 430533801, 920374588, 265584344, 256157600, 445181509, 753505197, 505871494, 200326683, 268541103, 345000057, 255054314, 678436534, 227385413, 446234941, 949015910, 609684250, 168983077, 128081420, 186287512, 784690112, 831381394, 805594745, 61276100, 762673401, 854681684, 231296441, 502697478, 213887199, 500790557, 709108683, 280469964, 860312965, 536053272, 815360647, 222889330, 958847973, 615149134, 529651509, 904575618, 969177268, 717938446, 178224832, 476214937, 27189501, 841308866, 310476735, 916944126, 151576304, 705534560, 796870432, 656939518, 995278562, 321001207, 509240568, 843648493, 649418321, 569217958, 622724239, 261980844, 732451192, 876546464, 482892896, 1131173, 696177972, 996732632, 502856060, 974070322, 568751178, 501390268, 358528803, 953592629, 410099645, 967514116, 266503685, 87294224, 426181974, 649211096, 336354128, 570402640, 329010026, 632093569, 565423623, 851958966, 184121220, 92334707, 908827390, 962109553, 98035417, 281979182, 957051266, 796511159, 453474112, 491336230, 310001980, 64565310, 909956429, 428110474, 547091004, 707428658, 126400418, 291448760, 793760970, 71913289, 988630918, 522448657, 459057170, 618986047, 798181809, 341986174, 352788654, 767189388, 275008815, 707539590, 90472582, 891112611, 34941283, 77118785, 571243694, 234344303, 337183170, 344196100, 213479312, 583627534, 955584798, 129192391, 453809152, 127897309, 979659463, 335164685, 947167555, 730570327, 364105299, 408719202, 186623249, 379408682, 166218542, 824012794, 114146416, 320151181, 843651266, 466164547, 791565888, 40441785, 168713773, 88551472, 522538084, 571101025, 852870673, 918728422, 47216895, 595478700, 745630830, 763648932, 117974533, 469456447, 421642263, 899951876, 518157372, 411026414, 715611728, 375599540, 376195326, 354359862, 657470747, 400312647, 8386180, 556143980, 506694024, 716184362, 398018664, 800922738, 549782343, 445420372, 959920489, 101363769, 401964202, 499904291, 788644267, 47817075, 21475513, 808244603, 507751321, 841412222, 2069252, 947350117, 645756955, 779691519, 97916207, 750693177, 781637660, 986641996, 644822938, 524956011, 707936708, 396604289, 367637281, 107762548, 727515738, 454916353, 395889013, 701569247, 579816226, 983429294, 593458855, 687361813, 896910714, 955850971, 190390949, 819778081, 926439673, 198907793, 733465107, 112880809, 850790490, 573648588, 925707032, 35905416, 366306509, 89896798, 384322799, 494842421, 602238513, 227968320, 207912718, 248740548, 241547058, 884627145, 641699117, 291903633, 659441759, 971292156, 834105986, 450297491, 815844257, 177609952, 773162484, 694315341, 612126164, 277155861, 935750250, 610953385, 749658066, 782708469, 767604346, 317886897, 660673244, 200526013, 226962746, 89925762, 280487969, 836944427, 194215881, 448201200, 815905871, 794562445, 823419935, 558822144, 936562793, 269995700, 261759788, 553876943, 447601301, 4123237, 38141278, 846497632, 521504671, 36591002, 112267480, 714308067, 249585893, 103443110, 483987415, 626937394, 847773610, 513600544, 576463121, 961190400, 687347566, 629917391, 102042757, 937535232, 289299606, 159341164, 110063382, 671721345, 111878808, 521945764, 946903338, 811592571, 311559306, 408428746, 58398858, 495263333, 419583327, 656756054, 258626927, 546833135, 617140639, 425299893, 286311385, 736072722, 294073030, 398180935, 246561533, 187505309, 169324196, 467819313, 766663252, 983056701, 500039594, 221270810, 218735781, 726043634, 696048227, 501185940, 596944768, 42199598, 199140184, 526994573, 562203318, 114552307, 360585182, 390649447, 330211715, 361705059, 921169233, 612790669, 69879211, 420414953, 60696922, 209715572, 168554436, 800972821, 520135261, 114898069, 491307668, 174992657, 826980796, 961472531, 210583947, 885458540, 491838720, 210937505, 803277396, 936871195, 618307763, 421604584, 334331500, 603240975, 275276352, 791150599, 205324580, 803965266, 941332325, 731642321, 190146997, 113398985, 626850227, 244776575, 480757881, 110316082, 524463667, 778488519, 527378302, 414405534, 329584198, 670747321, 292974539, 985251367, 562634791, 808555372, 853903251, 113671248, 146592689, 934864332, 637373325, 189507805, 331820118, 395454956, 689482843, 796641759, 3755842, 406662942, 103656501, 717025933, 597628481, 345984907, 513368152, 246656174, 833873373, 874812700, 838083798, 628252418, 857031501, 51089178, 227998995, 533696924, 249497164, 403320902, 619219205, 415499541, 249737884, 302423201, 990281403, 909148064, 59383451, 716676508, 414877717, 691017995, 426722362, 226097327, 491464853, 412224942, 902936987, 965711845, 417939782, 360383249, 269926451, 182383473, 431844679, 892780832, 210494913, 105209101, 809023209, 258352369, 707767570, 741463875, 34919826, 542262798, 741420234, 291996688, 290680742, 125245721, 164919338, 360387690, 404759473, 261414447, 232282343, 137472965, 658399496, 914911784, 344411578, 544532858, 928298872, 207767468, 205426630, 97973644, 91322375, 99941969, 857714184, 771505323, 369162565, 605267488, 421545866, 670739059, 265105723, 759500779, 854021809, 134744094, 509778789, 291906328, 936098783, 459940294, 758845596, 157669475, 512046951, 882176076, 67197190, 123237196, 986091713, 301117298, 773897190, 487064309, 226033494, 170948361, 219661312, 296149672, 412127249, 79576113, 474917514, 470352968, 585124067, 868594661, 509951671, 847234170, 703780667, 427572969, 982463660, 143580776, 456070917, 493109220, 768684581, 696975125, 936904586, 106759154, 709244849, 979221363, 942303484, 120313740, 692238236, 58726307, 990743282, 107975736, 457402325, 905564629, 925451943, 772875462, 652987482, 617836076, 688685335, 118176250, 995558208, 577389639, 868882384, 35732093, 604488270, 145450975, 145447347, 788368876, 167964151, 558557956, 813577714, 480992750, 749658027, 793250785, 514013231, 215826511, 73140329, 903213866, 295201718, 566026186, 940696980, 384376798, 981784775, 615670136, 396809443, 344038017, 717504628, 332627239, 381372775, 296656090, 337274655, 81829696, 108812167, 837761941, 794872143, 172910079, 441675745, 139903673, 961975287, 715563887, 128158308, 551171964, 133843377, 904267721, 680080606, 995070413, 473239572, 676185128, 874661715, 505213717, 285753449, 651122928, 854255137, 522016904, 810757887, 619997178, 335037547, 377623310, 655706399, 238810304, 405264725, 326614557, 425622648, 775159644, 734366907, 721701074, 788996889, 325248695, 564339683, 328786714, 115624198, 279910418, 306087220, 407535634, 586605334, 281491531, 35437497, 163866887, 579784398, 383554296, 326270690, 318667376, 436183164, 690133734, 607437139, 779224565, 891927642, 368861580, 234221739, 381133084, 783453767, 937799381, 849770153, 161906667, 989471708, 576643883, 185512495, 791760166, 894370966, 444725859, 968276119, 797941220, 68553464, 768534434, 833530142, 741448043, 181884337, 483601908, 970948077, 564149558, 419180199, 693522365, 537603512, 883410362, 294690194, 462412207, 453073118, 163365038, 195189430, 101640220, 855662378, 740688933, 412733937, 459041014, 160951372, 408751129, 22968452, 617245453, 592285837, 734679442, 428366587, 942248703, 645723586, 101948558, 608248244, 650230098, 580646537, 771830998, 26465677, 429765294, 318339808, 918129459, 233135200, 919895526, 112427303, 38184802, 167117534, 589437829, 238140967, 773478590, 628359954, 227660259, 93653622, 573380144, 87033792, 485880555, 679872360, 8558127, 680546537, 360571698, 354346619, 769483350, 112819589, 87379673, 70634924, 739589010, 891165337, 858479946, 695191726, 957908688, 413223271, 610092460, 944654517, 938684418, 920436178, 285048098, 107860236, 364512790, 499825116, 237509095, 181794077, 545124736, 119737342, 89333056, 291865185, 891159170, 917438639, 126039925, 505436937, 725691144, 416653493, 449299923, 505792130, 436015071, 616020809, 162057329, 880846112, 206562562, 200690396, 302211332, 415063956, 849657539, 877901892, 445067872, 358125848, 303693232, 225781357, 689519752, 675015174, 977868572, 826471555, 310127380, 762262988, 278571164, 553568331, 402992116, 370905487, 485411015, 917597663, 548434060, 335248366, 667785296, 422580312, 521214865, 107868441, 777291646, 463528474, 376273881, 166096111, 836777768, 966660725, 184819745, 570560247, 940385987, 679948708, 313594393, 748102588, 668936110, 738263663, 570204285, 202723919, 403733646, 846911245, 582806612, 936730957, 581463691, 488041901, 494263335, 98054766, 670119499, 319475261, 959958308, 965150269, 790600967, 924168448, 98205065, 757304286, 414253116, 673561681, 725873077, 383024738, 763252796, 216598076, 839234282, 273022067, 746258846, 620773863, 814446072, 539762850, 664949871, 994223148, 205192075, 365379893, 893362216, 346476908, 700835691, 520616052, 710321456, 446022867, 61621083, 121686796, 927282732, 888532097, 424461015, 122112739, 162491159, 909915316, 415575881, 498260272, 794686124, 165635455, 367978467, 288450357, 799717843, 534948458, 635200622, 326850776, 146285610, 906397625, 798265067, 67295186, 759492167, 53670486, 779291096, 813700520, 945387108, 793898657, 617346586, 600514867, 4199667, 45200881, 339263675, 219842486, 849081061, 617305754, 639402875, 30681418, 811644331, 75092687, 830923768, 674867340, 125860712, 811650557, 427519732, 389170815, 794580206, 805452341, 200539662, 947440535, 723456176, 526621810, 594979778, 600977603, 492611034, 198703850, 542642163, 413815553, 686280044, 603278941, 162099738, 296607152, 685523083, 15292653, 35339533, 900104130, 682583247, 850557373, 168768245, 796758845, 62745924, 449463023, 953327579, 26257502, 807979790, 580914167, 371767697, 539079418, 99250252, 990960473, 896941598, 504788057, 26602383, 43526064, 881533703, 773893061, 480663473, 306926317, 482615079, 118410316, 87328870, 581207398, 482026856, 331654229, 299979865, 224775736, 582761338, 922511712, 251499419, 936269241, 827729170, 626675992, 669371774, 851378396, 140214826, 184183013, 262450168, 849153499, 221186711, 418760211, 103946904, 675883238, 532713730, 599488217, 599723293, 352486334, 603236266, 773806565, 374819880, 137198828, 579494625, 644762024, 959638837, 767814546, 269084296, 80108927, 575219783, 269288956, 574192933, 50271084, 255713434, 779679852, 892056106, 178265927, 164815449, 694248821, 325602180, 811677621, 741585163, 474573858, 65847016, 957799383, 826115319, 28059896, 790583012, 395160409, 380228196, 28236419, 614588812, 251797760, 353498678, 682511180, 28353845, 76301769, 8909080, 935502441, 869476208, 595104861, 793254890, 833687046, 387025044, 658020347, 759218341, 193540584, 247093520, 342171053, 662908629, 867245730, 724420259, 710795834, 240859334, 458838416, 838716541, 366368433, 544473440, 85980905, 10036221, 616980780, 203183643, 37574802, 58449377, 947350699, 685931550, 335090424, 132213592, 697160446, 320511176, 955177352, 268195037, 605495939, 896321807, 349410947, 928459711, 438394180, 899416189, 158726621, 154983854, 201635535, 160885421, 60450504, 350643409, 122631084, 222544614, 256716383, 289777643, 289264962, 367490889, 419288411, 851977121, 922459191, 173468126, 648722679, 52075363, 325954352, 547400214, 423652405, 628835510, 836069557, 897503506, 530300480, 448143006, 47981885, 644759050, 292221261, 107629203, 754425398, 813664428, 561028515, 548502178, 323206528, 840411103, 673131109, 373637835, 465411557, 388315391, 203343842, 932310779, 377554993, 853249214, 536435305, 918984856, 466923030, 10585757, 531910778, 988388261, 992184244, 535483796, 784051960, 890870285, 14187946, 436777479, 707187203, 505936995, 161418518, 716479360, 963659597, 656142269, 722892419, 209453419, 497889154, 610209844, 459055600, 282025187, 384987431, 57758543, 665631567, 368244263, 411371055, 601855179, 576127320, 685858727, 138910262, 194516233, 245038161, 144762171, 703685744, 368613064, 516958437, 255390303, 940932253, 939977270, 466428665, 809642868, 614461159, 363748187, 912268527, 299080232, 736091636, 170173014, 662124118, 620541501, 108614502, 659705850, 508097276, 587157447, 787154497, 586218081, 655429724, 249359385, 372759738, 776456652, 824925496, 867256777, 353436949, 992445280, 354376121, 670299122, 701771389, 472050075, 357604811, 900083861, 250717098, 121205680, 924568940, 93775521, 436997171, 792250154, 485607213, 275205608, 695853067, 20791718, 851574121, 773448857, 819737592, 164800085, 755508341, 323696830, 479204610, 869202230, 276105, 24911988, 304988869, 425199683, 583423366, 604899326, 212121489, 964983374, 77147113, 659130252, 594863049, 824778188, 721144048, 403932753, 993798012, 988173257, 279407579, 6836653, 8780889, 545483644, 168138207, 964066714, 454421660, 29860691, 985532023, 502769687, 448011379, 656335420, 8970680, 874630792, 85504069, 611904517, 405726716, 538184358, 598285376, 125597515, 476929216, 543860228, 542303056, 408125309, 466569299, 313251195, 914154223, 929358465, 394825025, 307896357, 641145109, 57810286, 429151761, 282881917, 660908678, 793488980, 564884710, 238156786, 232691421, 440738567, 859832029, 470480809, 575256345, 502279987, 175049248, 604197116, 429794085, 454830110, 53023918, 425215018, 866339017, 702239167, 774922503, 782076175, 107723003, 313845136, 550019145, 37252240, 649031433, 470167554, 937011442, 886688874, 644935076, 904344582, 607576657, 82758879, 730154403, 943505248, 961962122, 16851525, 71149618, 634710578, 174987087, 670059317, 608622607, 781065888, 250093018, 235276302, 398638378, 792696029, 443029050, 78639503, 51899454, 85747757, 422589683, 411973495, 115416241, 910554371, 80227157, 479364446, 969152322, 138450013, 22458933, 889844534, 503757338, 659886331, 617675494, 970203796, 475398040, 540600274, 247565044, 667251483, 949931396, 674175423, 142496772, 106262428, 747808821, 889882099, 808173265, 534293994, 802670605, 116795485, 55078552, 629060424, 767668248, 328993502, 652497593, 225152281, 731818512, 25978143, 860585238, 433368999, 30861832, 846752372, 305984801, 794465632, 191393205, 512756049, 572830991, 768075543, 291711528, 725956378, 67637041, 449063164, 29629240, 774677732, 364953399, 616917655, 342835659, 648822778, 474964977, 253965535, 726996504, 412103272, 179380703, 574993276, 637487241, 433249171, 714244233, 100582709, 299771601, 459907507, 754653124, 405285575, 382780515, 113083596, 821254454, 1424140, 138269546, 900899474, 43724406, 594196904, 770234969, 138496628, 434339367, 439384440, 761957428, 272852378, 594418987, 74408175, 63815483, 117044237, 286092273, 663340976, 287428137, 169713247, 922143857, 289641715, 710294602, 129629796, 233310430, 806497944, 76362972, 36898562, 557499559, 77972277, 741008175, 85047798, 618211593, 12193201, 977605311, 877439879, 448978593, 152994395, 856709303, 294806206, 92196941, 168406225, 571440019, 273394505, 858386453, 929445251, 609426393, 650094725, 293557636, 240969200, 876387011, 808921962, 315620848, 677726947, 162029795, 44246728, 664850325, 428421288, 737642055, 94144296, 532080287, 90901608, 166953717, 170103627, 45748858, 469496968, 322949069, 816994812, 400528895, 388612359, 379925315, 999426796, 225103571, 806681941, 734073769, 38695115, 413039080, 574907323, 493508472, 34946954, 964681345, 43602079, 474442766, 573529566, 264023115, 338661265, 987385732, 387860818, 972657475, 198482479, 566615822, 738388118, 142225023, 32356403, 911372381, 541899480, 153284232, 483827643, 560088485, 669877696, 394088189, 917168223, 2337299, 449251512, 224033270, 69457809, 177977878, 313719878, 814945883, 607623549, 958747126, 877742494, 124856589, 98921154, 430673322, 938357675, 860936210, 446773474, 527517195, 971269067, 21463157, 314873359, 579677973, 668479939, 292407898, 365784124, 106034463, 815117313, 820035674, 243197301, 529913808, 812551823, 888299225, 109316782, 786640438, 364610866, 811789727, 406344325, 909666783, 889436193, 760457915, 685890140, 274765273, 131307077, 720813547, 408177907, 378500338, 529041231, 848930113, 720426202, 422528874, 38866720, 923181230, 450577980, 27293452, 319289665, 229665356, 254090147, 213305952, 761826467, 981958302, 738727543, 760212944, 861243921, 359523888, 22108716, 398615174, 691340880, 245230714, 801969388, 569968190, 358645406, 828317813, 846611345, 780076617, 600187430, 416488631, 904323719, 560722092, 485025548, 138695307, 631236592, 561497767, 562432211, 402198202, 5947262, 7160876, 989446084, 455512971, 10525110, 825881592, 704547845, 226446413, 938131905, 10817648, 278836693, 849207945, 223922089, 921168690, 48727103, 978670423, 455167059, 492575640, 508792425, 195443877, 413560890, 580911947, 220076140, 111620259, 327990788, 630894773, 262165088, 992387858, 48787614, 785571217, 674564515, 79283982, 530690983, 230585856, 669210759, 431099970, 206851451, 694601575, 623107297, 214644063, 526562952, 900824904, 757967451, 911635777, 660276815, 78858786, 881552801, 847216815, 796383562, 648321793, 922486471, 230031260, 592835297, 50636535, 895359917, 779672991, 743287739, 867053986, 852209024, 313246168, 933394630, 125800065, 481759060, 796043308, 41473285, 185547521, 218802933, 454429577, 422078887, 26224248, 915079951, 707100192, 167970402, 763407932, 795066075, 757991155, 534591996, 251784845, 90377577, 647723622, 296677965, 566721324, 894550548, 727124427, 19996419, 601895901, 694562923, 633332876, 271374316, 380391082, 246343419, 385415569, 553539632, 295682717, 371797927, 845106955, 328346653, 964479423, 270145787, 555863890, 989486949, 965879323, 637554987, 983376226, 612655622, 118426625, 87213139, 239813223, 894314621, 263660883, 523531950, 76925986, 814784863, 102006200, 755574000, 63278476, 656804317, 62207978, 842329970, 845335210, 707185632, 675759135, 850047903, 629457115, 430734874, 559447371, 498634761, 683499080, 763631597, 736038095, 100021356, 300518027, 691253940, 57233871, 996877091, 584676841, 229566681, 924592445, 380899150, 379175563, 746084239, 313440558, 537063117, 326734099, 47537351, 47584217, 99091122, 442354051, 61351516, 416793728, 813064853, 985152683, 233079294, 535914610, 713632999, 188291189, 816303538, 782783452, 384029565, 562176651, 308798026, 565593968, 516468480, 968448259, 274165709, 27551471, 695219323, 997878456, 128557167, 991074123, 426101143, 428524673, 217147772, 448147115, 928452927, 81299889, 112404113, 516477549, 393498957, 591204298, 245523248, 378234026, 319529300, 525716275, 306735563, 420482937, 260776605, 806312501, 82738374, 891658072, 561698367, 857257438, 939157878, 385318664, 461144129, 611208611, 300589932, 900736102, 346385058, 763562481, 998149802, 143876798, 962870423, 534126365, 316526408, 791076997, 405914427, 478214501, 42545757, 500741134, 517819020, 316711778, 889048142, 797334599, 846125764, 364331930, 146420303, 593291598, 506545764, 147164400, 826873558, 97751541, 73842602, 159202518, 12794693, 985409151, 424688415, 277730889, 824155210, 645821647, 342695955, 574777827, 304769273, 810509011, 792780210, 145452364, 136049671, 881452595, 653049716, 563607266, 446980100, 658844492, 696244180, 437677771, 499603963, 81906518, 94978977, 311326361, 726977703, 900220532, 641047433, 235250169, 20733135, 418238237, 138333634, 691225150, 212106454, 256907871, 817851099, 760614210, 416880674, 300594302, 531645998, 728403973, 699028635, 419524773, 648793535, 819815207, 938959628, 711794942, 288569223, 871082241, 104635415, 497544651, 526152060, 455110681, 872795685, 623276424, 733514133, 147210589, 28684245, 556838664, 907551745, 459874760, 588441482, 961488665, 705641294, 144668435, 157677425, 338172254, 86091967, 12403086, 32252523, 296753469, 470851279, 185201202, 179015840, 381369509, 791410963, 553627747, 385212802, 493121941, 19913585, 589856815, 493221793, 660899196, 588979627, 71307331, 546122318, 241115590, 651799017, 929026993, 608157135, 100740738, 883101071, 864426957, 695487339, 991086993, 183006753, 997788712, 244844445, 460511697, 903604412, 102166871, 993149081, 711736988, 292421255, 690132692, 179578146, 205289666, 529422358, 580421000, 532992942, 168345340, 45661955, 126883269, 626569189, 782852799, 137822392, 956746786, 46683680, 252277945, 432788028, 901516415, 948830305, 466582842, 620541162, 317142329, 199581271, 330324826, 85635576, 132761028, 460666247, 930604635, 999602924, 246265214, 645757199, 676765793, 256854689, 387507835, 459824400, 724023452, 604725215, 580758291, 367858860, 477839808, 841763738, 934006166, 270091776, 961959831, 899051, 937940795, 658005305, 622384284, 481524109, 369403137, 377160686, 847689964, 551618609, 999481087, 306387522, 547762896, 400551690, 815267761, 535624645, 112187275, 252106063, 65550674, 746479755, 451943196, 153946788, 823199183, 674454493, 54821893, 955562973, 7994279, 999394417, 332941866, 898861133, 382846110, 722984735, 310734451, 716707261, 2603944, 309527122, 379661424, 696740773, 589173966, 895620093, 323209125, 436685413, 503741546, 133555740, 113546645, 671512610, 704560604, 551694410, 128339104, 174746823, 222516212, 328676712, 449135187, 743268750, 749098082, 642856476, 535241662, 515494627, 224982255, 256571605, 562060123, 837318038, 666579047, 501839067, 315695193, 313042220, 645098450, 890164486, 499495135, 791045160, 49714755, 972630299, 546165061, 203156566, 506582558, 168254686, 691293039, 221567381, 577053288, 645100801, 457127005, 313125961, 678249470, 422183218, 183871659, 237638900, 217744, 401706661, 847575679, 942204312, 651630205, 36646013, 421329455, 151392217, 394831511, 426137947, 68693773, 76752295, 508549606, 814491712, 704223945, 367771044, 463060477, 791082204, 722582380, 503052359, 332758108, 289904691, 150987406, 879623884, 330332532, 732205128, 537777007, 679106291, 762701071, 759191294, 989515824, 733838021, 703575064, 889636773, 241725194, 105480430, 311179051, 942358542, 235654162, 372491508, 189416967, 518605140, 525791054, 96115595, 550606815, 965763486, 930867221, 809532157, 750438305, 526897836, 734554714, 527492200, 620043605, 225320327, 669377667, 302436387, 369432430, 328595744, 462181936, 755369662, 238768661, 678951402, 630441305, 989982963, 235824185, 950797174, 258772527, 543806809, 166574749, 663897642, 588315514, 633749711, 66616614, 269571863, 359088646, 966466714, 517758009, 296266107, 759693476, 8359132, 913629493, 784566713, 183002837, 126024384, 221347742, 222295800, 700317326, 188742875, 303062465, 497783415, 259148303, 716836609, 443646732, 473050039, 281337006, 633085659, 905571655, 927468928, 933385451, 555182720, 257384531, 573317295, 161216371, 356571428, 877157629, 681203986, 354556681, 872081670, 389195225, 498296046, 584420791, 161804471, 642962858, 600443687, 510082638, 794145540, 651438301, 180398628, 545150286, 814115675, 733515348, 261367470, 43047674, 460087208, 396640394, 759733173, 49100656, 740993214, 402182700, 201577743, 301420961, 304657020, 772680557, 672037408, 894125857, 443528755, 855874712, 132899322, 987290747, 463648165, 88108423, 310809165, 246918242, 675226430, 987949493, 338219970, 369786787, 343978979, 827187757, 421287052, 289704354, 422351462, 35001306, 709260626, 473283424, 983560427, 495890369, 932594759, 454791356, 241203789, 71956416, 898727060, 573394215, 440394847, 12111849, 704580644, 856892185, 790797810, 209044629, 246252013, 718465713, 43026503, 669596943, 389729087, 205969540, 405197327, 318429362, 738448637, 274318018, 759756893, 291732082, 1862424, 603877691, 610033314, 542465846, 314224157, 651333096, 856785952, 621458024, 558315993, 356191937, 564351047, 905885076, 638816591, 564437953, 503214166, 342812709, 690772840, 143618002, 709854137, 138115519, 658860564, 975014405, 484855994, 704636486, 263099033, 597661119, 505215673, 518976622, 138867899, 55914821, 859690518, 179261610, 279037915, 193595916, 964392730, 222419098, 219291524, 177172842, 257649193, 537144597, 21113882, 378808261, 897290969, 112725618, 304411897, 85939993, 230798361, 987399029, 523000279, 57952795, 85937137, 5554369, 892681555, 709771628, 802692077, 769036555, 969896468, 184526712, 498491896, 188101400, 633758061, 749229274, 6578619, 775361540, 760042079, 185181309, 87654322, 130940849, 409767109, 100783973, 520099917, 962608877, 395754902, 585127804, 223164457, 924912148, 265447980, 463933572, 974446708, 818906787, 313822289, 662852715, 865091214, 363128618, 130105553, 336605293, 106355385, 864255719, 979926239, 46039829, 567979209, 368471724, 865339564, 692277802, 687539037, 509373282, 345572361, 652508336, 906956647, 264131065, 89336714, 828105787, 312328692, 523941110, 62604724, 87044595, 991645388, 707167862, 357878733, 848654456, 495040005, 411781908, 163375862, 433134942, 301743427, 850469863, 924434695, 477488652, 91288496, 345753369, 963025383, 936101986, 814620445, 430413249, 240715461, 357181245, 668933908, 11369068, 869256937, 361149431, 201841628, 486527035, 526261597, 616583221, 633642673, 864541658, 564097580, 694382716, 836725974, 972447909, 178327148, 692775195, 573136235, 91136205, 503434911, 621378464, 351617590, 810923894, 607163755, 88209251, 2592000, 345988513, 526343495, 608080280, 851381522, 994463797, 901242263, 868482097, 317459228, 755362815, 294877804, 951806535, 858545222, 96627936, 688545564, 847980474, 95255569, 161740382, 98139743, 315224812, 752952626, 414335670, 652426667, 6300745, 92050433, 576988142, 239619895, 185033734, 812260822, 126090529, 465764022, 71441763, 441600994, 737268075, 37417959, 211728840, 276266998, 60559170, 244119533, 319275846, 640678665, 626037883, 952927277, 180198708, 540162014, 245949788, 273607388, 404900277, 615542998, 511522829, 353954965, 529882681, 353831111, 50045074, 365617656, 39840210, 210089753, 398364028, 993701888, 682845316, 237327590, 810829878, 399099918, 659559818, 535305890, 918869019, 560233145, 223494479, 938181821, 684416479, 828177081, 682621640, 413464250, 914212012, 323073629, 833879100, 712664037, 812305696, 159372013, 535576186, 556091465, 509012019, 985913688, 429545803, 991456829, 358632182, 352444359, 685160450, 536812179, 884297895, 59517643, 112877925, 295623225, 247987902, 950792149, 486250934, 971189829, 497007695, 611719426, 261775170, 500009629, 413760931, 756636038, 900835858, 645414668, 597245646, 307251585, 921355039, 286177295, 411471258, 148072624, 287651948, 171137201, 693810171, 875934540, 389297862, 4821862, 510689355, 845324110, 889606432, 163955884, 71635292, 43282423, 298949527, 812473723, 765620529, 500729564, 408998481, 809683496, 4247962, 13507534, 953147026, 367093208, 505843017, 964071714, 756482598, 204883758, 483281711, 479964107, 264269841, 419667125, 886998861, 901007152, 341454957, 370054055, 332573018, 95455630, 663916762, 818441255, 656604135, 656443385, 377924276, 707947651, 419383145, 894787955, 95936968, 452916866, 353212976, 584527737, 40088883, 493661137, 936122698, 155127625, 388336713, 745342182, 825449538, 635449232, 301695683, 747899026, 36362228, 767038792, 223318777, 880576796, 177735442, 570680264, 985996388, 533022417, 641770983, 970620199, 269057262, 496761856, 903954058, 291143851, 257270803, 349706063, 345122299, 592930270, 897044022, 917651385, 378763147, 601254734, 507671555, 823844556, 926338268, 381518514, 290896795, 710438006, 370417176, 30142324, 410834024, 272847462, 314672444, 6577852, 27979477, 323863301, 468546137, 766280303, 219178376, 401959012, 851385599, 531104221, 192349925, 486123630, 142014326, 516152532, 485424683, 279358485, 531925238, 1501439, 419213030, 229408357, 111687350, 953722221, 605919626, 83493385, 921134468, 29289096, 996211547, 932297533, 673577644, 191438746, 5306715, 990363427, 883154458, 789785296, 220790417, 468041815, 430902952, 563303378, 516863864, 972567220, 735270891, 926679942, 670734466, 74913076, 922851654, 97693237, 588791715, 28959679, 842841761, 846029174, 515444024, 242001344, 165300189, 383085598, 729936167, 191203359, 216832584, 688975214, 900658233, 569844654, 860897133, 270689380, 749098265, 772315139, 887994426, 764780779, 10493721, 661480835, 443249773, 217054099, 627474631, 450720789, 260668981, 311820970, 212257568, 237446733, 603100351, 713217179, 416638389, 799872037, 585565675, 347335681, 895372141, 486328723, 97324451, 73877826, 522263085, 343799383, 308397801, 144715860, 344759221, 76410559, 964228735, 898824917, 747869261, 782125894, 8730751, 501447214, 267262881, 214349732, 35778713, 686174832, 586105934, 563652372, 743617671, 586688257, 491681570, 978034380, 697190672, 814695863, 954910223, 846809845, 786084357, 159850722, 824371054, 204257660, 830541021, 137430560, 69293572, 491383709, 214755748, 797132742, 684674228, 892720557, 480344690, 380461455, 363203194, 414022585, 469667991, 832093935, 466204564, 856678483, 450966587, 352102000, 235077636, 187253861, 264327352, 893970828, 815515074, 611433154, 23970645, 543539673, 994777006, 354329460, 573553729, 366696712, 126642036, 533997542, 971172606, 665072517, 803336858, 860757792, 880948842, 727077080, 53711739, 721416232, 104239751, 754408036, 204103061, 499251014, 764278340, 534482959, 609970680, 409564541, 187997415, 117632739, 381577554, 751291578, 182851182, 544608032, 868604869, 546803864, 750931937, 72140541, 551204874, 347044620, 788539915, 517375126, 983615914, 687391283, 183468128, 420937409, 423891521, 602938968, 891207050, 310738691, 112215586, 616004568, 71562330, 297944257, 374903086, 411825573, 235824956, 782304968, 644916892, 197201402, 485648609, 196606379, 185732743, 870739581, 93937424, 105824027, 8036624, 283295286, 76941129, 55521064, 356046440, 836480122, 301690316, 178040905, 128678724, 18812835, 878227281, 638339608, 535103953, 390182054, 188996041, 489157609, 127308362, 790871642, 145503625, 317104761, 729283103, 68364637, 463082436, 508790528, 866157525, 292431367, 804313589, 301037908, 228258079, 540037086, 906144024, 193216206, 478457097, 707643381, 655310284, 255248926, 910918576, 540416575, 256497053, 574109005, 68643844, 247007677, 84528424, 795625944, 922876110, 898449790, 175973648, 109112243, 190040714, 288222488, 650223331, 326389327, 616166589, 997912057, 258270950, 651003569, 854865871, 840019094, 451287484, 198346303, 809293319, 89008667, 907359159, 287300603, 855922995, 796618203, 635391219, 50099615, 151376296, 279604481, 550620013, 523654166, 208429415, 91925165, 163164157, 736399271, 796865733, 224719784, 449825677, 341020526, 178753004, 413599717, 826769951, 115636021, 687525584, 534171095, 26460282, 349942564, 885737955, 354254326, 417102135, 114573919, 176617160, 572985003, 213894994, 464210375, 69652168, 78229471, 115627317, 437720444, 36187609, 189336340, 680484368, 349253501, 664613165, 690477531, 845554898, 473502639, 274101129, 981232567, 890102143, 708198798, 738965518, 186997185, 538448873, 33718534, 126160967, 60021210, 602468829, 859023115, 909017628, 512706445, 806086588, 928406969, 644357939, 805919104, 199881982, 52998976, 989408685, 959405541, 123519049, 821061212, 251515003, 296576460, 836697400, 444489868, 729818937, 313307262, 111093859, 894515371, 144837293, 293706894, 847369400, 658517475, 170589234, 561388009, 250781501, 189804889, 186829848, 117740947, 651727072, 879247290, 306641632, 899023700, 807428287, 263076968, 699187152, 566761252, 710076413, 916438034, 71881991, 612506482, 665093136, 864910394, 186913272, 520183205, 484412719, 500219526, 767260351, 20420121, 447614187, 509493989, 482502638, 526737528, 352094193, 27680739, 628876861, 315531573, 260559167, 434619309, 835019659, 264172843, 889409639, 668979467, 230051042, 751515325, 575615217, 589852492, 990888055, 114958842, 23208393, 652930097, 851161194, 575247062, 951350239, 635783891, 583687666, 313757269, 869061053, 756924010, 95674876, 293576416, 294223899, 52311777, 662636596, 349915224, 375184702, 754294004, 922565439, 683441266, 778351874, 241198398, 121607947, 55935724, 115882614, 116695909, 44097740, 131130532, 811377946, 219886780, 9809968, 41598983, 916137861, 555737214, 763817778, 146782818, 454504249, 955616647, 763334588, 999953961, 180118426, 500540416, 611899660, 165809825, 698467347, 55564184, 244602444, 893117113, 335656852, 283657343, 702985385, 128360129, 994861763, 844099583, 570317507, 164770065, 854557583, 982658952, 174486174, 478168788, 26476179, 957198132, 52601858, 252630966, 584542967, 967915529, 654106795, 523945511, 530150434, 343314651, 195745038, 875670280, 282714607, 69953991, 528429450, 421605720, 750712460, 902394853, 540587285, 715147525, 310046748, 802663786, 863985091, 521715689, 558306482, 707578462, 101737961, 911079542, 236266321, 969477997, 351175880, 604245544, 874527511, 983062364, 420093702, 880274316, 587404804, 208778578, 120683869, 5433629, 708222922, 268343536, 554682307, 973630884, 454736710, 80559592, 462540814, 48867422, 507172507, 392108497, 325389472, 676401737, 552412998, 788492352, 947084611, 909231406, 832450478, 591100175, 928397123, 398287394, 907448612, 430611272, 230828109, 157240178, 42257308, 240043493, 63628908, 708279578, 28842940, 429606786, 799164475, 874467646, 424587433, 688959722, 21476458, 244625856, 100845763, 526240464, 205562018, 445358346, 462928869, 156664730, 167472456, 856602900, 813761725, 307192504, 688439360, 699372705, 550978352, 535373456, 122642672, 717440996, 744428141, 836012706, 727882090, 345840762, 629985186, 460620608, 455608651, 706764659, 351363601, 980283833, 120669912, 315895769, 334412695, 475437159, 653527320, 196728314, 635175165, 143358770, 974028, 799029416, 103261140, 289948658, 950104540, 210668725, 364968024, 756140620, 62577202, 320398524, 928738183, 794638565, 400717470, 501714851, 539066646, 6059919, 341112263, 886419410, 158242306, 531089361, 478101107, 330974948, 863471752, 814535039, 984982061, 591434230, 583407497, 88042262, 207593, 607984221, 294185867, 250010462, 452820185, 17200642, 281841131, 699985021, 844095497, 577978106, 702731616, 712251358, 736856356, 602853622, 903941996, 52068250, 111031746, 83968958, 93346561, 454494683, 234514627, 711931357, 148249862, 237333223, 81333325, 803911569, 99815162, 858677807, 982467794, 103380487, 94779780, 734860762, 666413030, 882368797, 55642198, 906555565, 991942189, 612124137, 393654071, 837121057, 326909880, 233176842, 134489470, 236450054, 122845872, 689795015, 253346455, 927352158, 989690243, 87882502, 610962919, 444336258, 408747002, 746497922, 306511536, 24574176, 484065884, 124118550, 447630357, 208742433, 31094160, 232496006, 793074836, 588104037, 832565290, 1262754, 793486623, 103402765, 15854171, 161331163, 199302692, 416920007, 182741146, 393913762, 821141268, 784065609, 28415802, 933072394, 809141050, 485647497, 248162462, 530423929, 956138197, 816465402, 503972730, 300926538, 406411431, 372622531, 270730541, 298106817, 501509856, 928199306, 461144042, 620983855, 584887753, 509925135, 275814140, 797613162, 920457630, 191607406, 955722364, 808526282, 854589372, 173055735, 593327596, 431574875, 560196022, 122849189, 929055326, 502766797, 322001196, 916655856, 782711566, 921806672, 299673525, 405178844, 180838434, 602505467, 411540219, 286020231, 478757382, 244987590, 848396059, 470433273, 654271729, 436182779, 118896054, 384270415, 685717064, 204237957, 401240277, 655592752, 956186204, 213445923, 911279383, 525480570, 934663548, 518162215, 188830110, 88337467, 733842353, 503341179, 92907682, 141745684, 392057578, 215497150, 479186709, 318456635, 346293326, 722735128, 187182399, 24384234, 708501248, 474223491, 576239018, 113240778, 564112704, 698326586, 3282263, 212766267, 388314041, 709371093, 957306237, 335379869, 394360619, 137985758, 794386256, 529354301, 264969798, 451660919, 104455818, 605505581, 30887666, 802694864, 517513835, 671272118, 261719190, 213497427, 105886865, 721657926, 132882380, 807656987, 717276431, 499362928, 239064803, 285980885, 982906698, 14600595, 764381736, 530965800, 485145426, 911560551, 197197094, 938666526, 233971650, 757768530, 414715032, 278598628, 154783739, 749624878, 118097296, 397622488, 188742994, 334762925, 9109680, 257074598, 753112222, 682439340, 106532092, 60377380, 322512224, 52675537, 689692864, 619300466, 127290194, 64591104, 406637637, 256156422, 49742133, 208360380, 406621809, 869997709, 103172307, 683371049, 41808098, 677438624, 89522049, 887318739, 806761287, 753386606, 453426058, 470970374, 537522478, 288377219, 137590604, 237352624, 518728274, 950216429, 348067947, 434430839, 542154697, 583137725, 398758388, 690251035, 953552213, 226038154, 92644012, 438788733, 331547521, 768066261, 466272036, 818545615, 79571825, 444985886, 495475994, 899941020, 492407680, 718651055, 254250491, 720877854, 992818869, 172736105, 340227478, 280313662, 571336932, 582976395, 602282571, 102080747, 806299138, 545829732, 415195101, 861173881, 894085902, 834565546, 105864102, 492630217, 214850077, 160175355, 674908139, 656306954, 510483845, 499956746, 704020712, 394695391, 855866732, 337785331, 154987581, 561063954, 516624409, 334402820, 462396093, 605727375, 7041798, 8122713, 227064356, 94429630, 650358977, 605932594, 8231043, 878111204, 436354882, 673276515, 349749214, 68798847, 382394237, 167181389, 304692105, 752026470, 385816600, 109544920, 309755464, 305157355, 874494693, 287396851, 679580796, 629701611, 971137442, 69994032, 884588390, 47797303, 351907776, 916895878, 340564386, 461248965, 890782711, 252024993, 705939669, 86113835, 940519466, 737962923, 371661832, 237532766, 352340159, 515104527, 367642529, 719390132, 575008, 736335844, 327653152, 893377049, 738379037, 837997136, 470527361, 801087679, 992417795, 233115947, 181869420, 615648154, 118645187, 366968012, 553594817, 174731799, 967799889, 134197573, 276040532, 860828872, 291236774, 260399448, 745967018, 475878781, 591161825, 384484793, 812982406, 314316452, 169773421, 125307688, 459971544, 64787817, 627428112, 317368372, 913279719, 988636704, 558474465, 600192309, 20802928, 995900797, 226813269, 513026251, 802818096, 404888855, 836739807, 32024802, 957516008, 467543900, 98008787, 938609376, 24833782, 171692276, 32296823, 160998199, 607796337, 674389334, 967723663, 961693290, 570494354, 423423686, 834713030, 343178395, 976444357, 717173251, 647507516, 376879519, 637964290, 667700152, 966898840, 759754757, 987813214, 980224508, 979122450, 647382658, 886787925, 987689244, 152995736, 275238508, 203172946, 16906631, 198716576, 402395657, 559082310, 346399888, 847304461, 812209257, 921641078, 834078905, 151408505, 913185955, 384520028, 735038372, 671907766, 413248270, 140364373, 977753991, 806819103, 818574237, 473965859, 552006203, 6708830, 104369184, 777058456, 367720725, 429601797, 889036897, 456171492, 951418753, 489538106, 315162871, 828239658, 69017132, 500266715, 399517756, 728408184, 917343470, 942399752, 370445578, 196294521, 785651714, 831846136, 186520118, 800347884, 877019901, 59012523, 168665782, 370556746, 557992327, 242564635, 98073493, 194665613, 733847237, 466985004, 121072155, 54059971, 711714700, 549771949, 366495843, 779445044, 391421587, 398528185, 770206870, 647979599, 346031295, 658561826, 870284087, 872103095, 662439710, 751925216, 924457410, 404421655, 452398906, 977612935, 13405135, 14479199, 400383619, 662963496, 287873588, 285462050, 13258204, 877589585, 17007671, 7548323, 166565830, 671894748, 121312244, 601371738, 514620425, 377247336, 322457498, 325103744, 127171471, 793827390, 642175510, 122509338, 613298410, 587983242, 574776332, 429719894, 893360233, 298670977, 900239424, 248454656, 955085809, 342872955, 835125733, 906846888, 482817966, 35476404, 808660997, 547212715, 776546980, 381317302, 78073103, 597812598, 281377466, 299528372, 821349866, 88050230, 80924858, 392181058, 816307445, 797369250, 230156161, 75008784, 341478289, 787866097, 508603781, 532399394, 294126039, 235908058, 6288591, 121261425, 553988459, 167383013, 395320466, 526668898, 976591169, 160378790, 599416366, 842278656, 797022127, 14740102, 603698116, 753105523, 838895108, 363179375, 793652824, 621263825, 960954091, 202835552, 507357289, 231586568, 982676391, 455505533, 722845350, 451955330, 617946345, 64404616, 949903125, 829467993, 240410557, 677753339, 892880584, 32464640, 184697684, 920043551, 844967819, 31103778, 204423176, 481319560, 928381190, 488153989, 140974736, 364693903, 758001534, 1428927, 125887550, 969503389, 897978937, 779274115, 179708034, 931953118, 820648845, 582878786, 841253393, 271518567, 156694474, 309464143, 538851107, 599805641, 455477118, 800383429, 235496150, 950318971, 855039558, 132596468, 470552823, 849245793, 123239720, 860276109, 626052148, 804396573, 299234148, 509814755, 920235615, 934579532, 91735258, 689773155, 118219530, 211125734, 937056215, 155825446, 468942429, 941132541, 197732925, 509598142, 818680408, 900215803, 497926094, 587273633, 24856421, 13051839, 730450444, 440438675, 891010108, 80509889, 480503135, 547536255, 509940698, 526491574, 605508540, 739999317, 704175290, 444844574, 600194975, 248384785, 34729962, 68223475, 404338320, 627571261, 609840498, 68798495, 780836460, 131939394, 267905575, 707153845, 236536864, 782081037, 17710582, 656937594, 918371971, 883233977, 747594677, 78672655, 686610095, 411067202, 82719076, 488460431, 564933473, 376040775, 134274474, 477074023, 312466247, 866669190, 615198073, 619103911, 69358725, 69841358, 267848676, 186361958, 241228729, 29962049, 351120434, 91491991, 957739792, 859816722, 290864736, 919616851, 873551453, 605778154, 730007147, 40100991, 696858732, 965668390, 779898958, 223430822, 981463191, 477330504, 708415278, 902873260, 905397685, 697540329, 968604849, 185048206, 648943751, 598099721, 514460595, 465682594, 177708140, 606830453, 239500710, 800740588, 18185433, 80113076, 247156299, 648198711, 206592048, 123882368, 101994453, 127269052, 320206659, 271381275, 646384257, 662878015, 62946828, 637230402, 759076040, 888480112, 109183021, 838375286, 498462807, 183768442, 485118607, 78368707, 760322022, 892771733, 372324344, 233094891, 50507580, 413721875, 870332146, 912211704, 736283979, 472983684, 614189663, 739856210, 750505414, 387031177, 677570535, 216332472, 525285363, 523363977, 664117959, 192121346, 886234086, 437781832, 203848996, 975222150, 563327640, 372858633, 323378091, 431736313, 41634180, 515506416, 995681474, 288731265, 896401407, 672828206, 996771707, 467429052, 25831315, 531196716, 777547815, 675079931, 905690354, 974637025, 292804499, 607353620, 947032782, 326567421, 167459306, 154469316, 54912638, 9205319, 780981067, 144557864, 413070864, 376321115, 752938881, 938074968, 631566075, 333461061, 302805973, 977200839, 277484216, 929098441, 401041405, 988167924, 985786922, 586188328, 909793670, 597484194, 380055497, 606211882, 791471831, 873551903, 526987633, 871158748, 330757998, 671977686, 791409145, 520313483, 603935073, 85675156, 997988070, 930834834, 892840302, 200346258, 857002881, 966952788, 478957456, 265003786, 260516141, 527568261, 405787917, 815084565, 997458480, 842489173, 357688139, 651473599, 397784353, 442209500, 121049049, 850979009, 220977571, 486809951, 528986759, 700928645, 42886514, 505367911, 323858185, 991117939, 165064325, 930454716, 954058860, 958104536, 228036174, 999361940, 700730645, 178587130, 62830189, 769683226, 768785740, 336588261, 82981301, 833156039, 238899116, 972342750, 939999808, 958357133, 705301225, 41818692, 694610288, 264888312, 699273779, 308241537, 614237719, 286228754, 289520345, 693470208, 221159430, 640179388, 924697462, 516622296, 749719745, 205950984, 197293187, 851660009, 363862910, 128804163, 706129083, 872337515, 602655625, 686758316, 997238385, 96616329, 858440872, 555594872, 215073828, 482904333, 776708605, 911192625, 463960622, 705916896, 163996311, 563173798, 95414770, 159692984, 663202073, 939994067, 510669087, 161346672, 584739736, 607837224, 249112749, 966562141, 458583223, 304877158, 598029976, 670325834, 38638445, 636637015, 61089033, 645994339, 343592132, 870105058, 83178247, 12564794, 928860544, 711360652, 247122877, 470153284, 974839509, 503788913, 251553486, 858595476, 191436057, 500957713, 306303071, 685664099, 743795830, 470906540, 888420362, 956264917, 657549097, 223898652, 95562788, 906060871, 501508780, 115576808, 921066554, 718804072, 715328218, 284112024, 42354958, 368987198, 852079628, 102716850, 96636738, 891190742, 429415985, 858306270, 665559422, 213861276, 337208608, 2874520, 868476072, 919790043, 664043449, 419987770, 265437383, 1808218, 54662215, 356445455, 53020297, 565360174, 497446930, 609576191, 246417479, 966049176, 980744295, 826866314, 498898921, 487420970, 169298864, 202280054, 385419732, 705368061, 559350522, 112067029, 728112815, 998959209, 42786598, 930039833, 834965724, 430845318, 876958713, 453973484, 506189174, 240467972, 862766024, 456419282, 168452815, 2895769, 200149058, 298695387, 751671229, 684928858, 287197990, 129800820, 3833762, 432922962, 330061354, 821766487, 440982966, 321823732, 321094401, 892963492, 503236123, 478602737, 137318430, 155415814, 32256621, 626969951, 990970473, 797119949, 608864606, 638888712, 62617995, 359013774, 654272786, 179168049, 788196724, 351241061, 331159366, 322778876, 70309037, 690579331, 823468200, 363354335, 822061266, 587567129, 414960364, 692377368, 600857048, 801020403, 147817015, 877233945, 483163614, 892451378, 392735723, 579237088, 185963519, 140598278, 555506866, 921660303, 835181610, 411658679, 762480803, 279737605, 609646494, 79224334, 497390659, 973009731, 647481235, 859433769, 763374499, 439830852, 21827479, 892688565, 65593613, 789013157, 621813356, 379268459, 232945862, 786867966, 888825425, 724728958, 303855896, 54510165, 862760352, 402890690, 90905500, 797076755, 280112310, 538768139, 927333524, 219094471, 43428027, 26808906, 226779036, 198454812, 534444527, 236162295, 41895533, 351979179, 84106011, 91567635, 287680995, 557056764, 115654439, 31393724, 60512479, 316217724, 204697237, 889627758, 158928265, 77616850, 821433245, 466491853, 559614165, 233932635, 564158439, 914451548, 805079320, 561733799, 21553715, 610137077, 982729610, 660998101, 192853550, 349503007, 980683986, 970340380, 169417503, 2170880, 897469581, 818713480, 829458047, 569725022, 209449074, 188220831, 695816763, 441029321, 432640460, 161101190, 428053592, 11598633, 403434880, 227173928, 537387402, 826812112, 266419502, 711721345, 399446247, 671108989, 284373955, 348843378, 619007297, 666470999, 316666369, 879610392, 39224731, 864179630, 898555986, 278607762, 670875455, 941774430, 869015221, 40571528, 340130028, 625848640, 192597657, 224605698, 919423729, 891458608, 286182461, 248163771, 489264409, 898158931, 809077232, 182966855, 767877929, 439015465, 519131393, 348776405, 859453524, 610883380, 957513136, 334840856, 784056943, 793128330, 193930652, 392325749, 844493558, 668503911, 312224940, 930508807, 897447706, 139664458, 327163222, 145380663, 939651441, 960997589, 429354571, 942131720, 858126483, 398918006, 739045682, 586295718, 49403482, 943126138, 77890972, 204411426, 572230613, 708150488, 859396492, 610587134, 683760381, 337551020, 918050953, 748353547, 14693141, 527713398, 420223446, 321920773, 783400583, 572641785, 698483373, 206283263, 203458505, 835418910, 488369867, 662070228, 149020605, 408248517, 621666966, 217280657, 146133344, 611859563, 495775601, 865657505, 698834207, 753619544, 476063322, 810914595, 761479248, 8175952, 31129826, 686327032, 75024130, 72874020, 199759102, 727799382, 535263461, 724763339, 823739689, 960079646, 297646923, 745141515, 474793261, 136117033, 297522498, 725557136, 827082759, 940567783, 663842945, 620230422, 446084794, 368893110, 447799307, 328743512, 662659722, 740892459, 287200211, 658088702, 627979059, 633822732, 521666506, 362637107, 410496836, 896235059, 484480518, 219425706, 877052209, 556465422, 573988533, 77823523, 3356595, 876735894, 227234220, 120523826, 818454684, 812815555, 799733243, 559284761, 754095653, 574375679, 754947904, 550831964, 242773645, 121414625, 168150457, 534005147, 135181811, 250551585, 371335517, 839495657, 620963235, 388970954, 614110857, 822851835, 461716947, 247293224, 766819850, 482316846, 411455305, 312481648, 158560570, 207721144, 154421026, 753444950, 104552448, 338090570, 387586364, 347434157, 908835115, 291250033, 24636320, 741247494, 993257938, 435476945, 131177624, 662268698, 713914875, 423375014, 466965670, 382459958, 350468812, 521804961, 817379792, 698471630, 429009385, 466876323, 114288863, 271672588, 319549784, 488884236, 152809694, 626928229, 647525171, 434923074, 672554609, 215398385, 187015991, 882002990, 853293932, 434923732, 994571320, 324753207, 602860774, 225389413, 974690994, 273780030, 975101538, 218386459, 180879269, 973958218, 361091319, 486224547, 636163494, 290898027, 420552290, 252800426, 54199665, 630669991, 493334337, 760699619, 884907484, 16046241, 126686886, 765408518, 845302336, 352242227, 186279402, 950219881, 617307839, 867198567, 973385373, 925389388, 215434886, 345155034, 229875647, 890785623, 199642666, 510340040, 816759033, 694866427, 386759343, 849614639, 501861238, 581122052, 36843963, 355026209, 105793531, 340990214, 993534550, 27457175, 663850030, 323556151, 830103580, 822147004, 621668197, 934022049, 871888909, 198919265, 866940919, 465685983, 181274605, 644467159, 818989694, 202570548, 902532583, 276334060, 171990089, 796422592, 800727873, 484461121, 388259967, 159788312, 339470274, 178332321, 52347578, 546304079, 776252694, 966545709, 88867613, 334502800, 79904008, 969382896, 827456802, 624551668, 234250772, 393562024, 483903668, 307950398, 545410839, 954892829, 142330119, 124649688, 210929032, 37129679, 702892251, 730765796, 284826636, 524539217, 837236852, 154828838, 571250330, 426700008, 626198522, 696767091, 352579646, 471609572, 730756410, 293999475, 980368991, 767950492, 159683975, 397556877, 762542269, 688860222, 666970832, 677756800, 650141491, 469780249, 63327573, 854509832, 746670121, 455841031, 330583964, 976083011, 246833819, 188592659, 790131655, 817835947, 569859958, 235280779, 205418455, 23053131, 691155744, 39276790, 431096764, 259545801, 500742184, 321996829, 216651861, 747388874, 316502122, 130529788, 739174047, 118980360, 884672534, 707743910, 631028300, 397362036, 176823124, 998043249, 373176626, 53215535, 612866022, 480440245, 797557955, 576944475, 379482069, 403423132, 947300557, 919644825, 270261905, 505501888, 819280034, 603136063, 672020313, 645970114, 468583778, 328187422, 813233410, 75096765, 979059738, 4432315, 785324106, 402721009, 302971147, 756813798, 440420306, 69243843, 449169919, 685079186, 89611008, 280699617, 264616755, 777461577, 583684019, 42138132, 423787325, 207722539, 461803280, 525396032, 494608167, 443246392, 680284769, 476588927, 387730232, 8897508, 382243964, 331237420, 82346417, 131686958, 103340112, 985671585, 487573499, 541953693, 800366029, 88012433, 452501283, 130354401, 932772983, 482287194, 501297592, 18591802, 491934472, 410669114, 928088328, 509553103, 423049336, 791666058, 823165247, 208221456, 395975385, 925139786, 612688798, 396963500, 934736685, 716427227, 666163247, 490069397, 313645740, 876360109, 871313907, 151142928, 226811890, 159537987, 576808837, 193405452, 70663819, 443562891, 260800733, 665841674, 671660247, 618989349, 57690793, 723776258, 336415237, 437615336, 530380641, 519552853, 8509865, 479961006, 936637600, 274381042, 213048507, 846896631, 723860814, 308768005, 890578053, 259618014, 680563515, 792587140, 643715970, 938534731, 69843035, 623983102, 370184619, 782191416, 187626514, 159530607, 807446843, 493199623, 382242044, 84326425, 690127163, 377811155, 275166008, 856442506, 52192989, 979122515, 234085682, 231713481, 844762047, 988885051, 565134674, 291042546, 268449539, 10722228, 711778934, 422261355, 201565614, 752826863, 694131339, 413747634, 861369721, 678508437, 734267616, 505008497, 817992696, 44473578, 837117350, 468823894, 853918102, 412513027, 262960782, 739616620, 556079391, 124993907, 937149675, 596356658, 147666963, 300119649, 306143482, 648011227, 938532622, 887092144, 914762943, 174105677, 913919348, 395484917, 821482866, 538603557, 411505070, 582342583, 637394364, 417781734, 464581893, 85236391, 452204864, 237979587, 604683399, 504496840, 369832858, 307273863, 358712638, 298815248, 349536238, 87778008, 155331951, 226347499, 749564195, 245565752, 86079855, 636260302, 202218126, 433689000, 781638293, 129351971, 903474816, 640766746, 706871803, 116149543, 668332173, 755865999, 955484492, 948525250, 276777333, 647787207, 890786515, 157368669, 574872257, 312724709, 164306528, 422571370, 744646944, 140482422, 893992913, 448886473, 83693596, 747460560, 463113688, 67081089, 240997687, 184051636, 308164878, 942010396, 738317016, 606487597, 818107591, 779707197, 636274653, 713393723, 650682741, 184935645, 91016887, 972523663, 36670727, 931325148, 76033773, 767117478, 283017866, 828211073, 974004491, 202661552, 328837941, 227698217, 22762406, 164390189, 456477940, 599004179, 885438405, 877099612, 40732958, 61827993, 861519691, 479959924, 300615979, 500635070, 400047688, 698565606, 851586836, 116121138, 389568176, 882603197, 385309444, 296945417, 739131354, 626985996, 945800384, 702023555, 396068866, 878840065, 252163226, 616088126, 349390055, 870950975, 5485414, 407537155, 867722867, 3108207, 977682103, 169285891, 717216937, 774723768, 61792055, 264360143, 366081308, 858681189, 237386848, 7061005, 88700296, 95185854, 199674388, 782532217, 443782281, 26091241, 8321866, 328859000, 974249402, 543534512, 427923586, 242492482, 928691729, 186217099, 853193670, 9311393, 695721773, 807670626, 32585475, 531356377, 199437875, 953273882, 993063625, 364686709, 639651571, 386072809, 336837734, 837293944, 728730811, 703933097, 56170821, 370061741, 674414332, 276447917, 274344980, 265495747, 147354111, 609624497, 176193020, 694217734, 544249455, 308291253, 773979876, 424156863, 525953608, 125860680, 441113371, 861767302, 327756633, 268436894, 515943242, 121219648, 393913311, 833826051, 99893545, 292261860, 466215001, 957340397, 377340744, 895133445, 172720000, 976148054, 658272421, 637284380, 840050895, 402644678, 486637855, 325943028, 898037188, 30903016, 641865422, 752840940, 616957878, 843191065, 337117838, 28674883, 237947854, 797244994, 10102126, 145108093, 571642305, 945583855, 990884350, 153380599, 302614665, 957201784, 194447334, 495595194, 528657034, 845961350, 231218937, 752906864, 984459668, 587925122, 323644822, 842690930, 32570642, 902955750, 255629705, 284664286, 772821410, 827176623, 176430489, 48046218, 870455081, 685478248, 241046030, 567698122, 698691673, 346813514, 153758917, 356539573, 429303628, 268936633, 522994583, 422835644, 537354927, 66490369, 896305008, 180674371, 605857336, 344136851, 149341939, 512777102, 845941507, 824212559, 474927186, 581932276, 330458618, 603855379, 632663130, 935529509, 284972334, 190659177, 141383143, 230760671, 702331926, 175801330, 372853635, 682333268, 155422002, 776849555, 664859737, 169543948, 685959483, 486278946, 706616592, 250765083, 842570873, 639405021, 424655108, 351073866, 663966129, 115902384, 69913440, 108980813, 237394796, 275355677, 328541294, 565755896, 540475004, 649027907, 578969188, 263865416, 466880237, 37680765, 120824300, 678615497, 96172347, 495213759, 550648622, 54952090, 999588214, 302864318, 671424484, 483422475, 739666726, 71066268, 687118774, 901204239, 38669788, 793025310, 969122886, 810764949, 41740710, 9894885, 635573026, 219597639, 203831176, 82974355, 242067010, 642341562, 92553945, 358175205, 136657861, 33411705, 863764631, 973491927, 334612715, 834819992, 639130828, 415705997, 752245901, 38222839, 898022505, 281340769, 749818588, 210205142, 460044849, 354375128, 729889865, 14581680, 2902051, 166440442, 319329874, 994036244, 621292030, 293545606, 778496010, 680523566, 985571521, 4721786, 658015494, 61011241, 173202213, 285770443, 68789296, 15619274, 304883550, 113172308, 713858999, 629760202, 709233810, 329489875, 963391296, 847835224, 366796616, 764316223, 139945671, 859618581, 844534171, 469026131, 534704064, 286816368, 539158832, 245772569, 730994426, 895051201, 401454493, 816667313, 193368515, 195081168, 181850634, 958647818, 555768438, 873089197, 292394207, 541050390, 527251645, 399757305, 444394020, 686817496, 477933468, 723894791, 203751953, 105284581, 415930886, 629390705, 603483750, 580468389, 103438097, 615677819, 515054990, 844770605, 236438545, 964844908, 422344550, 698903316, 160576620, 322044404, 345919382, 604741898, 603374017, 682253294, 345789320, 917284550, 323046722, 568701362, 620225164, 571027278, 533691520, 568345220, 605654963, 243173105, 798233811, 692859494, 867023059, 96606324, 928308283, 548838008, 491544476, 954734333, 129736819, 304715518, 816992988, 87562604, 966124452, 535069978, 386398148, 657172177, 577118264, 785322181, 633915142, 159289930, 80073746, 789807095, 410615159, 93213259, 160166140, 115743279, 269816694, 857338082, 229424330, 103247211, 201048039, 20839942, 750513682, 512657781, 135230767, 902873861, 434197608, 152368817, 502277082, 98702615, 582916128, 423302746, 968192083, 183764631, 841384231, 125828091, 850199334, 888043255, 810757841, 506550548, 633049626, 406900702, 904416442, 828581720, 683225570, 700676472, 879512015, 443281845, 52926636, 752629291, 133053054, 696177509, 426438334, 381914574, 578669667, 785715914, 503234035, 99281226, 89681250, 196564054, 387541164, 846241168, 674279280, 638283857, 715849689, 687691585, 781806555, 387704520, 232367957, 269401291, 830305558, 919364169, 602864207, 330675455, 969102888, 241225037, 88705494, 731792289, 701967083, 25754494, 16700441, 979412952, 535427316, 148186784, 480212470, 483694352, 758273141, 224838074, 912737103, 722766974, 988482693, 78203556, 599249950, 201314373, 614641445, 322739671, 431500000, 165672349, 10351477, 498443644, 357716010, 737563812, 879201219, 533714084, 909305803, 436012240, 560773896, 857818257, 691270075, 202138787, 634244756, 260264604, 49498471, 968452295, 392722563, 309298970, 388080353, 650253316, 111683425, 680050631, 139560691, 825432489, 358857477, 942844796, 466353624, 895729394, 359357327, 953009977, 246563679, 674518254, 949418518, 524588303, 638623148, 77167192, 348387108, 987513044, 844134946, 826832938, 42734571, 461604054, 32442691, 365414684, 958719316, 537942987, 955801969, 665569534, 311695675, 179627194, 599303930, 103072851, 619784445, 207877574, 922605738, 669136400, 476309170, 880233575, 868332168, 308882896, 85558468, 145085422, 338188920, 944096087, 423359188, 197740351, 746798103, 484613216, 564881685, 277372749, 295128870, 437659395, 434755955, 623027291, 169878460, 126547172, 257873408, 186492401, 602919780, 150013704, 951740946, 492540907, 255868170, 212179365, 803209932, 455032263, 832693472, 367982703, 379097430, 159847753, 767535701, 814208796, 249875252, 94551376, 344168308, 833319513, 916205204, 31702768, 436113300, 19360557, 730081312, 879410398, 270626518, 971446253, 599527402, 602353873, 866226744, 435019201, 286120827, 875654618, 179998361, 138641592, 17465295, 313385471, 129846767, 623390848, 114567388, 910861406, 897568429, 600724675, 55259078, 736716600, 972171638, 142700738, 5012079, 152088481, 521387130, 789643546, 270653927, 993297556, 249350484, 754593423, 680195690, 485573194, 992555802, 15069167, 533413249, 95292223, 663850817, 28020355, 398194706, 448161476, 700154554, 259213661, 67109611, 275247625, 773784865, 895406325, 731356559, 328881101, 525914602, 674376126, 841780871, 364341303, 159043445, 876495702, 159570736, 78288042, 323803020, 381573413, 176264992, 268763091, 436956704, 606431238, 440697683, 9607788, 53516365, 911530835, 116226413, 576419106, 754015597, 763997008, 288223799, 329556058, 821185129, 626023, 196992797, 944375037, 828045057, 95977322, 3176326, 489752585, 54121973, 348179768, 842228875, 75263231, 494146072, 390821903, 678403067, 432790026, 364274326, 515590378, 931219451, 997898201, 911861736, 701783160, 767844816, 977879894, 866536827, 625847444, 823138757, 420436943, 523838217, 862448626, 318783910, 248217998, 406767741, 267321748, 991855513, 76495842, 29892596, 85731251, 773600288, 47723841, 605790335, 580253666, 293095337, 583791675, 88726172, 85341120, 242747430, 333765925, 494608541, 316612052, 704960285, 101294359, 521405210, 989439297, 494560813, 948468268, 436136218, 872413919, 977275647, 588944609, 897271285, 491552608, 266650910, 713867819, 810766587, 991583568, 55280291, 701173981, 264688940, 534253557, 30584097, 416555931, 443115806, 477521478, 706222683, 503796976, 892184333, 586758812, 927676943, 791326544, 267952530, 559441039, 30676583, 312773120, 345982648, 681816898, 836985057, 209918012, 610577454, 36858188, 574256942, 687030774, 776482249, 74811654, 843943325, 785604942, 662778612, 617039024, 159307204, 941325008, 846496265, 964020642, 44585265, 466860417, 93348191, 36238389, 779809241, 827308928, 149855, 773778397, 337885278, 262193761, 675860364, 602274598, 812386103, 264080853, 550136861, 656715127, 202574403, 94721269, 545900857, 277060512, 56476876, 573213577, 124485462, 650958497, 529686837, 483980007, 982037412, 673285675, 401435962, 704188473, 55513914, 497975520, 894077550, 589645539, 340810289, 944268756, 254757871, 115634309, 389143346, 39381889, 111710755, 105033398, 755577839, 46683685, 912955996, 81569687, 55874408, 71075939, 169751393, 634994592, 404194517, 840555610, 62393824, 491178942, 369610869, 871040159, 470564758, 626833716, 650102165, 245981453, 473556627, 11651242, 449988978, 360741, 815922174, 714519195, 477735661, 679994660, 300328745, 433665527, 937558924, 990283694, 498366349, 100831911, 953119870, 724378938, 197914833, 371345225, 797650036, 660177055, 776941287, 696926333, 120703546, 834186660, 637389797, 739675793, 451583214, 909098739, 413184416, 948107634, 401901882, 87710418, 605252609, 920520384, 465170372, 698235330, 75749278, 585367956, 450712447, 210390692, 301895405, 565118424, 798268778, 236691814, 413477553, 398253951, 839075261, 714082308, 826631860, 897746442, 43645940, 253417707, 582597357, 920396581, 972099693, 328886289, 477932017, 974060932, 332567720, 184712961, 857290571, 388767912, 219554535, 920557513, 392573884, 912060043, 137452126, 890728631, 384093698, 560837991, 739799800, 795815903, 509910033, 42703322, 225628997, 531960430, 149245084, 873331055, 242416129, 23854835, 814227151, 171940763, 642308605, 721287976, 661268883, 520720564, 65445406, 892742948, 385207067, 726294911, 637645911, 617322211, 660058733, 378494384, 407779347, 228786590, 692423427, 235325811, 160245219, 442624470, 879074082, 61660334, 744664903, 767238224, 547980877, 189559, 215954427, 403985029, 177883695, 964547633, 286240999, 117676667, 632364980, 517697835, 530988274, 136031045, 382601585, 161659736, 259892159, 175181274, 179422157, 582816117, 568900456, 975504723, 248248320, 982012304, 405205171, 35241591, 406112309, 623293283, 937518409, 103720584, 32366718, 339863151, 63016323, 284012916, 321104745, 978930115, 914800125, 218580365, 959598703, 22063500, 354558745, 152169567, 411804326, 498608890, 487470809, 481419206, 257534290, 683491713, 595615122, 985415279, 754140634, 430356789, 858410469, 241565679, 203004095, 573634114, 667845563, 700582724, 534568423, 437433620, 870194362, 85566084, 456789958, 233695098, 719428070, 28386568, 220908603, 897649123, 592528999, 150266140, 768988006, 244999600, 177283111, 502647445, 864405904, 45365657, 966091553, 62970807, 913305541, 921862171, 284583349, 924140461, 983513517, 424380443, 675050925, 608176301, 871264660, 472231727, 968610626, 408495235, 472664238, 826136333, 855030304, 859438002, 671871010, 887858827, 929686621, 753030110, 332806971, 942165324, 783849658, 683041597, 246618963, 16312487, 889671924, 843462962, 485921321, 201570072, 270622567, 842379928, 800265186, 856271212, 721452638, 721321114, 128032392, 287119364, 225704955, 534366, 360103733, 284432649, 222464763, 961898250, 952693120, 296179305, 898285224, 80177470, 933614106, 651832297, 216322419, 867363441, 934993913, 49219835, 94480418, 682250185, 626373839, 558930973, 961425373, 336806092, 867777916, 715924941, 735286422, 604971678, 580028381, 293646832, 787305657, 504994646, 985888892, 720714880, 61045883, 215987901, 546486636, 525223202, 147521816, 577416332, 157198429, 979577541, 283052725, 122434097, 384649174, 597448517, 911395778, 890017105, 98878523, 427361337, 72815271, 689967585, 447252036, 582439279, 562128405, 178189876, 659126074, 562107835, 313122040, 582792632, 668826838, 264395479, 442438285, 712897631, 121906694, 187551033, 903511725, 402406738, 921160083, 841075421, 839601787, 771866692, 630782366, 870773935, 429239887, 165167077, 420449925, 40153279, 199764443, 520114823, 912895591, 862054319, 59767282, 18469913, 475138119, 458201757, 962939642, 26455849, 828694472, 820628474, 46173813, 157735016, 879902090, 695495803, 636332570, 947549043, 933079424, 227368378, 608792966, 689387214, 32736439, 585880118, 945434051, 289218757, 165544478, 768818186, 661106410, 392857956, 38315863, 728885112, 762395946, 10970866, 610799956, 641057735, 755278920, 976678713, 529176187, 473520306, 411993344, 31370282, 556133290, 911002344, 839239463, 758050764, 469375643, 672355758, 810599715, 789223348, 412104277, 132830485, 278685147, 785753538, 444423851, 255692787, 333800018, 323049880, 906427702, 400404101, 916328623, 961162301, 614317494, 479284724, 531329976, 730909099, 333326076, 297625124, 960769943, 27873943, 482195449, 521327956, 819155256, 322369396, 452468006, 154351257, 564071278, 697983206, 668477353, 39399142, 110143154, 817599453, 961027237, 335768685, 748082680, 987425710, 880280855, 170131354, 516655745, 340369799, 900719207, 730642059, 753813972, 822538654, 450896701, 761072773, 685929496, 281208567, 251759107, 260141348, 244885227, 926161777, 290628321, 751718574, 532953269, 229228109, 854283684, 444501045, 442718468, 243746778, 245673107, 957800571, 859888128, 279904528, 693768907, 66413722, 391244341, 466069527, 213536675, 952844037, 348420473, 488441623, 337687846, 796047369, 134822518, 513226912, 47190782, 820946925, 493255368, 483413345, 7840504, 956822226, 875262115, 872858800, 233301678, 558466985, 139873022, 235511495, 439839586, 244251846, 58524373, 163403252, 313096132, 301210778, 649145869, 760441242, 685556902, 247603999, 696764655, 540239300, 984589610, 393641567, 607891001, 748682669, 538923979, 829427205, 906479796, 680413886, 977143241, 751836956, 226690286, 345232420, 747081377, 626690824, 345650344, 59626906, 943911429, 563939067, 384338624, 933985934, 326481492, 426299675, 399495707, 303394260, 386041828, 80725332, 633488669, 858067892, 822528810, 615436403, 838243837, 752651190, 288654604, 750730602, 602673149, 866204032, 279009206, 107047670, 840955199, 128805321, 809534377, 594846688, 27622626, 325335569, 999654801, 803699780, 737408220, 497404736, 681368771, 516198433, 185540977, 352918727, 436598589, 459019782, 187233515, 303206780, 7838288, 167527073, 984576181, 611236963, 999613716, 577413057, 373940423, 75321018, 830558405, 36362482, 330936542, 346891362, 338264734, 510701807, 151062509, 28277658, 138362800, 287199596, 878068334, 586333134, 51624016, 96729979, 250935119, 571209188, 75239320, 874834724, 167595327, 804407015, 297405731, 610231363, 312061743, 810042931, 154147105, 82706233, 127091951, 694612148, 380095254, 633651716, 147502945, 230116369, 912082910, 142936360, 200984919, 521693212, 36959740, 915803744, 434822476, 753944913, 12110781, 687682425, 308713606, 232232009, 778744186, 919874465, 452648653, 84159292, 163803050, 545048450, 490037498, 130256244, 133114252, 154031114, 671657620, 98673382, 768315540, 340322976, 120911876, 624358002, 22242129, 609300840, 262876745, 309464320, 752416136, 598971644, 369921169, 490574586, 243722730, 146447460, 639094364, 685203180, 54560601, 55731621, 888470592, 48515955, 86523487, 91521942, 684837496, 348381627, 119933089, 691476333, 726111744, 166818545, 365624732, 703641794, 665870837, 421215205, 738960464, 565745235, 953345, 820384395, 252011232, 391234177, 507860627, 665737542, 332483186, 531424601, 608400903, 392305016, 903059756, 774283648, 683766197, 517233568, 851427755, 88843449, 528489791, 497992864, 262395442, 651706849, 383780625, 420391657, 580404587, 566700364, 273934192, 937138471, 570720706, 646456941, 154586928, 881364233, 18337849, 271179854, 739894815, 862652909, 425792564, 969703085, 958238043, 599221912, 708965544, 808616110, 802334789, 135124457, 236390217, 323666351, 393882548, 306224916, 494574613, 614107781, 147957220, 657402750, 31228270, 279252421, 458513492, 998335091, 796457159, 132169623, 149749037, 245374585, 70884235, 112835534, 581783899, 867199991, 184997618, 902453665, 650774467, 973966295, 750377174, 801924800, 326844471, 761712035, 230358742, 930028497, 350104173, 521944187, 646797937, 906265832, 526160154, 846548442, 118992394, 101848214, 520365429, 899165286, 398171507, 198916027, 103934501, 42010349, 30279781, 684635036, 943200467, 212246349, 14949338, 611966393, 580149489, 488400716, 871615165, 931235334, 445234906, 527252808, 533722323, 270943774, 945806721, 817194532, 439282112, 415626314, 715184093, 74616876, 624656186, 126655352, 364391196, 146520641, 494973486, 796832933, 246326835, 617741617, 92881536, 471153724, 408801726, 337627985, 413636261, 657453103, 362860504, 561483648, 806740725, 418791459, 992696247, 532426618, 202785419, 914192970, 267187271, 634496984, 356447899, 36498461, 754053916, 224879287, 121840516, 155681241, 781957245, 952540698, 652622661, 330197623, 823022375, 669855555, 919467872, 165402371, 364554122, 365342585, 106223835, 702779740, 664523854, 182700393, 303169284, 200916899, 461831288, 556955538, 504083210, 835435909, 938084367, 823979942, 101837650, 549114622, 316177448, 907894813, 128924239, 217011755, 640034382, 630260236, 884218465, 776948748, 547632761, 527510282, 359125641, 755325646, 711557776, 602129221, 160219448, 558632663, 400474891, 866994669, 305664051, 654175279, 800747407, 176160544, 521632053, 290936038, 307000401, 147069773, 300051339, 845676969, 351918783, 329701162, 967637464, 97935712, 529032521, 625633084, 253527034, 765733527, 627919221, 606820260, 504306238, 340488804, 466447535, 489389, 724698826, 662251268, 122645166, 519779554, 655628108, 522351862, 805134121, 558262722, 606715303, 219162891, 600643147, 851462970, 954727908, 568946516, 326983428, 571985805, 787012937, 454086453, 32476522, 634641754, 913953067, 333067923, 835348715, 450829753, 496940364, 531773791, 494982908, 599842762, 882791478, 285760120, 634589314, 295425342, 934051987, 825049260, 931503012, 58738681, 122904766, 479678591, 684576437, 32101701, 989523040, 552507846, 155577786, 19576150, 292781559, 617781318, 853227069, 626113875, 621956077, 914633193, 120230811, 565033276, 231672554, 349572203, 335886876, 767520758, 253439779, 113883855, 536375548, 356429217, 256451241, 773798708, 830785776, 678190878, 221939323, 687465203, 832683949, 868759280, 674471943, 869492603, 195834155, 388081313, 915671640, 296941398, 687645005, 718297421, 600576330, 618496685, 145419185, 169834469, 868890555, 111600405, 198667090, 6214395, 708232549, 259699888, 838101583, 973850975, 371828392, 149561799, 446244749, 969812330, 11682813, 160107280, 300923072, 877751369, 456864013, 640722101, 928902941, 382030921, 674629375, 83906307, 31136211, 818081576, 612459955, 979799737, 801940675, 468214751, 668761204, 533948631, 649842857, 821284469, 197415824, 419107182, 453463341, 259605765, 505110935, 268499059, 209266936, 468016603, 440327705, 496356219, 577584253, 512774431, 9092660, 447140535, 340552933, 518166857, 359043843, 184125964, 925079283, 693469280, 843064952, 524402189, 319758582, 579067070, 175700616, 149684921, 236462659, 659216251, 346299283, 74900048, 282553877, 663979883, 665834726, 53471621, 748817851, 533521243, 627717498, 480105260, 210932599, 233084850, 102522119, 591589818, 892325981, 75292310, 58019673, 214090715, 834028990, 277910833, 584054080, 275416508, 948897732, 787362797, 110153426, 150314143, 110129607, 679094195, 810360568, 328837158, 343417499, 309473520, 622320448, 560959896, 401856011, 52278097, 356538470, 952164174, 150198624, 336041172, 502490769, 815137912, 467530918, 77682284, 262441428, 841651187, 580251608, 288364085, 294666148, 699785422, 239095092, 383388488, 776820789, 545667193, 103947532, 129972617, 198538818, 963123346, 931674862, 245486131, 993860413, 880039545, 115597308, 659933871, 653338139, 387991389, 358979651, 372694792, 405913424, 745845309, 903723281, 607393961, 37907661, 919037210, 303393086, 883492088, 699607378, 775904005, 23399334, 485124072, 712950061, 562727612, 4049786, 268550252, 401158485, 58021794, 374123449, 158509514, 515165006, 635202479, 680375213, 372357393, 511831717, 53941041, 743485352, 660642947, 922837782, 425336109, 377654248, 150609345, 451492296, 774941027, 904748043, 817960205, 134992582, 105347224, 385708994, 937980692, 862089613, 302005114, 499108103, 408851807, 830303779, 666116502, 75902380, 882496780, 336882986, 636244865, 72871354, 272665308, 355557071, 134194383, 876583905, 172172967, 84061854, 351721620, 449494722, 335950015, 640234604, 310898203, 187816499, 685892585, 739859955, 449397867, 412315115, 146460800, 681541108, 688146776, 345960667, 533394023, 126637698, 912239115, 957168173, 821055180, 169619457, 800504402, 831398455, 236259516, 461039695, 661354261, 339495968, 239216490, 12702696, 198188205, 262489959, 705590744, 371730623, 730653346, 921175021, 157899620, 585932413, 766779825, 613696274, 708428501, 225531798, 855837652, 330272018, 98486212, 135139098, 69351247, 913196123, 224602925, 123845241, 431731554, 907807757, 317953738, 831288657, 691357247, 552792349, 357367038, 705269337, 97902798, 607657157, 352649644, 842157614, 138699137, 271334090, 470276230, 611123135, 907767931, 483453289, 444924425, 437334806, 832343919, 482137428, 281343118, 778000430, 963083891, 604527855, 59983815, 553066773, 901662329, 312635666, 996498632, 97129936, 700766931, 187995335, 97481404, 84979991, 405620090, 152890258, 229316367, 604936858, 935693902, 364929233, 191717978, 28384950, 410037191, 142951274, 552888576, 746145170, 912979049, 901707961, 908261149, 914419044, 923821754, 527578278, 218769776, 42179130, 155379256, 827320433, 520159707, 164491863, 892415791, 602347383, 534459403, 90419167, 991878465, 460089837, 312589509, 364827585, 127216987, 637539053, 775989213, 423942852, 118356223, 798422028, 771843440, 152325197, 630898957, 759689014, 884678622, 328617025, 259970144, 38115997, 524270872, 317344325, 973627643, 263978947, 100770679, 105975714, 536553585, 952131097, 626866521, 813459879, 897604193, 564164365, 817373497, 398939441, 161373414, 645823429, 878258084, 955736640, 760320621, 599345978, 583962554, 755178011, 709786035, 9091406, 27832175, 701331287, 58080366, 810969080, 558464109, 534630166, 139684036, 213158557, 890187335, 739321918, 933003930, 999688152, 723014511, 976451525, 726569667, 831818610, 787597243, 570693427, 569624704, 41052195, 237938994, 62518750, 512523492, 637365512, 519067341, 187345931, 933504133, 166308568, 468555099, 752496049, 199170444, 676274053, 258711933, 811466987, 392616269, 593641659, 242850660, 991780714, 538397481, 581192775, 563708698, 835268453, 410370419, 562891006, 16422371, 575801164, 572789371, 553883063, 53794557, 250705060, 9303972, 257153799, 568998601, 93161665, 256023126, 918610329, 304555352, 762369115, 25195471, 23473416, 287882796, 885721240, 512562569, 721600383, 854231228, 116522408, 175276968, 40977267, 895244761, 929933865, 833100245, 810755101, 920966625, 644879747, 135429983, 808667125, 530175115, 985787840, 77939721, 11205182, 721286559, 709341553, 200131699, 603828792, 114471663, 52181675, 721160379, 742486464, 373535487, 444484822, 909676481, 687702887, 719368421, 496170781, 804567587, 255843690, 757076119, 927802313, 471396664, 531556608, 933238478, 7240640, 653915504, 3759382, 114097330, 932062422, 845022533, 989242515, 827458378, 891573965, 802494907, 530783174, 135684955, 57921195, 783854018, 854228995, 972619120, 822126671, 550455300, 28966584, 228261966, 66767387, 18704013, 507162960, 640773611, 559491924, 169048514, 700249653, 29950438, 721323502, 534513212, 597958952, 118098909, 551223812, 747628412, 523229100, 136096652, 733512076, 660539264, 84854170, 633962411, 180095450, 301609824, 197704786, 405670154, 408467786, 671021458, 966802633, 207766234, 200478572, 317792479, 931646453, 807604234, 691506652, 463438460, 954044229, 508914266, 523527696, 848653213, 412272799, 320645082, 301683876, 239963396, 990087930, 417334807, 8248454, 756924943, 167649839, 459857247, 86585071, 212039171, 30759649, 944786264, 379589619, 851179775, 24673167, 547385871, 730858755, 927937842, 398728506, 803116088, 134067994, 191284417, 264873779, 417545639, 801549448, 553892492, 204045307, 678229627, 727383811, 785521443, 144934380, 613643005, 216938465, 434489026, 295428808, 537917651, 172564536, 17120611, 407061146, 211864586, 520778614, 121037595, 347714719, 962258057, 183176720, 506194237, 840656603, 41487615, 53660912, 789701229, 811554368, 648871769, 131100588, 655061673, 55887964, 401888489, 391406675, 154105848, 767302649, 995410472, 588255436, 631130040, 437597034, 160029021, 445155927, 18493642, 741564777, 475027822, 665871079, 77578113, 837623185, 83044331, 61788275, 295572844, 540549839, 752275798, 902126556, 491918178, 409622890, 727601216, 101556474, 112107961, 917643491, 993457498, 222515653, 981001728, 935708395, 796710256, 193289817, 667018661, 439427789, 154092557, 190422278, 937111150, 267752912, 817145002, 361979333, 152495876, 410676469, 742116953, 666174320, 871543477, 941559608, 544069120, 230140187, 349840382, 576441564, 379213031, 524241903, 659520325, 849770140, 410288237, 15536991, 854363209, 414477662, 963589511, 768159054, 959609849, 218238445, 909651538, 134711141, 763018558, 585483435, 809823619, 908760331, 177882264, 837917484, 926076908, 653200288, 919351680, 888759573, 159921218, 248087835, 410826022, 423406852, 425131270, 559477802, 537231205, 122339961, 849565282, 267588404, 747130654, 631377944, 321852806, 576712050, 726167891, 857574508, 500828074, 859459861, 823653335, 421889199, 963964474, 718770741, 406464244, 167848727, 258106250, 258809310, 96485862, 112350505, 299841034, 681118686, 413759272, 196132842, 779011701, 362008486, 984383478, 593428659, 75815397, 528184760, 476649515, 948280227, 991299214, 149802550, 974866919, 933621149, 199940848, 366231114, 532325097, 10316824, 776698325, 697323020, 237097977, 421283841, 290230594, 96888076, 781268214, 372023461, 520197274, 457411687, 68366544, 108187578, 232816226, 352401534, 965398646, 161779844, 370678534, 353836063, 909397485, 156354001, 733026660, 648862046, 947174983, 940637246, 866281266, 810349780, 33326082, 971762924, 164202086, 520325353, 438600858, 309010274, 907099113, 419844599, 783965519, 164872602, 598979314, 290227005, 287918481, 736621083, 709762306, 52681933, 389468796, 1610818, 252253659, 877005160, 420942798, 624209417, 43398258, 309685984, 911874237, 81196872, 396533629, 343373856, 350071282, 259473191, 300361922, 988419016, 651698551, 123158484, 183634849, 407658602, 790808683, 773730463, 133489740, 938530099, 185873069, 828325147, 201283931, 89120471, 407846509, 287480313, 722685766, 213290380, 228059109, 716569455, 31450877, 653642443, 32961218, 611023714, 14392158, 953961131, 350115703, 815878550, 171721433, 89442247, 72306093, 551856823, 275690394, 792477120, 61394784, 170335732, 255956445, 485273728, 745840369, 646877658, 178914849, 6382358, 393248485, 114834755, 708084499, 398202540, 43329626, 525398843, 288735420, 854015240, 160132271, 575137387, 159108601, 615514493, 326004884, 929906947, 173130016, 198034641, 314986063, 876891951, 548876728, 584386805, 190469950, 724823292, 60914025, 194055834, 742071364, 301049131, 385390236, 892838096, 745287957, 449563826, 345786890, 944850841, 621942364, 173753670, 926035554, 335430764, 324212018, 653607965, 628376075, 44358619, 633686606, 507129885, 476772650, 800204264, 824546902, 23873039, 255706643, 23199278, 75477371, 918414558, 275699778, 209923598, 85326959, 426417815, 941504907, 671539246, 505239161, 738674371, 793068155, 895423334, 701492097, 629502363, 547327409, 513603238, 154358288, 89502328, 213202490, 660554056, 390896768, 484985900, 103111065, 534824195, 165017363, 8394000, 584527916, 204707679, 284874155, 629421958, 48635088, 802435953, 697537323, 492025207, 454583972, 342292919, 276276666, 457222552, 528972075, 560321785, 6178029, 395957517, 319853704, 817602548, 774982618, 399184039, 816996114, 108636227, 625302530, 492360104, 759463643, 56909108, 922630734, 178382347, 65161545, 319975084, 78671173, 243733846, 804724182, 225350237, 243193008, 595815948, 595641944, 762760054, 671736937, 173288377, 280633911, 111103421, 477455989, 94302249, 642479398, 30609829, 912374454, 633031300, 866349671, 212795543, 302025827, 583501670, 226189463, 31513715, 659498177, 785698393, 625452134, 940008490, 401968138, 259368887, 184231413, 666510589, 304265314, 202572697, 270250318, 677310584, 189941125, 609996141, 465663402, 501684225, 715973803, 763979261, 479070041, 215975289, 570699502, 27630721, 907881565, 797553459, 989711797, 223741713, 57553901, 673047403, 467978158, 267857595, 124116691, 819483142, 463075666, 344809610, 302471804, 637546137, 726545831, 500180805, 937486333, 894807551, 228606162, 900934980, 831837584, 652423758, 88064549, 521182585, 806886454, 143643573, 319074932, 848404251, 258780467, 201758886, 55200185, 509920392, 517661975, 842484669, 516977395, 282128544, 667531406, 137158150, 375705450, 24831361, 958508799, 13504168, 461640505, 382054774, 534111122, 2283241, 242001254, 754131622, 699715062, 361691916, 135176452, 59388465, 865434984, 482559366, 67479052, 843057344, 5895784, 443181177, 404218666, 247461974, 970819288, 729626919, 472375644, 865800070, 890767192, 137143663, 61243991, 662191727, 131591004, 149703507, 287445910, 278891873, 86145369, 608073781, 233920096, 862637274, 775497843, 946972829, 774715469, 766301490, 632521982, 660183005, 369356986, 950445077, 219961100, 535536229, 13101857, 148201947, 376157837, 337174942, 700800255, 354924844, 458596860, 62414275, 941583983, 577041814, 839784892, 873278802, 838724257, 388456198, 295135633, 449296936, 918821093, 10500473, 316703018, 558020240, 297298649, 998788092, 17845567, 120523232, 445641815, 967191109, 924043436, 438239757, 795850615, 572082586, 456787956, 497212172, 759209957, 696855738, 276969051, 913075863, 363297372, 480148539, 38648939, 111063497, 479048036, 260335876, 695916045, 952659865, 898576928, 360351058, 305485533, 627845117, 409434470, 215397403, 387179580, 541542385, 916807552, 474442728, 806945403, 668919787, 892834102, 745334417, 410001555, 812630185, 697617019, 716638269, 629955917, 840717428, 916452993, 782209465, 372890892, 878233872, 786570700, 789399010, 981486861, 866849805, 124269756, 355480833, 35337543, 431207982, 290490506, 779376984, 71385046, 416293678, 21266503, 801411481, 941130054, 602341386, 313251137, 656667354, 993092505, 430364450, 761122248, 955180729, 634764058, 37210541, 544255214, 970546338, 829851446, 55161509, 965629504, 123054550, 716552320, 666475011, 439007839, 758331887, 266369699, 895221413, 324127523, 134729791, 184955297, 802285081, 670130792, 561680990, 491409436, 312020143, 909562494, 451620290, 732552924, 358706477, 230514701, 705914065, 874657221, 477202027, 367005213, 317422931, 991769959, 24119627, 110510552, 905178061, 97806330, 268832698, 898085631, 375037455, 34693370, 155826185, 945755684, 36841958, 37054468, 717469667, 736178155, 126656321, 618953200, 793653086, 796928949, 795155710, 250577510, 354976314, 627654905, 388511179, 31547986, 375269932, 3919603, 742888486, 213254139, 647758089, 878321221, 949335623, 328055841, 599206539, 694507134, 351085840, 549428702, 834980978, 864707118, 426640720, 131825835, 79991508, 649951873, 279838363, 935788989, 281012726, 365984917, 555114682, 903534903, 835103429, 363139256, 441287968, 117238982, 350780308, 105931567, 903467365, 92187266, 438982393, 396918610, 731247075, 999753939, 669632366, 774278349, 243248083, 509512732, 69628307, 151988395, 815179320, 84251940, 246932296, 286872439, 667578543, 309744637, 378032707, 540114124, 740478870, 694042067, 900114146, 131448644, 534405672, 12481652, 81288870, 370356464, 774036029, 559409318, 843514596, 608100818, 585379871, 228626581, 529513328, 273750219, 906650443, 300920918, 681203989, 74972566, 214449328, 604078683, 132215755, 244657363, 961322967, 545686548, 635973404, 255819097, 459178508, 136223904, 9769136, 225294698, 825691851, 954991341, 423250846, 216559401, 995802387, 376405409, 850078389, 103872323, 975778964, 259514072, 27904548, 442244945, 746233386, 708078717, 422804735, 846847825, 491060476, 574013155, 437426594, 657096860, 316420388, 609793302, 68970504, 217711605, 895585814, 378521655, 660177635, 492007508, 819508175, 674341158, 52471419, 437513907, 634963615, 164463252, 193953675, 15788537, 831676635, 36642011, 732881214, 512666621, 252158254, 706944969, 910739184, 977415219, 99855472, 503088794, 151192519, 63767164, 883480894, 669813848, 365192287, 530532541, 224682320, 923487324, 997509223, 596363187, 314374415, 288824519, 63604972, 629482641, 980294308, 439375585, 563572669, 398455119, 643290840, 660576569, 486715362, 387757138, 563644593, 715373318, 17068974, 455789508, 909175096, 494994563, 65277136, 654988891, 396991131, 142670906, 670240102, 449568580, 724640068, 719791697, 605961813, 729322559, 344322920, 821184980, 726385423, 536036274, 324857514, 678127181, 744590, 266946158, 919131824, 209654807, 850849619, 414389055, 663450271, 423293284, 365908501, 481604066, 394819824, 57309111, 423246879, 327107459, 963800223, 761174419, 318476809, 180270179, 687519631, 288550132, 129962095, 593112674, 895922915, 744260114, 867185366, 413786392, 96822105, 534879005, 618580252, 513325929, 597279155, 312996899, 8987814, 273318251, 590491126, 790302534, 557421714, 814833914, 444509802, 61585036, 582661715, 453245956, 293909382, 765863364, 481862619, 444743715, 933553734, 35227137, 608488208, 93038747, 190269146, 735038818, 232761169, 531802847, 911781592, 51445721, 961098438, 587306031, 576486482, 359060602, 287317342, 643753804, 507935116, 987470986, 238440751, 342287588, 761061278, 651517131, 357182704, 2289896, 35955033, 339703753, 787815709, 189722987, 54488797, 344776186, 699280667, 23799814, 796943813, 953694824, 585042760, 241103592, 837320820, 425289505, 724916034, 830039941, 822897011, 773227881, 242146289, 817986679, 903106243, 621707701, 878516716, 603374167, 768744047, 210844005, 650689547, 596168955, 82201878, 605611850, 61076390, 434363227, 370637076, 483354830, 489151603, 437249951, 192648623, 723119890, 265607330, 554372313, 248922969, 991066807, 869694948, 429122976, 984239920, 319052819, 772945568, 30222284, 16814861, 922600417, 749199329, 16393728, 391869733, 656853896, 856751428, 592650068, 451377092, 852582931, 888099626, 860849217, 740073858, 249507947, 782070354, 135236910, 893929259, 643271327, 2350974, 882319577, 902720558, 73505071, 70092170, 860122776, 540623577, 204071435, 64667427, 74841646, 491178542, 279780771, 625299725, 706605326, 957999541, 769777799, 811052016, 468105925, 489687315, 703715031, 653821537, 921273899, 151787486, 351046839, 22823010, 207980857, 996637228, 945918101, 539628193, 65515648, 492455357, 615718150, 63993391, 840810824, 22688870, 390852472, 838854614, 144449576, 591252850, 895226364, 486558628, 413871531, 427669354, 697995662, 497248765, 149489889, 704169923, 52606057, 955089072, 540856173, 894120061, 289832883, 283234000, 155738833, 487732391, 849756549, 439781264, 593662867, 385306891, 361043400, 383585581, 621284160, 593039351, 388701809, 211115330, 826975878, 324192992, 883490358, 515695, 160274196, 642743263, 728954579, 171783, 948477683, 253404099, 405624526, 491451728, 150914323, 670996885, 969667943, 626961933, 272932615, 890739833, 457173343, 17182393, 442663150, 591699335, 726910792, 511938962, 701560592, 356286419, 492898311, 452754524, 972144556, 605653656, 69684522, 465809980, 817754575, 518778138, 563168207, 938186953, 635526656, 705567307, 945510473, 258403554, 914224156, 760580292, 873694752, 444055504, 719153014, 704707258, 291054991, 221964855, 974070429, 267789469, 511077519, 628963111, 320744679, 552235564, 890427060, 118563914, 552674176, 856812365, 527546675, 862570515, 289549126, 735742687, 872639239, 816487836, 104365511, 627953775, 866095865, 525102810, 684822611, 785710925, 289899723, 808003338, 209779729, 840714177, 133431865, 650269118, 980872961, 587710649, 323207859, 562252340, 423257277, 565196258, 533635342, 958233316, 653615131, 252700833, 948776671, 153854522, 272027349, 333304962, 269393156, 564233444, 677065954, 210727639, 101804934, 915984417, 712589878, 999142927, 744103229, 792755205, 273675944, 274166778, 403689694, 444333839, 639537123, 361046007, 411968445, 981555686, 90499979, 798360001, 966720002, 315110019, 36313522, 103203775, 366601400, 834501303, 337825733, 19789613, 952616248, 880822308, 839271329, 44940255, 804018081, 350490421, 949188929, 607127465, 319920686, 304633, 229302525, 53181380, 38901428, 878094717, 816493121, 39995508, 142833014, 18871250, 755342113, 341503559, 586133343, 92530711, 280633454, 154229649, 149310960, 318965470, 348797152, 962574968, 792551622, 399652597, 23296170, 136480630, 508540201, 784801689, 452281039, 552087592, 448905712, 513374595, 678041853, 81085063, 608523429, 383382155, 110192707, 86371390, 275048479, 326101965, 242990667, 287409291, 989183304, 95261837, 232630303, 204573217, 695128145, 628484522, 941264317, 317738072, 252254053, 951605665, 17548891, 804967452, 681546628, 458459178, 916407757, 135218592, 273437122, 430057292, 559366591, 54739552, 658556246, 625846710, 441701725, 760145727, 831547520, 264652777, 492203529, 856382721, 321522793, 176483956, 523741710, 61365291, 130955403, 2331815, 139144584, 749315394, 779960226, 769525333, 72034138, 17366008, 690130885, 682284105, 752380268, 831776628, 418792725, 232140010, 205551226, 128705395, 756187103, 694281488, 746354323, 487894171, 501165382, 64876002, 674101636, 637323767, 534843416, 74206815, 435249567, 275487784, 677463618, 772951751, 569617607, 852402600, 163773836, 487117873, 236219160, 373314717, 838991432, 203603120, 105861477, 858682112, 800013923, 943328556, 118467087, 763141612, 865168550, 169455264, 905746324, 555072045, 48899851, 145497338, 896024470, 888249365, 239429701, 602767051, 36878189, 413679341, 892520267, 707061223, 719210965, 808315611, 557473125, 368090683, 318535749, 545470375, 219549567, 241022346, 806237959, 34347712, 30377468, 837781544, 263754290, 397348515, 502626638, 764133023, 249234162, 191549329, 360549481, 509666270, 858459052, 109656795, 71391726, 423691568, 756710953, 568732456, 174799004, 112794644, 919156225, 113923930, 711225456, 170997137, 428141653, 176424542, 209208005, 782575619, 888836309, 488913811, 568873060, 23419875, 256555515, 746432343, 192938850, 597693168, 624620230, 585645982, 166573146, 623181601, 373764817, 864784181, 974463397, 368019045, 48958349, 230186434, 245267356, 576891574, 840603249, 291826505, 677737836, 147923137, 16082552, 650687167, 586664051, 610973076, 108477473, 879018078, 518002640, 654966763, 330873599, 722508439, 710706608, 298885538, 864180224, 414391301, 25035780, 412641329, 771775104, 109498180, 870169847, 332232644, 219854288, 965998470, 949914669, 486609723, 731573831, 718205676, 497670479, 55181327, 213885881, 534734252, 292534398, 317239619, 514258996, 745906005, 737498014, 231351324, 231511461, 537870870, 782482199, 278076938, 472406125, 978487310, 754525369, 694107882, 391573364, 917419046, 689080385, 37387195, 128577488, 497631452, 903346549, 950651822, 899757703, 84457538, 527859819, 839318627, 742824270, 280629244, 890476936, 596896368, 779280576, 289908425, 573494785, 576105259, 888640438, 559577659, 315100454, 446219887, 87523500, 93297229, 576498068, 572407036, 937664953, 623366487, 673184060, 683640863, 751573952, 217053481, 935126214, 130539088, 812509921, 630235234, 800845248, 439189308, 968918496, 810569314, 36068406, 330122495, 354778543, 984998107, 148485162, 241878029, 395135031, 918362344, 796156478, 47708423, 716409297, 813140551, 286591921, 860295069, 173171691, 590784213, 724493571, 853097732, 805055408, 691807643, 767109176, 624857622, 315888794, 756409210, 803613009, 711321211, 439264122, 583689795, 218273554, 847278823, 184384819, 858209805, 739749278, 536852428, 234596526, 268836706, 291020297, 952126727, 692162650, 730623909, 696683913, 375537007, 712262127, 861683692, 95410373, 9706468, 935471577, 948121251, 561938167, 563834434, 818684978, 758621225, 815730643, 560276249, 780803910, 134625128, 113906841, 562222590, 921609714, 987225294, 161689542, 941256192, 195940756, 501073592, 493833667, 823890347, 278423902, 585842725, 538917475, 982488820, 911370644, 340619708, 129310061, 304640353, 773729910, 449379650, 208982033, 4381288, 119864747, 533460918, 537192392, 122658876, 238565717, 499496927, 470442995, 167576777, 12323919, 637790459, 470363909, 811733000, 70241025, 514983252, 501244058, 511111253, 970335582, 418735820, 668987434, 762683141, 242665293, 923978537, 926456103, 782952401, 422384367, 390504444, 883371922, 84174350, 707713058, 505052720, 32604450, 983468052, 189843293, 224145332, 333858943, 837275378, 859277456, 44190942, 12869758, 495372487, 571091611, 790332469, 549576719, 969469683, 452014461, 601160669, 607040431, 278349406, 570991152, 465862940, 322082229, 896409440, 27340376, 968915576, 567718900, 297569336, 4698304, 205565347, 479130579, 3367048, 669974767, 282259538, 912760594, 25671560, 297581395, 424034821, 761270569, 864182180, 955506000, 249053017, 656596635, 293210689, 56381743, 809861893, 218316252, 147439267, 145188930, 363554385, 534365857, 965603659, 790226643, 491978995, 674604002, 171654414, 341548761, 23672592, 483527570, 739978404, 78852452, 954930363, 611633115, 647744885, 290039001, 791907043, 345949818, 724881346, 785756524, 926135386, 579629180, 485412193, 553031359, 896651197, 632082820, 213597966, 663084624, 440394742, 808907739, 123192912, 827979864, 63206984, 270607657, 723026845, 445830971, 253342296, 633460906, 408246773, 475527322, 968879927, 978041086, 771917143, 842721623, 102973980, 716100174, 391397042, 239161500, 661457528, 103098682, 302943534, 591940424, 92161699, 394133348, 586334381, 164349445, 519795155, 226026286, 300251720, 810087002, 393688602, 96453876, 687239422, 162246710, 556714748, 14545230, 410335404, 295881672, 897752342, 871338125, 762466422, 65073608, 958799679, 924508023, 624371226, 376222854, 682103631, 593076420, 920742649, 179249115, 796398795, 335421836, 770013242, 77631434, 995747562, 700770014, 730889602, 117614236, 917753787, 855719765, 7883592, 531153869, 533504387, 820363624, 112693795, 857548497, 710910232, 841369576, 720759530, 987323374, 708313251, 316560117, 236329434, 179459898, 818288680, 561451243, 711730654, 85239284, 596054952, 322166478, 386032878, 184214883, 592941479, 528275192, 413854134, 608183387, 956989690, 411703582, 454224001, 631812664, 823280017, 598388603, 86403285, 555226095, 501013357, 387625355, 499842345, 455309122, 837537418, 585713127, 393196374, 451238534, 422952026, 935023217, 427746069, 225583619, 406453598, 833557758, 286917164, 632127526, 159672638, 158217410, 602627037, 936774895, 78394063, 979038355, 635233281, 161534228, 903452855, 462014284, 319743680, 186604975, 457392534, 941484915, 518491874, 542834810, 177508926, 620115789, 470301, 116875498, 65848234, 72627029, 243866007, 37835797, 364317187, 125547707, 981707312, 266773658, 403675056, 826583676, 125413879, 634504681, 929133743, 388844453, 657007285, 441813797, 458638138, 641947840, 358940486, 86336810, 158049378, 865589625, 259386905, 936596689, 56161438, 689386630, 874502985, 286043414, 910740376, 730687008, 480825672, 59186784, 516257958, 487283681, 736430128, 801943263, 146670481, 97615250, 955253827, 583116167, 557976224, 109706952, 546468598, 629015735, 573190981, 510087885, 587527994, 735145497, 804155216, 948102488, 778695087, 733715994, 169367412, 631096035, 450688997, 722055021, 731412352, 38746164, 698578808, 692487663, 30900324, 599881782, 557717632, 337655971, 450966232, 870583341, 932640803, 759541514, 439407254, 471314947, 437670170, 639573247, 849223334, 403460023, 232715728, 639185476, 815431686, 806216078, 375562543, 898350631, 944612903, 284758966, 852627073, 155442913, 200635552, 423491210, 814415978, 286546549, 380532448, 271032666, 426786550, 848419237, 234916607, 317289048, 93994827, 790572514, 601837332, 142562457, 733947917, 317464674, 786352324, 536370257, 711863368, 675593803, 474732728, 524947799, 591299037, 631966733, 429339641, 73179125, 572266032, 594069194, 325442204, 24060666, 711768880, 409077553, 340374923, 632795184, 216485442, 115866298, 449533595, 913931365, 992920226, 102775069, 375131115, 431762323, 963042005, 696579783, 219281892, 17889853, 335302370, 559316109, 895390143, 147656721, 184993576, 662761501, 959384532, 894124573, 338907753, 318084315, 540182318, 170561768, 278182604, 682252849, 467563365, 814958734, 152212053, 915953854, 269141592, 82941424, 906595574, 123115486, 796008138, 932568481, 298230596, 454687572, 269546372, 130303650, 733572702, 900739227, 342930689, 727162202, 173464327, 435750375, 110895060, 751575039, 688260307, 653313122, 636635946, 864132436, 111636656, 391850559, 630263529, 872807879, 369739373, 668357511, 408237592, 39695185, 74082861, 84678678, 305755053, 221401323, 611668439, 115138797, 112377455, 824793899, 4022015, 72648384, 767618200, 697212031, 809894668, 888431222, 623191145, 593008097, 786743119, 571710637, 110262180, 59032821, 592464327, 346928870, 831066857, 394885840, 677190067, 833272531, 643136693, 740800565, 988394086, 817321282, 864049609, 273088792, 51494656, 596342965, 541822177, 340826637, 769111153, 101292947, 272676950, 681053229, 334942362, 347577686, 791792733, 313427075, 574832373, 620304785, 933765188, 17722450, 695346173, 196308770, 529629398, 190101278, 534368259, 126678963, 370959868, 368637864, 543487017, 242457627, 836272083, 398755067, 683401940, 151077748, 660595588, 716267688, 664304508, 573107785, 820988014, 455995655, 961376780, 803340351, 151226498, 460275197, 609888248, 46686883, 778708129, 440835313, 841538378, 551253619, 927105053, 953909114, 137532043, 472183895, 550494791, 540369362, 220761043, 243972237, 254414534, 931354322, 163783314, 342502958, 418956748, 13341987, 398667260, 774480900, 420682384, 256360022, 714072724, 855848120, 93470298, 811680626, 424510661, 928111324, 619061082, 400822447, 413239969, 37637814, 240691744, 445520173, 92006799, 786656045, 152002597, 336775478, 29276302, 828342458, 4018081, 444873509, 828555741, 379344459, 618803103, 930617440, 17852727, 206371666, 204778742, 318410449, 131521799, 550589094, 313499842, 844313811, 300829878, 97029227, 759493310, 35987534, 294197005, 761458030, 690032988, 601328239, 320523282, 602056370, 272234047, 945421417, 548361697, 879977380, 611616390, 347878657, 404486073, 497906400, 629936775, 215763179, 412782322, 238583586, 108460140, 432267121, 440648866, 379056314, 456204336, 895510019, 104421554, 376817455, 731911420, 544053866, 240565652, 604866992, 867770011, 676717916, 829737348, 476166731, 757717620, 827547366, 262520080, 222962931, 767343231, 834601696, 983765498, 454257470, 422510699, 719556556, 949400848, 765956795, 38716985, 239020774, 524810897, 237725829, 335161674, 287287888, 359309320, 135097665, 837223878, 197150886, 802118351, 845777164, 888883546, 260926363, 258171762, 448551189, 875452426, 661146583, 264638013, 757220558, 317005907, 458648556, 706134029, 459772509, 368863635, 111567616, 564377875, 776989281, 770739417, 189164558, 105170555, 23616931, 102400513, 827692938, 571000342, 856855476, 821929951, 156765165, 367232725, 878327573, 476212113, 794558366, 348910754, 883221747, 645327150, 438980990, 461478213, 569686386, 594008065, 671924173, 343469891, 823929225, 373317738, 93863271, 5393374, 916636428, 18650388, 884454104, 45600484, 667788987, 124952022, 930647709, 301899945, 47684908, 63062379, 306529876, 907728630, 344507646, 846787906, 877405524, 115142481, 216611590, 82535209, 518874621, 165569655, 949937841, 92818173, 672937903, 558485652, 421838613, 565760882, 164149426, 107200663, 397066850, 49830729, 266767341, 84503336, 668179451, 159313810, 880876394, 824427090, 664781554, 72420127, 632065790, 494586539, 662954433, 400324494, 160008720, 468253479, 66082949, 96270478, 403090426, 594387555, 188529878, 860090050, 168141082, 654773560, 76799026, 136974661, 682410017, 715691872, 14050366, 23803887, 911895444, 70312241, 973432589, 15818177, 307401668, 906703027, 564131332, 80139345, 886769822, 869583200, 916485569, 63736287, 247214576, 241630694, 122486033, 12376963, 997722411, 506985848, 850482160, 167673601, 706249255, 724500778, 62229697, 172991884, 388762636, 501385564, 746036761, 950146049, 464042669, 167772854, 412709193, 49270080, 661885587, 956484659, 958376588, 818423855, 175153854, 618929257, 997590421, 753358191, 787969591, 999391837, 485881135, 502278903, 366838695, 17540756, 407358842, 668015907, 147381443, 986797365, 283307064, 850161841, 535526228, 477334157, 934937603, 215688141, 819372383, 919333728, 338790598, 869973043, 242715117, 157621529, 806986720, 734183060, 191270539, 320236384, 523334029, 297167583, 148601119, 40640292, 264319143, 424392654, 550990574, 453836064, 382087134, 978799062, 554290488, 857395887, 969420175, 770230412, 296200897, 906221889, 556777336, 250397867, 720168875, 89120758, 714116255, 232180123, 765262978, 358310849, 758165315, 390034050, 874298640, 629162397, 784839443, 954578548, 909950856, 847741078, 130031374, 370658352, 630770416, 884941698, 22863833, 281360843, 675753060, 517042165, 126282691, 851128526, 478195262, 124654917, 124095012, 888777736, 386766899, 830080486, 95289519, 109542782, 599692294, 956593943, 549329505, 936557024, 458101327, 852200492, 919324917, 603789279, 241350782, 757636452, 103612458, 139612813, 150505222, 978040385, 783393867, 138945461, 497384619, 682778886, 369845276, 960202203, 946664868, 109689450, 891647681, 680669597, 802708061, 768367503, 750301122, 384755061, 273768794, 951829162, 264351368, 807587096, 262076856, 148049755, 343913184, 838974195, 575467268, 913723967, 270789354, 795378152, 381394350, 681952186, 154754498, 698548430, 654343589, 790852721, 697930053, 807334798, 706668542, 673021447, 135023426, 905976489, 322677837, 897050609, 915431323, 708868306, 781838090, 574260582, 883255942, 477239344, 857304547, 873511114, 107130376, 702832957, 239045766, 412023414, 178904366, 984704232, 793957753, 644402727, 725994736, 574647457, 275877817, 210016322, 227986807, 659046413, 323749564, 290693230, 165419519, 457988828, 666640220, 19974725, 363354163, 175991248, 670435347, 490055302, 97956130, 275706925, 652242265, 554256754, 242615025, 550039772, 569574089, 862639282, 234278375, 887972599, 577813254, 466493027, 447567643, 276777113, 332154580, 98891717, 623620843, 904536110, 928847010, 898909580, 649124510, 456983954, 201591635, 169207209, 389423495, 957426367, 659830719, 418763848, 969660900, 617995855, 555080571, 669092702, 215137639, 459940407, 951830964, 173032438, 817157221, 450201297, 147788905, 292304042, 789603408, 586353293, 511262343, 44649777, 635726901, 766059979, 252804444, 310441679, 193344832, 466242379, 647314372, 590680037, 434038236, 454572211, 787548188, 365627481, 657439309, 265122777, 890868399, 877490424, 466697608, 32227835, 427675691, 825007884, 928180095, 804082351, 58290991, 894549580, 415704605, 843753048, 996375803, 833404901, 466021835, 418721922, 354842850, 624143591, 847753107, 735213781, 159420754, 641498649, 677822051, 663647198, 855679870, 789489179, 874558210, 328772833, 198956094, 267032766, 61463217, 316435678, 362117479, 428164937, 58517780, 60498455, 204252445, 954051514, 103004950, 967873395, 815366877, 409362071, 992271929, 52285966, 519019570, 518320541, 744571379, 850889106, 635978002, 539769456, 886545714, 102772758, 577651367, 874277676, 192612398, 373148293, 861323580, 297474148, 17063413, 711401055 ], 5380 ], "output": 6534007224903 }, { "input": [ [ 950872315, 625312612, 475222858, 893262391, 473676466, 792298771, 759426014, 607463050, 190815945, 552824332, 616924935, 554006527, 976973723, 849667049, 307518936, 263447517, 493176630, 724268380, 936113621, 834871327, 880053220, 540819044, 683232826, 146420186, 26607019, 754306635, 183942310, 227129965, 658383931, 721999252, 273429940, 312124166, 793116752, 471083010, 428272209, 545976380, 767841982, 945283850, 891818780, 634357092, 817421710, 252458099, 439822092, 90193114, 144818170, 626250334, 412903753, 750768174, 466423745, 539409795, 48538187, 72664617, 396281616, 389459821, 925737234, 539625601, 18078149, 745738327, 322946406, 314198821, 854218637, 785856729, 852413525, 78009389, 220783729, 764470543, 937933177, 254354744, 601225346, 650552977, 538565476, 688842882, 553456400, 994275746, 443182461, 555440876, 812703835, 514874642, 159005663, 690446043, 631804274, 885790425, 262262203, 855915753, 107424644, 725312912, 899871315, 211828641, 253044543, 138508386, 488327840, 979830176, 61301487, 957248271, 811066988, 817215716, 487285651, 365834632, 263497850, 937348729, 441949775, 374720362, 799980490, 372593503, 213943359, 71729780, 54530844, 940964098, 807335623, 822279569, 757864996, 359361059, 244695928, 740541412, 282222010, 769333318, 549924854, 479433621, 385448281, 638597445, 774084890, 406786055, 805105969, 877813637, 43941827, 133547455, 800526958, 512912385, 48298692, 444123130, 578132712, 46825434, 541646425, 536902070, 735042170, 777135828, 131930886, 857567306, 233369274, 383870843, 871807751, 430066668, 546134023, 530762040, 564403480, 5888579, 90311716, 814792466, 115046731, 617173988, 724389348, 445590438, 429722389, 582835901, 976983252, 632384913, 882211421, 247135470, 885817018, 161033633, 194941792, 224589267, 199964453, 718996799, 781470283, 805780378, 65891910, 727898265, 581952482, 111449277, 499090632, 302380618, 469400111, 470469715, 155107229, 569736868, 936052270, 627867893, 523374937, 36243177, 196470441, 93034867, 406841194, 146048783, 646911999, 468026815, 215511025, 146107747, 385936554, 110362524, 137633504, 677157435, 243483533, 15087804, 145374528, 590255023, 961207959, 756210152, 72450017, 518374759, 844088618, 966147756, 161852806, 187553748, 23344185, 107668345, 851939874, 91829689, 599149617, 685236105, 76793765, 725476657, 501674774, 541367623, 861161116, 601152950, 173679329, 749212392, 134887966, 119038099, 50965524, 310603080, 62162810, 129975653, 973724550, 873826744, 189240042, 480569446, 346985818, 294668571, 22226275, 548403057, 116236476, 112939534, 898585747, 891403380, 591098810, 282170820, 297167774, 35340605, 687122382, 261880810, 292508007, 67375257, 687003312, 160399392, 39277282, 918126691, 981161384, 279242517, 582532747, 662213876, 572740055, 93650929, 829960295, 11968731, 212506579, 594677143, 58105772, 346210202, 638557343, 551026610, 337503434, 311341420, 306796133, 687118327, 462174043, 280211367, 353721, 999128117, 14022853, 181650683, 543029899, 9422759, 297888196, 389389584, 721096602, 164701874, 311563076, 240663094, 925701962, 547035677, 120130655, 331892080, 88451674, 424591489, 549772746, 207231649, 506692121, 846506431, 906355996, 933079803, 413582459, 85336345, 727398662, 504772073, 59677855, 237736694, 643848470, 198041547, 767543245, 272276699, 511965613, 558186866, 447171452, 433754713, 530845762, 197275207, 961733816, 246311220, 676538281, 517044249, 291823794, 886499449, 581746374, 414523808, 440670611, 931140061, 860688104, 871282863, 417946413, 677411783, 638842959, 225211702, 502008010, 948629537, 804251360, 652450640, 193894965, 644239087, 439699754, 620334140, 72585706, 93604448, 904767830, 965998477, 707046814, 463777021, 196165222, 638156158, 496108197, 46708023, 845528604, 876890722, 562419430, 755085991, 758803346, 77461497, 958714626, 423185879, 944226307, 871049435, 872859864, 340018304, 140258202, 790565158, 702004161, 468168542, 14589309, 130111359, 618569486, 14142607, 584767575, 258422408, 177855666, 31131760, 329601127, 404866298, 540988602, 148279250, 378289821, 213467975, 762655587, 921287511, 933443677, 997571422, 304490411, 713939318, 742955354, 597663647, 55604899, 737593924, 414547949, 663738754, 740396555, 348451866, 382142185, 563902590, 800903739, 391945917, 76639554, 336738856, 853581072, 869548282, 3539074, 640303748, 674591017, 650477614, 724648562, 987125087, 163056848, 474724583, 845293306, 890650172, 465195002, 998331483, 820900028, 164282683, 923421549, 969857636, 933477388, 536659093, 641887737, 877850422, 159507906, 175853728, 670317186, 278728553, 505298036, 233992961, 311382187, 983700602, 841340273, 564351500, 646807751, 957088889, 120136024, 270175188, 236634664, 847064453, 658230473, 121038068, 336249322, 448201221, 42319329, 326903998, 345532191, 371739275, 348351973, 260996902, 546142382, 34477369, 35432158, 883096023, 756586890, 784518686, 389591040, 894571210, 650936648, 348879909, 633187064, 302619500, 214325139, 849407345, 38240074, 565220284, 574815313, 852120121, 463166902, 769534830, 31528786, 958399122, 794177606, 484815237, 329116731, 516084892, 46003211, 860183628, 251208258, 580199312, 690576739, 618746741, 157485180, 920809353, 628686191, 263313011, 219332257, 45914883, 879997536, 663307993, 427896125, 321730518, 423509196, 296468669, 2868938, 197086163, 632296477, 135344504, 317015149, 932622910, 857457775, 748962772, 348920474, 260014938, 108899527, 681781876, 448155576, 297420753, 503762189, 127048878, 374120684, 233549403, 406082066, 891463154, 652000429, 486972126, 411520022, 178756114, 474803911, 979211726, 607664376, 214231268, 354388735, 461943072, 830791037, 288876484, 869694400, 508664823, 541289308, 170267050, 182058667, 119322682, 706456329, 738310400, 228160794, 329426715, 156477557, 503439797, 410763721, 395770211, 767642887, 468044343, 166371784, 665285755, 340215525, 554428083, 869336011, 190026945, 258821807, 184199501, 306710679, 351521845, 388798777, 51941073, 453321230, 530753199, 319528500, 598560131, 875863468, 395324702, 251967093, 172589398, 987626727, 600175940, 767193964, 872604537, 809485197, 173809433, 556188391, 328891235, 308303901, 597194452, 541032517, 409658922, 377502010, 745740967, 270764035, 785554497, 530917362, 778860892, 784002907, 303225768, 438223361, 153809413, 626765208, 817267317, 130488770, 444327208, 373018751, 606748883, 104060770, 641075637, 126897266, 939126829, 23620312, 976253364, 489632646, 680397958, 308040945, 876949108, 226448783, 846903289, 283633189, 789445269, 90936226, 968249956, 876422017, 847165759, 166248889, 942617213, 92666549, 575474198, 495407104, 196281850, 898010696, 609170420, 15633303, 251639904, 3181933, 851864119, 115369274, 94121848, 793192131, 925167665, 486714862, 260314231, 952233224, 116427479, 676718266, 652352443, 520173368, 35183845, 655493735, 454322686, 943869312, 435004645, 626248013, 165977143, 749924502, 498431349, 32944261, 964621930, 730085870, 779023390, 21025997, 66207746, 921314047, 621066136, 952935505, 601740370, 74636414, 951677233, 756646804, 96264445, 942789120, 276622814, 25491662, 793353505, 60501055, 423771926, 338554506, 695986338, 648678270, 333100189, 314419474, 620564492, 259017862, 384120444, 188759369, 563996446, 580841572, 161282950, 84814418, 552463280, 732002062, 726812779, 271887036, 837171619, 837489951, 261037350, 818451733, 303052802, 617311829, 671190099, 506651310, 436329140, 245983200, 419177120, 597595733, 434212211, 230716863, 566880238, 975399880, 268829181, 621683946, 638648009, 240936317, 744819071, 281235357, 960204952, 669701033, 472787982, 455905690, 760246864, 334818485, 58928077, 65246803, 908906326, 42168401, 770204607, 324198562, 630785975, 150894176, 676148085, 356381464, 880319402, 650413531, 79281388, 438935196, 366650457, 975590233, 886461225, 939392241, 521480516, 478490400, 786332039, 283611033, 991458188, 595406284, 939401992, 574390580, 12717914, 12223802, 191262309, 98606383, 58423271, 709832981, 221087223, 817874454, 61545794, 990070908, 252414121, 163347975, 567415653, 680022897, 501427721, 662177682, 392461391, 664162711, 84349152, 755506180, 758299672, 734662356, 46415217, 880727085, 136068500, 61165391, 438339566, 404093844, 453324372, 985997489, 279736548, 705167997, 112539519, 760765922, 690858035, 551214579, 50212788, 264339985, 81996268, 170881705, 126443651, 814913140, 644189309, 184659879, 499865221, 805265452, 385212108, 874885154, 393938078, 530265714, 807991252, 677831024, 854600059, 565043072, 772843942, 624700026, 667084384, 995544618, 59868927, 932407197, 561787780, 780860262, 218559839, 686715015, 942047319, 998627103, 471191937, 280788864, 907464372, 300791982, 617521731, 294151305, 836731837, 966000270, 942357250, 815094400, 340366507, 139878365, 758884901, 707639770, 997363219, 940570986, 379308587, 956877839, 874061693, 829895200, 203142047, 897875912, 215511659, 74817575, 880808075, 646652632, 728734911, 597004574, 945612251, 865903517, 276245593, 754764936, 129159197, 850098312, 286811355, 620624760, 311602388, 108590382, 27274198, 494418336, 812650969, 164736357, 852083859, 78104939, 19897029, 363314402, 949901539, 688621605, 327043724, 85393335, 916400233, 994162519, 117664610, 375785261, 555795028, 32304857, 568102654, 53491284, 676899154, 592159193, 163214215, 897980689, 485618169, 171759592, 107985122, 973221061, 447742749, 155305618, 975236950, 39319507, 249643292, 416816224, 33026603, 526044054, 381046402, 779091394, 253540061, 883863481, 389717777, 613884403, 402221449, 483493814, 895640493, 776671216, 157532342, 534976906, 1516601, 305729207, 855060836, 373557362, 838210081, 55594537, 304600972, 98265940, 479624015, 134214624, 396005808, 780746680, 647766990, 105418886, 771453934, 183161863, 786010948, 330819305, 375414940, 610936760, 398479636, 570296717, 925381665, 882272445, 861538475, 30699896, 158743178, 999181378, 480050743, 510760464, 659754302, 231089952, 428631540, 418306567, 603285974, 563553219, 993224504, 559193707, 743688580, 471957321, 982454432, 95315652, 175777250, 695240542, 504014866, 371580245, 283973327, 38434217, 194833370, 207073320, 875751156, 709656568, 550334845, 455265122, 682957501, 160190384, 39209898, 531383853, 463446901, 767919583, 387407485, 371278445, 353562330, 872434112, 416298277, 482335916, 823452161, 187637044, 663223806, 580096811, 628732508, 678026831, 739729510, 797385343, 953683246, 479478323, 762201555, 563206572, 453615308, 240290836, 392650878, 73056004, 829285094, 665424048, 18391097, 828728840, 593369645, 688172952, 218199888, 276938696, 901004961, 565325806, 547740235, 640919323, 437168612, 246382397, 838342000, 772753084, 820230927, 53649342, 176471041, 346976182, 134785778, 557732670, 573131723, 315879105, 635834850, 14833199, 465372492, 926811707, 934065353, 168087072, 168126778, 15631031, 811202512, 790962878, 853899971, 787302054, 614952456, 313625304, 473080115, 531364549, 630222242, 789220882, 250687431, 886044357, 744360085, 9846501, 798776558, 384465953, 609697265, 114475590, 696426968, 783527436, 457667933, 522248082, 136975551, 935178247, 363194735, 532376067, 209406902, 580331312, 400967161, 902934391, 293815303, 16293185, 455239151, 598919352, 87983179, 543361392, 446738724, 860876195, 10213669, 126963157, 802150925, 752130726, 573312974, 201557192, 130259816, 532315842, 580166676, 720539372, 851741326, 697630139, 370512130, 278425840, 520448986, 848140056, 986355710, 399722940, 747667347, 540512355, 911871730, 383210850, 865995871, 150200046, 434112125, 593131367, 682197385, 372929464, 361461831, 854077372, 586156500, 220224985, 71254104, 2520781, 223794731, 371214718, 276967963, 219440369, 551789536, 712757304, 793011829, 199158971, 958573482, 943986824, 910952625, 910627081, 28397688, 64813083, 49698952, 726938529, 392312119, 696753348, 383511287, 92082824, 827832285, 377955312, 697748136, 640686374, 224757017, 13972871, 556790827, 211295027, 223401750, 501236567, 924436164, 701395842, 436799849, 783468391, 17447574, 385934204, 950845057, 399047989, 438887803, 305998076, 981077556, 135597128, 164469925, 65377509, 797886364, 137303320, 542954036, 190528932, 764347062, 730742309, 642750123, 954269953, 465193202, 46036287, 623103555, 125949975, 305796780, 792660174, 354618454, 248820162, 297756497, 111898155, 603529171, 531993687, 206273466, 373244583, 312829402, 15197944, 41130787, 944738827, 551366165, 84595738, 501967624, 767246088, 660690873, 685942433, 150073713, 471621420, 25789413, 541412745, 256047710, 670131122, 27075480, 407044673, 480447661, 667236765, 153253556, 738937839, 554142127, 516282470, 100655279, 122833276, 655103555, 160576204, 657817658, 56142073, 13240709, 619569310, 545388392, 719255443, 541371327, 852517794, 270021724, 458611841, 263148653, 24426461, 493419736, 505148635, 655119664, 328471630, 26582190, 758374200, 397108803, 510700508, 235664840, 691568713, 551155912, 226537685, 713309578, 206195916, 274677983, 919205622, 867197676, 597366117, 892237435, 780835887, 459794038, 156619588, 139829016, 388540075, 184693365, 973646103, 151825991, 424114166, 781938202, 823617424, 386997429, 751961081, 808405022, 734973394, 385219437, 894347697, 877228134, 619767106, 236056957, 216292323, 547680947, 900369139, 628531185, 453198736, 938495368, 537556174, 283951493, 686936400, 683809919, 443169263, 549824175, 205990651, 279499390, 887930062, 744644145, 559678675, 448564631, 932652080, 364966279, 416903717, 752018038, 789961336, 656856238, 768416877, 771300989, 143535336, 91832759, 190882291, 395322859, 255850066, 604490958, 49753102, 460533267, 297355664, 254100459, 342553864, 401316493, 497919479, 64750580, 748809151, 787228310, 74934985, 457563105, 386747252, 247183613, 722402984, 971760645, 638677968, 949354266, 926759948, 628669059, 674568572, 755939432, 765016385, 32250165, 977093676, 702446726, 408184884, 473586208, 484621686, 33724328, 227998923, 311503887, 672972962, 111547651, 498943417, 274980978, 264788962, 750429110, 265667831, 515703276, 584545516, 329929213, 420496790, 103467685, 181775758, 666021681, 170074858, 625687218, 273594883, 89819525, 860109582, 594320667, 267769325, 703584778, 508014830, 838275736, 39995694, 734633665, 365603800, 853763140, 266741787, 599946805, 484342815, 834259248, 908760094, 979994901, 299805753, 230755489, 906356243, 282562399, 353928929, 18683796, 556700886, 557437818, 718466733, 400683265, 319652895, 560261289, 933034263, 883910654, 477301120, 982889786, 852555365, 456048440, 324604929, 599249926, 933088822, 323171106, 449810202, 693433211, 432698368, 312203460, 220174732, 31350404, 211588036, 499906639, 652657708, 940624943, 677083009, 980206716, 243807512, 851229081, 98102935, 840051088, 737605800, 64441389, 975628420, 562767193, 57527303, 577001978, 406506445, 216044866, 867745548, 384466301, 145687653, 127034812, 141239111, 170245504, 180387775, 814900946, 255347444, 219511886, 183248110, 913251637, 233786828, 619871303, 268985598, 547061959, 994924906, 733685775, 736242286, 625431721, 445970111, 616108303, 903900565, 809361492, 271374965, 197225079, 618011264, 735624476, 671484316, 186632843, 220880846, 440983880, 236361501, 986988556, 918888835, 876387404, 570351406, 818166894, 429545139, 465790978, 228083795, 51872699, 757234877, 29941509, 830239854, 695288458, 610732756, 364102539, 694670743, 309915333, 440837494, 611176903, 786857530, 537416388, 358938870, 161410863, 941371635, 991653133, 246287242, 618586165, 616163079, 229296733, 204805126, 220189210, 409904355, 678967450, 174700362, 346477787, 17733840, 493139885, 796498047, 538087685, 947907941, 138423405, 264961181, 667287601, 874766999, 975647204, 963277420, 279791040, 868855083, 168097936, 724054427, 894058240, 259339269, 809699030, 22053657, 776716757, 229244072, 722700576, 759427999, 33339439, 734653330, 860727653, 551419593, 731125331, 860940847, 446182392, 19183380, 721448714, 354768182, 828165374, 147444083, 983833026, 805289999, 396595991, 964294689, 407793285, 397829812, 647632793, 293433602, 611411339, 416266461, 340736623, 961744392, 789130559, 70010812, 740158083, 401308096, 266257340, 394277661, 308611218, 793141192, 354234270, 587354535, 470644070, 482599428, 931265699, 859356942, 789699237, 74765809, 885576547, 958028376, 379124656, 997387453, 469308275, 355137334, 105665009, 847601102, 178448387, 17961590, 957777546, 894796638, 760240763, 307896630, 947370133, 422578719, 229356793, 562134361, 549526240, 352712302, 494205567, 840458440, 424977563, 917572822, 130830529, 177809287, 667668511, 696477292, 951653577, 569578970, 857191858, 271935351, 509356456, 592530351, 267336136, 958102527, 268588699, 27487276, 635049130, 848900050, 820855055, 116652376, 14861648, 281420656, 820141154, 181378666, 826779548, 993609642, 6174608, 224553072, 970432856, 418346540, 137301661, 879192533, 573780511, 752287758, 219134913, 238492307, 288526510, 566955712, 717287655, 858841093, 655593411, 399088751, 688319593, 688445297, 241901785, 320386661, 538502228, 296006873, 585057064, 444506161, 924785595, 291424701, 569583533, 890862194, 957606859, 15462748, 544262777, 435251489, 751933370, 342036099, 783186283, 508777845, 521035102, 414835961, 533539871, 857069585, 993214210, 260804371, 211902408, 237847296, 686303264, 892815051, 922991571, 905475449, 637980673, 937986030, 399521189, 360227390, 265628828, 924752755, 438695573, 478900922, 871549320, 992098079, 499337576, 411360819, 469936885, 194919337, 172921843, 106590850, 547694296, 676689672, 794154737, 494633364, 139627228, 160731567, 439598069, 350862849, 709963096, 657529312, 666777733, 248484055, 870087098, 849018346, 869755087, 350626831, 542517924, 771114815, 550024334, 737156640, 279758744, 645495202, 919896909, 520854455, 435205095, 150931866, 300027493, 78698592, 303717064, 520208396, 328506756, 73630120, 907589976, 810509865, 554572425, 325360764, 626292479, 608985111, 686636847, 591540873, 4680071, 346358881, 522313994, 970162737, 487955386, 509338593, 461424732, 980114832, 29172731, 563238445, 193542963, 30034119, 278622527, 806695855, 302539156, 263818442, 574211357, 981423921, 935406146, 912656721, 118363814, 922020732, 94015546, 331089813, 432537392, 371574158, 438510783, 419892846, 889615321, 477002941, 85889776, 772200924, 616311832, 349630436, 356338194, 626579394, 78088458, 505092238, 900017679, 231328530, 50180766, 913475182, 725683843, 891069203, 367218238, 633419950, 749297570, 884579464, 495323913, 559010443, 459227158, 562220446, 487941821, 278748350, 358841987, 67961952, 96765580, 268182732, 75377045, 959713987, 127393333, 409513097, 562532475, 304574734, 380529537, 178399477, 290193036, 818523839, 688216171, 187561565, 606373823, 280483116, 48765832, 679743937, 892886500, 970714047, 876690832, 235754848, 71256322, 122214768, 30188340, 62741888, 735063428, 53159033, 187974799, 380582773, 898418517, 834290571, 174366499, 571398436, 822575244, 953877541, 740162524, 314352936, 32576221, 288009252, 524688, 879052227, 698529219, 152493500, 86686109, 912994017, 765265057, 633451706, 594695982, 685298099, 47820848, 295012395, 234597144, 17439223, 587000676, 657155158, 197980531, 786283311, 991068172, 746739152, 746550539, 241309173, 445558801, 318162548, 728607224, 387005911, 570629939, 213319937, 572680481, 977472222, 35914763, 29701155, 83812817, 471960110, 639952698, 211790765, 537328584, 114559696, 413146379, 490508401, 432783429, 834578809, 142486140, 969577999, 631459683, 486695201, 971218574, 712376853, 854413037, 768113381, 836702659, 514448946, 808727348, 32381129, 657975922, 967235018, 830465683, 218141273, 866613233, 550843938, 266041174, 752365739, 424456950, 695576006, 534122093, 314298041, 343954871, 109285163, 90128374, 40077321, 842850464, 365558070, 338714324, 662099903, 454775011, 884615799, 530536449, 530854029, 813371023, 567504077, 901051476, 409599430, 49555747, 882153131, 97344541, 760343202, 959600670, 860417443, 514596984, 279132012, 795394073, 941568303, 896118607, 316842047, 380418977, 572278371, 795691391, 433643797, 816910579, 193041481, 732249730, 19842308, 93776529, 753270715, 245414025, 565350465, 218349157, 693389818, 441069615, 396766883, 281536605, 772105948, 244900441, 66817433, 712144781, 233746539, 993344125, 967088684, 658071795, 626090608, 235912351, 586311449, 182092651, 68537384, 97128087, 103545877, 378805390, 132729281, 349406829, 524808601, 837999395, 736345847, 952938623, 329059359, 675148528, 794955066, 368494608, 617049726, 592897875, 926917554, 848064701, 423937831, 711758009, 584553017, 44968645, 872612173, 794000660, 166213227, 540130702, 170130956, 4549146, 386471945, 365037354, 616038081, 922301638, 875913217, 712239299, 86595280, 447515057, 236110453, 703209516, 533916510, 729905694, 161080105, 545531061, 137832507, 329304362, 888373201, 235048568, 124240284, 168828472, 403104832, 779064305, 244487750, 608370149, 480585049, 163718791, 678040752, 698565342, 360518697, 458205609, 546035694, 705270735, 101370375, 238895176, 166857715, 380915839, 74849761, 554084436, 971576555, 756120523, 87271169, 57002888, 394711252, 541720389, 506035056, 112339601, 133187024, 704610996, 334109078, 564176775, 486011225, 200464214, 344175727, 939620204, 397753879, 558334594, 872007554, 420135397, 437834626, 621423102, 607689067, 994987388, 251562348, 524634028, 415830806, 698624276, 778489635, 176927369, 247321155, 177826876, 627469353, 205921032, 459096868, 618034759, 737632648, 781128868, 790084177, 826158776, 602592750, 942232826, 265705323, 272618428, 434040298, 471078787, 953220267, 309018212, 987622218, 981154250, 205796333, 985031161, 354525506, 790443099, 84205248, 102611697, 889090690, 717804604, 458336776, 616569954, 995461807, 230936968, 142342883, 524916566, 103649986, 716548114, 50161485, 50841200, 953203139, 163207314, 179513793, 945505138, 363178699, 247836431, 741976282, 652220592, 973675170, 89434252, 365836222, 422175898, 587747155, 511937515, 391824242, 843584875, 206158527, 357834352, 494750295, 381522735, 583892969, 549843912, 274934614, 420345389, 709762677, 131693244, 822480663, 986442592, 378755286, 476488186, 99191852, 766610664, 329994135, 150374193, 398247584, 858359105, 45654268, 160468476, 761757766, 671780127, 208297012, 574907907, 695757659, 240658952, 258207942, 170172519, 437643006, 392359350, 84355382, 356758964, 659192596, 487973054, 595974922, 858370118, 115578186, 699677051, 996460777, 967478556, 506827937, 876609767, 841288214, 43861235, 733038293, 700155233, 757936641, 623666003, 565517356, 418948640, 810499973, 347048705, 440112525, 846630630, 820743580, 673847254, 982518761, 272325608, 183769212, 356878058, 535811772, 910589634, 700230861, 116716034, 129400257, 688009538, 48138400, 377222325, 614230432, 182735090, 169549313, 769769468, 265245420, 304498897, 484415603, 831604149, 453959574, 29343842, 572389024, 969937408, 449114204, 912067979, 216598130, 483552689, 276499167, 443060164, 434740533, 246151851, 471329281, 811315814, 902185523, 740480019, 539675099, 911169093, 111495301, 407163486, 731294764, 430281901, 575840293, 619141857, 914742504, 987150671, 174729176, 437963324, 206456848, 780456986, 367000366, 166958098, 628711820, 171828002, 583189269, 815286918, 264853055, 172848924, 229944668, 609553414, 816571754, 712780456, 752047964, 241546403, 183054104, 892767911, 271841692, 637110405, 905414635, 908254219, 146892204, 539442654, 458206507, 686752955, 111728016, 29500973, 754795313, 949790310, 146958092, 610553929, 124262032, 653531191, 212215136, 67264145, 773272194, 262374096, 222955363, 11863875, 970445806, 844551226, 340681612, 220064071, 509467362, 189420329, 197389004, 258721482, 300821709, 949347194, 962555810, 798449820, 3209879, 220168378, 374583154, 568517618, 260187469, 421137656, 267083846, 680454758, 844972265, 287256377, 625601204, 370629338, 420565769, 16067299, 822343338, 161895418, 481294155, 594547223, 824445648, 339371336, 937450272, 885609244, 53705420, 451381694, 18748458, 684074692, 826980269, 718575025, 635458067, 6911185, 566113367, 933941993, 194771009, 42980786, 575583609, 715702618, 40373695, 281850070, 35706968, 242245420, 268709028, 473581247, 453766832, 413000429, 567855578, 840324059, 748061156, 938797473, 233230104, 164379586, 9752081, 959747078, 424291319, 751699471, 821971458, 304539296, 486348937, 944081055, 227455525, 304945597, 352201496, 555197567, 639908543, 469959688, 646236504, 222396575, 347877568, 203040706, 821962576, 538703960, 580785548, 75994429, 261451365, 278884770, 84686026, 998934460, 181185539, 965797870, 791729416, 59187947, 67743070, 532244519, 350957360, 538735045, 72948868, 803404467, 240591574, 785084839, 31416838, 618325678, 1508610, 866616182, 647569323, 578498586, 682587360, 785256291, 430896820, 762734163, 504164002, 141192212, 420975878, 299984112, 398531197, 752008172, 178459999, 473389938, 895694213, 266256466, 43154295, 11562470, 104383671, 53357823, 627641687, 43022458, 631583319, 851221575, 85967426, 791657202, 983852819, 167103724, 874988900, 466799337, 974715637, 298741760, 686395935, 111993542, 569721205, 116186578, 524030374, 904204997, 697016680, 168103929, 454862101, 189228570, 101818286, 968295340, 853078961, 843634200, 477393456, 613315860, 502815209, 428680549, 605101832, 635836797, 442562336, 512764564, 390664696, 116194464, 60040791, 397826104, 163173703, 736337656, 997767151, 392282142, 300435532, 375340089, 142475839, 987767360, 195876347, 811813866, 519606971, 312732880, 346646353, 746120420, 989233736, 497376213, 183585563, 837418563, 281928099, 788374097, 489995642, 346742414, 505214682, 597879749, 282233357, 993398892, 264153876, 693792804, 303922694, 362025448, 991575960, 53736667, 232642820, 205823690, 411749885, 541842975, 102166503, 254259883, 74887282, 135400712, 240481449, 711632968, 303273890, 591326737, 395797646, 190082111, 480109518, 494095206, 945802046, 452134229, 342371599, 805148277, 838983302, 852114117, 145837111, 536449826, 973171884, 884572250, 97144304, 791686632, 864585110, 166108903, 154375556, 870539276, 367686136, 186118908, 506409102, 667467810, 263105366, 763090704, 923511445, 76485970, 273472614, 35846118, 80773107, 944361278, 353668324, 225028199, 474244467, 829832755, 391879412, 958072286, 299841473, 859641907, 234655532, 408019441, 321541332, 762971000, 277327572, 594631891, 861853846, 101936723, 571634620, 100818891, 634433211, 959561567, 802647065, 419021437, 412647028, 841558734, 708871096, 969252008, 653224684, 6010848, 814862586, 115595205, 947623830, 203357430, 413743392, 896433052, 135785627, 278618092, 41831664, 785910091, 338718325, 1409944, 761503963, 476771941, 18484095, 143048459, 273708984, 865709651, 504857697, 805005191, 116107348, 882896006, 20742765, 359852524, 257888218, 444011165, 748965721, 839517118, 936860958, 42843489, 589204463, 427216684, 687218850, 628631679, 673993106, 541664288, 628659765, 826936287, 71220316, 308568915, 168456390, 576383873, 189522980, 785992699, 84359999, 232324462, 340478036, 727507246, 907587149, 10084611, 866943432, 985169901, 827172901, 843307431, 133005533, 553021643, 21866531, 632895923, 363932737, 614428413, 542837868, 925147541, 223726106, 248890711, 225291105, 95277150, 363326644, 793237027, 666953728, 904128607, 814801633, 744386370, 171570496, 200249638, 717524953, 577369577, 145275126, 352011002, 86549511, 581383981, 507842239, 237610368, 137398190, 336167239, 499794806, 640445215, 804928020, 18250945, 704459601, 399878730, 444277019, 596367217, 95686768, 608399270, 740409848, 173865020, 134747083, 740947963, 143340021, 277176300, 556233805, 800240702, 904232460, 130304761, 804120236, 501404960, 140570942, 287422209, 268235804, 956647113, 475606480, 356070891, 271337139, 361742862, 369619230, 513260199, 184088877, 580315056, 956444815, 838147903, 123958873, 626453318, 904110859, 607781308, 270529811, 553299604, 137774622, 181728843, 698195663, 4058842, 117018517, 399627075, 807395935, 249847501, 160644541, 537647029, 344103868, 692951177, 721854409, 48596200, 446743265, 82067517, 801082967, 801918621, 438971683, 832230750, 996003648, 370510008, 169040830, 40253013, 614338572, 446789714, 119931728, 879291740, 969150340, 44451340, 154759642, 748653241, 498021657, 681127433, 112495818, 502437537, 528278992, 871989762, 820147982, 719725530, 380846973, 565497325, 785637225, 572770627, 253441079, 739971406, 411249350, 310016487, 378354976, 77398917, 706334099, 774213726, 778491960, 280078841, 821328461, 865340961, 267697119, 111857120, 719126237, 634131892, 171355217, 629923546, 922184066, 422196292, 764859429, 80283474, 949584924, 599425518, 311567960, 582959316, 155537054, 281732467, 129678843, 138002756, 214776534, 551000207, 170538878, 180378379, 598571641, 719438423, 835029289, 651060256, 308924407, 304863258, 747531836, 267066180, 169959520, 191140699, 458284276, 705833216, 632220322, 565540014, 477107569, 260859390, 844467914, 225587628, 498633562, 856037708, 110720795, 165207677, 474757965, 278552083, 72210989, 917129581, 254987176, 467965008, 305387572, 919878088, 903671352, 553544593, 425608208, 593127111, 519625167, 7871742, 237314222, 936385546, 949010244, 100861116, 603779710, 203170119, 433346022, 461695589, 847319730, 313413128, 255644839, 988316532, 798911309, 240654923, 333519727, 708485133, 104726034, 273560838, 962289609, 524969347, 545184623, 439614733, 757869030, 950889020, 929092776, 478611563, 648697977, 930525357, 396220120, 101767900, 997009004, 595024466, 209393383, 315240577, 349036150, 631626379, 772146832, 785405781, 542006261, 644429142, 637738541, 415651170, 222662324, 201821790, 949492684, 95327057, 642440689, 36432704, 878055728, 288776281, 812370305, 383290471, 524735405, 681673750, 769211745, 269522436, 496036336, 798086527, 619690428, 659694563, 395244702, 20028748, 212016133, 572923238, 634625330, 296719928, 452105912, 763818394, 823684984, 37570300, 262609083, 435747250, 204747910, 700680572, 754456054, 857464941, 699484965, 614734985, 39495258, 655447442, 880861770, 546877907, 167482336, 386790782, 851047260, 383753010, 544398173, 153240122, 325618649, 650151760, 622373306, 442597723, 389297623, 894848503, 874812240, 159504984, 563988941, 802031553, 846520497, 240410449, 119440843, 471836738, 746345897, 83307639, 455768165, 759214260, 572309360, 590152474, 805313499, 321496597, 640787206, 402338381, 791624677, 527381329, 42836827, 656671092, 631200553, 399786020, 36163280, 369723129, 154659485, 792027576, 441307715, 636972228, 490821419, 865069126, 103161899, 560835647, 428276456, 343597510, 181336139, 47852548, 109880723, 956388415, 304523514, 973374225, 135217139, 391421050, 371873099, 89400712, 912491618, 513209555, 993284485, 284291186, 516041206, 493771997, 566690353, 394500108, 937933166, 820562164, 602840501, 305858610, 301503953, 976248514, 744451936, 378858845, 462719054, 113258880, 200958696, 443075765, 874986002, 211037234, 137339320, 845766915, 53417086, 892302841, 81231548, 599171366, 429476435, 62496848, 514255414, 582360569, 123992282, 51154333, 726355728, 801104634, 837778307, 253585066, 753197102, 819884787, 860580838, 767980360, 820123980, 800425547, 823475976, 520824320, 896005955, 704730379, 80802910, 552544781, 138235860, 584033555, 881591390, 371875732, 804989991, 33580919, 10714569, 996953990, 232133865, 72106732, 451181297, 905435352, 9579363, 11929605, 711038813, 693249752, 519385965, 15531795, 563791109, 361994619, 144029722, 876990177, 713994671, 517617873, 942388385, 852605261, 972817577, 446616095, 392451052, 330910834, 372373470, 172116782, 672894737, 351288694, 105122805, 436228817, 162104984, 80967765, 291579740, 156045288, 492156533, 6124723, 15155635, 358992802, 734683189, 495804738, 916094105, 776831273, 961055308, 841849136, 865853595, 96095384, 150725748, 354002217, 803829156, 374364172, 613819130, 73603382, 93409119, 601831956, 773521672, 646127296, 958495139, 537517252, 823913853, 673355061, 985730416, 789981887, 93297222, 644647162, 637040534, 656779701, 870513392, 159158760, 904029601, 965116125, 134973084, 348392294, 468326000, 680557303, 542697038, 814029776, 35867690, 660354855, 27560531, 211450713, 508006340, 531540267, 879229133, 306571861, 659113870, 647411964, 536527910, 284126859, 639145122, 776631919, 71115224, 181614713, 112466628, 766101541, 454316953, 964531922, 72488016, 150725249, 406184366, 770298440, 16965616, 369452403, 658307680, 95171826, 123633528, 488495566, 224975737, 726405373, 568422554, 911974173, 113487429, 346184117, 845608833, 876241011, 690057066, 169009917, 978157428, 316428902, 435079682, 961140564, 591145994, 942520048, 632772591, 359304395, 870636567, 435392031, 471695232, 512560782, 865896134, 417099276, 625451312, 302063629, 483360357, 175339848, 881151210, 141408412, 494872393, 720315226, 352919847, 857838490, 203409774, 580584284, 511400041, 84596151, 944703006, 805461556, 824078093, 339134782, 837550984, 721630757, 32124249, 594323432, 663819205, 294602855, 650717572, 370481939, 389760145, 64464917, 406083642, 560038777, 863917934, 197864063, 827475371, 530010363, 199456816, 470383227, 750706919, 535057933, 923234471, 409886820, 728958897, 99290736, 376646241, 989882216, 364739447, 875042055, 429609323, 196243113, 40526342, 312137868, 824986007, 647723902, 882858926, 435573080, 503495311, 308441705, 252734807, 832954768, 539215638, 348312504, 160096328, 148503500, 55042670, 272506419, 955343586, 469244957, 852787466, 96948617, 591149764, 694626961, 625229098, 112472361, 436790051, 765802194, 649264858, 223602431, 980436696, 964208581, 681672353, 731018771, 652387874, 433485988, 651315447, 486823006, 58103358, 496652500, 412983969, 177818378, 570965687, 81729692, 500644698, 432488096, 700041495, 556244680, 88184109, 96492673, 558200632, 14874788, 769147651, 218589892, 902190858, 207317529, 404017678, 584196285, 148367037, 257116240, 436426808, 587565325, 309463841, 822802758, 991177856, 404334403, 457600264, 13516027, 910971634, 37568684, 426767567, 718574803, 935428133, 898102998, 234256130, 798228272, 322007834, 445311273, 953065277, 73930948, 680738537, 385238900, 849387287, 179866080, 59673718, 468971292, 826371893, 896501073, 126771650, 921036545, 514821407, 467956654, 674576611, 616483194, 704386028, 405270905, 290175633, 728633569, 712933875, 663916504, 87821912, 266072994, 33882051, 842332628, 374481430, 667998240, 823860038, 211108909, 514389584, 503173288, 675724389, 589190955, 763622507, 244734876, 803926230, 973745570, 927736572, 457081320, 65683833, 503181596, 754900533, 647992815, 838832147, 324062766, 942504862, 876232154, 602129135, 223681724, 417395263, 836341466, 895836298, 852498025, 544270155, 467485553, 281732976, 900592217, 300090990, 890476639, 640667628, 485435746, 606521367, 945626576, 637051294, 130254636, 378299488, 833033299, 334173419, 398309426, 348384353, 869220320, 671673237, 834672673, 390501083, 995183914, 821614581, 788971477, 930911862, 306957151, 304520259, 960423566, 286366212, 891307991, 58623027, 365758829, 967824575, 821792430, 345855155, 126259186, 658643846, 524324509, 550842690, 291409514, 9560105, 313584325, 593299200, 103635800, 264463882, 22069784, 594002157, 720644268, 574460562, 921776938, 722714682, 381342144, 815421118, 753520695, 950197115, 731094745, 878326111, 154472426, 612207447, 563187791, 827783370, 37725633, 10276574, 727403911, 993514695, 202244276, 192079564, 140608456, 492753245, 506197202, 990185611, 151880598, 861295363, 386009264, 133395627, 887378599, 948442877, 2300651, 598454721, 724949667, 812208273, 485928185, 501514138, 98769395, 164614517, 663503715, 396615538, 317663447, 633878459, 28536073, 173286991, 106122565, 145075047, 306023700, 421515453, 919778014, 499065244, 242904476, 431721543, 911787912, 785932525, 873725931, 563198182, 467264907, 283139332, 261752110, 669176179, 37192524, 945301360, 238046785, 295213965, 238844631, 697976534, 82488950, 191220120, 275345116, 41189904, 849595359, 314976540, 601151060, 307810270, 90741487, 954280860, 782068626, 327419798, 820151888, 226350797, 655769285, 703424240, 614027260, 194818854, 30964282, 99890315, 787539266, 492754922, 897434068, 585072461, 914812231, 347125960, 952859192, 426065872, 900355319, 285131230, 264332276, 228909734, 209166347, 613420759, 84034616, 936514485, 986687237, 896548428, 833837581, 532336427, 355561621, 541077587, 559339322, 840307135, 312099875, 502565379, 584908373, 307462363, 122214038, 598849399, 456527257, 850246299, 60310325, 533538772, 140064044, 487191994, 772160380, 570737058, 671765782, 882298818, 500805374, 674767235, 599534312, 314192595, 785712661, 71938984, 685469597, 679230381, 796675485, 317731866, 712623261, 386517383, 404579434, 5963376, 179820313, 233779756, 420518673, 124092609, 886962167, 647846577, 467925909, 629971044, 610520750, 694618293, 725454694, 368699192, 718399899, 691016171, 339268485, 443650068, 386390432, 413019127, 56773525, 416639310, 18885983, 307384663, 587171899, 482142764, 760585097, 777554705, 584933482, 957191224, 653268215, 53729283, 859456103, 305958960, 971274705, 154552817, 633310263, 723468916, 488660101, 937586367, 602923124, 617325851, 19077465, 420077523, 21930599, 705044149, 788224823, 852639617, 887015524, 361006852, 797958402, 305992805, 20423374, 198510240, 273471111, 610639159, 678845509, 170121186, 509810576, 707416914, 815198974, 11959536, 52805671, 227021219, 152438674, 302562880, 79886211, 297521373, 708723476, 27335499, 956981844, 190474466, 788226081, 27414704, 826315258, 459997753, 190385745, 734629254, 801675837, 763628030, 369189783, 454023640, 175779373, 69716610, 957493270, 137402000, 762739292, 690430334, 342114248, 754938191, 153462795, 763734079, 446378950, 956546560, 850195405, 386754154, 970892405, 587153490, 774464555, 993427686, 298422324, 715050166, 987854017, 125016459, 478903501, 655578393, 484030630, 473220133, 518477539, 84577169, 142062261, 623152212, 703622100, 11734354, 149946266, 957587611, 867907705, 472441826, 402248218, 971314966, 939568815, 706958593, 831573523, 487213850, 73859574, 755133224, 714472456, 703099194, 617807413, 67296742, 410901969, 89723596, 164356297, 994109840, 98118950, 565831721, 274943814, 616274387, 956344686, 988446965, 628828001, 152525889, 32669769, 426759533, 934024148, 641719144, 556167326, 617010711, 665812170, 483817285, 819361134, 287560066, 598756696, 271912593, 246070422, 280695253, 912509472, 102291261, 438841808, 737418100, 475510216, 232244029, 481672191, 743153099, 127350105, 798926270, 240691099, 41896828, 275182096, 300505368, 71188945, 661859905, 601531350, 15007801, 360944828, 991076057, 87795392, 959816670, 815914430, 654461337, 285849455, 482879032, 932760316, 898481047, 260250258, 702833424, 282341614, 755142533, 64015231, 642255209, 919497604, 528226693, 68186435, 915365652, 455577839, 423397067, 217851337, 324896754, 117002540, 325678858, 222771589, 491422751, 787835807, 738635795, 658066763, 437116193, 692322555, 482904844, 827362387, 347597210, 575771082, 728013284, 195967412, 937354077, 602798725, 447517468, 102329737, 196877919, 703570536, 596490715, 780421334, 616243154, 954925528, 914499880, 18375819, 177099535, 569015181, 310393628, 201898378, 954736875, 482869356, 550603952, 358740209, 664031528, 374906644, 412761963, 62501547, 104275185, 743753105, 962864251, 234721798, 633702136, 632556150, 534439738, 944799319, 645930325, 850732035, 348195603, 942892653, 191675475, 938428926, 907054585, 140795095, 863019481, 371244638, 887339005, 790542336, 428182310, 576178898, 113951530, 490514099, 184606367, 770199844, 63243954, 318733220, 38173790, 387926136, 693892342, 847659281, 928696699, 618016314, 157636861, 849874502, 845980886, 46617340, 473444557, 314714303, 118258063, 101387159, 103687148, 666655335, 229203144, 316476506, 144334739, 645267763, 49209955, 232112404, 86509122, 458154963, 308117855, 267210390, 594544406, 381179835, 584540622, 943480704, 990127164, 726730691, 345826374, 281525416, 23185504, 723453196, 226516600, 818204076, 214600666, 492755433, 964918343, 996784780, 506049456, 1789984, 260403475, 885618138, 174707859, 59390426, 438909539, 984526605, 748777526, 582993692, 993146133, 437004628, 482677134, 961845721, 122788859, 369596877, 585155797, 37072566, 697010646, 214618919, 104184328, 917419443, 162565679, 191934577, 619733082, 78994583, 287766503, 74320461, 248090229, 711108405, 129081630, 270831844, 710837384, 979675790, 750024624, 976042782, 927284652, 757028601, 694643467, 790720767, 664143954, 559553621, 411980131, 719608280, 599856947, 402209404, 275454017, 163452513, 587263576, 449291283, 550656661, 719270883, 770811035, 262268517, 770279038, 380890314, 151709294, 316766269, 415135334, 196516286, 941470595, 233222032, 477291634, 447147114, 734532224, 694848230, 781180404, 582140541, 795708182, 116730721, 526253565, 618056481, 145993752, 297121633, 887563613, 974011436, 803293166, 371151444, 556185429, 845356413, 39077533, 982067989, 984921329, 431284997, 363278306, 674704520, 882084037, 606816596, 299961760, 697284351, 108395881, 33839909, 832876427, 573604791, 225158162, 431770781, 622968162, 295605652, 171929224, 524380650, 729997282, 872810181, 924880546, 995248344, 187942406, 199703286, 248181630, 160850213, 141918139, 549359378, 836842814, 415431408, 13367846, 104390464, 493940779, 384242004, 917024321, 507333785, 626401492, 176779669, 747270122, 638523993, 877120668, 574130744, 823275790, 496030410, 313523113, 606264213, 533745927, 332400947, 866089022, 33043754, 907891239, 490215884, 381893605, 628092280, 881396755, 558180409, 941746724, 194200468, 669528222, 939663386, 147594102, 418709581, 362942378, 270912388, 429521917, 616964799, 498382926, 880498460, 805900896, 843497703, 989501631, 334252637, 590682381, 30661330, 153502076, 502901211, 118646150, 136114219, 112664749, 502709498, 210571451, 701048267, 655039320, 644905335, 839266734, 326851346, 746022820, 375232090, 795815967, 563822018, 114849686, 968561618, 752062013, 28614336, 772118949, 413645872, 932063144, 425424156, 435964784, 918647771, 318441945, 618031820, 314062450, 446928267, 513134015, 42476619, 684358605, 296589039, 224536270, 901731652, 785963367, 937650185, 518052188, 329510502, 614844460, 581769851, 861700633, 477510383, 39522232, 424445172, 401815433, 197357573, 984518505, 879027211, 616557162, 443421840, 859710771, 371038069, 355860321, 499524455, 496158725, 774413575, 918723620, 738431542, 595546953, 115690857, 34215475, 975969663, 994624426, 505687245, 360704130, 371097712, 580589047, 418604206, 927132944, 850026051, 846706255, 810096717, 790843766, 406577127, 21615747, 775202407, 783778306, 872945942, 79376633, 239446433, 899807069, 783058826, 419567220, 989431582, 372476058, 744065048, 837002814, 98637728, 218113552, 737537922, 344756805, 944421304, 665443665, 92662360, 893210678, 876494385, 728280757, 485885767, 555373589, 211645690, 319520396, 337276864, 13799782, 535215138, 745859401, 129624992, 846086381, 383220692, 440975078, 342326102, 588677956, 860005344, 954122570, 337568379, 80683342, 696247507, 741371534, 458322611, 267153091, 426743948, 697242476, 105110345, 687796451, 625788656, 43049462, 51068189, 866267943, 974337204, 378132643, 213567626, 806483916, 745136761, 172469251, 906575307, 489598860, 182588928, 807387691, 819435247, 426687470, 933718155, 972636048, 670769083, 433383126, 433789733, 756465134, 204626590, 16901336, 849716157, 415339207, 804375818, 477947063, 99615652, 56637856, 145922113, 181844137, 560375987, 770107509, 568465228, 899381451, 187337236, 879679411, 407856040, 775900186, 914872606, 323114497, 76404574, 599020800, 370498913, 306608098, 970403209, 524203328, 784454194, 788255482, 367896834, 607937610, 106718805, 515774604, 28289012, 190581089, 419241952, 731917596, 44083664, 579481723, 537767879, 923861677, 664201655, 39202661, 194908750, 933267669, 786846158, 900128188, 223607719, 492447706, 267303985, 783251848, 111927963, 262567963, 243222288, 579021759, 673532901, 582939054, 455132463, 623254323, 968867545, 708455537, 782780184, 788765657, 273078462, 864365388, 373213215, 303008948, 918647891, 992176923, 101154818, 955988731, 74285684, 754899471, 936472006, 390440759, 910768548, 434878220, 101158791, 915805331, 305187192, 764748663, 490934860, 700978476, 114871025, 564272785, 94117507, 564964429, 718223146, 98648978, 387646611, 369961569, 258283483, 353176308, 456819113, 1622074, 960226115, 378049734, 466346800, 402075570, 387420166, 966395422, 192079314, 963850509, 322890040, 155065894, 765663687, 393038215, 796828626, 367413910, 405060991, 977323337, 910810304, 722504502, 237583646, 581439875, 375682791, 309738118, 996366449, 680158184, 151177750, 351673829, 179582049, 686453908, 505900155, 275449399, 743676071, 923796289, 681584678, 12888366, 499673173, 415552110, 910364946, 182961118, 636001748, 7595292, 737156599, 938391828, 741915173, 201451596, 445159779, 201099136, 524697019, 189597093, 812374053, 342178892, 414213529, 687266118, 166823982, 538061827, 37412824, 868061934, 235603252, 372090420, 408494641, 106228479, 350508115, 504539931, 563638874, 560991258, 487066403, 15610650, 964143484, 478655562, 473459963, 836174070, 436072219, 61188548, 675413765, 211557033, 91380239, 223077940, 727816050, 890367087, 629037430, 74810118, 135267367, 189003217, 663675916, 34260839, 455401168, 663992510, 355192670, 794146235, 758048506, 465549207, 707226532, 809713875, 742611273, 763201883, 63581116, 299140065, 884393522, 199408880, 888991810, 553823731, 6474056, 458055012, 680879214, 3104874, 909155892, 812294346, 494894757, 620237573, 816668882, 416506927, 273135685, 676964177, 845688749, 393722545, 923898026, 783024990, 703053509, 117664594, 872168073, 199778319, 255604035, 227801888, 138075188, 349318504, 587219270, 672083711, 680709113, 962462618, 70502923, 818857774, 934010786, 711450808, 959558401, 795129495, 238715446, 96458277, 60119799, 849793038, 202511503, 287573848, 303859672, 497027048, 824628650, 896587044, 220440786, 92509283, 817174399, 59841505, 387266134, 537915762, 275575679, 812419377, 422918278, 832970924, 715150448, 959506409, 445897057, 414198740, 226937795, 195229945, 400855513, 810338407, 761141184, 572797129, 627112529, 765967501, 435319982, 33411000, 708238174, 340597527, 699598394, 745143681, 790567779, 176523122, 612744441, 77175015, 907884393, 251331232, 660928077, 302518303, 976123704, 583122904, 151339815, 293741239, 925683895, 585559821, 687907524, 89067164, 214046336, 873931488, 660345573, 313378526, 473667105, 955500931, 779955758, 336804842, 423630848, 306288204, 157006104, 293349395, 268248552, 31589231, 69648300, 735489897, 33063678, 14036087, 200633964, 703248715, 972595043, 133919193, 531625159, 813867204, 736581594, 373576991, 819526854, 300628349, 68354538, 67617032, 287604747, 78594818, 347125168, 500356295, 159691844, 914543678, 762632396, 794308086, 108179408, 967748760, 219412488, 933220657, 341605302, 26161223, 921146486, 437738951, 41945259, 591232144, 391881493, 226546143, 880672670, 998067439, 470800242, 417401009, 966138421, 412964916, 384166834, 804986273, 125743503, 440989189, 154438015, 31818327, 29782610, 181541786, 383520225, 129016995, 900775564, 451821004, 12065294, 721337326, 367777973, 369059389, 962729539, 104673846, 29382505, 210806227, 900943169, 508718768, 774499333, 425833630, 364912584, 208287594, 311998428, 828525762, 45064261, 932446895, 22729340, 406199759, 913100498, 46928066, 535922843, 461536916, 425667744, 771664801, 321191319, 526943762, 221769896, 513302228, 30925985, 173487166, 607683991, 839456111, 403775367, 592554483, 255135045, 444037454, 128695177, 218863901, 47035406, 239610512, 187255504, 358578671, 68158743, 292819350, 511712705, 607709619, 14370490, 30955204, 773105762, 862569760, 938634368, 543054864, 369625488, 596018253, 333046681, 892590600, 460442769, 776310964, 966627811, 345940085, 431065096, 730254503, 979617647, 232247425, 993235179, 343942189, 832782852, 975116131, 332320354, 509935108, 953653632, 611094478, 142886092, 992925832, 443787696, 101027509, 98038839, 465694504, 826755148, 417463379, 276194738, 504717760, 605352273, 716313576, 614206747, 240685833, 161649446, 327472514, 381601891, 239603652, 596656979, 600463453, 420618441, 780686385, 314949345, 836160618, 14982269, 47810907, 287601040, 860711720, 389817127, 123414601, 614378484, 843836594, 927331370, 886129789, 423068998, 524420550, 37479673, 209681396, 3675323, 690531240, 924275427, 651475074, 471835012, 137489719, 280898443, 826181854, 265868180, 777142648, 685877861, 748209373, 568075957, 790400446, 945534726, 169348858, 685398597, 611734508, 508051767, 225170180, 757464013, 611610988, 594522969, 395071449, 717412221, 265451107, 221352050, 571581441, 359263784, 649808179, 103915362, 956886368, 797762625, 25111383, 378437713, 334489673, 251395293, 28220909, 244141560, 15681076, 617602730, 374127623, 245352115, 221142080, 479621303, 402571374, 224296380, 911106432, 265668704, 999197810, 550213382, 439378708, 15258472, 267579615, 707752220, 820838783, 486451050, 240226659, 346482608, 965639020, 767308232, 461917151, 722252142, 351892500, 242617168, 98711019, 918338797, 702255661, 41500311, 758628254, 336970887, 943997057, 993430806, 748649, 645354643, 685275957, 683090246, 583192354, 981749897, 189610209, 521873284, 363992665, 756440716, 390710165, 960873070, 202315803, 937557187, 865848279, 475811945, 763247652, 384838244, 55824657, 279837009, 962077068, 62060687, 55592691, 670537507, 650441223, 118163360, 971452433, 365596697, 747135720, 979251708, 679181823, 352147237, 624606136, 978936322, 300266293, 680396145, 244561553, 566619359, 741821586, 657263301, 597515354, 984251949, 553604841, 630910951, 435908883, 470033138, 830019979, 688936319, 245406366, 593354973, 496282905, 578452647, 984803777, 71791068, 475676540, 334325363, 817038542, 306819884, 753617010, 730689779, 182616386, 394539373, 589708936, 48421550, 675045146, 953899722, 562282587, 644191505, 70743614, 329463781, 975041060, 961850902, 842772303, 5980228, 935253231, 594168391, 264119854, 261535014, 131443161, 700215728, 37258475, 236174980, 88652664, 724093912, 611949966, 983526169, 912372719, 224977368, 651766228, 217792131, 811892702, 363378359, 591696713, 379024602, 385713783, 150121857, 22251310, 687653346, 214509762, 641711750, 528933537, 102614520, 920688114, 14529916, 96845115, 969332180, 120092205, 245269034, 729153072, 384662431, 325286827, 813933473, 447279285, 680717221, 708494400, 141805098, 832425307, 10013377, 3680037, 988578233, 45739471, 229542528, 192948004, 428300522, 360888067, 647359156, 693430203, 764309951, 710478181, 242149097, 865829517, 540402160, 854564190, 669082481, 807037885, 205888596, 370548114, 977905910, 597510514, 103984026, 573801769, 27918238, 311932262, 245677295, 532630908, 460313115, 601317016, 905607717, 555945776, 871848524, 69912255, 933590151, 881702941, 100249461, 315037048, 298180221, 876432694, 656568920, 985927563, 835408783, 403541428, 485336870, 819470916, 670692711, 237891294, 790648062, 830010055, 927847403, 230365315, 792042839, 987595796, 841279773, 280519407, 618985419, 692306392, 799188773, 425534820, 603571943, 54228389, 483860750, 630503669, 101390408, 668666499, 706509332, 822336892, 889434908, 615359753, 405295977, 499149255, 718909335, 779799993, 71418401, 393052947, 437597342, 877331098, 891731064, 444960613, 66889432, 599012069, 855933972, 681305477, 428268447, 47328063, 578110354, 61965407, 322172670, 675152869, 506686248, 440725974, 868773276, 402375968, 661238550, 624470988, 232076769, 757687498, 665227739, 492361212, 7454875, 418120812, 513519357, 371666469, 131249155, 730029947, 284550647, 574056951, 900527701, 113775516, 984787191, 3848410, 737042075, 860909494, 42879930, 516612658, 133877647, 804040926, 854434035, 401507717, 967961280, 146648606, 861272065, 729495027, 759167663, 728015236, 119467646, 124707780, 43798517, 375584129, 864921129, 103247372, 410116558, 851428816, 172736906, 989634524, 612929148, 677886496, 878179529, 261407218, 766503751, 883305290, 151320837, 355182965, 4932900, 981740360, 200241872, 644632483, 470914854, 728324354, 117847237, 534425768, 697511341, 307074078, 66473268, 452047205, 468977736, 353251284, 224352509, 886933465, 133480714, 980396484, 16389459, 711856510, 456082475, 348660945, 458976012, 937711153, 308551629, 202656235, 708399972, 20473415, 891854054, 793121829, 396837484, 302986649, 401774383, 567057408, 401554238, 998544015, 306474316, 56878088, 519993378, 4539632, 451565324, 189949076, 264803440, 99010968, 538683725, 257589020, 392589193, 388021235, 281139470, 966053304, 201481554, 833809925, 957292086, 857438361, 996500603, 901188422, 358675351, 735429981, 500579192, 512046717, 484472069, 469996399, 44823624, 255389424, 919973950, 351864200, 431654060, 108191612, 676595298, 346916485, 489523622, 68887984, 884344129, 20375066, 153535853, 765263336, 322926881, 491300540, 517000077, 373808116, 328968974, 600554293, 272304436, 516880385, 782747737, 825982999, 306179847, 218505274, 16637183, 98678465, 701191673, 587653848, 55086801, 245519103, 882650660, 786210664, 614178016, 196622402, 796271529, 564725662, 777273783, 171547352, 389687741, 164054231, 350506999, 21632248, 115519004, 255043451, 224691057, 230986239, 48698603, 407530474, 165495152, 558468845, 42899869, 694908291, 414492924, 986319182, 585169529, 165085747, 673073853, 218482278, 670657396, 25293748, 836208571, 585309468, 700630955, 639508509, 555728597, 302560322, 290988859, 914572178, 405409772, 944382590, 77922697, 593621197, 28459251, 927840851, 46269894, 169193285, 485525861, 455798385, 942667629, 575484177, 916439469, 563729564, 779015565, 376238537, 256878447, 368718848, 493811306, 562379388, 695157395, 367568050, 40428836, 835479528, 339739788, 70585037, 555892002, 164277832, 969059174, 285355337, 211915831, 812443511, 122238521, 2741255, 259634735, 30771520, 87218207, 141949754, 90433682, 502105999, 299687350, 23443256, 768753097, 111039418, 383740371, 631825559, 616743700, 77715489, 829118489, 348839809, 677474606, 681974867, 812984386, 38946545, 436661532, 434185663, 893902342, 63230919, 46325961, 279049108, 972398576, 782350238, 358367947, 781246042, 742529103, 156594285, 162558004, 446701624, 246728635, 53130564, 744927057, 34890207, 812155500, 635619051, 934464139, 10018658, 274754950, 366608076, 992177021, 62254380, 719933218, 154319845, 839256569, 811224583, 461285270, 212544535, 781001765, 841345820, 389165537, 754663377, 191711554, 913604923, 633936792, 643777794, 307028715, 612568773, 17478854, 853131395, 547733361, 401828387, 707661081, 510772470, 913335382, 698921558, 299285135, 444876894, 873234365, 843478509, 455590889, 633814239, 490196946, 707189658, 413951695, 212718915, 929855129, 357128530, 236717954, 289932370, 335250550, 959593143, 33176035, 745509949, 545554304, 283705860, 171961994, 519043339, 563733199, 452311777, 706710577, 905797638, 871073079, 142585697, 961823139, 553971488, 714334490, 522466308, 599936646, 330965122, 60567985, 555665559, 183573581, 968670434, 624748542, 355127708, 299884248, 665060916, 422815194, 840758949, 692926465, 273978180, 561227676, 985427247, 680094268, 127356739, 649161866, 376401530, 571249166, 683089561, 644347015, 853290562, 404480887, 601075896, 836342487, 128618577, 8236352, 257089228, 147956592, 468245552, 448242362, 16497790, 615702919, 479864486, 613111103, 877130038, 606425697, 249341718, 538175788, 474708062, 614622636, 752002634, 716222312, 160102140, 145565258, 281445394, 865550079, 199443599, 344111136, 418559763, 899583388, 486653683, 238467231, 585642661, 178370720, 197750388, 927356509, 879737653, 578186053, 728554140, 941603016, 832415652, 737180500, 382104798, 785691779, 262307916, 412185415, 854523818, 322285248, 666754204, 642174703, 172527517, 640885329, 423632367, 140495737, 661733763, 715478346, 928911535, 516942925, 704821220, 941554532, 541058038, 116627651, 997224668, 523660454, 17255309, 823117362, 885182780, 748483500, 920006237, 347074004, 440658334, 823020229, 185728228, 926743509, 567753368, 771662999, 328255996, 273443184, 420244801, 615623521, 426559387, 517477879, 819516976, 113056956, 681147807, 138710992, 624371636, 61606136, 437239451, 735155747, 397079994, 643205989, 363699707, 116530934, 539129263, 861718221, 913532441, 819034514, 426632155, 556343397, 284512562, 359952024, 159435365, 750615083, 154295336, 634416361, 366904141, 171794460, 935834968, 751951682, 737284841, 575358196, 206720653, 696297162, 222627121, 273010997, 855338190, 790517764, 51047940, 347457614, 836254046, 18476940, 478696172, 936450192, 164323558, 660007699, 994663385, 665097245, 770411936, 738976233, 417718161, 728856206, 52819162, 16854094, 272937043, 61971190, 566382529, 381689486, 645691260, 934289604, 754468182, 429749995, 404374253, 278898755, 311110582, 439335286, 338530379, 487183382, 774303060, 688636775, 965260914, 484725478, 622391166, 379437235, 43038861, 279651031, 662836398, 775233517, 966233255, 903600989, 760769376, 313883496, 636660503, 693801270, 866686118, 263499064, 502409036, 623559113, 690015667, 372680494, 445028501, 328134643, 90458582, 171562421, 842676591, 11219942, 93835004, 763490647, 500253371, 653119580, 730605110, 673681194, 440781940, 897971807, 129547385, 882691537, 783669395, 927567591, 685632034, 889062588, 172361420, 114798481, 149417004, 695028406, 66906813, 949772492, 486271858, 346230944, 115441323, 312827554, 409273832, 283253971, 445842529, 682473304, 460645191, 10472249, 450408637, 126897576, 792749405, 659303817, 663518953, 600847243, 521715158, 274015936, 690616088, 471492184, 264470964, 441519019, 227693310, 280741549, 608942153, 161070061, 433581617, 501216676, 573582919, 776157638, 461536577, 838116303, 689107288, 34455229, 559520203, 933580693, 203278278, 121628921, 383010424, 452521076, 177160775, 784759177, 905119133, 783780054, 580970536, 951836029, 213286759, 946515158, 58301805, 960856150, 964460380, 360588917, 239057771, 259873407, 126769434, 219300928, 743725414, 387346292, 540132228, 238753482, 657331588, 920791252, 869142550, 733197594, 655535951, 639782905, 887218081, 47118432, 234302516, 972155269, 312385305, 128499014, 295267649, 626792751, 278085411, 957351017, 937150411, 934428846, 121829919, 754364524, 541163010, 645787350, 22780527, 987716842, 42334174, 416108236, 925637229, 779469746, 403450338, 293831393, 100412836, 636673622, 701612754, 313507517, 742578891, 586879076, 268461905, 191876525, 81727120, 249645734, 75445441, 898255621, 368806588, 107767210, 446789732, 112865496, 289761348, 284408758, 4705704, 788280704, 913143958, 24760315, 58604170, 36405042, 27557407, 118337368, 140386442, 375797236, 246302974, 43585337, 261350535, 582243337, 287874194, 420585109, 841004401, 644327559, 917262717, 228985693, 564505474, 177435589, 552368565, 192579340, 590635154, 669603668, 961682726, 381633339, 411368126, 751456639, 197327909, 138335099, 832161622, 692510592, 569492829, 369161543, 966894557, 107009633, 907837099, 917705960, 821296575, 512481984, 467814182, 420385643, 104257987, 909997359, 487570348, 106141112, 249059937, 441131052, 222712688, 278859490, 585005343, 28334484, 106924151, 10077251, 345212951, 380492695, 77002296, 118771258, 579994131, 10120386, 737635456, 705003995, 616206203, 531080412, 557046118, 402212037, 843922821, 133308716, 872988737, 473222647, 707031906, 387458885, 676681626, 163515475, 759175533, 496741402, 560752832, 170081456, 365855531, 550498898, 503218306, 615751838, 99129494, 71859895, 807345203, 263468380, 932646251, 898091741, 56022426, 92304315, 428360523, 357409559, 888901287, 917459278, 473670300, 130264634, 762237534, 416682609, 968364144, 712357210, 503553132, 603683233, 184545002, 604845753, 858441123, 695927840, 657101605, 696173831, 503957902, 302863685, 558508657, 278126246, 956026950, 884429090, 142432864, 137582469, 802605267, 526102914, 558250670, 846217843, 607974284, 897674404, 216638977, 339685253, 407141355, 754252919, 474927569, 126137563, 445290300, 635712242, 753297503, 406081878, 411845871, 926511531, 260639047, 672642912, 592799352, 695727472, 294379155, 22409054, 493627354, 192946085, 148236479, 945327982, 493330332, 381391819, 382337978, 432825176, 632752844, 50887774, 706159557, 830498761, 72629204, 628162100, 903685444, 402758479, 641101636, 780990426, 395120631, 985463074, 637816758, 553212179, 510595714, 339763439, 888530152, 523863042, 47417721, 646856646, 777121162, 960309524, 731548436, 58070884, 472102123, 864926505, 161188416, 302711341, 635796581, 241081943, 525920654, 30945179, 15794718, 635237383, 108547930, 192085270, 682281647, 110067112, 154701688, 270575532, 593181857, 251138157, 611124588, 545248889, 84961680, 234706705, 521793176, 395376672, 632985451, 617928944, 75842968, 178670373, 125247667, 528956867, 634005892, 632799514, 632420284, 731566315, 743396507, 954411628, 15151336, 90102453, 393969203, 45328284, 608999991, 603998234, 122984592, 346470073, 655235145, 618628318, 450570452, 280297923, 505186406, 413805747, 879075343, 891884717, 463882013, 327000293, 674975609, 832808548, 705920475, 208810486, 106462701, 288890873, 864324543, 266986714, 204659068, 298890672, 572932125, 88376299, 375923246, 139145881, 398804783, 11323380, 429650818, 715589941, 758903477, 192403446, 822072563, 842736178, 733550723, 415846988, 158867445, 902833568, 939176106, 746679896, 639106573, 868254771, 390557321, 179692346, 642022070, 878254817, 15116214, 30461718, 519936416, 57502942, 400222523, 370625410, 853570115, 448823643, 730402285, 896733293, 476659963, 278207200, 154071255, 920633147, 328709802, 78078217, 227905088, 514310809, 498731188, 636924854, 398203146, 241571964, 422310257, 976780699, 433847254, 274974723, 50780445, 944550413, 234446736, 525562396, 397821175, 15053028, 886651734, 996748163, 666437698, 613342920, 282605611, 166221289, 388276043, 360098718, 823088830, 714640303, 322614646, 77137406, 694664142, 493463947, 127057521, 566766552, 631970786, 407403804, 602546821, 848169806, 66972813, 510903082, 65950735, 759856846, 214441257, 262509126, 196990563, 226276661, 914074335, 167996932, 244226331, 200135934, 209891614, 876118955, 887045943, 767115769, 437210403, 506423941, 589057747, 997672979, 664232671, 525788019, 65695703, 920023713, 600728008, 663288453, 357737278, 208704779, 594329886, 446987119, 407549821, 137814170, 132540561, 113602389, 484612058, 481058750, 445620966, 624729983, 820707582, 809933634, 720249781, 780101801, 845916303, 783906778, 998689772, 276618359, 144312546, 504757951, 429521851, 355946348, 628962059, 704757706, 4790407, 792268673, 262983242, 323702694, 963161820, 504951301, 534187383, 113329323, 389100527, 329564809, 544948618, 757495708, 563676034, 81766526, 721157722, 502054730, 353179358, 379680752, 706882485, 265093108, 604645871, 19016072, 640264418, 580130971, 970678854, 895295050, 337855111, 698196167, 329898427, 13239534, 677691840, 194227039, 74016070, 96404703, 454334834, 580913730, 622084278, 714505203, 169175453, 519241285, 245183251, 634555436, 291131056, 483350417, 453501525, 857009646, 496516484, 885861635, 703238002, 82145839, 792089965, 761839717, 944363746, 15019319, 580034852, 776896537, 719124632, 406287277, 12966729, 592761229, 505828233, 523129306, 111726530, 276642525, 29422399, 706301654, 930533094, 55173280, 648453667, 424481030, 886773069, 380718835, 854451737, 463229889, 367992268, 634424398, 899257948, 325279509, 809447876, 341595305, 157134057, 117356680, 888698845, 337788251, 171078171, 288091367, 890679698, 639584882, 742800133, 59731487, 755257028, 28331092, 722873887, 301493612, 779803751, 583167881, 993050111, 765094162, 604314062, 544270711, 157231576, 931230264, 843821519, 143763695, 94414139, 41006406, 376586251, 958357004, 22468523, 812160471, 951544069, 976286331, 994717478, 159219322, 512278946, 172177331, 931810394, 626672694, 447961873, 435429261, 375129827, 328675028, 855294655, 863214751, 247818457, 638118545, 701444509, 467153540, 870823471, 996471026, 129682636, 403604365, 127666529, 534881359, 715724135, 936175874, 326483003, 426656857, 887214151, 283153989, 377904090, 623043842, 339204510, 125324219, 323184115, 698924598, 768888601, 904759439, 918337281, 14727683, 48882792, 7186889, 314042249, 306432284, 826088435, 842400823, 335003480, 988014209, 793962037, 487083304, 690519189, 482539055, 157095859, 203115227, 275457210, 997188842, 875635082, 767335009, 988518740, 561308768, 363636314, 88023177, 611383766, 293449265, 14346164, 109743873, 692283170, 327155455, 13438231, 391844173, 448443902, 747548020, 826078996, 447822828, 72546609, 220981857, 35905778, 170128559, 785810519, 930073461, 223948582, 632065857, 42685860, 920598210, 751563089, 3088851, 330757209, 131948758, 743188895, 948070728, 495489158, 784895960, 326731721, 369108163, 94314775, 947438798, 719322836, 477118874, 163580200, 167656670, 635242534, 498553832, 66716279, 854261379, 987708625, 481603515, 789972559, 173902923, 220087041, 176166090, 862292283, 400229418, 347362798, 453396652, 549203974, 457467163, 35672342, 124337920, 697234594, 313263107, 940187621, 195880167, 777193059, 672186851, 171218172, 973153274, 932882543, 571151103, 857153666, 947791823, 815597324, 780637961, 308206287, 436950605, 40816720, 309210033, 989026690, 750619556, 382413415, 739002070, 187470485, 53093294, 747379326, 373842404, 361078815, 81588745, 39981515, 850338090, 600319032, 473366263, 187892680, 733402445, 439687813, 612442839, 568439305, 379003470, 489149079, 79295865, 73059373, 978921508, 219995049, 140298215, 715469695, 721527286, 192723206, 221737116, 497719855, 43976062, 106813635, 647821155, 185573304, 450408845, 227521903, 348692643, 675142698, 328542633, 915243843, 343639848, 695781603, 537203920, 262128682, 13221503, 851280789, 850212872, 744955101, 386718570, 666983637, 418005323, 931832633, 264184345, 237904175, 288233162, 629043579, 534099039, 321820916, 864794520, 293670725, 622492868, 832899996, 944446396, 48350739, 456965795, 956554008, 821946851, 578782530, 809785177, 221983937, 439954230, 663110693, 820801114, 263492642, 674744109, 370711025, 522232824, 863400320, 318953432, 855875406, 71070542, 310367545, 757018390, 78460917, 259636590, 54446122, 267907088, 874836482, 180605527, 962223957, 359180187, 177588639, 889043735, 174762012, 47293599, 303908905, 510177363, 998536271, 528161097, 539041400, 283803545, 656494559, 809586894, 90275589, 612433326, 245182927, 549281559, 154073397, 223240392, 465831500, 217444246, 652035081, 701877148, 184584905, 25153375, 263885562, 170188540, 254673973, 584929615, 231174893, 824141183, 510232447, 9845633, 722685549, 921556175, 849015945, 572973327, 14880017, 783905950, 987139441, 25285991, 152616887, 226888450, 129347036, 311815112, 334416565, 868877658, 162073451, 639247693, 475788693, 963191171, 728004390, 509957341, 352388051, 135124119, 694529651, 513496136, 403595933, 904021885, 237589492, 618906839, 839683413, 550170492, 162534670, 41890582, 33383309, 564155337, 516844272, 914359273, 205513380, 711327370, 693014946, 221917172, 728781878, 371911403, 489777877, 582772272, 654857084, 274929645, 899449519, 419567734, 170797031, 282591549, 145850864, 979443573, 861903708, 768556655, 998395563, 504819698, 187441575, 805202255, 537240528, 401501699, 602401751, 858825453, 649867670, 232064955, 668864619, 587976746, 602374388, 93807868, 699898128, 507016319, 895718519, 670684078, 462398008, 82711449, 801129565, 585146610, 182252178, 624613744, 266172439, 822418389, 485190595, 489617337, 539363529, 686925371, 697923954, 306531841, 309517026, 824143118, 649176712, 777016048, 512624392, 500251239, 733276160, 453876486, 347860549, 122166363, 550024939, 993130582, 268963845, 826832119, 261722594, 505106780, 1567726, 106863402, 393565189, 284176642, 793678872, 573990344, 351772643, 681948223, 792286913, 650316072, 745304714, 545553998, 474860118, 720719025, 414947052, 29974440, 821703829, 165378135, 759740877, 31205699, 791705782, 569462166, 743630725, 843241136, 267275387, 725070969, 216030185, 155987993, 805815756, 15409804, 220406825, 105307953, 452938444, 605906828, 238180862, 487203721, 27563427, 798893870, 77099140, 353708718, 551438994, 232490361, 724868186, 211719349, 919483297, 607273815, 774894229, 274767379, 325046842, 600520844, 112248817, 571084473, 224189623, 884437000, 964988533, 977021677, 499207506, 954178288, 649565152, 757667192, 941183533, 598317472, 601882223, 706337439, 610481947, 196663963, 982508401, 974840758, 652037711, 569350823, 315057932, 924210674, 839235088, 960109559, 728725655, 402348984, 161846555, 316152545, 243322676, 138418193, 557674023, 370523231, 729248543, 510850451, 189964911, 473658789, 197141027, 470653982, 943318500, 545013650, 451918747, 217611847, 242167645, 537493778, 429572263, 304305935, 99000371, 842485684, 187767279, 873475791, 788739661, 199021382, 890192631, 621815068, 663161973, 94702630, 987607212, 51978662, 364917096, 48199435, 78532848, 507813602, 828098946, 96157172, 137405358, 72851157, 351843342, 585065396, 549386810, 254962368, 976865449, 487820231, 407820272, 539898481, 242364287, 726129504, 9349768, 443449584, 767059599, 363352794, 291791323, 300363400, 502722982, 65810470, 985716822, 813474133, 676698976, 752959539, 470036914, 478969367, 736595238, 454426572, 213252747, 653019790, 409790230, 602715735, 998251221, 906074908, 491241710, 506099141, 320508779, 357053022, 55832418, 568082896, 641282280, 198735276, 930957878, 70993191, 955181470, 66457677, 693479259, 899756421, 819608981, 260922778, 191223925, 654144565, 585437760, 718943698, 77322025, 999267025, 433293332, 543421478, 915452314, 616583278, 510574140, 236442204, 87695122, 511754113, 469552522, 279325111, 397120116, 534133402, 372363668, 91208592, 629510355, 175032084, 508751892, 448915949, 14632908, 577445698, 833144835, 422605615, 769016118, 442117090, 895690476, 646032696, 405519155, 124772673, 641062056, 903969581, 46266340, 915338026, 258113962, 629177879, 506481459, 422728804, 168492731, 863482146, 636883413, 19049070, 804140002, 336451677, 814307941, 320545740, 254420178, 363121030, 572641629, 379614187, 630001153, 948361652, 34496544, 95514314, 602715136, 116568833, 803591252, 700489826, 96263206, 285618608, 572262933, 147386010, 495986768, 734765324, 847790757, 9244392, 619121939, 312025628, 463623178, 384868927, 805487122, 613101069, 642215578, 674703616, 102465460, 432029057, 164701086, 313497793, 782464867, 460345411, 625204317, 815797282, 720785173, 923877210, 812732389, 66815749, 991800896, 601018112, 394537109, 309555414, 667769629, 892460859, 408469883, 939895909, 460413937, 668184102, 511689036, 729982871, 692825326, 685247526, 903854532, 329481415, 14271379, 406351606, 955737198, 133048341, 684121167, 525760056, 532746486, 578553733, 447884222, 15761416, 206005597, 248093663, 999628277, 938482111, 496360905, 604230561, 70083723, 520708923, 303963013, 768351971, 300117672, 319001010, 762247860, 644637974, 795741258, 842924412, 97576185, 994998094, 398835803, 684016502, 193718857, 275608360, 81247584, 912191948, 914467006, 520180930, 62208319, 757540656, 855372950, 515162838, 720240633, 507550838, 853241402, 693652416, 474504038, 187076205, 296929438, 355460165, 344932365, 99679843, 713095178, 624411971, 279688205, 812930967, 833933065, 904493921, 574910548, 842475046, 962105113, 546716521, 725827202, 235230692, 771826305, 729446991, 459939258, 959986363, 669533182, 831203674, 29612114, 394553190, 974593992, 273419042, 699856097, 61528305, 543073345, 618389650, 20878334, 851950701, 198243463, 900280750, 366846474, 485687046, 690617561, 643127729, 6201837, 137151500, 599202518, 417762348, 951689746, 712295060, 533876616, 663904123, 332276116, 500702253, 409074470, 736921664, 692171519, 669757074, 462680399, 999607160, 875535024, 378469973, 792908906, 218754343, 399138948, 951050470, 637239539, 625213856, 857486171, 406869008, 736652622, 530219799, 733582584, 771345143, 754205611, 306773873, 468568343, 537748917, 939775267, 145116018, 23213866, 995677044, 667117362, 802311001, 962702546, 510084739, 847476561, 643339354, 1867385, 421731271, 372373038, 338025902, 979042485, 207776692, 327827248, 483014987, 322433861, 376572647, 494335647, 597581929, 333021389, 222181398, 924191690, 21168744, 676404227, 688976030, 169387850, 402981506, 415783619, 175685687, 763562373, 754233428, 685803456, 36314798, 526656042, 569756321, 77739829, 561990832, 502406338, 49512070, 249748179, 646999476, 62836587, 737428065, 571963363, 527727582, 406104566, 809934789, 844483362, 541536248, 751908078, 476694732, 380402205, 193012199, 919071564, 697604955, 659366251, 767697211, 36015753, 916979482, 643460340, 546985171, 5416235, 739056204, 365669214, 229911337, 439719632, 724174987, 124943658, 772888329, 271657881, 98708153, 467716568, 5403964, 255600897, 453122454, 562919066, 426136748, 133126533, 112475558, 407861800, 507870637, 911605996, 582810357, 580507975, 683913299, 68415317, 374080004, 497563717, 524906008, 146709168, 489606006, 677550975, 301875076, 896537300, 34247836, 89418502, 754576355, 252906982, 151213425, 476671427, 597538664, 327977894, 521104371, 18670326, 11800490, 438607809, 574285782, 352607268, 171925717, 316299767, 996008516, 861157556, 247993593, 345114449, 982284872, 120256184, 943835880, 385301290, 331489776, 878735549, 915578679, 906028702, 571908693, 610138677, 528721686, 827198557, 319724008, 443460815, 423389353, 898052513, 822901578, 853318292, 484491782, 537407750, 198638597, 400012771, 454099477, 261202687, 624119604, 959164352, 21588293, 491832702, 843577818, 296762367, 181528874, 103182601, 244934402, 594982891, 255974585, 279251670, 604340792, 253196107, 128799321, 743206868, 355178618, 393947837, 79234471, 640135615, 537751638, 445545376, 854280320, 325666940, 348571944, 729404209, 330843334, 29174380, 277420851, 194701700, 500886187, 493387384, 202986082, 513176446, 145820363, 516628883, 281715190, 956542918, 117776158, 852977427, 955335777, 441146573, 810023294, 123387045, 311963159, 658945560, 350824782, 649658222, 67491388, 138948465, 395612671, 85531094, 512321448, 183414103, 457652366, 953971221, 978658992, 216042811, 222628465, 749819328, 690163634, 959661955, 80338852, 325411519, 17743249, 38576049, 589509807, 294145472, 937842621, 690801122, 476116675, 858560410, 5340013, 858869285, 288986128, 541823952, 678299515, 218535113, 698174127, 618115866, 660882616, 988674460, 677474130, 517547209, 447699747, 818688473, 5134143, 446113437, 511933121, 246336644, 765934582, 580943766, 89710123, 843997746, 919190151, 9817970, 814581523, 379733374, 884902971, 634079039, 627681792, 786302790, 328510238, 991877248, 484448318, 267374083, 647843576, 721309672, 547971455, 699061194, 389003734, 500514900, 179378616, 831204647, 69662719, 568473594, 147091481, 841482673, 449286741, 225192524, 628322721, 969193113, 156094672, 795774936, 765307835, 962000601, 268452780, 904373229, 605877294, 730074754, 686032979, 951162999, 711808985, 168654485, 141473664, 649986581, 13281121, 661490244, 499027681, 896254168, 946469794, 916151016, 927265230, 783066216, 259730172, 261166855, 473268930, 683451142, 499467126, 388334344, 2418988, 159442096, 408839297, 554065070, 114708452, 43262647, 605515700, 341355106, 728201583, 530499239, 51361308, 541372475, 506390940, 374766128, 462432281, 846826912, 788966950, 327992085, 77368116, 56121750, 996381131, 430388856, 889649855, 221817420, 990879894, 950442757, 939465293, 390664334, 324857632, 950998606, 752797559, 899308788, 936719317, 920786508, 302679185, 325044164, 98935474, 462190803, 678606257, 749232999, 465062878, 511069143, 459278823, 921595202, 728950013, 69810792, 140684879, 39938220, 248092825, 751649162, 687971204, 639601551, 700643895, 601872362, 633313531, 194216898, 767447774, 717322536, 633951447, 899496075, 26380910, 599419048, 424629012, 922247420, 421263311, 813535601, 56754245, 123783224, 264473452, 850539832, 599657615, 540976661, 768663226, 492394765, 736608981, 670919699, 941808063, 202416884, 654970094, 871627780, 834202837, 869011448, 134732637, 536939963, 187659227, 954712949, 568656077, 118576791, 549672397, 330150063, 60822413, 15239634, 505005428, 858791390, 976359063, 568424197, 442478374, 821785305, 77934936, 640051851, 592427243, 994410228, 58883181, 684235733, 564145117, 165792097, 799717797, 515055560, 97418456, 912069005, 848669427, 310900000, 468622869, 685446467, 99164588, 127695961, 839553485, 857612564, 46422008, 159061677, 258558637, 893540219, 512478512, 559422616, 156975128, 571867570, 344773497, 940463766, 412520710, 3167704, 977594114, 680165271, 933692866, 86839755, 759155327, 150565543, 725493383, 643612818, 403688668, 359208632, 983082652, 125498784, 943004153, 383612607, 390613901, 720856305, 443971020, 37853178, 266841747, 372971272, 515661248, 89144999, 530282952, 41031838, 947751075, 89602420, 870978231, 331213121, 804182548, 824805771, 295261248, 769973079, 900633690, 591190911, 115371109, 876909055, 657853498, 262134034, 930974466, 934475079, 829269743, 712792819, 501630860, 973047980, 188283067, 711584341, 705183948, 144405751, 628441777, 486402411, 399075843, 207365943, 349649927, 635683094, 255166581, 668462375, 810884828, 303391274, 365285860, 114229622, 609875177, 366898170, 159851870, 718804339, 732228555, 773374919, 3681551, 315686633, 764507783, 179155038, 454712867, 302099252, 82410505, 631036666, 510667205, 130101133, 577952237, 257603294, 881048570, 429222433, 547996620, 580617137, 528115375, 38511889, 479268379, 448654536, 730205912, 378347919, 68570068, 830467276, 34754551, 442251220, 687509341, 45858499, 960638396, 704674274, 156441574, 913569950, 236538892, 369148247, 128394279, 773780043, 521285360, 233800584, 461969607, 19736711, 664744648, 589883202, 627586619, 557946599, 131627897, 956912652, 945011803, 555990022, 229096626, 685231288, 658691416, 384918382, 947100061, 70736693, 82602749, 152360991, 683714595, 344734465, 737535958, 515865369, 457088870, 68562289, 97790329, 346923539, 205841439, 336551970, 851244112, 941868034, 560806207, 403572319, 706514932, 427479178, 454625470, 302631529, 875485868, 522295864, 360142789, 136010233, 455335643, 742466721, 740457769, 642870904, 429617633, 579063713, 104985869, 525188185, 951909045, 491482199, 410667356, 22123312, 55066472, 140825941, 603767029, 975397565, 282069854, 740234666, 951936178, 109383767, 422189897, 338380630, 173527727, 35811376, 979366066, 557611976, 281759105, 356438761, 479692292, 929412676, 106939627, 689547636, 62345125, 754361348, 214841480, 188485514, 199085891, 782603333, 40203588, 246496354, 863517937, 978922646, 532243533, 384870763, 693177554, 536862982, 18571363, 487984466, 717731202, 332878916, 8426081, 405891763, 521836912, 767081600, 922085824, 520180914, 945871688, 820265740, 557307752, 88066277, 755501758, 516530864, 865235500, 88513792, 529512307, 970711599, 280450520, 729132478, 776731282, 290955748, 13752881, 393438987, 780912068, 783020841, 254261521, 196307768, 225357414, 390788907, 494673779, 232905291, 628393913, 954539531, 384071999, 665833272, 462281312, 270347724, 244295027, 83946601, 908022492, 840266104, 196400062, 789229189, 321873497, 544156355, 38771949, 85539543, 56579729, 564781153, 475795934, 298499607, 741244472, 851039250, 594252132, 265815501, 93463420, 597195395, 133405325, 751654707, 50782492, 569139666, 17448981, 859911877, 302225624, 73061701, 691364434, 160162590, 466903343, 333232935, 703865271, 204723259, 369745361, 73832386, 676465654, 958075143, 28116662, 252772428, 555289152, 518185724, 466259261, 536202653, 682426347, 312641186, 343789368, 946381226, 363218762, 265690254, 535832904, 866207772, 807632586, 485136324, 830881614, 881415747, 519910051, 922686192, 600181840, 119767122, 291393021, 433286453, 436479648, 420024076, 782683410, 323235345, 863867641, 862969946, 604520958, 913078193, 282699333, 942372184, 38894953, 41071803, 799241658, 152361857, 618291018, 874007362, 23205277, 676095946, 28667265, 51033024, 418109751, 649561431, 204911438, 6564303, 964351127, 283129752, 62694791, 699339320, 333163650, 950368768, 185498614, 402916841, 444849457, 35862114, 964803850, 470083040, 144131026, 304186412, 375155959, 393097987, 202894860, 801379510, 399380677, 378890475, 98227924, 607823520, 151130846, 948284443, 41021347, 729036060, 665905251, 750210861, 18888850, 666776197, 349980071, 430179851, 503515592, 366365120, 534759102, 760282141, 580957218, 360336398, 165155451, 785216374, 23416667, 280502552, 537855153, 286974884, 328203335, 516974542, 427870321, 8368038, 549758222, 382821025, 659443213, 443916087, 804411010, 756505027, 619760880, 970035392, 921771391, 415822672, 683756217, 348412425, 708929752, 286539926, 549860495, 263307917, 360900339, 9588915, 585878395, 271154478, 43880824, 701158341, 176016991, 643453454, 841286132, 78772361, 504673274, 105252144, 177060413, 225340431, 730284814, 417638647, 206121318, 75554836, 295852869, 746801819, 24297516, 994158021, 231167198, 117389112, 485221571, 996118403, 26850924, 394284030, 87501132, 16039783, 102463526, 751840544, 213535890, 706393037, 489693966, 482433236, 948938011, 783740543, 584242205, 412075215, 579914733, 442826295, 720060763, 297282266, 387049160, 457193487, 953682896, 459350590, 610833576, 498630640, 234633329, 879523964, 41074869, 447946892, 89433085, 3123736, 578595872, 1793975, 391420455, 677092938, 278650523, 35007202, 671274007, 234706931, 919729597, 135563327, 809241085, 415649293, 545203171, 959712035, 932346208, 321449181, 32511794, 360690342, 521465398, 810554017, 50024342, 243442119, 868277259, 530059114, 285390943, 741358240, 793681749, 970189506, 203649185, 805540000, 448804622, 26026320, 434803538, 127850135, 83305255, 631395440, 486720235, 181024369, 207429937, 639497118, 671717726, 37203925, 677156204, 78158, 349745730, 390195717, 340181975, 30898864, 845326405, 38350823, 201213072, 786265885, 522533522, 333659618, 341037394, 273439839, 696232591, 160944548, 305673076, 416719526, 941483616, 401960337, 242811975, 52075266, 160650045, 37624031, 473810159, 432025610, 754948717, 943519567, 727398382, 895859587, 968710859, 655446574, 145425701, 636331263, 286199123, 758095916, 293282644, 714834554, 435145917, 490336927, 292781775, 687810, 409139781, 537232218, 607613496, 41607628, 115955312, 255403933, 220083343, 378577454, 390151208, 888762685, 468252510, 160264682, 502488716, 874569122, 397897935, 169336420, 89462916, 97066212, 764329376, 217168066, 798575748, 10071447, 882595392, 908044364, 905979447, 426674374, 524242481, 894836280, 733989283, 110334416, 89386419, 89453143, 651139958, 66490923, 629882909, 20038640, 909478160, 468302468, 362025397, 667998137, 947563579, 991753828, 278739240, 286254694, 865576904, 589905361, 620640896, 79547418, 752357569, 868140731, 878782721, 731356760, 118970114, 408873549, 680840592, 447275280, 683737338, 261311932, 527010694, 780934136, 492558242, 343315731, 329472397, 737931092, 319463430, 511177034, 275180087, 24541290, 445039728, 214601818, 209396835, 521520680, 134855175, 750335829, 418247566, 519860899, 595056105, 28975731, 915388096, 85634185, 556283904, 539791032, 691467907, 9314719, 284279688, 697393351, 83388332, 29789598, 665462813, 587934701, 116302226, 995783230, 41255935, 364557917, 832875731, 273985344, 271952041, 540321059, 936940105, 602815672, 884576758, 99963905, 960946546, 608945530, 510609022, 704422737, 980526259, 888202637, 309156647, 67279418, 765498042, 556919012, 136605613, 950342040, 317198362, 942571008, 920577110, 751840391, 428394310, 788998678, 724258670, 99914550, 428986453, 636824720, 932924647, 104952942, 536951439, 831483879, 773974525, 83281043, 833363758, 540658273, 391945314, 384353471, 668038303, 839755347, 954400268, 957419112, 198051699, 178974138, 133847415, 7132252, 140745930, 244151045, 304390831, 721722303, 46771547, 213599578, 849865821, 541338878, 966978246, 622905674, 95722593, 426807315, 505811158, 288026324, 114945587, 611173113, 723850537, 249818192, 495822416, 732645700, 136584396, 464247655, 886489248, 613977204, 689991237, 903338663, 773290997, 319485591, 529994457, 311670930, 514703945, 58923644, 518955770, 210766732, 626947572, 48913123, 800460266, 96222731, 628286062, 13452950, 825050217, 461547704, 28947739, 381539623, 473728114, 644193288, 768991643, 698374500, 930835500, 721673224, 150916252, 245030731, 371936875, 310681769, 710054684, 259875835, 792132105, 379215155, 222752158, 443065253, 190174433, 632762579, 230036030, 827500960, 619431462, 675584139, 599682517, 545307151, 988800579, 691358645, 111326311, 663500199, 358031628, 401229465, 210501045, 992515570, 78499359, 874288043, 900649749, 519911810, 719944985, 881176007, 887496955, 956058369, 819976357, 508633743, 971959602, 989824481, 741319813, 163297282, 849698648, 210818212, 702083034, 480822786, 309487430, 849837247, 392510645, 131178879, 876689527, 682973186, 37992547, 384767861, 31331403, 900363420, 788764170, 636499497, 184372836, 767300896, 799502812, 800360361, 305022894, 791454840, 863969113, 116495089, 23721953, 949846439, 323158182, 402981651, 875926354, 413123615, 607908913, 677019772, 596865898, 769944736, 807622410, 931908131, 579099510, 24352041, 437435902, 162365653, 378892617, 80870814, 79849414, 260835703, 612112719, 240713950, 961311900, 138449266, 444570584, 392745460, 620194914, 700875615, 349343618, 499311248, 355883365, 590364381, 30291098, 130047589, 438939898, 304396956, 369680209, 644071451, 779509401, 530416640, 332927854, 930997311, 354958709, 901818752, 93345612, 514428196, 988735968, 681410662, 78027837, 310440408, 525327545, 349187351, 489272282, 809790782, 609169699, 720653507, 432793100, 13706388, 3933230, 743061879, 951759533, 85454104, 504348042, 386926810, 127021570, 983819132, 113270757, 835027542, 10971368, 342151164, 257904613, 531065790, 231601903, 848075497, 128974781, 869952197, 513236464, 594762521, 253568484, 24253307, 235837502, 195396724, 436998690, 138877469, 346072695, 229931414, 256208802, 217080128, 737464915, 979899666, 744885208, 99259784, 218707328, 304084296, 898021684, 831961395, 814836894, 818571046, 175530212, 132622131, 585514434, 169022757, 501849086, 379551415, 914002180, 248459504, 246209544, 206181861, 242737977, 208221799, 699593518, 865059834, 663897471, 282968385, 846231241, 535674665, 459770692, 826960473, 441201470, 392603456, 183695389, 932545495, 592002493, 480699410, 641936001, 831754225, 115043386, 178435698, 556562236, 667270615, 521355641, 908545968, 469466238, 183336750, 949801111, 219750329, 897340893, 29325925, 726211109, 985672035, 952108769, 695937499, 330455806, 973450184, 283659276, 610787048, 981946996, 780723624, 960144711, 320276729, 783198736, 486407323, 679205000, 950227364, 93535990, 63513930, 449802011, 991843673, 201351549, 75694345, 659017077, 724338607, 606125586, 758385397, 753741260, 716758484, 362311894, 573250151, 15255591, 580415235, 9352418, 250539241, 57718401, 40960060, 209021371, 261681173, 233272115, 124308384, 776625818, 341494108, 93063132, 51332503, 818601300, 657379625, 626340391, 37548545, 665738120, 579167767, 904756883, 964551570, 823840015, 577863933, 940784382, 584658514, 667909292, 906932194, 163137599, 195307268, 42908115, 39197379, 683703114, 494252293, 8893170, 482295583, 958158786, 698405179, 69066566, 241598516, 248930786, 900950392, 689645874, 103838010, 361390667, 57567015, 370221916, 543857239, 204882414, 991117736, 774643461, 793587541, 313338479, 288888630, 274632822, 30906674, 47384519, 367688136, 881511239, 785241521, 913750643, 150669948, 934666827, 997186218, 678284713, 776757965, 617882047, 436733672, 587520939, 290340362, 484050358, 427550573, 600428532, 824836032, 332660339, 320584154, 74364605, 744498024, 177929755, 323979223, 980071174, 386474445, 151102461, 673230141, 114081185, 723151214, 932139065, 782526358, 942529324, 81580930, 593993899, 283561366, 29556229, 809592930, 600904483, 801032978, 546491365, 120887715, 30419152, 366013897, 225613844, 337466953, 927085520, 656628586, 474564194, 308033779, 744820956, 92327468, 231852908, 463311734, 629934509, 62384410, 232387959, 907168414, 747346384, 473507438, 695270781, 1371836, 227114663, 312560459, 356526547, 720330214, 309170749, 432361794, 194128152, 709191224, 446823773, 828965276, 162470227, 122601048, 342207481, 333833289, 884311182, 549035034, 209669713, 864360260, 131462441, 60992203, 763412916, 898721131, 249823823, 763516085, 516222187, 284400833, 586777634, 711698959, 318478712, 527511252, 486958652, 700150557, 79089941, 829931811, 823938946, 521375199, 422595392, 683773743, 543072679, 519457025, 146469295, 700924683, 64752319, 967794301, 267514734, 213785832, 74055421, 16787207, 256176776, 930331276, 820761392, 149899776, 424684169, 873519614, 196577429, 501974599, 412454899, 692894710, 890765001, 944443955, 247015895, 9932025, 630103327, 931256788, 946215567, 412167484, 726530478, 149403183, 154731955, 772672828, 990275797, 203408350, 713306994, 771567531, 875264650, 546846307, 563299128, 235483329, 607492480, 257834466, 387918484, 233543551, 631638934, 555794256, 218528148, 14553509, 43905865, 543933377, 856178338, 310162470, 442679020, 440143143, 961390524, 835431257, 414888710, 24100703, 167760239, 5300519, 228159535, 634579098, 410808334, 88315940, 177452307, 475189653, 843523133, 522836635, 524691296, 259445011, 591472612, 232034826, 934934172, 597474194, 951952396, 859581300, 173049561, 481103381, 270843184, 105872293, 359842369, 745699673, 657287254, 617358854, 307658405, 868216657, 470921280, 613395037, 195717343, 175193904, 284348048, 130416505, 809933207, 989808173, 625461940, 963753511, 963666003, 531697007, 706795946, 585413151, 943738371, 664728290, 218277389, 108513168, 314828762, 30455915, 728529476, 185790175, 936970575, 503938639, 521954259, 278914792, 916175937, 234299620, 784181041, 373065434, 798443647, 534846667, 310700053, 902350459, 285663009, 962638396, 663961606, 314683012, 616032053, 472052814, 615664606, 160341389, 795092363, 956161778, 316126903, 455864503, 802515835, 545948905, 447804201, 325666549, 944604832, 207460604, 208279904, 929984986, 369049103, 2995083, 130312589, 464106748, 344995136, 583047526, 910579190, 427267994, 599788193, 431051548, 544420779, 292961304, 977201163, 415758243, 664430372, 545756800, 245061691, 436667007, 479495715, 558552358, 400282613, 955178905, 98596464, 434755276, 165346128, 884169302, 492168131, 616886080, 361157674, 829516039, 442306126, 99946450, 194302634, 4624220, 332808577, 338222279, 834585240, 253244261, 376969917, 146072764, 904083673, 448738432, 507109748, 890122542, 628382667, 946152288, 473616889, 145597209, 707572915, 444978212, 210932133, 107748793, 390563885, 468651294, 538835790, 460892397, 543996974, 858317132, 418836773, 223594086, 151565412, 1140034, 237808555, 777536483, 305060609, 47949831, 224768053, 638529440, 467675262, 525042507, 57995580, 463929837, 526119733, 997063071, 476065141, 658411723, 340359861, 630852897, 678893692, 119448968, 240046760, 275337065, 61891686, 269530080, 496972155, 866880305, 472782438, 644659026, 741780349, 645778127, 784940703, 546147390, 290231198, 291515379, 541840933, 799660707, 8980173, 792994209, 292570952, 494515221, 308212772, 441686401, 701893453, 64502722, 508682677, 545044480, 475883784, 750783684, 625548387, 244338077, 341219487, 238808870, 625065810, 140976944, 858264137, 477686915, 57419113, 447913823, 997894454, 118985314, 47109414, 286361833, 18533340, 973271475, 18784410, 22957203, 144382032, 978464374, 953122379, 667686114, 780761875, 125092441, 477580102, 818266997, 452701915, 583213416, 827338271, 514706750, 436147902, 740320824, 885531866, 439945174, 974128851, 56790473, 493671028, 107520895, 918822120, 412755391, 809379408, 989543347, 884793269, 591450917, 173739217, 53450647, 517501339, 350299878, 718936833, 288642222, 505734451, 339959000, 398633413, 260485594, 485459273, 405850570, 264494772, 843602553, 916624326, 684223851, 615659699, 868888132, 519625904, 341006493, 760273311, 633417247, 291575956, 960468335, 166661679, 113671555, 134431745, 576143600, 298232629, 33761038, 716984874, 921058498, 175167994, 825088581, 551639433, 474026386, 971755670, 142546313, 162860537, 389495574, 494814813, 339112489, 34157359, 505772937, 889972999, 326195493, 815562823, 721375213, 194786142, 512009767, 506123545, 599534814, 169549071, 849899543, 243573716, 184827141, 677583743, 660729952, 257661870, 855327656, 883952200, 751361581, 733555758, 383769482, 854288282, 599999035, 171611291, 931031166, 50375019, 113338071, 632322430, 576726024, 350143230, 159923383, 683013523, 63695062, 976549428, 159045713, 863689421, 360064339, 978751215, 983279613, 571173391, 948931914, 170154788, 150189543, 130404702, 920895077, 434692183, 1388391, 138604238, 484117779, 468314285, 611229118, 623278997, 943277944, 48203650, 309940518, 741991073, 915916791, 395812435, 629704490, 585398242, 588091708, 983532648, 575909290, 670508048, 911130047, 197549023, 154660591, 940163028, 486584148, 537912417, 301921944, 814193056, 162777243, 341564603, 219126094, 827635415, 682984090, 892587970, 482633984, 270886867, 788425012, 345467815, 304367144, 907013098, 461678125, 707853437, 667594078, 325564218, 826773803, 403206273, 929480084, 649689107, 114681602, 345599024, 494772178, 95825740, 185652892, 266324928, 146856262, 492055157, 124912191, 94452250, 320284566, 884310138, 787544755, 985364802, 956806433, 106859718, 844421242, 789940527, 853206319, 660369570, 728133794, 898167656, 590937269, 308397798, 440622929, 118707654, 599908551, 414597825, 231504109, 410022261, 453278178, 182252231, 60663935, 627318616, 3409880, 104286185, 419310807, 184824355, 432227508, 34414412, 221651988, 224465268, 337696836, 323462139, 687051931, 209559321, 356675613, 532407339, 734088035, 851350812, 131136186, 226125958, 933696856, 116018649, 119307989, 221295352, 40875426, 281735490, 224238054, 757886840, 52752228, 283000193, 964343039, 30635331, 412397045, 60427542, 12626250, 474696166, 213860179, 502308163, 513181124, 553501033, 507790875, 121145563, 725664351, 303979357, 658067220, 498378258, 121127399, 289370845, 540689672, 54650580, 660240169, 749416793, 241466955, 315982748, 602982816, 853102361, 944328667, 563305694, 49708746, 18311351, 502342899, 46292411, 959024360, 410582966, 241793979, 55629603, 745099831, 390812889, 564252118, 637367341, 605918193, 354615439, 196506752, 382686366, 705179059, 2119841, 193830751, 64900513, 387745984, 568518125, 365296293, 96897034, 804700587, 237989693, 986519945, 425282022, 473016700, 322747196, 288322888, 53720585, 995004825, 955683870, 835419551, 654151797, 710402550, 208576120, 219899576, 390938908, 651050458, 56810449, 710666553, 896477802, 43924082, 854063663, 836444198, 182419807, 885523139, 37291889, 911400316, 313034616, 307950776, 563028246, 191503772, 3679457, 816890484, 942770587, 230363222, 335454597, 552579121, 788987540, 272491789, 410312464, 891795638, 837038042, 687761903, 685019527, 272407120, 10684393, 474508264, 758352955, 135044102, 2514178, 531218368, 911800125, 917054624, 245514086, 496809409, 877039015, 874641538, 58852528, 718375873, 441225331, 856574534, 941347733, 192207811, 19570994, 471578167, 229120204, 911003049, 42718974, 915987995, 443559856, 842811631, 519616535, 760088812, 178259255, 276525985, 227775398, 260211345, 668709663, 46258692, 357668755, 106334543, 156828690, 50520433, 426121976, 60813240, 346056246, 950383764, 269409447, 641048321, 120482118, 39925445, 409736323, 759902195, 354507118, 278278865, 698238953, 688503468, 22962456, 44785569, 116582783, 654541867, 683749360, 276772091, 632091841, 730695931, 893444296, 653851675, 363252343, 100493465, 134556422, 672305026, 940795927, 587593290, 133251024, 28433584, 222931690, 877908389, 723515976, 760007581, 887964026, 222853427, 681103737, 77986681, 695037080, 78141818, 496949815, 674804870, 794438488, 133949100, 891730098, 114126339, 621745756, 245439745, 427086308, 240243212, 77134613, 481062325, 582560535, 435772102, 123611640, 325683638, 917710192, 427949261, 761519176, 761104803, 61695870, 110046608, 549157564, 230241068, 113870304, 739524178, 347020878, 382831455, 664990093, 767784631, 216915021, 227611184, 473528405, 634632456, 847510921, 318923762, 625584178, 890594425, 663844659, 861413787, 950501071, 822969601, 246120343, 633230711, 758292431, 499601306, 461521856, 547236882, 47877427, 70051078, 293694676, 353414352, 107422381, 336636731, 11141643, 95554315, 183478410, 990820009, 201793084, 717390338, 488064966, 129254145, 856939008, 191765122, 238083812, 512435476, 554440234, 349143366, 704221456, 378286602, 66662359, 371022713, 35366793, 833954479, 114925464, 885047520, 102020282, 909489698, 294134984, 678447355, 354784530, 586396945, 950698504, 664814714, 121126023, 728205216, 943211996, 14343544, 414803056, 824425407, 733870408, 51660622, 964723067, 89396437, 201947592, 809598148, 716151440, 923119965, 395267085, 115464698, 878268862, 608758166, 239629768, 932276784, 955859773, 492850642, 355484926, 618766153, 904577383, 904468545, 662589438, 535155547, 246258314, 73753023, 777981469, 762005284, 32472073, 11620588, 788910073, 407249080, 445403652, 776730113, 346792600, 614331208, 63514915, 573369659, 325367741, 65402108, 101803795, 675373516, 564243215, 278731725, 403203336, 389913937, 447371246, 420507114, 321890304, 727713185, 123866307, 702784448, 833836511, 599289696, 911236609, 284397684, 799559647, 926084255, 86995144, 582952043, 999900197, 853404466, 357092269, 467661906, 509030438, 550519079, 742736468, 463688960, 857337608, 804894765, 47084594, 694590991, 582573238, 574700411, 502447375, 984285449, 977700757, 574266862, 809918625, 522089178, 448241291, 253763814, 817630027, 380044258, 664040106, 151039485, 289898682, 671598047, 591980384, 904995853, 707348143, 319894855, 260736672, 311463006, 922472136, 136041386, 260192208, 278284352, 459147084, 90310737, 212280255, 546252919, 767060535, 327172598, 650682952, 643645670, 342782864, 908684445, 364145328, 381053391, 680343746, 151136787, 675130086, 404679431, 815664530, 350573610, 205826519, 924337372, 254188656, 166170068, 970414734, 685201183, 921277972, 796479000, 872523757, 204373612, 763950563, 115602636, 422296, 63212474, 441954645, 800457322, 117420515, 78063824, 16076810, 385437978, 875113956, 345221083, 832906827, 992353248, 397184779, 678592201, 913951726, 995938712, 867257083, 189745923, 884236692, 66825822, 523137534, 270082503, 840268099, 842444525, 213543298, 301456797, 359753211, 421647870, 453486075, 480404981, 286288348, 203143783, 507022646, 727470044, 859926754, 101555455, 403787059, 396461352, 457125566, 513096788, 771987289, 709407826, 148996258, 825975746, 229919243, 994980269, 834705080, 867462151, 22954666, 864663356, 139429121, 740750498, 447507082, 384117680, 699673165, 547434222, 839597496, 293661775, 523576099, 382941432, 115014013, 298246192, 686969610, 994600395, 259614022, 655557352, 303419207, 371062661, 552591038, 834369622, 898886721, 385977477, 212035689, 636718372, 636699767, 647512520, 578901752, 320506186, 223140570, 973827519, 63450368, 851920506, 457773678, 617733414, 868197142, 276348594, 325487514, 911620244, 578824728, 963344889, 427626623, 150709204, 675540012, 163223945, 395184718, 577987568, 702171188, 796655673, 189806370, 941292639, 542135287, 216894676, 543616536, 906893510, 878337784, 979032198, 7457504, 875488570, 507798255, 865527148, 946171254, 577084259, 787891757, 282839586, 927726920, 144417249, 378119603, 487893077, 731236947, 829037766, 788620774, 178489157, 583043390, 929720392, 828464430, 803735762, 372839242, 689982170, 4147386, 484973905, 445600132, 90237324, 437381470, 807547921, 516924817, 293290710, 350703430, 798221248, 607415896, 630017142, 874192591, 884398680, 446273555, 401604218, 283683372, 510466946, 165000653, 295411165, 450086156, 500386692, 238204525, 568097156, 477354157, 74422074, 100769883, 401604700, 164791729, 595309316, 546528745, 655818432, 845742556, 193881629, 937175544, 819543863, 670043750, 910882238, 30922513, 990265301, 867620908, 979761589, 587328444, 340525250, 154751562, 871115451, 397864461, 396232344, 511755471, 818755880, 701701551, 654309866, 560058620, 600953351, 703228661, 944329498, 963710183, 762697912, 672510642, 392545865, 288163069, 392360234, 548856374, 647438543, 494022782, 254563120, 398049740, 577996330, 966792780, 531126154, 222022529, 257530152, 482720845, 15822018, 364213778, 811670229, 330008418, 847252608, 848975444, 800444639, 367995806, 244362239, 558307807, 441243760, 500395162, 438304053, 193606848, 151318927, 919791422, 187653157, 699374021, 892108783, 343004215, 696402588, 225056705, 237242194, 679569624, 41162402, 307892490, 375530036, 118963624, 245271222, 242096765, 882650571, 870465741, 558323894, 419659284, 316223801, 763949405, 470300476, 297816969, 483278285, 285034775, 613454466, 635461080, 169271695, 459601783, 217542948, 770715240, 226846838, 155755401, 243782777, 743285125, 605708651, 82005749, 319278816, 179130441, 498579209, 145187543, 908321488, 833204632, 975661884, 753487175, 603845669, 847740990, 898812932, 958810082, 194238573, 471442854, 223508803, 456389681, 411020085, 687620097, 713782698, 798834530, 389667686, 473607184, 650085158, 677173783, 950165786, 154056332, 635992184, 763260792, 729992582, 443965305, 244195580, 124992347, 505899264, 104072859, 318475616, 206916052, 167057059, 789276488, 217105780, 608572446, 513558164, 582424506, 602340842, 838670816, 752507712, 801042579, 161797574, 918699086, 966011890, 171660980, 422391994, 153473469, 797951378, 486816574, 20385900, 962556281, 706727768, 99586220, 653021638, 352138066, 4056267, 155493621, 705096662, 264949008, 264776957, 856688282, 636154613, 97419037, 877461163, 788861471, 762614591, 956242144, 94533228, 399744298, 131699384, 360973330, 174982330, 621991731, 654305547, 21441859, 196832977, 297006164, 299720369, 169397191, 522230074, 640440346, 170288583, 370349660, 647144960, 966380524, 975242244, 218199747, 989084568, 522979876, 419686669, 744219809, 173819030, 369464708, 705257764, 374845811, 490188881, 353324163, 387661345, 587527543, 679166003, 163261062, 946475933, 462320535, 276405629, 621429215, 802732396, 839019193, 975490151, 806238239, 120642852, 470109429, 126244545, 281139913, 964108443, 778965745, 917940940, 641983416, 439198660, 651977227, 904400814, 281659365, 94869596, 978368337, 212379303, 45952110, 973527463, 298483867, 245866898, 288417900, 424278747, 262520101, 111660666, 571401384, 853093322, 703668748, 136760475, 173864665, 509338516, 64179902, 137687726, 416854761, 893802039, 193832301, 521041603, 208769007, 889451771, 500233210, 935047599, 670408549, 438598433, 573719962, 178329663, 941707027, 669690559, 252481766, 756985875, 892195990, 459315204, 981915937, 964821666, 82397733, 368223706, 219592813, 876167945, 971195017, 364017749, 924007423, 77852553, 836393473, 496662043, 57082133, 234496275, 244713717, 897761322, 400218932, 930189816, 233215375, 893179906, 413657752, 331718596, 1533511, 868692013, 328720881, 204280401, 390289619, 843923001, 789998055, 504660493, 577706736, 831262723, 226098438, 873850481, 932252062, 537672632, 372323767, 655723320, 17751803, 497005971, 9199422, 546542863, 879117467, 721210322, 954116130, 444301767, 803865165, 635909719, 832278316, 186107035, 841037899, 833587706, 869833830, 274857045, 962609847, 74333608, 609211709, 563487677, 546209399, 391325008, 895363584, 322920112, 353135659, 568131049, 473734256, 195157513, 673038590, 144534277, 876729868, 394604032, 112063171, 914696967, 655374960, 818028909, 109670403, 201662409, 410033379, 130634462, 148009157, 152621628, 909878880, 21607757, 306409279, 184733094, 413654378, 569828836, 795801814, 205124407, 864763702, 991892719, 98398535, 415370361, 105350244, 984062871, 40446244, 635093917, 394250361, 216787554, 58251762, 844397644, 984495068, 696813924, 896326256, 270833560, 942345692, 100572556, 892505214, 454243699, 314322469, 824838430, 983018079, 613231220, 505828545, 647577539, 207398527, 802822926, 731953931, 912514233, 59972181, 832338967, 640516311, 364983245, 670984761, 94665897, 516440867, 326892723, 814968773, 202966962, 829181977, 524295068, 714058875, 13468288, 240582259, 411213158, 439149785, 601968032, 32490372, 310084640, 357053336, 291197427, 649950673, 5107445, 23613266, 887971923, 112304249, 104315724, 915936686, 461811989, 65040710, 335912318, 442216269, 243160456, 770933984, 445736787, 272433862, 64593132, 211775278, 593585407, 839564156, 633020326, 496381289, 499728758, 296954226, 858827414, 516328557, 823916095, 274751835, 922329559, 346684692, 708512310, 751108351, 99342774, 1045661, 65889898, 979921944, 299716980, 942807986, 143376933, 847233839, 97965280, 616692419, 425204046, 256654431, 58276106, 464429854, 123036316, 113904992, 492841813, 613252793, 691242116, 122839519, 580080874, 517326007, 494840760, 18997984, 514427724, 525335446, 854431222, 64678941, 753039790, 39175270, 916744941, 37125131, 296301342, 85579347, 713675434, 945993426, 769466387, 567971147, 281467655, 51657222, 367499336, 293487492, 415950156, 443622076, 434225358, 868071617, 701564926, 587562327, 291326220, 817095998, 498506297, 814912981, 795899297, 886146461, 520294855, 312499361, 157349597, 542197999, 401218874, 486871933, 30502583, 777112126, 730712767, 639670167, 643045319, 222687268, 525300400, 496797365, 64826723, 938069280, 164315428, 978700507, 814092249, 918133709, 215266194, 113107001, 46858652, 165437012, 948153442, 785401770, 387968220, 314240849, 321197174, 691664510, 946606637, 179688751, 310567442, 918268378, 160043408, 683860381, 993053244, 331862241, 486903395, 435543580, 744857312, 917630564, 885416839, 705029040, 818064035, 534571312, 946164086, 155042053, 587888661, 802583842, 527210376, 205575397, 32777752, 595956963, 540219135, 206439579, 35944074, 460179513, 124666080, 101734738, 562763630, 831595167, 831845642, 818614388, 990535658, 898761833, 585814790, 641403685, 631581539, 521949146, 475422256, 347784291, 634650873, 158112754, 967593134, 715858035, 74116597, 290909034, 644463596, 292023434, 883337853, 233710779, 767356321, 340806328, 6012820, 974267374, 554443718, 485161147, 892372650, 238453072, 138828201, 796636963, 845929526, 254950291, 284700220, 221925534, 480297843, 604335903, 44307730, 381717226, 296402776, 315241449, 167456267, 999116649, 191027120, 230781080, 75896738, 934066164, 548801296, 465354597, 985077709, 950634087, 236479063, 518031481, 322984221, 830798346, 30737208, 785315672, 494582271, 770889844, 315785275, 52254088, 17698518, 843664718, 129059204, 513786643, 423492876, 436214878, 125600898, 431013689, 282772730, 71941430, 839078495, 872254346, 594393999, 654971844, 67828375, 721806570, 75068055, 244679378, 598302381, 622161067, 878472107, 837664354, 94115836, 460886391, 512638119, 661757425, 504325330, 371352985, 166563836, 450832023, 106611050, 411978038, 87343626, 952748488, 894167901, 349598842, 377683550, 617139723, 926381598, 806718027, 991518727, 483214940, 202672066, 819969406, 396522149, 459475688, 945454070, 304375432, 271742702, 158693860, 822618893, 918939958, 362133663, 690332264, 656788399, 23507404, 744654791, 143077261, 622764123, 569520370, 121541449, 19644973, 205076878, 704139390, 594327789, 717176961, 582514674, 14987139, 725823884, 124792465, 126795336, 856947674, 537299999, 991605503, 40307159, 484418609, 645212433, 889962160, 274582086, 583752995, 345980206, 202799742, 281215948, 263877489, 754703634, 636097450, 813739296, 145141330, 780728474, 252380904, 722966231, 956108289, 701927169, 240285338, 505846704, 449838159, 334773327, 396034391, 720135521, 675914119, 432963659, 118245711, 707468073, 94050175, 570432212, 304653872, 143082810, 290239863, 772996899, 689004905, 503920368, 190820682, 741109134, 799304630, 392294086, 605451941, 82370511, 22887713, 888728558, 478671786, 486366766, 434243871, 460136375, 9037327, 631040639, 931687721, 548185427, 849961783, 859478918, 536527028, 143478094, 759797408, 896363993, 357561101, 10440984, 616117004, 704984600, 865622048, 880752440, 608283724, 112100775, 310392151, 330462709, 358378118, 958786915, 402417528, 619033002, 692629886, 431562436, 512964353, 71931640, 518801801, 205626929, 528602938, 871012047, 453000402, 274188832, 425109267, 899799645, 372630534, 11492657, 16326280, 478205690, 792612884, 579833421, 46684993, 553721444, 957411236, 993923445, 970678891, 696097555, 199208009, 3152989, 739972973, 705350220, 177832721, 337266723, 209071171, 703574870, 452734351, 657760615, 84336880, 941626864, 890106469, 825911647, 211491893, 514141409, 26794639, 895425045, 549739403, 464246647, 592605515, 111020687, 496364438, 6904299, 945629647, 481470705, 161912145, 727876908, 159824340, 65017336, 342200842, 731962678, 173486882, 825631188, 431973617, 457968896, 387973074, 337820954, 920353587, 802681275, 831329816, 676649185, 543916368, 628048350, 757088244, 406504276, 152732557, 657914681, 545847083, 851709006, 909405825, 634310164, 95121690, 582389828, 304189171, 316159526, 958034953, 379133949, 713578396, 98763410, 431638410, 491379199, 471295080, 191825946, 702290910, 323961936, 424262502, 877801220, 110889552, 37766626, 833136792, 138030389, 397719794, 959696419, 73983425, 548084826, 903255072, 794798964, 29871100, 646597758, 115982262, 618404287, 500764141, 232284572, 609683909, 267786523, 198346707, 159828728, 48353867, 352312926, 320143443, 608016993, 290298584, 576289725, 724842938, 188499274, 904291502, 606960782, 11264739, 978560332, 845141595, 21877532, 828732574, 628162910, 1717410, 983812193, 517539768, 167549028, 520722805, 86911136, 129904728, 212461503, 880904659, 953966785, 981327227, 679353584, 182151470, 239171238, 385451665, 144415371, 576246081, 771074805, 763694359, 509261323, 992241383, 237388864, 569119929, 856662625, 140587266, 492494312, 881249019, 61093282, 836250034, 606694266, 337344085, 541035754, 813849297, 441251065, 217276829, 769204748, 972872005, 18708440, 107651247, 631317299, 8830188, 832557124, 347412183, 714115309, 929264664, 92533750, 507592496, 467671141, 356430016, 138625818, 499161035, 916182052, 753053538, 834307992, 869223732, 602349062, 918503490, 324115047, 44228678, 943550949, 471971420, 987547478, 744169323, 513329408, 289470119, 74336625, 518540013, 605567362, 711363473, 499884291, 854471073, 438689901, 952291543, 781443345, 553153386, 424449760, 217756598, 91333984, 59298859, 439629448, 619338200, 548939645, 25658389, 651980110, 823749341, 82307246, 54554678, 798981426, 437345976, 84202735, 201113945, 125578032, 992036240, 738167800, 93331304, 487690349, 770872890, 680387515, 902284711, 472416294, 485641950, 49763080, 291069344, 929065301, 251340452, 866405127, 283230571, 84144177, 548998676, 343844058, 662509818, 581692023, 145643535, 123481340, 460391379, 912019347, 686182530, 910062271, 745452949, 595751753, 482952127, 179871549, 434217355, 971358098, 117078790, 992031486, 708460185, 269763904, 61865632, 471754827, 150156892, 788705649, 943142003, 908548918, 913873524, 524544618, 809491292, 652952691, 636438784, 905725569, 511169812, 785792332, 216263751, 966049389, 521993700, 945107095, 376449821, 218462924, 995017471, 781528592, 55620325, 181286915, 292985123, 709564699, 915255752, 744564513, 543051403, 714134606, 695122866, 894128709, 985899667, 453141715, 726053083, 647566028, 66242134, 746549868, 456461064, 922344151, 213622318, 72903766, 351868895, 551888340, 544878495, 118406110, 531057147, 429509563, 597130334, 44996179, 992892862, 176048373, 478509232, 205848436, 343594040, 193924666, 704886759, 194464327, 416242194, 651365950, 272092576, 623903207, 423822223, 310099505, 110914799, 89352896, 107853149, 910741021, 462032830, 406762278, 665118239, 446071714, 367629333, 901171654, 825407753, 574492369, 128573263, 356374465, 19685686, 743976611, 620756004, 7393940, 224163637, 620595444, 43287200, 897894431, 22858387, 855580427, 525125740, 488926775, 674076396, 290751823, 534880579, 109216322, 567453612, 809345917, 132763702, 445078080, 735130609, 261530524, 848274754, 527770051, 32570066, 611949028, 116195021, 986090912, 519751759, 956666346, 718827324, 863564114, 94673757, 555681980, 311620479, 621910424, 589783696, 567687180, 647057445, 753670732, 156133993, 651052258, 895019191, 420793120, 597684301, 912924193, 145908877, 206777093, 253211465, 389983296, 889338868, 123656570, 736026148, 266502146, 383784199, 373236209, 749230587, 451477001, 623907663, 739798573, 818148983, 132534375, 745933527, 257976795, 923856045, 859992344, 825808300, 992864442, 286831027, 480871603, 51277557, 959924085, 928390306, 862724761, 830012387, 665220903, 861496020, 20587769, 806490241, 730751594, 88280072, 723764494, 444127380, 715232306, 270861090, 884173871, 519843529, 586466051, 430915610, 906969770, 535041857, 465286, 31320030, 775405100, 983014387, 584422280, 582834156, 489064541, 282715396, 519761387, 86136442, 149188595, 498128778, 598076216, 444314517, 353357700, 187719521, 479821154, 864681173, 560352118, 882072716, 41996032, 124269746, 389264223, 695529803, 897184540, 352349044, 620445565, 669646488, 426775457, 366550803, 770282512, 798042961, 969242188, 709725713, 356614739, 681492462, 757177839, 723696908, 53334301, 767738803, 308826317, 526158230, 262435640, 479243621, 987125358, 849415351, 430013649, 547869520, 981312432, 70492145, 543900201, 284254618, 67060376, 443846390, 37840922, 130734595, 367720478, 212968418, 425237969, 148964866, 877167823, 243529676, 902479833, 3961194, 242457354, 889065550, 819750339, 702061277, 448000079, 530361083, 140198757, 489078086, 477409288, 463856011, 703762028, 344819889, 505286742, 523163119, 855848086, 991881276, 938728170, 681059190, 633999189, 735401850, 78418097, 818046246, 10578400, 259647258, 879670955, 777856442, 580198433, 425161162, 229535411, 346250233, 290320348, 10712583, 147921543, 479864347, 646861970, 71851408, 248322184, 965552863, 180851597, 95706626, 19799142, 479480372, 768146497, 255358080, 964770180, 848188566, 296622293, 118413418, 488139998, 736139600, 113745919, 922302859, 878072227, 841857959, 255784662, 181209498, 20794375, 276544599, 221171790, 887863023, 759892260, 110003294, 823371746, 326420296, 120789158, 453913680, 586560259, 794668772, 252443716, 353447938, 685829112, 743504438, 703644715, 221354635, 507127341, 590138785, 784902872, 194127984, 447406968, 190188574, 133389711, 587860249, 967899, 823203137, 419721811, 461095109, 580647104, 334755529, 976877247, 688932123, 343042789, 781201589, 232036596, 751900768, 329055765, 538582459, 202970937, 484493264, 334599811, 897139366, 652172012, 247100714, 174871616, 235542161, 39594362, 488181239, 150848992, 368926348, 48392169, 981957501, 264379205, 765850504, 540798675, 429384267, 23576575, 575578296, 558914427, 325034516, 807973313, 92255638, 195776443, 25941108, 351423541, 657167444, 943818487, 898934943, 729966115, 913397234, 236135371, 997404045, 93315836, 928590011, 37045232, 715802219, 5205601, 21379827, 645031648, 372592362, 597576747, 37552148, 757649159, 1535135, 439523860, 48127071, 686322120, 886885295, 59046050, 449932648, 528722923, 567542518, 231757378, 478421802, 115762128, 958127420, 267667316, 960569832, 775885684, 101005835, 835558845, 996110319, 543829120, 497545196, 319802479, 670313732, 662540979, 452141349, 191763509, 478981941, 95428174, 398158240, 634019995, 461676417, 264027564, 886792923, 411497139, 625078728, 853570433, 350787918, 749099548, 34654322, 333033654, 818050347, 450449103, 990063766, 835842758, 75747485, 626606900, 893495235, 404067564, 787203112, 595350231, 679546969, 322492519, 212950779, 389977181, 852633491, 93528374, 122790785, 434349899, 931454685, 622415849, 662445315, 750541334, 834931502, 7295751, 812115210, 796215832, 405690602, 115701818, 605999399, 52406395, 981840218, 543742972, 170264215, 71375207, 175362294, 514684090, 390976268, 616769672, 685173157, 812608160, 348976297, 762149423, 422609141, 387429969, 670075898, 694027025, 828458198, 480728075, 470883142, 986315696, 770892592, 837154520, 12301853, 9529078, 462111965, 998078562, 804837308, 12507573, 655262362, 61889509, 847346069, 151572607, 386243656, 160471096, 329640052, 290210491, 814459971, 167422312, 100856394, 174587911, 975535561, 295058545, 71558114, 484578195, 961533046, 158973696, 845813331, 653389461, 171737547, 866625327, 530394138, 599414620, 225094669, 670108533, 3476502, 289246347, 170566171, 549521416, 539227463, 820817412, 968524486, 66229615, 946332656, 594852122, 563578254, 709183830, 59531123, 259902392, 4950147, 433257361, 208733620, 347513829, 969367391, 941168188, 698382794, 265694265, 208272605, 265639546, 249835030, 668683153, 457262012, 549749485, 966394967, 762822153, 739605971, 497785706, 503006494, 974970022, 302652177, 375641700, 395343694, 74610158, 343306566, 528254281, 41679446, 385051269, 496496621, 477736418, 734770386, 336495320, 96838632, 932123239, 913077589, 639302894, 929516035, 698908230, 132614690, 554257940, 627480634, 313306299, 91508814, 256643502, 188001248, 978672530, 359649098, 380227871, 689845718, 427411953, 287527961, 363885731, 452891338, 5589169, 843656715, 185083538, 680983042, 543939665, 836106307, 795656287, 37713246, 391790638, 910074999, 707736828, 253214276, 346959385, 477020082, 289563384, 316549390, 176356224, 674986310, 734906971, 804966409, 737073549, 342932057, 769984671, 328908010, 531710497, 313332555, 756025865, 705637184, 109808087, 682911082, 787573470, 157707168, 72097264, 253729085, 586354835, 196534262, 282611377, 449576931, 746941305, 826247754, 803506522, 498240615, 63700009, 261160223, 72495499, 17824306, 750362830, 706881514, 728239078, 738687910, 27218584, 629803555, 398187910, 670228437, 952301649, 16060362, 856909078, 100985147, 38724957, 37407793, 91549993, 424851347, 112453214, 894477648, 288153071, 841959859, 395154322, 927042388, 432261446, 871027276, 739188943, 357107587, 594869326, 392513672, 642029829, 262426315, 659458478, 66062295, 90308639, 55157504, 700802433, 800523960, 580153380, 154130759, 388354089, 575104645, 575234203, 923399857, 483071294, 798847678, 209302002, 153828602, 285523581, 556582282, 115539566, 782672029, 774504475, 698495765, 71727184, 885524760, 47392389, 860809275, 689857029, 476597651, 906080454, 251725800, 109034305, 265321595, 713219264, 756879500, 694267276, 548920046, 490987791, 348567941, 168637145, 958367248, 126701003, 707972810, 876974809, 200287112, 173018157, 64436350, 97049150, 927578356, 135093524, 121696062, 424833386, 556613473, 481590801, 247861965, 499134443, 502886807, 120469875, 376821925, 425795082, 788663681, 369529029, 833604957, 678598648, 607529992, 678499851, 605328278, 702965782, 50774269, 599359304, 976655504, 695416793, 294094726, 491496190, 801287709, 282407131, 531298882, 867076857, 362168040, 994814262, 881140327, 208421871, 526347213, 331926969, 542216652, 618300241, 572942489, 114882890, 319994805, 977548936, 532324038, 226856813, 705801462, 620116533, 891904889, 735190976, 157175059, 774831141, 707043536, 114003995, 391592255, 713759601, 246475686, 845681205, 80487999, 155568234, 600520185, 998647157, 165242617, 240335621, 993545316, 283878080, 362602265, 888553402, 379998607, 305082855, 937398053, 94007159, 857851198, 368275087, 527653656, 637469177, 527197083, 71773744, 166822874, 394556520, 293060729, 817743445, 869757656, 947728217, 547127287, 180427302, 428097752, 608237951, 226226919, 604821002, 45611913, 76351742, 66511125, 168678693, 575902431, 234235551, 904520685, 340914948, 128620399, 713551993, 870507389, 723313973, 339728020, 789949060, 720178995, 176286475, 941654545, 382694088, 838046602, 562369988, 954584484, 70253526, 318248487, 537910884, 441360372, 709846889, 427049081, 980742653, 623384712, 55126366, 428613432, 791669001, 1845795, 92020063, 924490074, 566107672, 840251545, 742744521, 351527449, 741928359, 581620280, 54296000, 647878368, 546212758, 420276495, 242348319, 786906322, 519358203, 853412, 950244614, 870128944, 423395051, 624608586, 723951309, 4902982, 826583638, 473356850, 324859682, 868710873, 740299530, 360608543, 210102920, 121878373, 681788741, 288906067, 566705187, 389236293, 491491791, 629931337, 868444643, 258728388, 898924573, 418327211, 540344051, 748858352, 578083264, 128787867, 722221899, 416592862, 472064357, 179246408, 509180874, 882351120, 589920735, 388656199, 151831602, 891339053, 737536250, 928586588, 118576909, 345926037, 787244648, 358816723, 817037707, 756445659, 592529275, 982683416, 174293358, 896894803, 967343758, 420018381, 992765088, 727898587, 540132406, 45783478, 962447685, 318350105, 238292647, 520887705, 520988052, 996932272, 694661790, 487146433, 749084767, 552726737, 988082278, 804749819, 913850455, 359726741, 414308791, 361578614, 91607420, 601687619, 32564197, 157095720, 249972200, 519875701, 114903674, 886074962, 841416803, 47436785, 241117547, 408217098, 913381775, 154758604, 773221569, 499684379, 596274578, 702983890, 316326760, 773437627, 164950716, 558099393, 347909986, 112772608, 956470160, 719184939, 589967470, 246932596, 964944498, 105995922, 588166130, 599328584, 428225031, 426064840, 794029348, 22018219, 769679851, 873526544, 424149786, 435406375, 91204096, 515753123, 408758278, 240586496, 270448531, 96362908, 723852030, 771888146, 187388404, 180475733, 812018014, 466336774, 954927934, 842085924, 807062906, 343224869, 159423712, 438800643, 554833023, 461245033, 155331074, 857201028, 386345538, 185112525, 224715187, 696710824, 268617544, 315349906, 878875228, 188712272, 748589234, 769204037, 251844817, 695355101, 989119907, 47885506, 848098709, 257367603, 435708943, 568212339, 617987269, 817687618, 16786744, 441572936, 709582661, 795650877, 401041221, 706790800, 915800269, 672122685, 923038860, 376634050, 667295632, 59225347, 434554852, 63812266, 72048880, 981051790, 392276092, 501867172, 611929969, 233887908, 197446651, 536846298, 702098830, 734350680, 831126720, 651751691, 56293042, 280998563, 211048668, 393711763, 473643563, 60734093, 620648291, 693277154, 625179217, 533955295, 28070611, 966929802, 674281008, 661662085, 563165900, 784074061, 882037247, 241013550, 920447714, 932933561, 521785436, 383355413, 448565591, 890710821, 798257045, 494619172, 116740330, 336421568, 755824884, 855875535, 208962052, 880942171, 227119669, 599263790, 643619999, 528097330, 188523853, 611060295, 670715711, 543914198, 555267070, 872040389, 707553494, 558018544, 945352235, 613149827, 265269097, 600509489, 398177934, 237297429, 881489245, 429044613, 499882720, 343330797, 20881610, 300109194, 682637079, 180700806, 605933799, 286131272, 272872181, 335386290, 147195484, 273805483, 1208189, 225113912, 255939965, 575152443, 366275397, 711174031, 125940932, 858709193, 81506367, 970336302, 77983544, 21398779, 327584552, 644551354, 629655837, 39976748, 282539313, 473058910, 848916628, 253478029, 176908141, 738574468, 87046859, 775983095, 339865562, 735092681, 971323824, 737949544, 227701254, 502097849, 485176836, 328761043, 31536320, 266323066, 92586776, 967371105, 693144116, 806309116, 947173586, 944477155, 917703529, 479381050, 563415557, 395691967, 133472564, 832824950, 695294836, 541065955, 70054197, 279513193, 499657581, 329689617, 190730574, 488653291, 477195383, 613026565, 251035923, 476582144, 62999139, 295045708, 128123068, 727814084, 877280986, 776900265, 8344720, 877035663, 560462265, 601328474, 829188086, 353374577, 966321721, 608395271, 665381188, 868777927, 359807995, 80792915, 780937892, 788578934, 772618210, 717081799, 443990423, 845627811, 101968167, 69092561, 793486493, 359641960, 901850174, 979423279, 70075914, 515686052, 662542480, 297284251, 827632949, 881746601, 219561723, 110321868, 815257801, 731846686, 321618716, 778402430, 692284480, 789014507, 715111275, 576292050, 527558530, 110260967, 805874891, 706232081, 123402327, 539214341, 271552360, 464323938, 763266967, 364671077, 53272155, 500232311, 958104247, 76289079, 578564515, 46016969, 427303230, 727393661, 960609477, 901713458, 919652204, 252064651, 51026524, 697398855, 136639626, 658105268, 216380098, 533008389, 132358062, 966503776, 793907325, 688519377, 755504347, 430651221, 790306277, 977412083, 929095634, 261371528, 114536784, 273181426, 123401784, 158717065, 736011582, 218247468, 109599391, 288707145, 448336200, 822960678, 648452658, 211779004, 594439098, 291051627, 651945636, 265783510, 7920589, 146261608, 773485218, 77933145, 139313909, 477605728, 152691134, 877966776, 686902314, 585633272, 634192741, 827173634, 43350614, 869911429, 862584728, 918075256, 170467965, 275964230, 111076486, 199725542, 136246206, 630717551, 964982588, 988734710, 119214502, 89742629, 548088448, 13873717, 925166447, 81382960, 872604799, 621891431, 596168527, 47900174, 58650834, 655041883, 464144173, 313848391, 866390076, 201214921, 187113711, 815049324, 119561605, 57608257, 119088053, 668081385, 447829870, 932886147, 331846950, 659329315, 153142463, 248303336, 426304426, 91894946, 813913863, 569419297, 377214575, 444198145, 584528346, 626991090, 731597279, 539541226, 32980173, 759299990, 935795910, 167415764, 748052295, 485520580, 806781502, 489175870, 516188569, 555076872, 543654160, 377313896, 51689614, 36916973, 612650961, 106691807, 501163515, 653757199, 247566718, 628792075, 181595815, 454950181, 549005755, 674259280, 90996120, 310792165, 585823930, 71827401, 525818219, 140303178, 206502498, 44472456, 937110885, 791808666, 440260818, 929341377, 351393796, 278741914, 121655715, 324521369, 137968953, 514931195, 268712618, 649952668, 685191971, 892407966, 774236602, 549098024, 117007236, 532886952, 124460120, 722208186, 694629436, 754727335, 908052598, 670549709, 905765944, 73642131, 534436790, 788219824, 957714584, 252962141, 817498900, 938568646, 161589351, 239436907, 249969682, 3033999, 216382646, 851888215, 243645028, 575976556, 228061513, 698935577, 377220920, 176755105, 800885235, 248104746, 525068609, 262768007, 562723173, 885825436, 646924635, 353272770, 390241099, 712676933, 609834963, 194175032, 277717065, 514376885, 255124235, 193638672, 800705380, 689978921, 952959946, 821502989, 837035548, 72175034, 32868511, 822613733, 311647409, 766263125, 875621879, 648953018, 955558859, 54186323, 512599700, 88475102, 360051825, 883002856, 531180990, 294716688, 867205699, 818983262, 603304255, 999011293, 179799919, 781248083, 884024433, 728706740, 181797404, 846089749, 174988708, 532181168, 117869540, 124176947, 249836535, 114807252, 931072932, 344947614, 257184798, 625601987, 233433378, 386572261, 452383052, 34322767, 697243140, 537861798, 301206939, 322540041, 856862959, 218032791, 169343597, 519449867, 622099764, 512425353, 438496513, 469693771, 716332893, 478487322, 764794258, 55514330, 339085197, 694181928, 28894316, 917524815, 817495939, 730952121, 247308991, 191902592, 91840327, 922313510, 567018934, 232554821, 971206957, 362009568, 139720472, 81607755, 113003182, 800485110, 712831837, 764438102, 965699163, 470785947, 532285107, 987518867, 102323606, 738132257, 377339265, 90595319, 161949201, 999267083, 237615055, 732211304, 159179642, 502272855, 408292572, 594522436, 378257430, 956482959, 613570015, 496961710, 943706988, 447258746, 924534317, 133365116, 511854494, 328748632, 262679319, 213287050, 273284585, 397953532, 435013625, 803794058, 367361387, 784013694, 404836029, 410344611, 299676629, 394798528, 494896449, 726487780, 773521337, 729292101, 611943444, 908528835, 282879497, 258173225, 460953425, 591314472, 25061989, 99579623, 937087639, 24108234, 771839400, 63281329, 139849709, 73732556, 737674253, 150258277, 50765593, 121635462, 307081881, 440483985, 69097694, 698601420, 747711522, 559439379, 846648085, 484751673, 815968065, 175266545, 569284496, 916422211, 833660251, 549244840, 981994547, 180804066, 556521472, 783930828, 269860781, 54284126, 717130168, 232687221, 903871884, 925779130, 818557586, 200424632, 315984965, 607502356, 123614770, 591741995, 111869003, 258616631, 843987162, 352147500, 912107722, 553722092, 225749711, 760445486, 784661483, 691060263, 647954808, 323811173, 580511394, 434187299, 643333197, 177679048, 554356475, 286443357, 327251976, 926626230, 278184982, 201100623, 714931946, 112246532, 214940, 100920308, 43114671, 576010273, 124667734, 954721658, 965590300, 53521355, 512301666, 798244351, 379162051, 224089191, 128838795, 563061919, 731311791, 858863001, 424240907, 822381299, 512478615, 704035247, 445343204, 790422394, 573565394, 716282370, 668325033, 942215548, 541089938, 163291701, 868830470, 303683053, 642255192, 719865938, 196976296, 778121496, 61583303, 923850411, 906558769, 472362533, 554159960, 676634451, 996501758, 533500575, 320863769, 411377231, 488221137, 524890476, 216149721, 476539818, 927281538, 646495990, 102652937, 558288334, 744767942, 952641079, 914743366, 454756258, 358687697, 383344323, 631891062, 372739228, 199644458, 249757607, 478411722, 50558140, 849602106, 817394100, 236218910, 409993338, 896797591, 468002963, 627315796, 414373868, 761531106, 979158356, 749830627, 911256183, 296702928, 513385183, 480064387, 807241916, 840168006, 928241852, 270645803, 504974146, 506593664, 754527373, 4163673, 602596462, 209630850, 575809542, 625268541, 532291357, 456240284, 154663713, 522002669, 468618216, 500167497, 971046378, 60740242, 447532274, 722553702, 722475526, 1207272, 728008515, 422642637, 768397268, 183145895, 310711040, 995721776, 691312992, 450732592, 529663684, 321422115, 509105909, 79413476, 14932328, 893766048, 100152102, 970279933, 879970809, 217716253, 559057166, 281238969, 520934587, 121770126, 419530495, 781096267, 618311917, 31988344, 979544865, 287973653, 427824433, 329594884, 25102448, 627304681, 500432335, 976553090, 479059253, 383049308, 182336629, 555416591, 741880282, 181540045, 516479533, 677939354, 324726008, 463638232, 503354389, 690169584, 686986380, 725473267, 123008851, 597152323, 937713368, 928376704, 82352534, 360679888, 449009168, 207992023, 106493601, 125688221, 582669062, 22816791, 564986605, 822191429, 205284368, 183336184, 112731770, 43331205, 957400396, 697778981, 588955338, 40823939, 117265594, 749336993, 396514328, 546579443, 702303308, 801349246, 105892037, 241101831, 707567908, 562979393, 230139924, 601257026, 102807107, 139831937, 865136482, 549891230, 363692583, 65173207, 487305456, 418065111, 330646097, 449638807, 827422425, 936239549, 61129815, 207246781, 738853685, 376058310, 766668509, 231004216, 420815520, 184584620, 69992947, 888955966, 970619693, 210162872, 936214477, 540134873, 441054031, 837531794, 840907225, 296015822, 920778115, 581359397, 589457252, 136852995, 615017074, 441136183, 868336956, 474616273, 618322639, 164309315, 390287474, 341152556, 897505369, 551940647, 621400868, 935791651, 937078780, 856369392, 923184536, 583053494, 157209256, 504254281, 142077677, 530715934, 868985666, 945463167, 97627436, 708227920, 403459871, 500566496, 976903896, 287119686, 803467398, 739364488, 519539990, 606712292, 835458982, 223997193, 457237535, 251283309, 746329439, 429423091, 27511194, 293809414, 45780428, 556707381, 564603215, 643374924, 73886876, 820044952, 485556924, 847276287, 910211445, 974080182, 135688371, 791972920, 216559817, 358985583, 8274556, 43824343, 805245611, 656921244, 80139658, 346131356, 326342145, 78798741, 251981198, 946941489, 672602608, 900336124, 84226682, 30116941, 448159946, 128746524, 950329287, 620859078, 293394288, 273144954, 354314486, 612921042, 766081730, 621842238, 884889715, 824639179, 614133715, 196710653, 356998068, 526317281, 735331432, 311370591, 827590093, 68965470, 70295550, 398853352, 95372122, 835977873, 262155024, 180095359, 221346594, 79605239, 93573618, 544715431, 722210074, 196665241, 294437242, 481814841, 1744586, 304920935, 673440548, 943163189, 969911478, 75687399, 564158341, 223840428, 819661112, 553802180, 430393262, 924066022, 427749599, 831227194, 970773237, 606742670, 340297005, 632513072, 963891840, 178800079, 934586423, 479479873, 493201643, 618218591, 37509512, 635755359, 536383413, 374893411, 572487954, 355382879, 427626959, 300792651, 714919480, 453628101, 45758915, 403780501, 982171049, 121688658, 719635744, 222001795, 590295160, 883775545, 998220053, 250147810, 235533494, 104685998, 346815522, 391937114, 791949339, 732206070, 281470461, 733794104, 698496972, 555196657, 305141921, 285745986, 780414485, 192153043, 152825652, 621753409, 866813659, 560438880, 679059680, 225783718, 484819570, 850092966, 231907280, 852217676, 637155148, 545491519, 848396117, 702091303, 640220116, 664867888, 864993849, 810354109, 405816741, 288018108, 296000910, 709660261, 610694955, 450317704, 713267382, 141358201, 243976953, 346847844, 973897510, 45052311, 165163846, 660662490, 260439147, 785991872, 623765980, 892594791, 222829741, 522063836, 674289390, 243112888, 729658358, 667445251, 584580778, 377718491, 266609007, 659940802, 914730776, 141914772, 83137551, 877860046, 617413034, 361882681, 642825381, 111105654, 930268786, 93687330, 825188100, 249764400, 51206759, 966818927, 24378921, 727801244, 883764290, 190475730, 827213968, 995803414, 855086348, 533342566, 902675934, 229222737, 541299263, 971780158, 557021978, 422499247, 579709915, 120817148, 832085260, 894886380, 416761600, 556555548, 934241614, 90013585, 401318936, 189586594, 352367525, 127092551, 417154336, 427731073, 881758057, 100585583, 257736717, 498889825, 905676422, 374938052, 71731076, 65674281, 120609981, 595141823, 276072714, 592993621, 729805975, 606986092, 7755646, 761602617, 106262281, 512283318, 124263195, 639049673, 712652450, 374701205, 614143204, 465867471, 773247707, 236632487, 815005383, 819787403, 226758138, 803770476, 495008585, 952317336, 828234525, 911746097, 120137221, 414545016, 690141200, 652542697, 451337063, 190220404, 553133648, 729012189, 126779022, 803380633, 842331492, 686127965, 87230005, 551776211, 235071371, 222282643, 632401756, 551346809, 502531242, 245323423, 94202322, 260393509, 670083730, 799281840, 393987853, 284039057, 850778857, 214574417, 116706719, 489351489, 669701427, 777046713, 281840010, 174242162, 567032649, 303041479, 314149499, 708209560, 653038366, 452633305, 75718985, 122304756, 237627064, 165643501, 918128688, 435353670, 872083034, 88564650, 459021657, 154226650, 942173352, 776627107, 692219719, 318924343, 98423848, 733103386, 466378296, 916187949, 262725993, 425034405, 251859824, 485285174, 653222032, 424335964, 48246851, 77065063, 553352636, 353578519, 215087858, 453227412, 609047555, 796026484, 341233878, 725923919, 798480048, 506713671, 390514838, 734948511, 90017669, 606729598, 536190900, 725148576, 549657279, 300128820, 491067316, 40314124, 849808460, 905936068, 914255105, 683014940, 68494826, 945107023, 162148878, 78386081, 521282325, 152701839, 303512016, 652298890, 931781596, 346714653, 763018350, 700517734, 750928315, 747390292, 18962350, 701173362, 699178807, 418029437, 42122822, 228372507, 11975383, 337461208, 345783620, 95433929, 202867078, 987407538, 337634625, 224644604, 899467257, 58719933, 743247890, 779807067, 881930213, 412552349, 244975140, 826680504, 389506274, 517518670, 656688798, 338238517, 32484305, 34741848, 343942400, 608832813, 806457016, 205053969, 597847153, 886508340, 39454901, 696064593, 636099108, 971655726, 257368383, 167550924, 77268323, 762106656, 243648272, 873160749, 320019756, 573527787, 865800924, 722935768, 679779414, 641302535, 44960286, 843713943, 277249396, 753076385, 779135016, 368209873, 772469886, 173231440, 486344361, 754775813, 150602328, 845027515, 614296988, 741500477, 949894673, 313303298, 342993102, 250391523, 846478992, 607312717, 707652297, 912866774, 115406420, 581568211, 121618125, 706157785, 213534050, 665134801, 819250632, 999083446, 635498664, 933618803, 452862743, 494168211, 966490091, 421775322, 192159319, 617981248, 482003491, 978863183, 835126214, 856845078, 226258123, 462672823, 321445369, 520802896, 515635576, 698125579, 717458531, 436471193, 99695528, 174615578, 321708326, 455750472, 477194390, 646137286, 676288501, 183207798, 234066262, 758129867, 192496515, 107522922, 996405480, 960705584, 581236497, 801787939, 904724020, 237248591, 167621137, 113768422, 213332681, 769727092, 782394688, 441455918, 621136596, 743467514, 64765340, 310603838, 804847418, 386455384, 394304869, 755698361, 132935673, 416495236, 48940179, 414244284, 317666868, 364142359, 254447078, 776174511, 746469365, 782932100, 767129240, 106878850, 132096135, 197651607, 447437448, 404813071, 294338448, 66336847, 557353047, 62258246, 620876043, 448007452, 687639434, 814404429, 500251873, 595257988, 165187712, 479594010, 176149403, 280125706, 742009688, 564653636, 439055817, 454674233, 544646881, 493506037, 863636457, 369413158, 504691423, 784880891, 720279843, 652671560, 902316663, 946054097, 129008636, 279617402, 102385743, 249333821, 866998284, 282833730, 963319692, 219422717, 419885847, 135648505, 578492557, 612468044, 274388937, 473854640, 191587247, 868735873, 393971206, 926210719, 175617770, 985869270, 868160522, 848588679, 709393024, 89570181, 103855634, 72794275, 432615310, 836897074, 225744577, 234345477, 146796633, 794656183, 384436011, 984542172, 28206655, 932885179, 884778886, 332032257, 952321260, 745375267, 592058089, 722912506, 369651582, 52407332, 295955464, 352013268, 548207322, 933777188, 163009544, 560336829, 845426081, 789671187, 304343286, 470339685, 701335465, 607028239, 691700120, 982282539, 784285275, 548158700, 845338238, 884810186, 115968962, 445223876, 235705719, 693566961, 859415805, 401216873, 457782732, 460214268, 268582740, 10956756, 790438875, 827783293, 176044576, 372198986, 404662090, 104043366, 431186147, 407764753, 707125048, 498881489, 240692053, 463954175, 514768233, 78313000, 811008861, 644515743, 29593058, 804177020, 851317158, 931450347, 533669786, 919097707, 766313339, 30364025, 572260489, 707941822, 1114870, 949368198, 876274399, 163143861, 85818693, 980607677, 137363333, 440234136, 981233469, 130481110, 979410666, 622397407, 683601641, 600773485, 886797918, 276483257, 585880169, 823776317, 831326978, 180379340, 922212347, 293497016, 7480582, 443572895, 832793387, 559434099, 422028943, 487595950, 731039444, 385110674, 145892571, 915633562, 507761482, 953069906, 396412292, 404481223, 377467917, 875140104, 152313679, 626996507, 992221943, 179034849, 958306430, 160880268, 295467307, 297375667, 717824716, 752329900, 324577487, 403075828, 178351353, 702901682, 607323053, 943687883, 115906707, 818500066, 863838135, 33613209, 987017846, 700565262, 883175037, 9660674, 36931456, 400406742, 321080196, 418893303, 350978752, 286703999, 989190142, 762452430, 305667745, 457239156, 442787547, 76623540, 865817631, 255785031, 260143406, 266605276, 843779028, 608377062, 541284572, 95096201, 201023669, 479953580, 257166867, 915209081, 627038902, 473486027, 201041761, 68215817, 717350089, 330477711, 10620607, 161740513, 959175907, 141211676, 784995473, 528591478, 604974904, 661154723, 356868672, 759854976, 818318101, 852740224, 977978606, 981988795, 570947835, 916456285, 285695638, 475650490, 43447238, 863597120, 545127486, 417057693, 661681646, 567730886, 705782766, 607155446, 229061026, 389542066, 760524863, 839347701, 833188639, 528791965, 588275857, 210268679, 320797359, 739514027, 330158830, 664752922, 481095742, 423435030, 385387859, 33840962, 300099602, 103672014, 661942468, 153965753, 431464182, 125853428, 299811052, 351957430, 240308448, 585271966, 105563761, 892747383, 531462995, 742050542, 220839073, 173447542, 742695697, 83285008, 717166779, 72630384, 784970726, 795107073, 105254519, 666977367, 644842331, 328447895, 657522999, 754090688, 329242503, 748644048, 780534713, 575842039, 340233556, 106850776, 115192517, 417873501, 14280141, 754987247, 324006498, 555858401, 973681047, 125635468, 537149105, 611665383, 922758297, 126291076, 833402869, 629656202, 978121428, 667900571, 772932208, 449816410, 480352750, 3856119, 719118898, 52479321, 181069087, 265377246, 7263956, 919686523, 934412598, 278200539, 762733817, 428971640, 985003216, 537709016, 110318209, 75294160, 317157688, 730424279, 464763454, 592164029, 659291356, 584369188, 127250528, 669316164, 840270332, 414811277, 66216581, 194980347, 25713562, 570575530, 776515561, 974477008, 45546396, 997268763, 750810000, 950806855, 568746458, 428031123, 41160010, 462347216, 769509404, 842990382, 656519610, 47661422, 313043845, 957587738, 532604407, 823387000, 781500405, 599935364, 74898879, 631670645, 942505876, 698735346, 359074065, 782271, 456949885, 176784254, 376242564, 956794187, 430554093, 973020783, 97398161, 382896493, 971098715, 188571939, 866414032, 714214517, 489785272, 565422198, 363281385, 75781290, 33397872, 657698825, 512810766, 867013636, 99980320, 374354519, 880748264, 922622129, 640920847, 461928146, 465425811, 579031672, 787838795, 361144172, 8121935, 490114639, 546092169, 275680144, 342125377, 643039450, 132525611, 789163798, 779840512, 771783380, 926488057, 602695472, 92363126, 92949647, 431829413, 190361389, 911619152, 692646407, 324010069, 922637516, 683736756, 624848480, 28652063, 218467548, 734459092, 385705045, 685382570, 762695719, 709290642, 394809879, 247284195, 893254383, 133158772, 802469029, 145772366, 271322515, 179286749, 447278406, 36022638, 205282901, 238450958, 509224473, 443942827, 365670966, 696563282, 389417693, 310185850, 695057984, 804295700, 375496666, 609869445, 520298930, 24992573, 640559832, 789433875, 903126224, 567765133, 89444256, 443986158, 826081781, 173317090, 469221920, 300927082, 416666876, 404881858, 233528249, 87490070, 984744868, 109452497, 433124430, 155435166, 135850484, 632534509, 35495975, 749983287, 203674748, 448899155, 834326709, 166667429, 928321821, 531395052, 979558658, 911451102, 823881477, 368020061, 859105346, 437514256, 838501844, 335659314, 719239728, 699165855, 166364767, 130993373, 784862028, 819780321, 943914340, 806260492, 237536152, 91470785, 809572437, 986931268, 840196795, 630021688, 908771946, 894714401, 256630476, 711471648, 464642376, 689159036, 48014809, 77062302, 816074856, 170652260, 648979407, 779311288, 732337362, 473038112, 962698328, 717407185, 802302838, 152708236, 718668712, 652046218, 98493651, 107616360, 42211389, 166019242, 675459455, 976377191, 241093886, 201917191, 488940523, 166322788, 429176869, 207710833, 22095234, 587293116, 862010405, 374692443, 563329292, 112476009, 742900881, 502708748, 879030386, 145776921, 353060369, 29151461, 977079681, 754232331, 48100306, 687242943, 276055135, 768330640, 64148273, 371881649, 716002901, 211106917, 109389453, 936326052, 967718128, 419946307, 705464328, 861594648, 667329433, 977414985, 821973024, 505791123, 246164792, 755779721, 147879970, 447945065, 459506886, 56605198, 187123126, 81547748, 805322003, 289122881, 814943668, 37161671, 523130150, 142076740, 566129656, 88999714, 871656963, 349650707, 692917304, 70594033, 220146860, 173466062, 41362985, 722132222, 918733294, 835385353, 501392601, 827077384, 137390524, 664332316, 461983604, 792739472, 758620348, 7685672, 599054215, 949151416, 41684574, 352589665, 240487070, 748848006, 49643787, 147342033, 877575607, 98908602, 345578316, 678386359, 646481740, 938383465, 817772868, 121803321, 721989515, 791787154, 815109501, 966146771, 756709252, 455593934, 249979346, 229809981, 999407977, 646912655, 945886664, 393128705, 936626168, 334034586, 106708840, 556068086, 813792043, 526893508, 152744821, 646719218, 598048309, 570298532, 830380806, 898982756, 548694447, 776884324, 498196150, 848219541, 37840771, 521129670, 950215092, 30613634, 833096342, 732482379, 64231104, 799110110, 535043215, 686001230, 640747472, 293112096, 221100885, 644888660, 305727542, 616592206, 106080325, 358173638, 531219930, 847836151, 466326464, 769131047, 403654482, 578269493, 76339810, 716980511, 871430002, 495622732, 467385967, 750330715, 335997276, 744313777, 231675997, 841014247, 943110993, 835614637, 253432779, 623195913, 722508248, 250309046, 399128618, 544659954, 437596455, 752683362, 301412938, 938008492, 467924901, 332096848, 579777469, 643028446, 443740670, 83807854, 490704491, 325551177, 754902134, 849113882, 655085862, 911743786, 212015775, 163071038, 542859479, 177941234, 268313764, 428281008, 834810581, 219878218, 688135665, 690681990, 126864198, 248195770, 596513639, 279158309, 254646724, 547597104, 977190983, 812224897, 92940061, 407803031, 979977761, 172341697, 270501498, 410888308, 375004609, 962949637, 284039400, 99278492, 677361914, 292839676, 165392606, 878152462, 596788670, 428752827, 650658179, 989325692, 128644180, 361810504, 268650160, 692882219, 514904087, 536931983, 378102915, 451259061, 205291197, 204907208, 890342501, 565557918, 235973076, 41009915, 85184510, 103344007, 12181266, 745154141, 272140322, 831531925, 399804757, 796632286, 849379252, 908207302, 361284708, 352322295, 315417471, 725448995, 145298592, 980430973, 428564589, 578209336, 374493602, 554540408, 765477346, 108708530, 603530453, 723674787, 854105985, 73789956, 439493678, 102531315, 657982748, 757321434, 691191130, 739840592, 351385416, 333117476, 771255499, 123360870, 863917807, 383053408, 69507901, 460496638, 383755986, 642361029, 786226651, 239769919, 327066297, 620961909, 149872568, 448558606, 328611438, 925394072, 984164178, 565200117, 909805285, 370844835, 631459038, 575724276, 34317991, 69629789, 995078532, 79618123, 323312954, 168948043, 644550425, 144833234, 415967025, 142938195, 542362753, 291511897, 591164879, 734622188, 325148833, 174984247, 433305599, 86090332, 878487594, 32628744, 304499961, 260309742, 565082131, 830151593, 517138753, 500660983, 384428258, 559207580, 176335175, 767144071, 843723566, 649920437, 396358761, 91319493, 939283521, 15934150, 829602407, 70318257, 35092638, 626395292, 702017651, 283829037, 80918332, 924256019, 745655342, 290297416, 460607563, 612994867, 923417914, 79360859, 180743857, 927992928, 156731162, 22352212, 705209149, 136083669, 162914333, 948716233, 412327524, 685333705, 871829750, 666635038, 985611008, 484517550, 635375175, 868747135, 470491899, 114338460, 659466137, 423707915, 688571763, 661907224, 499472938, 139173302, 476695636, 546153162, 709490295, 329473508, 559599412, 917399712, 832488468, 950132084, 558150331, 340291583, 534065523, 143759262, 140604801, 552265051, 419805202, 394333562, 274230190, 999139135, 18458537, 667078440, 447790990, 380267427, 623707686, 244909177, 741469897, 815847991, 770089723, 204791023, 382687708, 326252008, 139423586, 934232593, 22175832, 217351068, 969654554, 94356124, 240996267, 112158910, 183926704, 123774107, 680112134, 708715038, 158854777, 286375389, 854802066, 715406178, 995184951, 749610299, 114470777, 361587537, 480034779, 81175163, 535282133, 351186082, 121501818, 782088607, 11612950, 506477327, 646871897, 669520227, 778255852, 956768597, 689624064, 970274097, 70730651, 981414987, 539807134, 565619545, 956294019, 222940927, 442538774, 434070594, 843561725, 803620484, 313874968, 294459266, 5650794, 330255048, 772860404, 2592833, 465445752, 171325128, 162168719, 537616439, 769921127, 966121268, 140056828, 93981205, 319968944, 247527154, 878709369, 853892373, 925876838, 615205153, 960547435, 560816880, 826711176, 165585497, 153224928, 898369638, 454673566, 895632713, 394176372, 248291431, 747963284, 729445255, 352782289, 460485854, 758677112, 269184030, 989214607, 284274239, 570624883, 566319589, 647018787, 90335686, 527800188, 781029609, 696633779, 642308186, 820191654, 352243800, 2747026, 238659244, 803504301, 765623122, 886238413, 967789123, 26892659, 650289029, 749601316, 813499415, 900575097, 526792114, 996520, 113889472, 141628509, 302050888, 492294541, 776093160, 772690503, 880368835, 340483594, 550919346, 387005901, 77580677, 451224203, 939808307, 474343612, 637386877, 572583028, 849644699, 185923750, 958524295, 290501141, 761994853, 830049032, 117885041, 109894947, 616359049, 117771581, 645657401, 958286650, 271165523, 724778895, 546106931, 132571354, 670397549, 85667882, 979525534, 997279863, 646367279, 413743373, 582644752, 672612747, 340768161, 663542451, 358067218, 380565371, 204861949, 141851135, 236420409, 21282359, 840522486, 287595849, 816352789, 208481814, 764007812, 995574466, 569916635, 1944291, 691327910, 213864769, 496700162, 271907709, 51951138, 983026829, 418284923, 990434236, 52741367, 288625475, 777473656, 809235785, 300512269, 628883284, 71787454, 996924000, 238041130, 971891471, 82025510, 339357838, 267041188, 682333869, 943495471, 396008946, 27198250, 642832949, 852811844, 854301951, 291837733, 553237101, 441754901, 573503741, 765081620, 247338823, 864406838, 13227688, 78904796, 614795608, 943594997, 256656750, 654776420, 485746140, 654071152, 379458887, 600669442, 310337727, 905013982, 126880982, 191291497, 786868894, 82412684, 398436423, 395536395, 917295662, 923723501, 987976755, 708001505, 286271263, 215710597, 413719036, 295569886, 670423137, 454056004, 915736272, 669954940, 411017281, 293837162, 823355063, 353303073, 569241188, 956884742, 182573453, 595439485, 831712346, 275618094, 348038455, 400227310, 657105582, 796996022, 211449078, 261617886, 812069909, 923786604, 39389006, 752385244, 998430175, 623408076, 820184649, 559070114, 497482269, 606716867, 560080220, 717313859, 299241346, 833564811, 519814761, 136585185, 540206850, 520883941, 341549348, 776388011, 777794786, 965504036, 832907409, 753577763, 273059426, 757331597, 35087761, 799149396, 608864678, 484962227, 740114857, 739056230, 183375227, 534989058, 581930491, 408922127, 889478120, 522822859, 674540805, 893679936, 213005932, 148686408, 739117228, 723927611, 538185243, 363418272, 235033679, 480801381, 114045751, 553412120, 39071976, 608636628, 382212687, 772474842, 273625222, 339587748, 440529435, 270895302, 616016496, 924488212, 322015357, 756027471, 7264762, 789209508, 921054607, 702824468, 902383308, 315739410, 654935354, 261143062, 580327435, 316125908, 237179624, 891675614, 712246301, 944433300, 111810177, 250624698, 496357277, 324839047, 689730395, 278472050, 893925980, 323928947, 716163576, 833797578, 877079175, 25155169, 320099749, 577312483, 868146167, 471728212, 29372407, 914554919, 117191248, 251568601, 340513121, 297273442, 876949820, 307215858, 880100520, 649522868, 564566561, 448559809, 703819709, 825588726, 343431663, 206782561, 65676235, 267894766, 246560862, 823670595, 110131095, 500498954, 705604101, 841614126, 593093646, 307312494, 740006454, 779240022, 139869180, 643701121, 793173870, 209920230, 275470090, 263534228, 663496097, 578283510, 547253485, 246243498, 627470776, 459935427, 505774653, 189300079, 573656620, 890971056, 381827072, 272125702, 194640109, 954147811, 416947330, 898865266, 455433529, 493902849, 455633212, 28672447, 376442233, 968874773, 137035589, 496749667, 553456780, 522440679, 2188422, 846813696, 283087762, 816378312, 758484774, 873793303, 963906464, 579658086, 582016415, 495365095, 543902833, 244455870, 917895953, 624007033, 444057390, 518999780, 579871790, 581628583, 119625937, 955966063, 671584167, 553717516, 934010493, 160391769, 973939787, 578844825, 392009883, 371578031, 963205030, 626416843, 53626318, 189848306, 56368110, 122298867, 390678382, 876991487, 293285308, 491993121, 756254758, 416252539, 758694414, 259634125, 621952165, 173433248, 212043271, 588445743, 961987551, 887817239, 947222511, 735170253, 291820510, 722544128, 825771954, 399124972, 971205515, 749462996, 626549316, 703071403, 944194115, 113796277, 960676165, 368089145, 229340195, 350375904, 800765465, 778079212, 199333790, 566128298, 898698405, 959129143, 470559814, 824844755, 163018277, 572694308, 455908626, 193502374, 201835922, 347063929, 265085643, 635885852, 42477104, 633873948, 965201265, 278038121, 13483152, 12172133, 951088143, 33102815, 112011939, 905981399, 31731176, 373210616, 247601473, 257177656, 104901734, 514801425, 91348450, 90477673, 476623719, 143308679, 536377668, 951719357, 799449762, 624514776, 707556638, 460770673, 338018215, 856645099, 660488211, 319730989, 188117368, 723542122, 584807073, 275004106, 611863786, 774854016, 105420540, 507806973, 135755439, 368289647, 520839764, 600283186, 181144849, 316661372, 662473280, 819005344, 54812276, 541896478, 968599906, 994683604, 598401022, 538298255, 395070960, 353043972, 538580044, 540690833, 176670946, 755807060, 676681010, 962574922, 754730829, 273083225, 636055725, 721499540, 976441494, 288638134, 169860756, 717018633, 501663387, 788452525, 767910170, 273485575, 862847200, 6089990, 78235513, 219385261, 389218598, 118522519, 764987866, 604297699, 335932736, 533714379, 167100669, 570817414, 578604787, 282759165, 658168988, 833672957, 271155618, 706278287, 537883359, 427327629, 594798749, 887046602, 897318773, 448812928, 789062797, 882280698, 446978513, 379967577, 234289802, 960600112, 60514918, 386385249, 274622357, 532252965, 342791119, 709421931, 663477970, 644697217, 229474528, 125145173, 933576381, 431198001, 32674135, 828844614, 500515342, 772357772, 130823139, 49893804, 825722024, 617116789, 372813370, 855904042, 874448606, 433892522, 475475792, 932484109, 666952864, 801758353, 140297237, 799754459, 640386164, 400093784, 804599183, 380282882, 913364865, 350855199, 540564036, 691235383, 266455189, 601086037, 42509094, 407627788, 805790450, 617217194, 559725596, 101376229, 807215621, 957135849, 104695833, 340847355, 964582061, 302734049, 987514694, 401212783, 543047171, 15764852, 917389895, 607874925, 127985582, 268783022, 142089988, 478547426, 236201929, 853132446, 478233107, 514369501, 694816853, 861883783, 201234136, 728867226, 769754322, 829309787, 691133071, 51912492, 398687525, 657196263, 262337377, 393436889, 700780984, 44439355, 313710379, 356295627, 431275742, 369281397, 930843013, 698322703, 982404497, 407552311, 198213419, 771193664, 511472973, 937754453, 976398702, 612478919, 572994299, 284393398, 918088526, 83102883, 180938619, 506731909, 53419022, 106231058, 841292952, 126169081, 485651922, 499801774, 472349929, 584771720, 270174966, 185888692, 420601400, 224480851, 838590737, 49946682, 177887658, 722759441, 408116155, 829074789, 144648368, 500927016, 423874628, 901397990, 960302126, 856926119, 284533981, 730822351, 816065282, 688174705, 606928604, 634138165, 534816854, 602417313, 109236630, 234422794, 254100923, 853703222, 935422331, 732956723, 511320500, 264923831, 108596412, 958403564, 600636040, 945174273, 881363257, 76072108, 68129986, 337862690, 63889697, 823333078, 234917508, 753652453, 864675823, 42752633, 737881260, 797486884, 812564203, 329573429, 961943751, 756841390, 585647093, 671434751, 735013278, 791306841, 377615607, 222738189, 508910293, 372857136, 998750990, 763191619, 240539263, 706393593, 746700990, 670490842, 558183646, 308625168, 485985232, 999647226, 155788797, 199016945, 127149640, 423687523, 62290036, 839391139, 586055455, 473504368, 91365305, 883665357, 417565025, 756012113, 65712139, 996151308, 24505717, 101575051, 121235250, 151812413, 521642707, 664750719, 311946096, 892129256, 386559706, 475563125, 543739176, 675548154, 6347755, 104951736, 856467860, 423832830, 293498079, 807129043, 750920828, 808349597, 685733226, 804528329, 493641489, 828156195, 663651224, 900082829, 14475149, 467954361, 980489974, 691266929, 364002927, 389874405, 464219919, 475948378, 892365792, 237966133, 368034077, 4596356, 962863257, 486101256, 292848417, 973532921, 976864691, 483187395, 544121273, 351327160, 986371580, 679654272, 161015841, 2928428, 889324306, 361392974, 619463628, 905055767, 617190945, 876052769, 17555832, 922918805, 495531803, 606471363, 193050668, 988311870, 708654324, 120375380, 318232307, 507495037, 654763304, 656452275, 302118728, 111833127, 204414571, 838567277, 871488362, 619530036, 834474297, 635826075, 497364132, 886459594, 197909488, 808355819, 397292011, 777341326, 423710103, 276176291, 291143912, 595979670, 242106941, 367180369, 491804381, 437742918, 724353336, 257881592, 969207124, 340183210, 632475280, 781626636, 386689790, 920757091, 250637000, 780796800, 35734234, 394841192, 649864242, 797755574, 985460858, 675932438, 743081297, 178226710, 671189572, 743762293, 776646163, 878094254, 626500839, 53606613, 133060339, 36593424, 953254135, 858098298, 864677346, 644469860, 553159205, 18061678, 432278635, 504188463, 758661344, 491748562, 201490572, 680767010, 149273296, 910600100, 540385404, 521858441, 88662884, 701956323, 303280057, 3645760, 282654602, 472963302, 513269604, 888135644, 968565712, 95009955, 958330083, 410098952, 400521484, 289948641, 666503895, 445099068, 556442984, 84062382, 488584730, 362504094, 195583768, 599099866, 277692732, 307806735, 274072057, 395327194, 635340200, 579534149, 498729895, 992116094, 541302580, 524446072, 168082296, 36632411, 691907336, 109907572, 45135774, 401658054, 635663370, 735852766, 107854010, 669381623, 866477508, 893172518, 856293439, 141623844, 480288367, 828990590, 402027233, 43257489, 859492638, 344010493, 818741337, 264795964, 81541619, 195704415, 764380991, 448446135, 66279228, 751881891, 149322107, 940865601, 22575583, 976095785, 57240558, 303493087, 703194735, 538793278, 482903449, 978735706, 851349683, 46629226, 801925721, 370519997, 801227410, 532418904, 136863332, 717380968, 196865340, 82538374, 324296318, 99534069, 969748665, 418759018, 847370169, 759529530, 344163451, 777307569, 912720873, 78331117, 140799620, 428246207, 446229529, 503804217, 678521322, 374172876, 151214338, 829359573, 936643691, 427919811, 527025705, 489335057, 312642, 376445526, 562250254, 810273201, 392720924, 288183706, 886735419, 662371345, 542626304, 38763002, 408958360, 350319332, 954518619, 887450034, 890333101, 188853495, 725488933, 169507392, 17293654, 226871480, 8457025, 653239797, 185154567, 300715939, 142492987, 521929118, 448777883, 375395450, 290470807, 181028752, 602045335, 651567954, 812084872, 253252997, 17170404, 655195594, 648977591, 893884894, 583147007, 673896757, 872647433, 15533527, 337559774, 658741079, 604008916, 833554008, 108681913, 844345107, 750712365, 88892934, 573574650, 697043418, 485299133, 255608982, 692843998, 877279020, 321803810, 38515894, 753976241, 181702933, 74671963, 424928540, 250226746, 998432088, 725178615, 781492850, 397156001, 74308941, 252380356, 654970899, 32158329, 682284503, 507678756, 528099405, 735122682, 405224487, 765367990, 640153979, 901199414, 912751239, 989943298, 30231772, 648288726, 665830930, 143281368, 54312434, 687856191, 861142892, 502835274, 875079476, 230660483, 757794545, 709292987, 472206085, 755429072, 522818453, 80174596, 47366066, 826122175, 265879100, 925483945, 629074843, 410814937, 102777980, 55867612, 765309648, 531441882, 91713574, 305593424, 718580861, 721091241, 801198949, 702971348, 893252399, 977233529, 152928250, 336449167, 161798015, 665055458, 438791422, 33067779, 796607103, 319655646, 61708053, 38476439, 879432529, 205001008, 912782869, 423574639, 630500537, 746019733, 175379703, 694440705, 954114237, 399784221, 352421371, 591218131, 288077456, 806238246, 184108298, 566461376, 783496071, 437147899, 74426854, 591725365, 122835393, 448959898, 196219092, 183881715, 449410905, 701419212, 343121096, 133010295, 880002225, 751727418, 995448015, 700158, 271341140, 311513667, 176971383, 473555314, 824948235, 303875709, 664361344, 175817954, 237102680, 765508424, 379736688, 331962412, 631472427, 298229348, 809457041, 913145557, 151064279, 138077505, 143749187, 695443273, 181273248, 714640971, 997054464, 612677848, 705934562, 35272673, 469006547, 490770321, 71488194, 354832514, 479465408, 717194980, 219220333, 761197756, 727000225, 406810000, 137496247, 583184913, 578669488, 848144140, 801169833, 956614552, 799594769, 838263094, 998278149, 628051083, 457965530, 192894094, 474341722, 912192204, 76134362, 175384507, 438713101, 108547037, 730001761, 712347427, 75980789, 787276966, 576473454, 177567003, 177724775, 772684266, 88355714, 359775339, 472867386, 184014116, 541238005, 736237704, 183766138, 826095593, 829630201, 804451260, 504790152, 33812798, 527667482, 339679143, 754844852, 297730064, 805723268, 321917354, 721156057, 196940173, 71585380, 271655389, 951027240, 796283983, 53320137, 596431499, 797958574, 306489071, 284792442, 258275958, 840149577, 470971940, 749258505, 892117484, 77667323, 330202502, 158324339, 524157016, 296873516, 164619209, 934505738, 905236478, 862680631, 322148627, 262076613, 233527377, 125883983, 682491057, 639968968, 645738337, 695310918, 361808235, 925269228, 197688166, 87625141, 823496168, 5160521, 135490622, 743364417, 303929875, 859705208, 867673174, 719904725, 833572642, 198143504, 279313300, 380814971, 517521315, 252023624, 232604642, 527346413, 666522614, 654275837, 11436914, 703091880, 767172751, 815260795, 279711444, 273193353, 651952984, 184732875, 37314398, 774210842, 896816553, 645595016, 792196172, 693066463, 792742307, 164846803, 558341680, 951265637, 512385740, 539208083, 442002835, 95109649, 437374900, 52600775, 822983069, 957185504, 346693309, 410122313, 147163751, 491754584, 54404870, 817812588, 271061925, 165080304, 46747519, 181218476, 659194181, 636183475, 346528453, 525032116, 981876724, 851145763, 326845906, 616428312, 689932912, 199152534, 878251638, 993209339, 326922935, 363099022, 671603741, 387666460, 121312178, 235959363, 903884301, 401747822, 646504067, 558246724, 801327865, 410427666, 406592460, 471185147, 224877183, 679576277, 359535560, 821477667, 612460304, 385458466, 431618967, 137857486, 961194582, 519508944, 890497755, 936628124, 938785321, 330534083, 97972742, 108869335, 562912128, 22992801, 425669930, 469243236, 268826374, 422246585, 539564413, 705725066, 693627492, 148199700, 401396343, 469355637, 533872000, 547012626, 121050692, 386835834, 961265167, 80262360, 861907269, 899457184, 861027716, 258760771, 932293308, 848113278, 654093162, 421453399, 622722188, 374592823, 631143833, 67486026, 815795140, 807852014, 341268747, 790920659, 644805921, 175507518, 694240994, 967008144, 44058602, 530766380, 776537888, 125078247, 957931481, 201255052, 945113620, 627569930, 172972973, 459892763, 551814054, 962976637, 480370335, 642538786, 500289918, 79527529, 624815781, 531532857, 913487236, 837191679, 93799801, 322008852, 190813850, 186559215, 672460839, 857618860, 403290455, 172647284, 359576106, 68216068, 255221853, 172378537, 494962937, 830386533, 825534245, 873466719, 616898637, 641956809, 545582578, 277870389, 366799709, 98396423, 276968215, 53202584, 110068354, 901717536, 965706770, 742894868, 520427400, 235318799, 109383424, 95107832, 155799279, 281997614, 942389798, 938012377, 450670782, 636010191, 944269808, 575604870, 275946747, 263266167, 397046918, 841552975, 964392088, 348606974, 174135586, 180662599, 588608317, 619688483, 854780672, 237536939, 94623241, 696032191, 967338100, 686703112, 162377210, 147933702, 517191501, 863665108, 423879736, 314918718, 657923355, 779642845, 253937185, 708567443, 59537192, 96191932, 492703911, 455538120, 81534384, 536514391, 233380475, 602110722, 946933376, 526324088, 491020574, 412832036, 844290536, 161551365, 491340866, 791097804, 799984576, 345490719, 222581888, 264483310, 966893079, 294050341, 594907974, 530779774, 298348212, 444103917, 540482937, 253122333, 475884992, 723220117, 509414116, 157204895, 358417183, 148436285, 833069354, 821705393, 923487505, 347042450, 68595054, 524945477, 333514086, 375798497, 726189463, 213901112, 254300692, 940295288, 616262884, 820063305, 289137888, 33409547, 568107438, 770546733, 35518914, 611618222, 694721946, 110856476, 218393928, 753374170, 863666068, 356211773, 372209724, 576823733, 8672066, 936118281, 78459604, 588236627, 957916891, 687299520, 364097828, 2455008, 484909219, 553869992, 579269774, 278970327, 135228234, 541516697, 420602552, 477478687, 708313100, 178715129, 62556391, 710155376, 191407132, 457107675, 300551977, 32847947, 316625182, 892960011, 902899135, 105233023, 948029222, 803046465, 585226457, 176670104, 720206363, 620853145, 40128043, 929022457, 324978479, 420582907, 241206293, 812379288, 308253364, 929552539, 658009181, 726114980, 969751447, 607476795, 614651039, 591438396, 445155290, 638401490, 824081026, 174130605, 708468095, 375625147, 562202424, 785051039, 978073352, 774662991, 372715076, 387790524, 482282265, 184761413, 625302608, 279727666, 939982933, 856621191, 733117117, 754985370, 474648832, 168918428, 336546588, 214209455, 568040155, 599967884, 339782677, 93234906, 677504464, 348445634, 652176436, 644956749, 820626928, 562220453, 369815961, 247852600, 80226938, 53869203, 706625929, 979272794, 216867978, 846669848, 264103150, 854522390, 29313850, 443353763, 42184536, 59365939, 886719189, 235766152, 601280278, 624086159, 863848132, 614763362, 659543089, 691225526, 655715924, 162163546, 641506014, 81079557, 698675351, 965378193, 531008228, 126552862, 69946495, 559455095, 921267534, 442082904, 808017585, 494047182, 160620959, 412061153, 170460367, 221693057, 996841764, 996362941, 528114793, 409173525, 667781921, 469586439, 686985356, 856824895, 168949355, 678201122, 371114202, 524793438, 79785214, 685832163, 869478249, 928038598, 786425393, 832388358, 495290292, 275773535, 173759246, 894909884, 684263961, 924922150, 794444889, 977364873, 64528886, 638752702, 676933039, 788473662, 404700894, 275167364, 69273471, 449293326, 558199519, 170490958, 162275348, 615618661, 655963468, 582804404, 975875033, 152067790, 631953290, 237681936, 250204064, 477326880, 776804479, 396905933, 479025843, 243313462, 437768628, 878443577, 617068162, 64069937, 604787651, 232553748, 959975823, 185802993, 879429415, 374354394, 484032796, 58409774, 258738520, 817381848, 603202302, 447163761, 617369023, 80775489, 995370926, 756719188, 865204371, 514643642, 183510915, 416936931, 657320670, 765289381, 197167963, 343056014, 569708423, 558792472, 11886066, 458010480, 375512741, 60059823, 914092249, 409245196, 197453367, 614181191, 887586596, 532858992, 395157011, 365500535, 249719519, 10240888, 615406762, 643093609, 969508980, 547244804, 75919998, 967426378, 624904248, 216100956, 920893120, 326719458, 32015991, 119400571, 534149281, 878063079, 400044605, 59723947, 816274650, 236009472, 138980980, 295549284, 487551515, 566000471, 846730674, 438208482, 485915995, 609009373, 741452151, 761017599, 269437536, 690877791, 207319589, 133936039, 245777673, 386549736, 147115607, 392661436, 61384671, 128778166, 193188437, 785238210, 154637930, 154204810, 757456929, 572878515, 917473696, 825294445, 72442195, 139362497, 889165978, 350102981, 335989156, 918394938, 457901347, 913246756, 8962150, 565163991, 421675114, 371807546, 216212764, 529836255, 35753082, 697088771, 525990680, 545180083, 872637287, 700356243, 84867541, 629742610, 133740306, 531926138, 383665538, 631747314, 727040885, 342755893, 152381251, 583820535, 59910599, 45936759, 785904409, 143218410, 599353061, 788038995, 885261079, 107855477, 718399216, 304112344, 351490297, 623260532, 605770138, 944526128, 47474794, 756247176, 541019389, 443572243, 866338230, 699681273, 96481121, 670765087, 128915418, 443512579, 510424380, 871152983, 234020692, 883520022, 870306841, 77457940, 449397889, 46015962, 969706789, 294707833, 308023917, 700044461, 498283154, 234135141, 391026773, 788587119, 352566755, 52231896, 440969332, 220738844, 953653268, 410540096, 554978343, 526286735, 24097941, 539443417, 443251851, 715347323, 666137837, 399789156, 193011899, 895197252, 314283626, 206617127, 500594379, 640193655, 512035624, 26394018, 126054502, 287451959, 928720270, 715242471, 702443495, 694033443, 708476737, 799102813, 437182518, 101298051, 330811319, 655601318, 882661594, 532667882, 386082793, 887891564, 581226796, 462368646, 227126657, 521747485, 378082662, 17828041, 916899873, 553782064, 39580594, 690332447, 7583461, 416252660, 156712369, 190631600, 8614991, 186111528, 36190858, 716913989, 804302611, 681289462, 597704470, 838713077, 683646956, 603587923, 592369669, 415053042, 283818625, 25629331, 476611327, 806437209, 836094072, 702561860, 540982910, 155366602, 485330743, 185294773, 286015672, 322284880, 704725430, 826259799, 343012412, 490663881, 368307886, 275266229, 371965517, 254907392, 818243634, 755485116, 324345075, 506745262, 754133390, 815624724, 88846617, 453658324, 694754688, 196702591, 333353025, 237386331, 228105971, 984001671, 999641977, 438705724, 802641344, 559448746, 4011229, 188317814, 672578625, 368131511, 496382854, 584553426, 814986185, 262695894, 543706149, 750856792, 79003157, 505618629, 494888325, 419872394, 291870517, 493004296, 638380316, 142883500, 225385349, 121006294, 272351761, 682444080, 763597836, 270866443, 566638945, 292015916, 976767418, 948237309, 7580924, 675396778, 728656895, 825614446, 895603975, 286380425, 932401181, 744728531, 727348696, 942501968, 3550181, 297646091, 491251086, 772590937, 322841743, 333737555, 405820232, 760194700, 594895296, 664192331, 62367087, 612013990, 635624633, 975743369, 31320459, 971309767, 474522109, 720433419, 521212531, 122571012, 320545027, 473535789, 221041467, 641196737, 251578898, 207980210, 960138649, 379853916, 240715653, 822998120, 171291350, 141715136, 838453192, 378522280, 798989608, 384203667, 122939882, 118597716, 631178454, 323439062, 465753030, 569437732, 375684107, 590552178, 49565362, 842501854, 472705579, 148642391, 294900094, 123458343, 239716765, 49969801, 218495113, 606096717, 724143534, 524110768, 420336974, 163141787, 150497853, 317687896, 301617365, 998017630, 455270930, 825932452, 48908669, 807745939, 427786419, 192959972, 257446827, 487317808, 954680921, 880130930, 149146245, 889002640, 986064379, 104912892, 739734003, 35387771, 775658532, 611359495, 126710167, 417341864, 877803788, 28981432, 930744156, 373543376, 176992940, 741177369, 229121120, 337056733, 791757617, 13302003, 167794500, 518548770, 741519823, 740061032, 996539529, 414277321, 563473750, 402899632, 434293702, 382134216, 637179547, 572960541, 231374387, 912894198, 582099557, 555920816, 606569996, 64432489, 799531380, 517990562, 660601142, 548955861, 21004206, 712037603, 977144914, 876279955, 451976600, 181956165, 11426319, 631925789, 248933578, 288197195, 424963582, 735100882, 650128342, 723028664, 493905182, 227664732, 952639187, 193042748, 65111109, 170738406, 219991996, 5980570, 696978084, 125694145, 915526004, 18517287, 469407027, 188731235, 125167868, 154644697, 945759661, 605932653, 441343028, 196063708, 113808984, 943942949, 312079528, 208276737, 164816186, 308771353, 972097604, 972272986, 732649613, 252849071, 383256148, 472615469, 629244875, 326699798, 465989261, 853698249, 841724198, 521067818, 814733397, 924895006, 773456933, 76493170, 310304342, 58992478, 560303637, 282880151, 647834015, 587592824, 549802396, 834511391, 709174299, 758259296, 182514014, 143139777, 901473224, 679305159, 391616393, 102632244, 735620769, 161553570, 363949791, 351895434, 275599147, 696344898, 993937308, 128611109, 128795536, 452487568, 65888495, 895609496, 646391220, 664960427, 179213525, 449038864, 22511749, 661418643, 279871686, 471478273, 561260182, 483546132, 404501138, 567281151, 217030520, 782139409, 410751203, 873751195, 872928781, 3151335, 977382649, 615845118, 629298443, 444790398, 673450222, 8394849, 195893421, 669980498, 222356561, 286952581, 803437689, 539442711, 789576915, 605453390, 481294520, 604494163, 825364525, 774805285, 478859683, 955538826, 732621780, 161483344, 459101238, 685875035, 996542792, 205807715, 875212751, 457466627, 88050632, 562015194, 23531479, 138615320, 542224574, 256757269, 423635056, 780381290, 837782614, 293673666, 378753547, 921293039, 250639358, 768220545, 238158577, 264124214, 297718431, 146606414, 998063847, 695252731, 332045830, 316395160, 655341508, 174559234, 734850480, 863362821, 456837332, 459370746, 246116469, 990152123, 455725177, 906178334, 797053972, 555901838, 623087700, 599757856, 335594038, 251708293, 665317029, 860127693, 660282296, 767574478, 399417338, 149958832, 803682169, 235551138, 729207255, 928933859, 235313882, 103923791, 730510182, 92252545, 309530076, 860515214, 406936684, 820122264, 643312278, 395053536, 743023878, 696032642, 284597395, 567461207, 662332447, 776803789, 866974261, 624754221, 934232312, 153248211, 54388936, 813774926, 455432648, 246340284, 112172903, 328829554, 19849500, 162925544, 500955061, 31570424, 362308403, 681966593, 774694456, 895925204, 26275856, 882486810, 466015505, 78797477, 47756565, 614891497, 375647133, 681144377, 315669021, 712322694, 958170082, 171529831, 489135624, 19607242, 981286604, 525951041, 521378590, 730535457, 23623369, 308447849, 393879659, 963128864, 174494094, 811447373, 594103892, 436648457, 329655101, 464746957, 419604658, 671649494, 921349647, 946952275, 659977970, 604468072, 604798800, 415653485, 927934269, 637094706, 567676990, 414839924, 400535928, 477681441, 551653574, 459622883, 430752620, 48935917, 76512868, 475540944, 492027296, 350431050, 92258734, 224472592, 119971694, 546937534, 877646683, 767169112, 218948432, 698589459, 346437833, 822935628, 935434364, 559658650, 758723544, 355007569, 645291116, 970015546, 960754386, 882855967, 766558788, 658519817, 189304083, 584500526, 65308472, 941988818, 946409599, 800489234, 558242250, 829709790, 888418562, 324645573, 616391133, 810073202, 190292183, 439324259, 473520007, 785649571, 654499582, 630649408, 998495754, 232472685, 550500865, 19915334, 989297503, 409027290, 975431004, 603069140, 79165236, 109820259, 101684997, 200731849, 570849620, 993006483, 37035498, 322196126, 165253395, 818062214, 447889517, 140067345, 692777715, 664263489, 798872592, 929140068, 552386109, 918532432, 330476814, 652042976, 761326238, 904006365, 599832142, 687925478, 854400376, 611563023, 989571601, 945883843, 230382728, 497665986, 193809958, 378572089, 787902951, 57199639, 932982793, 444696798, 811737188, 289335474, 953270849, 382976196, 572118301, 273824395, 145328556, 754932366, 316606568, 485609096, 911050106, 449375465, 801014157, 530194156, 387509456, 189504774, 306823203, 399941175, 633818240, 903801188, 523384692, 558347982, 170946434, 419518827, 742822210, 380755067, 41128523, 897337485, 758922831, 978457367, 514265868, 317709110, 567212520, 662154163, 108422179, 843261307, 465678654, 957507201, 666485149, 600439787, 784689250, 774158, 776093772, 64769616, 786288931, 565732072, 689999963, 383980889, 4067124, 858040463, 283575471, 839966631, 213414289, 541854197, 567032319, 291820816, 257203573, 154890828, 622068369, 247420800, 210319356, 537679029, 542294983, 513053221, 431287420, 776948117, 915270178, 934772061, 465746257, 689753238, 985247146, 845238674, 74859756, 916356166, 793095277, 454062047, 212924549, 125302414, 578044821, 114562505, 592722499, 875556954, 59883148, 732339124, 115760409, 258558805, 62254634, 474699788, 617457821, 668233540, 930978656, 822672518, 235565633, 675181338, 235302691, 911347854, 759112216, 179075892, 86457901, 244470220, 807101848, 455495374, 291144188, 479937324, 321411859, 275750164, 700368205, 822566392, 15869612, 673540529, 435383587, 503693622, 291637146, 424992167, 870500874, 634073395, 535040933, 537639178, 10011468, 285898379, 995684383, 128403375, 196859896, 256810795, 531292704, 599936881, 918322738, 803235537, 807919358, 274633980, 555198202, 586666345, 949209361, 665088711, 422542893, 648354721, 38836393, 899849840, 854772204, 83205309, 403616646, 659666508, 489713814, 943931611, 259319940, 930407877, 713640882, 624448112, 51089814, 790682117, 881204474, 47973643, 337325752, 765596889, 353902725, 709114147, 950618941, 933947862, 454383271, 911078114, 999876393, 58032032, 278373502, 383604546, 39075570, 472415174, 366079525, 651702280, 442085577, 551344393, 332017711, 311546641, 618233796, 972238674, 335353201, 63637027, 250279851, 867555987, 270813675, 60765630, 789591766, 349037681, 535867541, 893004510, 9859879, 687238101, 41882972, 382153958, 144250803, 443700020, 591874711, 798163521, 322588226, 725446224, 615307866, 21580738, 429707474, 190709487, 31398206, 82669861, 854213983, 378461639, 251723603, 903583907, 754579591, 997081670, 89340707, 41981545, 140752749, 739133317, 243121720, 268856935, 246037374, 910780080, 926497416, 187708326, 262935313, 534385497, 630217440, 405218094, 532916475, 626284993, 70904092, 212507322, 410636261, 870442308, 123811414, 831349902, 463679156, 437514586, 284703669, 411913666, 465685224, 757003500, 595510432, 784419175, 100747954, 784861102, 808738152, 162996063, 661101330, 294856790, 643183517, 662578244, 531906974, 934067319, 929062264, 770916047, 110144076, 486527141, 745547341, 125655556, 135553326, 24326874, 69441415, 830107525, 257453757, 331472227, 203569897, 491401271, 410868184, 478847893, 369064523, 169160912, 796317613, 461291502, 8546752, 638815563, 357239138, 230470323, 204519562, 648882469, 546627265, 298874508, 88639506, 606655280, 489797149, 338309675, 593467286, 580466499, 848108485, 694988744, 522063321, 156353243, 836353782, 359058417, 43115106, 280238005, 543915964, 908013633, 6450103, 97562474, 596484077, 477042355, 92931964, 801957436, 180916385, 832048627, 872545846, 523651484, 746643372, 101281483, 415396797, 502106805, 362494912, 855515326, 725461736, 391683495, 263503376, 400293085, 633147313, 38147802, 818636400, 497392945, 403290989, 213144406, 352559094, 48707197, 31747702, 301675667, 479118913, 755710397, 147984044, 265482424, 878781296, 254089044, 828057139, 340910978, 487473867, 39302629, 395603043, 236662885, 749362997, 683350386, 926089376, 371674729, 165699559, 318190341, 346826684, 659266319, 635908099, 710532, 370306809, 702481913, 247403721, 543712820, 223465637, 472341651, 77474796, 725300131, 556010577, 221311013, 242966749, 376757977, 256914112, 184254965, 63651532, 33138957, 607949140, 597095364, 265575845, 980042805, 964695796, 255067547, 569246618, 599124225, 844008288, 793360877, 631814123, 362267307, 469052044, 638122263, 474019925, 699319956, 739680493, 396257192, 124092239, 36919756, 830267810, 205531350, 149247433, 991092352, 486404078, 697363274, 671947680, 926715244, 946455282, 725613173, 945372872, 569583232, 438804536, 477855005, 977010223, 823843449, 754145568, 396125929, 347589302, 339500790, 328182206, 578966682, 76271154, 744255474, 516612670, 309803488, 231909976, 851831509, 742189238, 251498022, 744207040, 195228409, 635213718, 11568190, 503510674, 895071219, 879786161, 536063738, 428758298, 932172257, 660828372, 665875564, 515338855, 58059627, 238595202, 481585672, 509362251, 488701693, 856234694, 571461252, 786916750, 465133829, 356037692, 676831559, 742480894, 638785701, 612401822, 939969375, 260010809, 442970123, 953975589, 100546600, 920290570, 477933764, 165537674, 544693356, 145130555, 614949055, 49076836, 671433790, 594766713, 172954261, 917067978, 703956275, 337997389, 956969816, 195227999, 509633627, 788562366, 721847567, 670185429, 256607365, 555469046, 680746166, 297670906, 699401904, 736871731, 560289021, 356358698, 855949793, 300266658, 170917973, 735540524, 819927840, 60093759, 378867010, 281929674, 583981696, 892966931, 654698322, 70785083, 27523771, 164646905, 970730128, 95254071, 954135006, 741097388, 223622607, 231294018, 77789440, 120908112, 66514899, 752138446, 810934246, 596353021, 487677086, 6808880, 23843858, 608875320, 250855978, 819313574, 466422674, 474537672, 856428664, 888950731, 81427982, 488639368, 846188961, 898313395, 59482762, 820867941, 245996454, 285907576, 963584146, 981042983, 493192119, 930131955, 166630835, 949911956, 477584711, 765786777, 182051744, 371409271, 326794274, 998419374, 593728661, 600102419, 536221310, 701469601, 859977514, 833720787, 485276448, 360746062, 821724145, 28553886, 131341590, 310682218, 38771576, 600152188, 927904630, 775445524, 825701622, 697999609, 838074773, 410331284, 842947440, 497927959, 88751571, 474365432, 485899596, 369308239, 732086817, 252145274, 641157851, 296496272, 33078544, 277631791, 54234420, 6544754, 575246100, 723922195, 484047035, 46744603, 742295836, 946695969, 173320072, 84661944, 129767201, 636529589, 216381427, 837432631, 608774525, 135569320, 496173725, 536281285, 65610588, 281239848, 625650945, 507231024, 260216159, 937951795, 172422425, 341156812, 821381075, 773220287, 184485620, 35220480, 320523879, 129008498, 837949383, 102928775, 345964908, 507163596, 695843780, 697305675, 244057438, 154468771, 726959100, 49150732, 819553132, 939842017, 711092131, 353921363, 749951542, 232656789, 106092171, 47728186, 222188998, 764051895, 712554271, 936880085, 393349548, 652749595, 741239723, 36004511, 505713958, 95103202, 373038288, 376304519, 44123350, 406248272, 295673823, 408881369, 570105246, 977764513, 193181081, 959118461, 787808983, 264532125, 951275473, 44765252, 494965020, 737910169, 774992486, 780033771, 692304532, 184239192, 17832979, 795712868, 443770692, 625579412, 704351512, 111707837, 408763579, 910208144, 128771134, 511489984, 365789459, 911621560, 669690872, 150061004, 24835396, 788771699, 826455449, 130888352, 347107334, 715844336, 163296151, 899965230, 762022296, 826523352, 621204305, 144918565, 293613247, 881849075, 886517851, 31201609, 353159600, 620224657, 334800460, 666755165, 32667269, 60366104, 80032933, 532675005, 287715054, 808922870, 147146125, 272600604, 220109973, 152298123, 331159070, 582427927, 296155258, 879033080, 319454743, 794612246, 401987756, 316521059, 94284573, 523279468, 83470137, 724476508, 942138658, 84106171, 578820810, 317458276, 496811211, 348036304, 59880070, 928962985, 962621295, 658783676, 358633096, 901934936, 702908301, 486754456, 177168975, 525757841, 696517439, 457129770, 394807841, 89396207, 863059776, 493064288, 72930834, 391707623, 393189320, 142334278, 889835626, 915252123, 218038593, 620616699, 620499218, 294763507, 678434370, 204267384, 229680446, 494814685, 718660520, 69695885, 998633820, 493241426, 988977593, 747146270, 280195692, 361575480, 633785328, 851611501, 651842530, 484613688, 166138763, 21021986, 820836393, 655379374, 829127873, 193685813, 301682599, 139576718, 389441933, 772371893, 463959417, 607877426, 710395815, 992828546, 201502699, 587228117, 259596061, 291310925, 673340416, 240962308, 184135368, 962272446, 698450848, 229728392, 247224828, 504880720, 506784441, 745226834, 658802326, 729101518, 452794463, 264383249, 95866334, 961503119, 841983673, 218488340, 705420678, 630692216, 50006954, 418970794, 640337428, 203612298, 202170656, 737510456, 786548950, 41203565, 842796549, 718984235, 75643172, 523254612, 235561468, 916549763, 32853307, 596370472, 294291239, 886594545, 447273499, 619179703, 862352219, 66873940, 226760660, 670113850, 282214435, 472844637, 228981372, 923154019, 979851486, 603619570, 464737983, 426403154, 314493176, 591153270, 410007459, 544719950, 999389874, 320913058, 850863160, 797851663, 953242076, 750153436, 917619491, 426342319, 631485330, 844149224, 996582371, 627225714, 520643588, 880080562, 940312132, 959812556, 449496169, 705431311, 362440966, 568311691, 953673779, 999314882, 182703276, 37751518, 244274777, 304030042, 839030565, 355879026, 886021993, 984130838, 455161925, 345106601, 870678038, 612680428, 159447759, 432784703, 886543020, 473525067, 781514457, 370527146, 84934221, 97270809, 5728525, 832119339, 935135395, 623586043, 520543234, 672085220, 960758766, 268364775, 365285186, 809345673, 416327390, 177249501, 133343670, 20197253, 411878476, 461459542, 181223050, 104866650, 243278885, 399017307, 9561991, 669151120, 646050295, 260380453, 302776824, 157066420, 136411124, 708458107, 373924797, 183838347, 790845081, 255794928, 895286760, 396457737, 509410202, 769816538, 507320203, 777844787, 910850625, 259850036, 464985012, 131413660, 97446350, 413301991, 218588660, 706810326, 507639826, 547496230, 859593420, 414164595, 347281858, 913330038, 577116217, 840340130, 20973483, 10456449, 464125871, 57395490, 637165009, 44656766, 954722879, 88729857, 843953262, 597005248, 198296280, 659357391, 723757228, 242814456, 437717179, 467736279, 939154371, 642817527, 77764122, 461579078, 564806067, 719090402, 311487565, 988516782, 298110877, 226004167, 204999088, 110575920, 395816846, 613059228, 865542417, 984408580, 513730426, 165071841, 383183170, 484465474, 441293243, 101997309, 233620108, 41525814, 181788592, 594475747, 697106407, 839552638, 897120909, 457141755, 150248207, 699822376, 396419312, 712085494, 466617566, 850753158, 665434572, 862239720, 760978714, 838580572, 567918427, 152322233, 784199158, 235805549, 252453801, 128853108, 694004080, 981278981, 414937230, 298821109, 821962917, 922695142, 126673392, 390786506, 724816619, 793940016, 560547007, 470270414, 588409565, 132858492, 407158449, 250741133, 618412590, 887041881, 653004247, 934361032, 266414242, 216521287, 490253205, 13871140, 418394144, 286239595, 878486602, 526300905, 15437176, 549667245, 901077514, 325400282, 644575368, 607495626, 53346498, 810968993, 371588108, 738947478, 231688016, 250055129, 20194374, 204924236, 849900878, 876472116, 605579849, 791866021, 313202789, 405804075, 409818483, 780942042, 253864531, 651786213, 834760079, 925074237, 851413679, 736639068, 291236006, 765381599, 414481511, 44929757, 246186246, 807264221, 494645557, 60486785, 271219784, 43979696, 682568967, 389137570, 197534576, 75891335, 958704511, 344874041, 209010655, 263433491, 328679716, 705399302, 861858283, 658074030, 53050847, 438335394, 5271383, 807770347, 340265532, 596193763, 112577912, 995085220, 34851541, 347708666, 447014964, 317767294, 289634452, 956623229, 849420202, 623352224, 893510899, 884021317, 844338752, 562184100, 721136507, 757895463, 917196933, 781042409, 182864387, 613218855, 360930051, 529725852, 480576875, 149818051, 628201664, 430908105, 153695273, 20812817, 529507472, 80246702, 178092185, 125954289, 290358046, 912255334, 813514486, 905365469, 598388535, 228479814, 764957725, 476351364, 973284409, 456634019, 771392795, 545925387, 627420750, 513149363, 12063288, 557632094, 935776625, 623352936, 136703346, 5067609, 538471206, 90052387, 572776826, 524098261, 959581371, 844798953, 581543630, 800033079, 230929018, 202876170, 887056822, 890203369, 429492544, 71688914, 386954100, 807303138, 801806994, 288568474, 187888255, 174432414, 355644204, 354239159, 930863959, 943457573, 106499442, 952005321, 176010358, 262147637, 298767045, 77648480, 1341731, 967636890, 404730858, 193419741, 903073047, 247386799, 873738527, 214735775, 656842120, 811989736, 887959401, 171479140, 601838523, 950421636, 883392881, 842316234, 906536497, 90302912, 52562386, 743401816, 542655639, 763021668, 705586734, 878751572, 255954441, 100287032, 998698995, 252514674, 422942244, 318695137, 199233342, 518345948, 601418220, 600175849, 342026415, 765283636, 197077391, 831178891, 161285528, 26199704, 793009996, 172524551, 274655668, 155000046, 206849746, 650934330, 414686210, 729921059, 408188586, 116268282, 782843925, 522741922, 751385399, 864366884, 955918025, 282925653, 372341018, 980538453, 939895325, 980631216, 690537744, 640264449, 228985559, 410619156, 741765516, 301807877, 626633074, 470521227, 301569704, 659029908, 320828646, 915253983, 744323337, 865470433, 894899882, 737120696, 261328285, 875399711, 570164173, 84170311, 711574920, 328257396, 34910678, 788196442, 679145959, 336312909, 736100858, 524062561, 576785346, 909202421, 298368506, 79815989, 966454308, 78101028, 345660271, 46432695, 447670479, 63221917, 634933888, 688938704, 209174822, 752208126, 632939295, 894359332, 819326541, 373775973, 139864489, 598315355, 481250883, 888761973, 249549916, 92135860, 384375698, 779278787, 853265163, 575091039, 26100426, 643111151, 566317062, 319332918, 322117396, 213214226, 935493596, 15223909, 430404457, 822662550, 404769484, 481362018, 232865377, 220240948, 339395792, 159258037, 634910561, 208415258, 92814422, 663029484, 38505205, 22430190, 538863247, 199752968, 157904209, 622636759, 264818601, 58579919, 584745257, 582240396, 530033452, 364999961, 646672517, 436182286, 756937225, 679800025, 365850302, 551654396, 86077854, 931738052, 987421772, 686039475, 646711664, 132210805, 225934934, 643260854, 560699084, 983496277, 259793786, 346576541, 213307721, 78417608, 588219229, 365222268, 296820238, 624162959, 840484916, 786458653, 549101696, 870145533, 180520068, 612785988, 389911626, 480531892, 602783938, 260494705, 111820054, 665555091, 856455217, 82005356, 785096504, 679527005, 597188224, 256251843, 557859146, 703967902, 436025853, 557112535, 471703940, 968608068, 102002131, 887147041, 994266209, 355763771, 918182509, 819323226, 197536509, 529026935, 709285778, 730718831, 203525323, 830155583, 204058093, 919925995, 456834714, 159263357, 408071478, 806327875, 987202467, 81981486, 984150889, 173233249, 960555157, 986058099, 703976187, 365627815, 56841589, 266976857, 409810389, 310634861, 232033489, 381801122, 881853235, 941516262, 682018327, 94650514, 790212758, 99603989, 235309975, 912115080, 6202597, 678036745, 401004704, 322006404, 745372162, 768985687, 407657983, 62050052, 167686072, 363172082, 634176719, 161393951, 444697907, 830835798, 955331979, 196089200, 22486724, 605277125, 304933382, 541530063, 807957589, 986859047, 890704352, 29462891, 495433677, 390382999, 143514480, 771865534, 460000377, 779828103, 504307662, 205481186, 827559299, 821802353, 119642029, 872290046, 732611404, 656517153, 705238518, 891463202, 862072423, 413899800, 23052536, 658796441, 506589536, 346438820, 766153362, 423032691, 786172791, 609466155, 67928874, 993554146, 410774648, 85207378, 437573046, 796475778, 800956805, 485310738, 591931208, 958240397, 106962746, 434327699, 829312995, 324738175, 441048716, 617096803, 877443099, 655917782, 741064962, 990548080, 950706614, 756896296, 192937737, 371789143, 849640492, 347299963, 276665768, 439464707, 381404985, 959204570, 422881126, 30096180, 502392011, 718494615, 84016686, 312434023, 684657532, 750761826, 534465090, 593259278, 606310407, 446160275, 752315537, 239820206, 104414218, 812574245, 69262538, 379222049, 924755840, 833865372, 928416558, 347230400, 181990749, 841858230, 727368430, 857033545, 869086061, 697629239, 56663225, 711784879, 932733556, 28902844, 483284588, 573712843, 759289306, 670466524, 632542502, 807646931, 24836618, 727582151, 467981547, 684793602, 882794151, 116565028, 687157042, 880331030, 447998908, 28136747, 687162264, 82177296, 165759546, 467714266, 388344166, 895966989, 503261756, 30042126, 182664923, 159646601, 236926269, 858639238, 232593802, 837320910, 561887941, 700109986, 868944496, 970135425, 181537798, 800920667, 720699540, 180794093, 774667019, 367021461, 962739859, 134558543, 82441853, 55176416, 8851385, 839339153, 282214791, 243586506, 936141708, 239792054, 855853337, 94277491, 868810070, 220390090, 407774868, 824331838, 510797620, 461806376, 902915785, 870532083, 285501827, 526531075, 411011082, 311275387, 188866848, 148962865, 608513526, 705353092, 114766314, 622844511, 436900227, 497653650, 876857501, 769034817, 880531335, 198338737, 113114057, 755224165, 721957228, 768978123, 879119125, 699471046, 598051381, 589877353, 113558723, 327697290, 77381175, 727637970, 416126515, 780720672, 742853103, 625280323, 560239378, 629815741, 4929043, 870595284, 235105423, 757121400, 623076394, 861854599, 209467182, 995765124, 108899339, 939018095, 627309937, 172689130, 114839044, 581773574, 681890145, 585922688, 89221461, 802356327, 393965125, 829034712, 666300912, 12802301, 927163042, 323889951, 924411641, 764355297, 384563448, 533093689, 429163619, 129111765, 86556479, 737457108, 841360966, 891180872, 822740119, 595379801, 619313664, 762970134, 418076974, 130214091, 437582203, 140912102, 48896761, 405708507, 875691175, 870102121, 366039742, 131554774, 379152081, 593360367, 533767240, 17033364, 449537591, 487654331, 931068388, 907543181, 842432450, 589061745, 676619250, 135393598, 474629359, 950875381, 540023115, 892238079, 280756036, 764083775, 217476055, 720433088, 380770539, 247409840, 894866803, 585057308, 190796604, 802722587, 787717751, 558152142, 274503007, 6613967, 371899887, 388571084, 914643977, 301706395, 808912902, 365957002, 182972666, 561165311, 58516530, 835327591, 714291646, 194323301, 301550821, 249001310, 891151551, 66700452, 361994545, 363984776, 382732931, 391514999, 714425287, 294337061, 318128382, 927625932, 701661582, 160999495, 749829072, 195454122, 128319434, 390238564, 79314622, 292112061, 476957396, 149833729, 460943604, 62615621, 295263040, 471581962, 647270288, 281572178, 290219592, 629812588, 753649634, 163716604, 603516549, 647790306, 686102078, 151496520, 782975368, 17366233, 473674973, 473185803, 199781403, 369538938, 329225354, 470686610, 869686626, 351781315, 577399698, 12420045, 788459184, 697900280, 901135443, 291992516, 8034032, 373531285, 81974897, 856378575, 10461245, 618605356, 852455421, 980080758, 671451881, 736932197, 510727470, 882431983, 324396671, 246298876, 920340703, 515927160, 693140052, 422395826, 992515521, 429512128, 396359764, 905907652, 186107241, 483155505, 109888092, 203330351, 697674238, 818307594, 126882388, 249306271, 284749075, 252755662, 992696572, 662434724, 758658621, 166946789, 8049840, 366077918, 642647945, 338414237, 466571984, 575886701, 8610618, 884779217, 475029660, 133841239, 928232295, 529388703, 759452656, 338295329, 44422102, 49445739, 146205634, 534766568, 306551329, 61610117, 402703869, 678948609, 648841633, 773859571, 270009602, 934754982, 654768882, 669553640, 708732327, 893935587, 63948495, 57873922, 612448701, 71867811, 947402437, 411077630, 413263082, 384513299, 964599223, 44209722, 588498526, 231328733, 489157645, 761581508, 380243687, 601744861, 631837129, 666815492, 838307740, 457585618, 199860990, 156314025, 525920251, 67524466, 940858768, 684357574, 422032596, 51907797, 842888340, 356007600, 505711198, 727494589, 92825281, 636454368, 763898409, 598241616, 636191755, 414655485, 863662422, 692909167, 625231696, 42621935, 598553395, 668848649, 803168094, 263570008, 22798049, 959470822, 330712065, 860249581, 6553478, 175868687, 318723285, 219650957, 622539474, 724335762, 329779966, 313357525, 16772055, 598318570, 25701264, 275926299, 683783493, 628540977, 656673288, 497280486, 900326444, 612218133, 587301948, 475242988, 744996444, 191664989, 230652797, 474589470, 400415618, 616970340, 961204555, 553129740, 108147616, 281122588, 155912492, 368849072, 798699740, 970685430, 410268587, 615124833, 819317154, 594720626, 649042268, 596426542, 236077200, 279480064, 510719685, 352712957, 381044257, 772177337, 926871705, 237550830, 770763988, 600554604, 148514491, 805388845, 386289657, 993069475, 25891191, 929773187, 921982843, 386666449, 799136271, 577093111, 486723740, 515655170, 247279703, 364005969, 197300102, 460579856, 845200712, 317959031, 582935836, 82082275, 433860257, 775963792, 321443492, 768773459, 412052237, 79780511, 272426358, 401325717, 842872921, 935783539, 702644537, 236102526, 68393973, 781009122, 165772151, 34593133, 151434400, 473619168, 983851757, 125538540, 979848827, 470795128, 37933376, 983885434, 351386422, 491031713, 859776053, 785001886, 439571910, 909327951, 880097620, 179142984, 972582386, 776017023, 115721828, 660401211, 666564858, 794183724, 363281662, 122506210, 347274892, 834544971, 543046287, 77255741, 738045070, 774929089, 644208764, 828610924, 145012687, 867990243, 977308878, 859036149, 745860244, 804534632, 550022729, 404382699, 493002825, 614423259, 334355546, 408787601, 906418781, 904676286, 481427991, 875827742, 363720106, 659983309, 271698576, 941422567, 365448549, 219385571, 687345839, 548308527, 427238378, 578623460, 375759490, 788502202, 417126427, 958799554, 931628617, 522206846, 729330935, 516498697, 599365921, 303852732, 886155712, 809561519, 206917866, 754142947, 110334346, 454336135, 635204429, 262584366, 373025947, 819853646, 975709340, 571500655, 469718034, 278642573, 197748231, 283513814, 14317448, 433356109, 434944654, 525743453, 145630490, 321841034, 775383959, 401920752, 771886611, 642464395, 972320665, 7829817, 926240540, 144115367, 341651219, 832187044, 281535637, 942017962, 626120314, 187407424, 664421074, 576585061, 348969389, 275328772, 798238933, 624377008, 616454166, 596235737, 8379125, 113883933, 555629774, 786036057, 414135920, 301594426, 900922932, 651952777, 543937876, 902311393, 591629919, 591442033, 410930254, 885561321, 425308306, 94964439, 409968942, 352489645, 71722442, 359517440, 164184175, 215920414, 766865472, 291607622, 63955336, 329482080, 162657033, 210486136, 617275104, 138131351, 471880614, 593763960, 788912412, 480668399, 133560150, 315830797, 620497846, 131443265, 825903731, 188263441, 608958636, 34118536, 125383819, 240496315, 778315785, 275819834, 752241369, 629702843, 37903114, 471152298, 558249800, 550686443, 363487379, 316891499, 972427664, 961343994, 173393361, 915300655, 453737134, 43769567, 17366642, 612152640, 179293681, 813285749, 275128137, 778369831, 660131009, 736119024, 570491573, 358625527, 401695529, 304751206, 920214680, 8444596, 550171115, 652341833, 41081805, 71925870, 988867676, 652778596, 295906696, 790487694, 515864392, 909752679, 109657262, 591520072, 868692923, 616185721, 716176848, 801166602, 644232346, 120442296, 693656757, 174594278, 177147719, 11300726, 346256908, 794847816, 281534705, 521474705, 754070617, 33204985, 924872272, 239770416, 356466015, 701052283, 337182064, 11390385, 135076392, 749079318, 121738879, 957276096, 401443982, 601085550, 397023244, 914749053, 404593538, 682163907, 186697120, 430876136, 241637239, 693110362, 205548031, 974101964, 562924394, 462748889, 979246691, 979357889, 964215040, 215775223, 336746812, 80342495, 441497465, 159652194, 273197063, 654170143, 428103888, 636159385, 631675594, 62173481, 535374406, 257147638, 575547245, 308260211, 671106940, 779891528, 424129680, 443632572, 862981296, 492499971, 31981890, 661553941, 434408501, 831245104, 136815622, 844774770, 608033266, 113973299, 344702611, 553943469, 485772490, 502811928, 788826324, 105585944, 802957983, 545810960, 223782880, 329685369, 498233399, 34478735, 146014971, 912468585, 37143521, 706594006, 660992063, 29796177, 728387088, 939789322, 837452175, 524984727, 340134531, 590847434, 897885619, 701100034, 29181842, 53469865, 805961754, 299177244, 919808288, 951154794, 856067542, 515458048, 85349843, 758747838, 498603513, 551682891, 391690910, 696024917, 980172321, 470273070, 688517398, 533444434, 742395930, 844867476, 914680398, 712964871, 81870929, 684978301, 20131544, 229160923, 143434530, 109581365, 304128209, 525196745, 95723759, 817992038, 920714769, 987520607, 691089480, 568296741, 463233261, 777370466, 258461496, 967943653, 639824523, 760825837, 505884221, 92832789, 558960495, 706396941, 1173258, 602027956, 444494594, 737288242, 434175615, 791493658, 869052622, 872042061, 189623324, 505432490, 560881200, 517076396, 812080538, 860514639, 211569046, 775917618, 614090468, 437622248, 989113741, 275447880, 969903531, 948026341, 128146155, 732946346, 998727866, 570558773, 133492545, 726186293, 949451754, 106183281, 733876228, 855857949, 509134848, 591364565, 559182980, 705223963, 100551027, 949238033, 715632519, 439973400, 198016942, 644573685, 632209581, 728179053, 515078337, 964907279, 297373089, 686901962, 669004715, 219778871, 121599746, 962756097, 212694063, 435858593, 761933269, 604367206, 134428983, 661585076, 98468119, 410189961, 375003278, 311126786, 992555422, 61304153, 620483006, 207669351, 163294019, 940987475, 318388742, 90831495, 256081190, 488565356, 493949145, 747920639, 679832404, 363586389, 958753771, 40163480, 782175144, 861882846, 365940828, 87862093, 999153622, 905994679, 450861119, 670002784, 52318326, 935896079, 270244348, 979383329, 703803858, 892236544, 650048420, 127450755, 348411079, 22082703, 102917055, 824877707, 3308735, 707621227, 559954408, 580538904, 330562407, 187743309, 561459254, 233698808, 461636513, 204351031, 643954963, 450760284, 689828632, 531619067, 982776087, 166198493, 436581011, 687364618, 547831136, 635099433, 26896447, 91430194, 513342277, 621098039, 28568046, 427207915, 298839526, 141927707, 916785377, 961407180, 621990785, 387348443, 737159192, 72021254, 360644465, 997963315, 126713737, 715885531, 511544795, 47185672, 483266376, 224845800, 854442777, 61473747, 480329020, 219124052, 241843301, 197794337, 40433329, 849402795, 787007708, 473598376, 310290794, 810614480, 678024003, 702574736, 24033012, 226773343, 843724341, 964424332, 460804376, 559049988, 406928282, 578125802, 992796607, 735188056, 170179029, 397929321, 284154426, 125319617, 519427052, 569362185, 419207586, 434006559, 20488063, 641271613, 401125982, 811011908, 932936695, 869919860, 797232887, 496024524, 696430727, 25883031, 897634128, 501093178, 645094100, 344687257, 558574539, 970813315, 761893979, 835998509, 165554411, 173684918, 237267036, 171899845, 165507061, 144708957, 726965697, 840981151, 334409192, 620642131, 933599768, 581907717, 11764752, 383657836, 68270770, 868473631, 166526913, 42113110, 190249473, 234350001, 425657527, 98485259, 788961226, 454503231, 777004890, 46171799, 444678436, 85577862, 646882391, 499065390, 282215574, 813088088, 332476326, 224982450, 861501348, 820972557, 926849433, 882313982, 536841675, 235140548, 322696618, 864791846, 287475311, 902939527, 426268214, 276800585, 617592668, 729677981, 332093, 551146516, 222556999, 671072796, 905125369, 438478474, 886727692, 312140233, 875752940, 395220378, 918772765, 17844783, 843196160, 210465178, 445674014, 857425343, 785249523, 253184339, 973085252, 562488616, 773546603, 668063863, 468537948, 147789559, 45166721, 155743865, 148316441, 540777442, 86389245, 796722930, 310975134, 118547437, 558959627, 139333536, 610925425, 404537123, 395837341, 397943506, 129380307, 851910459, 212369057, 927795185, 501547175, 918579989, 18554952, 923361385, 846101570, 605729191, 531174076, 50480233, 971236584, 196578182, 32492324, 715341947, 697153743, 864256107, 316583699, 810303229, 298423537, 266558719, 953155174, 869485614, 64103730, 845914, 43432302, 643536590, 930625592, 155077451, 522394603, 157500844, 687566980, 27473200, 712329684, 22600679, 772355046, 699078744, 768591801, 437035334, 916033490, 911830507, 324407028, 288556753, 882860064, 73674128, 622302524, 187588426, 435005458, 455766803, 959803706, 393576303, 243393639, 783056769, 440337873, 740018212, 396827022, 221155368, 408499245, 710493487, 781092119, 766592532, 944988352, 560717460, 643146596, 469394749, 70723301, 525294076, 444048118, 960812014, 602756757, 669704421, 844293890, 333447663, 488162082, 564058799, 770867884, 215056767, 486540740, 4034756, 927798820, 430937957, 175514635, 299041782, 979095130, 922005700, 881016185, 582724289, 415959103, 105561548, 716124035, 708161190, 17068132, 496164469, 621123757, 631396256, 970207686, 99578222, 727356277, 638194190, 432147883, 910433518, 20348008, 570068212, 519809189, 349135303, 100662523, 196372047, 996946226, 335170594, 234348760, 369936763, 79789460, 975806007, 710925458, 317639172, 181812480, 371924970, 700332770, 884322793, 596095371, 464933870, 734395064, 842774660, 108736447, 879247846, 68219035, 72771466, 908345128, 350688938, 204107967, 530176241, 216107703, 923890415, 835921712, 850189707, 694440130, 348314431, 472060807, 159050890, 590877641, 245112275, 632659985, 606323716, 439520089, 20451815, 835922448, 21359648, 283159816, 548584066, 195567403, 511914078, 993542019, 712744799, 742609970, 804364990, 417150018, 345354134, 297516741, 584537105, 347136319, 374600924, 406301294, 156311142, 182665518, 447891947, 860798418, 781566014, 424518198, 689116701, 643757200, 190492419, 687384854, 892709750, 944085688, 539545429, 56967286, 311175713, 212812568, 412425209, 218699210, 58244543, 281452599, 577732420, 188373186, 333614128, 148452953, 892550107, 908189185, 16359144, 466308274, 922600040, 244666585, 424613285, 651664303, 667256744, 670286879, 237994900, 434271938, 18470973, 52983668, 491347815, 106112481, 549368439, 1481514, 146641823, 106949626, 648416793, 726833757, 489911239, 280005284, 228504732, 559276991, 987183109, 76941129, 213365767, 419263405, 76044662, 422065353, 702661129, 133260385, 498483642, 889740513, 993105174, 230320398, 349967741, 760042837, 974928259, 466367330, 947412934, 780820117, 340781569, 233941821, 665651362, 201500304, 42656486, 119878882, 213700013, 661706450, 367077354, 202947912, 875962837, 764642230, 691062600, 110380257, 853828012, 137475753, 67991327, 661392041, 841368496, 910767044, 855513504, 549717006, 570374339, 382964803, 385359569, 825783091, 38754048, 1676862, 159739834, 104040736, 78733090, 584170379, 317770252, 957515997, 709750032, 30464831, 117265819, 218585776, 588748948, 687955778, 777791989, 810342614, 645011345, 113439201, 261720867, 595938297, 349652896, 692073592, 194339162, 121686191, 720060770, 301849598, 771379824, 857119638, 133851639, 637437407, 931080652, 432049106, 791170374, 886719462, 955865834, 683180279, 862853534, 425321806, 581658801, 579680522, 546213190, 866792632, 147584921, 584126060, 570424541, 127595110, 206015485, 811091602, 296133955, 467246581, 272871410, 492110754, 518130318, 750217237, 280542157, 866493019, 375375102, 704289061, 87543449, 872193451, 395916434, 37828633, 384879829, 329127322, 334459546, 896013550, 33579936, 169105916, 285018827, 78432337, 437881051, 768487636, 622895878, 900332856, 548738335, 31164638, 327522430, 333853578, 394279729, 808057908, 430789131, 275421907, 111770788, 981927097, 71081516, 166905551, 573394935, 327996497, 389934939, 602285200, 434940086, 149610677, 720828714, 158488765, 708466106, 217198825, 831994224, 767649752, 441487589, 864770463, 886137283, 880282670, 734020656, 704970432, 190492068, 976637392, 803515303, 59589395, 241071762, 805974661, 873972151, 173911052, 804775486, 254323828, 853643870, 744109422, 337870403, 877296810, 175589167, 669785865, 135020922, 15789012, 787400327, 915879069, 773505256, 624517189, 175462161, 541150561, 889043919, 907323913, 827341677, 337084284, 98241421, 711461193, 55603702, 301695402, 822407080, 730864698, 493777896, 355917740, 674424455, 483364679, 131659825, 863563024, 535690387, 406721476, 484433062, 167891323, 278541780, 379579627, 188416397, 546840755, 424860431, 295802598, 592366964, 139285587, 148363435, 822156839, 659914698, 840684453, 880010490, 982437586, 635905757, 723054109, 258254297, 184863452, 597289729, 893537096, 325930, 165143553, 975074743, 452636854, 553354211, 148937067, 232787634, 189303176, 437147948, 982765640, 554987534, 316531021, 934415502, 194196909, 439739260, 585387990, 215088853, 514660230, 729507123, 459492244, 381416946, 569527907, 159537656, 627262487, 584413360, 635861370, 203676438, 784902283, 91356402, 873695261, 88922982, 855711925, 934331333, 49115321, 886761907, 313599546, 488203979, 274728836, 798241547, 842125202, 909591213, 336748435, 554703588, 198342610, 829922443, 250348056, 770749702, 376789242, 688139245, 881514271, 12827009, 390880094, 735185720, 785664648, 198685107, 65091604, 11765785, 628693656, 58398040, 765226925, 349849050, 310603483, 644078881, 864225354, 198722803, 383194367, 110969369, 945581713, 361523310, 221175611, 866631060, 330102852, 529800294, 89052844, 523464823, 676967060, 300358116, 82910001, 889747793, 644805713, 679044181, 22349447, 587988134, 411739096, 468921949, 431689058, 277471240, 481832929, 693608681, 932960639, 618712292, 889556470, 310457177, 812066699, 538336557, 539458319, 968267307, 754330258, 469304759, 311621217, 769089464, 422030619, 737685299, 656772433, 961494895, 194712735, 669880481, 767878437, 994971561, 775787739, 906363045, 483094173, 610587249, 825852530, 624445948, 401802090, 310498436, 304417175, 449256879, 780801785, 672134731, 23808693, 271606559, 570348046, 333167771, 104847, 895651177, 20481888, 529161088, 507260815, 16119739, 412732197, 433365755, 156086041, 76150759, 93663939, 960411329, 437849811, 656817333, 26816034, 270636443, 690349122, 662375214, 805396248, 701558957, 647004824, 352213287, 809513531, 473452046, 674256510, 653518689, 836448567, 615075614, 170650108, 447163902, 258931567, 839939832, 42909807, 839508143, 475682933, 554971057, 635191293, 278226053, 886788707, 818191429, 451691623, 542107301, 864818623, 319092160, 892291000, 599009021, 845647347, 162211351, 4034554, 738867246, 276295955, 433435723, 99298580, 942858454, 727611529, 748668227, 642479388, 933585081, 97556680, 709730746, 85687677, 289407493, 488997175, 596677404, 1504071, 465773982, 184882871, 265370087, 299084616, 165627987, 110646360, 4144369, 422278159, 900785793, 47640137, 890190294, 553662044, 724938611, 831233654, 969619002, 262091426, 90355716, 467157889, 177982342, 668281588, 433756292, 79675916, 341761059, 242755585, 765333342, 522870040, 961688134, 555714311, 413799744, 386077433, 375242743, 242671933, 357926710, 663987052, 162779842, 732783205, 11289365, 674995288, 532082732, 969083226, 407645519, 47240317, 32330924, 865096413, 258378999, 553484511, 834731534, 973337092, 375022671, 339957483, 209221166, 965259376, 899232586, 494297495, 102540288, 296711463, 321684893, 708961881, 590674621, 963098562, 15554669, 434003661, 746436134, 21426059, 674136901, 507924362, 926204284, 189966807, 691392357, 784537011, 68843017, 471641624, 758154799, 529385400, 299174488, 770953890, 398348513, 408994528, 827210090, 174990716, 365759925, 803504303, 167960072, 665024067, 245658493, 766670178, 744942663, 398230567, 126293568, 737790953, 578906733, 103083321, 456440249, 577794516, 579383033, 877887636, 519400419, 756262992, 190038305, 817478189, 182881621, 135405041, 433426710, 205040292, 321438463, 941311215, 794000292, 176392541, 978984141, 193818530, 722435429, 636342792, 322697087, 634832719, 479684029, 625907539, 285443585, 460245104, 45398826, 724049578, 870746719, 655874828, 285916887, 924187800, 237598971, 218943425, 501175082, 77367734, 496278131, 998357664, 250511537, 543332469, 164536576, 920887712, 952581135, 732893184, 152933072, 331558701, 962842692, 930400364, 236816540, 285648127, 439697481, 235506553, 949074737, 68171311, 611926542, 729428969, 76937477, 485942590, 882525495, 380028045, 265258375, 681614939, 260474851, 835086019, 156165842, 112861414, 824912339, 799688073, 630743349, 751772089, 790613562, 422780662, 217942216, 551184849, 813968652, 622280591, 15864006, 750596787, 861828718, 657952058, 463896520, 120105040, 8940097, 349618957, 170393491, 532832833, 429787364, 915394349, 585598448, 800648995, 737652797, 312488909, 331791706, 889245889, 655520004, 199175894, 721747315, 929112727, 779328901, 368696836, 962203507, 326415913, 182037662, 757422365, 393158951, 4863521, 242757091, 117423859, 225334864, 411162245, 110723637, 491756232, 253090895, 532355703, 608578450, 254007091, 226768527, 123325319, 882718835, 219154485, 660211663, 935805882, 639113186, 802111900, 15234538, 97467189, 978206976, 833695012, 15531226, 796066434, 451760603, 634795141, 504734432, 301087340, 298086501, 380990936, 290887790, 959316071, 334778702, 329435986, 821275743, 578678636, 848030688, 240382650, 520070438, 847539666, 944793799, 633534454, 57217859, 537170878, 220869320, 988612604, 912748521, 880642926, 241460395, 427171565, 430970515, 790621197, 780241439, 242935294, 878974522, 748630950, 52558161, 702127433, 93136033, 319745257, 480387251, 573324836, 108766309, 113679340, 931165705, 934086798, 598550309, 574255830, 279354717, 1091757, 450301622, 183130931, 836253983, 39250340, 466580026, 572793012, 675985201, 705039001, 936205326, 92228354, 66580551, 667020188, 325644206, 901514942, 57523106, 51091812, 68280085, 40049006, 859215704, 780112680, 73660918, 788483771, 96385973, 453969014, 117917393, 642394904, 75036814, 537375792, 38307929, 212113476, 141021948, 18367103, 488450405, 132288054, 240323596, 590131292, 815329932, 21163146, 996182200, 100890524, 549582536, 860013232, 678040109, 535334240, 942716680, 136011242, 117868874, 174819161, 225567465, 396060365, 737470013, 960582777, 514412655, 358813500, 652638279, 73991370, 380363811, 222852365, 302887465, 745140940, 682747518, 236969137, 680575549, 409061538, 231705050, 37244504, 4965407, 872437153, 550270106, 433039654, 938378493, 104504270, 354341903, 361484826, 759828323, 314089391, 795217747, 929780470, 182760862, 87668376, 11525163, 819351180, 236460995, 287817441, 38155967, 774831356, 107482462, 177435379, 990853963, 100483159, 443419541, 405276630, 491371887, 874784501, 33943291, 225804743, 825373837, 33316578, 609852147, 666845588, 408441510, 306962706, 469673604, 764691190, 941545717, 766096067, 948634494, 185849581, 152669813, 750127723, 673567544, 446133532, 586797751, 304594273, 937414771, 654771175, 628585182, 563670763, 798937395, 621037869, 76535562, 168870834, 280038974, 952282375, 315969773, 267061192, 450804938, 75235721, 766192380, 936532158, 720098290, 220475539, 883297099, 898959150, 870253229, 196130024, 755905272, 35321633, 706454117, 774316455, 448262161, 547461151, 493684115, 937369673, 748907750, 178959460, 458472508, 731881400, 280009741, 855906931, 18625298, 406072644, 273730840, 461863884, 404259594, 759429960, 826757422, 399168599, 311230302, 988273763, 483437928, 714735934, 880411805, 10863120, 881735710, 796032698, 992823808, 443825472, 41160940, 184359329, 968307094, 451842248, 192037801, 403718280, 513611024, 732205536, 878570206, 298698797, 350764037, 93460117, 586988750, 958729003, 24499451, 762048758, 178994028, 398199073, 442996171, 778509951, 135126943, 260287525, 386953198, 69416383, 54982616, 409732669, 80785497, 101320766, 96063893, 805418156, 216682610, 13532606, 478635283, 629277766, 841560601, 631090583, 568241331, 824415458, 351262558, 442568158, 28192932, 447812668, 676102816, 988231127, 550893086, 945705290, 786220492, 136446436, 645987177, 192297544, 466908539, 779309545, 718041391, 144557426, 156572177, 18723718, 817958262, 8296463, 304709013, 390023790, 437825413, 860917324, 680750275, 51650117, 345220489, 751205463, 982828438, 305877609, 531539602, 98856536, 169026952, 705540041, 201204458, 613458377, 368579747, 651349146, 658721508, 121829244, 338806641, 365141622, 383075600, 225576783, 631552298, 694368587, 624889443, 78125641, 195641944, 622375263, 389167389, 763497631, 895222847, 284962477, 222441632, 617736077, 298197269, 483845780, 215623655, 852962017, 64122894, 49542507, 678308245, 282341796, 577657468, 201611724, 824087619, 860797325, 647975727, 769608867, 614711992, 336505308, 148076541, 329034243, 401545797, 633591355, 969652263, 99861745, 215483471, 214221341, 509454185, 768959727, 976330204, 138735433, 83711068, 791807780, 704321427, 301142799, 249590508, 770634558, 376128087, 861131641, 491478484, 343264525, 988726225, 487107882, 409213377, 756352179, 300914203, 29647610, 866945083, 714940211, 63211753, 848784334, 389613721, 570763178, 573953625, 564339622, 295725993, 759345852, 262120737, 265836509, 294239861, 485562206, 677626005, 559819633, 980783172, 406169623, 454041227, 942002495, 320758961, 465323496, 198254191, 153670974, 981429916, 145353508, 942115217, 128787344, 555028243, 742348678, 344495412, 866133089, 512226324, 600600661, 758929996, 999964629, 678508606, 411942859, 209841252, 689988487, 294912561, 775424650, 144841498, 739432499, 940457344, 319859131, 707603909, 493633767, 746600309, 609841484, 335363912, 573714710, 357792158, 709447764, 217676974, 702405508, 661640599, 423904596, 413494862, 761980404, 496103519, 709910408, 129443804, 322387908, 918760986, 272527023, 389456561, 698574273, 653166376, 273854977, 57068623, 275965529, 476261816, 198628240, 563007599, 223437807, 300398550, 540417139, 39483797, 67638054, 871576350, 188197181, 679646158, 627601578, 682050719, 822003538, 425425550, 538163759, 330500552, 367406014, 594755790, 807752768, 531068278, 950365533, 919337039, 299119435, 83248152, 713291426, 892889633, 501939004, 702420933, 801236378, 647639266, 771465997, 901084273, 107761214, 4233121, 321958717, 803562006, 870570701, 869694756, 415185647, 351500980, 918526757, 789346465, 422993062, 774918983, 601273696, 3612748, 505885447, 831252116, 473536553, 575412564, 809365723, 780665517, 217140151, 394158195, 575412797, 964851754, 706275462, 213900900, 558783851, 485603591, 283466341, 981127036, 284782031, 6170527, 2664248, 362141615, 43813532, 627667812, 263922846, 967268997, 78259667, 226110299, 497921193, 582813192, 15911863, 631481925, 373484991, 803571643, 536672918, 364745909, 243556935, 78998213, 136842631, 552483001, 142099247, 513004261, 356005077, 749064722, 214378403, 158192211, 413709701, 9764845, 748414058, 495712129, 835291741, 996535583, 772549417, 387600851, 326157235, 950824754, 773089914, 300410037, 660014081, 280404793, 661433985, 803862449, 96821408, 364818466, 691665405, 73621978, 587954085, 986266966, 349967221, 172460422, 487735618, 101469776, 853773309, 141823109, 201519205, 157646338, 644276900, 663583416, 419954159, 254784730, 408381951, 791281739, 497522725, 798527100, 924353702, 700632251, 478409714, 871630398, 171121325, 837508970, 321536242, 501407575, 891016024, 321069918, 135635610, 762966853, 546969539, 341667939, 874302075, 566924396, 956879234, 600453901, 19879386, 694682729, 783196315, 803732086, 37514849, 324531386, 822336400, 623863109, 833035158, 343019988, 414521919, 780452247, 417143545, 976886181, 936072425, 860087667, 909115104, 795962953, 438155815, 875189001, 934144868, 589017770, 687169821, 592237590, 68132410, 897334077, 233735276, 841657181, 258744962, 595454055, 707355313, 454012889, 536143152, 222206035, 774970630, 133192592, 813873481, 580594201, 135397104, 777242702, 621393560, 345489362, 840478657, 224724045, 731632241, 626855667, 547413602, 831498490, 472188445, 741183988, 43648158, 646264965, 9723243, 758179164, 948495403, 993537364, 911215079, 458283459, 82906778, 801719078, 690912755, 561069531, 21000988, 882439184, 51176316, 456940502, 990725378, 321434055, 262714538, 923977765, 992936301, 142375410, 98687725, 17566721, 46094315, 865450667, 208689765, 576119108, 792070376, 301986106, 757870886, 181321861, 498523674, 120843883, 571007097, 119506243, 862902567, 885412479, 928958658, 159433053, 738156211, 57562904, 876651423, 83700197, 973107195, 112160375, 119408040, 661571994, 504844776, 268140442, 319313767, 747870026, 52405429, 683810948, 907177283, 945011648, 958266507, 87858411, 626634291, 579310305, 744273460, 626012320, 984107713, 368211592, 632739309, 215059087, 262766935, 506492343, 469337772, 231038372, 647786940, 559222991, 989383128, 631372348, 419845683, 92625119, 59191463, 625691880, 885107953, 341274697, 973080467, 818353758, 253669812, 833729304, 231019447, 853235972, 468162218, 907891260, 596621836, 261113455, 609502962, 503588571, 741240581, 209361570, 707115801, 950957915, 169804196, 426942197, 821229630, 612108642, 451371149, 785131183, 912885436, 138594743, 341063302, 801251771, 386793781, 644314677, 985623852, 892411428, 984091293, 417026879, 798487682, 485507101, 880332109, 513669190, 978040163, 789966161, 70814079, 349417877, 741856729, 617953085, 320067839, 526826939, 38563282, 351641733, 300584508, 562265732, 71459045, 413472047, 347349180, 548702972, 620307102, 526548107, 599324354, 697775856, 267327721, 24305246, 273200671, 209739426, 468575488, 909360023, 434059224, 717680793, 937477956, 993792465, 197806838, 96426400, 375825976, 323132088, 39742035, 383030628, 359929432, 556275660, 240164055, 585896696, 406658926, 139979886, 178422636, 872379901, 763651728, 982657319, 323030484, 658555051, 241518905, 912823914, 416348916, 94315837, 175737356, 711765386, 348155721, 63160237, 201347018, 167304263, 793978192, 555116344, 810874043, 148036773, 72638766, 561708167, 461892542, 3572311, 114849445, 229957284, 726490636, 155258967, 448042399, 685810146, 449198455, 24930628, 17299130, 604705462, 769450157, 89996163, 901194607, 169310592, 902083059, 383472991, 974858702, 306422818, 106015156, 490950594, 352395520, 144944800, 187283967, 80910869, 596856015, 58187180, 725299314, 435358175, 347365233, 884902160, 48199281, 224021857, 678644347, 500473404, 673470888, 524591636, 932829365, 602709430, 475378357, 142281791, 282194924, 358320256, 829846107, 37019508, 498337666, 543996447, 132821184, 917339632, 271891635, 472888417, 720841995, 468972009, 773913330, 285545930, 458397563, 966915812, 62792103, 597766799, 647030973, 193847142, 562311358, 58210541, 600023830, 188019490, 886158726, 975360144, 221373750, 310723404, 798591135, 808439645, 401513494, 439554521, 887003995, 803774952, 137507094, 32828637, 247511280, 788911979, 900690413, 277890938, 452361779, 881029023, 523031550, 960471671, 424168191, 568189787, 422377646, 619689026, 316231301, 748930012, 710783019, 144740652, 900900870, 335765698, 341175443, 310609037, 220252655, 173630372, 533453930, 102986377, 825785414, 971565884, 27033130, 463205986, 163417472, 175855726, 482229677, 855635455, 726397924, 430880254, 229060233, 780940677, 947738463, 486966637, 481164255, 840555324, 504315466, 238213802, 296394705, 478320048, 283701682, 720004643, 207879552, 254901196, 635877022, 409092812, 338093862, 822310050, 865322980, 160514214, 336817282, 481469235, 816353193, 189386108, 488872166, 648727781, 969522014, 618565692, 414042365, 633074864, 643591953, 496585899, 387603943, 252827282, 196194896, 197792091, 361456279, 353901065, 881691727, 306099714, 763601883, 306781963, 491701508, 527836979, 559721885, 549110114, 305818462, 417123234, 582747775, 114570542, 20204950, 710708642, 837967254, 834140206, 891499498, 451824185, 846867048, 884061714, 601568056, 916490188, 102529165, 98126172, 277161784, 857330937, 356580082, 384736389, 506450263, 9744349, 22476170, 480976667, 527865859, 3579809, 746927220, 452183307, 327766425, 868699642, 701840222, 225275219, 335561890, 394949963, 971645902, 708645002, 763108491, 338418832, 756699525, 470629119, 449420481, 310758487, 610394773, 287393561, 825809854, 6746118, 107028631, 357054331, 520856309, 641439584, 46028655, 715978351, 222813808, 360655465, 333980972, 80456548, 999019458, 624817561, 10067142, 995503679, 565831793, 813356791, 624218204, 266422678, 83506128, 597995610, 489124940, 972153680, 78277288, 810771634, 434159316, 826642744, 428826847, 72575235, 465969707, 635870534, 80897268, 611515323, 845344997, 831387886, 910140340, 455378712, 258152731, 614037372, 835145127, 293629085, 433267316, 580069778, 46762320, 717436114, 179090416, 219792077, 574673229, 396099198, 685056994, 941617794, 986228504, 157887559, 70499893, 39903429, 520004861, 520096443, 200807583, 296204564, 741994289, 936906199, 219045800, 395175687, 404611999, 848928313, 214355664, 48217262, 314181496, 46536571, 563729742, 274106029, 660560661, 406982355, 466771510, 781899793, 634300797, 175103350, 234862352, 732693829, 732789003, 632293789, 569007304, 909680411, 341684632, 955292156, 405547025, 575184811, 926721087, 245214498, 886293967, 234420446, 213387620, 751769466, 658983110, 153091146, 999572855, 823989361, 633333415, 368947720, 104637442, 924744211, 178796848, 477687202, 452426193, 974717784, 445467264, 332492182, 106880120, 595612625, 58420925, 903849614, 602689612, 58107379, 512737183, 206869254, 851110572, 607719598, 413176672, 806009196, 284691782, 300682444, 948961501, 117297929, 440836034, 390750144, 536816324, 837428644, 828017470, 299331504, 241608057, 450601572, 127538221, 234317186, 249422496, 972742302, 333146958, 522894173, 308585255, 76888096, 117693892, 367759029, 131892366, 989130382, 407691335, 645941208, 81514628, 962695633, 731506962, 6016353, 303052796, 157066775, 915841251, 500811518, 376052045, 681780924, 147140829, 743849007, 868088134, 595389855, 488744562, 393706240, 35160143, 361280446, 335084359, 99699718, 491939553, 1525042, 477066890, 713589446, 145717713, 534597498, 45048138, 228348932, 854542056, 631604710, 910414815, 599313247, 446124618, 331347703, 329005870, 106414963, 612394565, 518253441, 388885556, 498523626, 322745125, 754626497, 445161094, 717994355, 562798855, 354111189, 485842299, 748198475, 936607582, 515733110, 139343597, 627353344, 544155964, 890850962, 854480896, 688667086, 152113036, 162703484, 469329084, 578659191, 636042362, 546696922, 401701980, 853654384, 977585401, 146655551, 921793342, 756122898, 436761936, 365190800, 548637142, 874645242, 24837750, 704121823, 332606672, 264129510, 234477545, 467482728, 119113285, 583088169, 907518391, 241199112, 573525357, 486385786, 583513646, 87048885, 429939491, 800628899, 26837523, 448079926, 677171565, 147764962, 386037623, 512913646, 900597202, 15301644, 369514135, 756626861, 229193605, 754121614, 187367912, 970554452, 830087658, 534281724, 120446244, 513256574, 74965264, 237393711, 28533471, 312415640, 144021816, 456662720, 47941198, 592673379, 74422953, 241789429, 35271975, 193075211, 647416445, 275767609, 79891190, 847040463, 816777209, 53504749, 617422466, 954390681, 292282574, 87168859, 440888094, 35908513, 490566220, 560129261, 49113358, 905752721, 21512013, 643407646, 707736510, 354939767, 118307017, 619204391, 902960042, 257942925, 496965532, 708795555, 827882916, 586274802, 431491951, 701812859, 160221975, 450304789, 583604155, 856502606, 151935215, 722382106, 31779245, 156825112, 517785703, 22502243, 191339349, 578108601, 686155918, 457919086, 813549272, 805893643, 629690510, 180299311, 276698686, 406155732, 101953818, 612209341, 827918069, 519372162, 794222056, 740435499, 259066544, 265141507, 515012951, 702070392, 44462353, 843775037, 765727438, 977216249, 709526945, 553440406, 787046870, 158648809, 694481327, 49295494, 380546208, 643984571, 261339721, 698446787, 703506055, 257516529, 31395388, 501345027, 1077951, 828244656, 568665898, 298636842, 786059178, 552107813, 469648014, 283244494, 939744591, 590866771, 525355063, 896383624, 497850453, 618131436, 443674430, 592851605, 985586150, 166213750, 38997657, 534066018, 954355732, 515938465, 242547000, 701468676, 960304021, 326628196, 111996519, 851597826, 912074305, 577956687, 726401031, 34486979, 567934888, 181256861, 706853505, 119991733, 211537295, 270945899, 237744212, 848171557, 226691926, 149536886, 649008838, 350200964, 377824015, 834602159, 823602359, 41464675, 722714910, 909616673, 551363040, 567247963, 350457525, 224838840, 506291664, 219821204, 807287289, 553618206, 201711913, 626071786, 54811992, 2397770, 952035477, 566846405, 132377104, 822933521, 26350597, 960891553, 33000561, 400294852, 899808985, 529533556, 452548406, 433971898, 433482846, 58096220, 283620964, 227791484, 583118514, 126520260, 194520498, 701667301, 470852174, 119133845, 76430869, 9272769, 294778310, 193161517, 347186851, 744434338, 244015235, 551432885, 474743664, 180921808, 579812912, 5723227, 916606902, 44060613, 227222381, 665502905, 448394964, 578966267, 538501674, 69766654, 985433735, 163172990, 398299503, 755853022, 630583223, 958353657, 416916610, 568784322, 675496260, 401581102, 969936665, 829519318, 802836855, 593382534, 342182809, 317470528, 256427687, 843748274, 411640414, 979543176, 84593690, 215864687, 186712216, 739832143, 556560906, 966232597, 280110180, 388684839, 839275144, 267515855, 122297469, 679988481, 711201517, 546389367, 738364614, 758244092, 263477681, 309499586, 691488643, 279202770, 658083261, 168174748, 446578377, 366827300, 816408503, 679820462, 757536693, 599746482, 258633, 623800722, 641668439, 471171781, 523279111, 38264400, 6868333, 516973046, 305901163, 675536205, 235484467, 530951120, 912932570, 679541634, 47367710, 718751292, 988370120, 228263138, 104193228, 342041008, 594985915, 358154350, 810673215, 25645282, 932861351, 785435409, 72151521, 370975870, 46115684, 175247612, 209401133, 903662932, 939208019, 242476714, 448323509, 5151723, 694898607, 706936976, 227596379, 231228190, 339901361, 841454702, 336247191, 203312458, 436135995, 78607189, 150995038, 456826241, 492888847, 390943862, 221134724, 858028265, 295438082, 675612947, 762214364, 177858896, 663994328, 344196405, 222298237, 462252259, 861543540, 906389508, 190110529, 273647985, 393416205, 293479892, 30115566, 605502910, 509991026, 967830638, 249812436, 419885171, 716098131, 888109394, 786145124, 317694745, 785128416, 510628734, 992604552, 76608142, 502195168, 682302141, 443067690, 944433634, 499559330, 58362263, 607705980, 726867599, 778215940, 823001186, 463168236, 995506829, 829758881, 95829455, 889268466, 853596251, 251534399, 633905544, 166803695, 517989174, 362550662, 209226633, 947801152, 565954685, 380028295, 169701955, 115444302, 766437041, 318195472, 673417318, 418155130, 671916667, 178509427, 534484443, 651607036, 251206612, 367991586, 886255834, 143356837, 668389115, 578444028, 305083848, 771629028, 574635033, 586062591, 395079029, 348153784, 909652440, 824250285, 342647909, 483466174, 495395071, 909289361, 885053183, 968781394, 301026972, 588386510, 625277481, 712042009, 246515585, 172264263, 998615911, 851878050, 223321329, 553830988, 162020688, 728736043, 927343180, 682618057, 176822306, 876085649, 247504175, 924347497, 455872368, 173547593, 736460310, 166169257, 32837404, 326404431, 818878025, 957481885, 125356786, 634110048, 257968121, 343467243, 454451778, 303365614, 633670676, 841171610, 357819571, 81267046, 979927583, 989281581, 512857148, 613538735, 356942009, 339557566, 63664580, 291435991, 822850126, 347076108, 199485243, 933975228, 256930873, 722015397, 559009155, 688850500, 790299994, 358243244, 265251418, 436754018, 824075110, 575672612, 116392649, 394390153, 254640933, 382777763, 863562975, 910732105, 293149029, 846163948, 310605434, 336586277, 802565067, 782681981, 276012914, 496810727, 490290880, 977092101, 449639257, 603233900, 228041894, 639091762, 858274589, 248445648, 998698886, 382884834, 194231748, 665035109, 602426039, 365917160, 6321105, 249114207, 281018349, 664458350, 582065639, 967220790, 84563287, 29564894, 750050029, 208310470, 144080119, 306348505, 51555206, 297659261, 975308497, 756684531, 821028885, 897530637, 260856195, 721654402, 309337228, 433012627, 20289471, 514507056, 882624377, 130783999, 775991527, 76002337, 696440822, 172208673, 261390666, 955919051, 704244680, 964840217, 151734707, 182660166, 433596146, 565950139, 545621549, 811961299, 387200549, 581165248, 11388428, 849643232, 561736789, 982209566, 477269572, 384698259, 543671662, 219993453, 381810353, 576223546, 5702033, 686777236, 17807106, 185041252, 636084586, 198877566, 64532839, 287090953, 593732981, 81693890, 560505540, 170657503, 112382597, 123426891, 290717448, 260562010, 493846605, 727082109, 660794105, 561135434, 170038227, 414360911, 521802819, 768517639, 240777445, 295612969, 223756523, 29162239, 929866084, 343557246, 975110169, 648010404, 339968977, 204398275, 202244524, 760325430, 343404166, 591646858, 646329133, 476189874, 916687621, 239412011, 726831073, 592764595, 522020748, 790195224, 390669190, 803384625, 560206458, 767065042, 628346586, 77304924, 772587978, 864561827, 205912872, 754210136, 344634539, 713343840, 170759259, 988449902, 78970577, 419748676, 991918446, 939311223, 714631314, 83272458, 479211156, 544674467, 656734608, 219754775, 923540893, 381857708, 300573248, 989839664, 22865546, 541730129, 141991045, 646087991, 959015159, 681907449, 670572958, 614862011, 474111569, 278348499, 545252809, 936584415, 599294877, 982725785, 307495501, 107579839, 977369399, 727322124, 148987523, 942198293, 42598579, 618229426, 903430333, 163233477, 173268626, 96572269, 764465266, 752841258, 833013151, 512850163, 190657408, 847908602, 436317934, 871750628, 302467223, 480876952, 901186657, 194138752, 602482282, 473233353, 274440158, 950363214, 744717434, 841415294, 44433345, 400537446, 755738717, 25588679, 296299944, 843631201, 866090710, 238943516, 776492753, 340365844, 676194731, 432281455, 157353684, 603572454, 544836586, 606018653, 979254720, 302821386, 574384922, 447684253, 946703459, 238474900, 802152566, 698524361, 653459909, 685709085, 261842895, 186342374, 75867447, 52333972, 267554288, 895338222, 317944453, 750736249, 126727923, 218956554, 668217398, 982927186, 59474252, 21634758, 664235505, 906938490, 200804014, 573958174, 650466841, 841934625, 458249211, 117991872, 50795490, 345382810, 44942354, 956074307, 408463761, 55589297, 772439055, 279312434, 992422842, 491593028, 343961082, 347685441, 785861822, 328441711, 575769059, 117835615, 761834283, 170724468, 97670190, 207004866, 697570980, 581682844, 164488269, 374761764, 357632712, 597602407, 966111395, 906721618, 269531327, 312460927, 771271937, 564908671, 447296360, 523803098, 169781636, 751132257, 841524058, 747155922, 32820379, 432922018, 128342295, 527404510, 893243221, 896141675, 731132819, 901622350, 967363574, 237570092, 923813969, 954351419, 537405328, 838798927, 211557255, 32486775, 854973412, 711183265, 441578595, 142379385, 908088379, 882769897, 462292855, 807522891, 171628979, 901115695, 675851368, 885081098, 869842695, 928305299, 614347967, 609746307, 299086462, 662008232, 553437800, 571324377, 921022128, 146994148, 608250202, 163480461, 248178156, 268429191, 536729719, 771534897, 907559937, 393325594, 333065742, 469440835, 14326844, 912154572, 94347921, 158277650, 833918070, 865281966, 827388330, 776511318, 832933448, 348922316, 108636754, 25843669, 839933517, 363297150, 570050491, 322487378, 129153395, 250233991, 822908352, 728063860, 361690257, 928325585, 597327348, 633393460, 18018368, 893060521, 146081576, 19034100, 818419914, 262162217, 180755924, 790132868, 54976926, 297473809, 987086564, 813674897, 805361532, 18299233, 107512012, 385332660, 68830910, 43602751, 458267094, 729803269, 521714560, 470845920, 50080065, 917782276, 402591701, 299517401, 628722682, 505460051, 892966877, 93641911, 90668397, 984633573, 601939944, 503623739, 120051348, 66262338, 161633137, 657265951, 294764884, 519256801, 353846639, 632724514, 755830955, 445003882, 566519263, 325350116, 829025563, 147254995, 672840907, 313238403, 838469797, 134593382, 149509389, 54236320, 667233171, 57262623, 342004516, 540830711, 54661234, 794967738, 121376036, 857986324, 954078488, 621243524, 176611354, 686292870, 599305756, 294040028, 800054302, 986119682, 332225435, 153283587, 766829710, 93531032, 967421984, 569109597, 390128627, 105171411, 225168626, 845762628, 241692565, 646780876, 163227981, 441372468, 286043605, 776151554, 89698412, 199090857, 697719948, 596413247, 174094955, 13597479, 647145912, 150370090, 296645015, 614279754, 677905015, 670989620, 225236069, 271018708, 192584680, 654846885, 694693751, 929414977, 8433379, 459040602, 908310793, 633924470, 506933030, 709058995, 369836575, 560029259, 575716611, 57625098, 201227317, 422591567, 326238683, 827201008, 819189431, 333049088, 543104006, 201611315, 61863750, 491973428, 448231144, 314356507, 803803972, 938503393, 595569610, 346552051, 698046157, 494386826, 294609090, 583794004, 510157892, 730939556, 728021308, 447802725, 854553535, 728908801, 224103401, 103446259, 892644809, 375562079, 785002319, 854742381, 21558541, 744478802, 228797219, 703624705, 434220319, 617826721, 472432015, 995481925, 380660963, 736131555, 952243169, 474484482, 467770409, 421612476, 927533311, 427578741, 422552161, 624179712, 318395792, 112507663, 936413481, 691908098, 588260274, 724189271, 960156885, 70393271, 893098883, 656532756, 166174689, 510948992, 448879894, 899638352, 606105360, 118094191, 405871481, 482754664, 174464097, 349726497, 601521722, 32320285, 34251494, 344873790, 334855548, 737545662, 590466759, 520011800, 501419905, 128286751, 643283816, 386096105, 623592600, 375257609, 227186174, 451312185, 696182515, 576125624, 412644510, 592718933, 293327486, 874765588, 682369645, 768323719, 648699269, 881544416, 178057828, 361466016, 807174593, 561779542, 67570559, 498683089, 675684073, 33969270, 389269496, 327622384, 751949811, 173017585, 684285184, 737781082, 231201488, 362534238, 168800460, 464039145, 600319995, 729268964, 464744809, 294398501, 54677292, 757501071, 829065233, 138335116, 313385789, 19016705, 876276984, 275881704, 67071527, 516575443, 216891275, 543894539, 376451990, 585822805, 91370683, 498748064, 497212209, 779025800, 144344185, 809326511, 39718585, 213541093, 932068447, 924300553, 602728103, 581057034, 108419214, 958213975, 791533307, 810401105, 534294219, 320326669, 914939765, 564941490, 868629663, 812502278, 673590614, 283060360, 265086499, 621256769, 7647433, 732029650, 112723208, 196463934, 472553374, 570574569, 808468945, 882192657, 14851593, 409603493, 316066594, 874995003, 814326167, 818805337, 108741066, 253931425, 167787480, 357169812, 151815356, 558096281, 123856628, 822432660, 68957435, 378932901, 479251597, 211759434, 442596594, 682943675, 993456487, 863306739, 120196424, 566183022, 741039280, 169273649, 36322703, 853591991, 189895978, 258185225, 337822094, 587903291, 854668959, 45639971, 568000471, 48922222, 429839009, 63600571, 989783172, 992753768, 692863752, 698389236, 812826277, 657892944, 557212466, 648798392, 11944486, 626207921, 34172965, 212620549, 338960680, 159482849, 279943295, 646400352, 856638022, 868662101, 444652517, 137502018, 755526443, 806211699, 1428370, 649240872, 524170576, 210198756, 62773627, 195858432, 997019656, 190277928, 596380321, 782224936, 951260363, 346109145, 144788624, 341296688, 442856865, 257245184, 782720512, 472799359, 138198908, 460657182, 608394564, 365678327, 84721551, 305229337, 684407193, 78019959, 519413470, 694583449, 95119393, 720356776, 833736168, 721913917, 266359705, 326729618, 873109834, 923670270, 952753587, 367227375, 234813535, 938229938, 347297921, 276282736, 361103575, 390407365, 821433310, 439374975, 48669023, 112468824, 57349935, 93073091, 92625863, 344558502, 900971396, 339336430, 595642257, 228558697, 900177099, 136708353, 596760613, 249587143, 288731739, 21912078, 686594367, 238706252, 790890298, 255004123, 488567811, 339480435, 222303390, 989538301, 6444910, 618516822, 569358388, 298336023, 823418289, 532076529, 626655690, 424365661, 687554391, 450811571, 347267774, 978375518, 153350174, 573073510, 578906629, 132653135, 195751112, 96453364, 582329082, 913499648, 641142918, 254438907, 504940423, 451059765, 597835022, 374165647, 920150224, 643866602, 824777845, 742856485, 516703353, 994440485, 935928340, 654938991, 505053495, 1009115, 621865106, 94784128, 694997526, 164224512, 946992061, 595478029, 748085504, 334530101, 632011819, 370106851, 713884234, 587051580, 912763603, 644474263, 266050222, 7897777, 897150726, 693271486, 121462109, 848872034, 223031825, 923299048, 725345674, 746168650, 400956991, 736136890, 127550362, 831991207, 516635840, 431377213, 976465866, 513235182, 605038693, 763398123, 465118461, 839820956, 62734514, 951663155, 197309214, 678133776, 982304752, 157215748, 664262296, 680892887, 28606895, 487817082, 418021719, 822309635, 901118290, 195839404, 99780497, 844044003, 416797480, 782745164, 873224549, 696756267, 786854041, 589742117, 987934990, 437537814, 157012378, 108716258, 586791914, 568741124, 154311971, 529104421, 262619350, 635822044, 756171119, 86120215, 539537471, 470622121, 586714657, 936293877, 696087629, 693825320, 334520625, 387152853, 662624378, 254627098, 970134568, 106699874, 471499298, 294884769, 154371100, 346793798, 177451065, 317113914, 927013563, 383130073, 659229282, 907308749, 280187633, 344286117, 458156137, 977592206, 782163340, 829532293, 42340729, 939446631, 834490266, 405059467, 200613065, 596059783, 881391032, 43135381, 804592539, 17017759, 139045752, 22389356, 308052302, 770110957, 822321183, 195942168, 75758219, 862241389, 526951011, 846363305, 34312922, 503635897, 114833561, 360890437, 834865309, 641987299, 181948447, 729802863, 183607477, 183997296, 800247622, 122839971, 994656120, 115628692, 798370510, 163297929, 801314020, 981930256, 246340479, 124551946, 427897669, 938465736, 916605338, 45028169, 4707264, 380008897, 287533323, 140275102, 144520536, 479575134, 647464472, 372491004, 342972448, 832898450, 523606391, 423156943, 738236765, 594321551, 86688257, 442436805, 834985139, 90964808, 902142165, 463105706, 379000871, 131486873, 212887014, 276792008, 864994049, 244660965, 982188425, 891685030, 855594308, 192567524, 92509905, 311340201, 40598947, 759827236, 942136258, 567148152, 700589480, 957380476, 57430229, 633228625, 867452516, 985617554, 341633947, 848672519, 399029577, 375236085, 104050439, 389772937, 984577031, 640525069, 560663608, 505688179, 251287088, 599519829, 595518919, 633321727, 784899103, 606082, 638089922, 757183944, 199346906, 756207842, 989357351, 614985360, 190277282, 814191204, 509954498, 740714018, 522596403, 834656557, 373347042, 641065734, 734185330, 863327605, 16168181, 235019445, 916317471, 245570693, 40472427, 197807238, 851401483, 286594757, 484928170, 5808992, 374617681, 310677441, 778844393, 651688544, 104543029, 903116459, 411814991, 332605670, 57612963, 944615720, 241676931, 850068039, 450721525, 301863931, 550110552, 78732773, 653074064, 693319114, 265755438, 756595062, 126168167, 59442969, 185309959, 694091245, 878664967, 344448204, 763083485, 270130348, 251757146, 355428983, 972555055, 762155815, 938990685, 142596109, 526004579, 958756971, 989543094, 273721216, 512775830, 646171253, 710808185, 41768889, 977756923, 250045660, 527453923, 839431246, 354239273, 503040182, 687446598, 430084550, 180864583, 301846131, 65148326, 702889443, 960805225, 207388368, 872704827, 552313155, 956737850, 960348068, 469790863, 787225562, 783457117, 858768260, 410488772, 240756084, 738307449, 37587685, 60375542, 835271573, 978456437, 285900102, 771068136, 498696798, 659520972, 462785927, 560342030, 821968152, 739431006, 779577745, 44218638, 124170847, 984908547, 929144069, 425930706, 795184835, 614925129, 796371500, 204677250, 908002526, 899016683, 893707882, 404527512, 557299862, 397918016, 928751254, 805859997, 107053365, 118979390, 259837033, 633858504, 926724351, 536722652, 717855256, 838551508, 47055553, 800283404, 553274846, 371231938, 399653452, 557812134, 371579496, 161804734, 248890783, 24494855, 862145699, 504704718, 414713519, 583114114, 341393640, 2882097, 683922639, 297601629, 162545771, 549418652, 49117881, 161653233, 714056258, 257517843, 768917579, 264426029, 393736093, 814536622, 757240488, 191364973, 57341586, 424452814, 529765552, 12792813, 488029240, 640263534, 678930029, 889315479, 824893559, 493047435, 425236552, 374055900, 951084923, 531712782, 5148204, 375187078, 885795570, 997266062, 767232249, 83618897, 171482471, 681785026, 370868990, 495714228, 350295487, 612268691, 981929717, 334145779, 809554332, 598211676, 95213302, 515539634, 488306329, 282177923, 361884544, 267013853, 267582000, 355002738, 569965599, 594068102, 290640853, 899708610, 911882205, 857442265, 177064547, 611183529, 419525094, 972409296, 389465770, 631536609, 952364578, 35659908, 540305990, 783784843, 783201565, 38672580, 878335436, 678519198, 589649450, 310913310, 583862173, 97162713, 382645736, 53823203, 700980135, 481500871, 985178521, 123275704, 561400691, 98517724, 966948361, 384589578, 613329835, 666451868, 99612521, 127496662, 698341214, 418811893, 96383444, 65065714, 657731095, 634263843, 282542194, 128373521, 473349735, 313641059, 224186666, 407692372, 88246471, 543084148, 567138667, 815364940, 986414447, 576136312, 510566426, 102058445, 232079517, 816378855, 590375273, 376536577, 403242638, 435638586, 590734763, 658216287, 918758172, 571396428, 761121237, 578887948, 450560955, 662542970, 447408122, 537557259, 654191644, 245826587, 490818463, 409163744, 424836606, 423010946, 862045204, 491088206, 207130253, 32696252, 426112071, 533377525, 81796314, 860485826, 696441266, 973349274, 896267435, 26517383, 792470171, 555656067, 768098103, 75597294, 843898791, 627314345, 46291231, 352630763, 269339946, 259587906, 600714436, 847427192, 171929860, 863110903, 194438653, 431536367, 369959269, 712630566, 272893708, 259224761, 291008051, 165894925, 706891349, 33545327, 349328846, 534319437, 429076559, 745809643, 423014441, 373082637, 174571301, 738733047, 16007372, 202016395, 56042681, 452864493, 574421410, 292125657, 344166977, 993534066, 828068946, 13830547, 399614354, 411769185, 34224811, 839670140, 873569389, 944317741, 177581350, 601317370, 495797350, 26012494, 98284853, 326399486, 955128365, 921318286, 514127, 432741803, 539819157, 356378337, 529404412, 302961422, 472080199, 899872322, 413511420, 766877268, 843312478, 940441759, 146409430, 283562579, 411721321, 999778503, 669683984, 766619055, 988855689, 167232068, 109181981, 418299722, 959321310, 815209938, 93190744, 352133375, 10899311, 494291491, 445290551, 988775487, 753276256, 255046502, 218484109, 352517353, 533894406, 483275484, 396999369, 189043372, 59357189, 34293747, 538611304, 923361691, 145523914, 638574950, 583336804, 203270664, 173003001, 776925975, 263823570, 178657930, 88453858, 292118848, 729483410, 283321007, 423471661, 347212821, 535159052, 576312326, 458710176, 537708366, 904358545, 310349524, 439206621, 278207949, 877313304, 643771268, 959120119, 175752713, 914251690, 776833804, 245351229, 750478170, 827693563, 703679270, 437515145, 445308280, 698104377, 991779259, 235455523, 505008788, 310845468, 176603043, 547494566, 330565447, 188584148, 171577965, 556507294, 692102659, 969869807, 625039295, 190586906, 191882653, 361901624, 804113360, 325223442, 878847438, 852942497, 526141617, 664487212, 855341034, 617023068, 920982867, 945055254, 900207653, 154961504, 897469076, 56849452, 299447903, 753249002, 440743993, 721656369, 203549434, 467721793, 591528486, 935361414, 429525696, 336820772, 16127916, 336871222, 389642485, 490073535, 117840380, 73480681, 146541664, 416933757, 24010130, 299379968, 54886989, 777459855, 674269414, 195726111, 385783, 871921401, 676814785, 914356587, 164508565, 521374916, 800579073, 706697414, 541244753, 807746838, 956066192, 679570176, 221642821, 340658867, 876189977, 662127345, 56513159, 862026925, 527461005, 705408998, 375187294, 186425645, 328145616, 908915735, 680907426, 360597990, 444032469, 193851653, 442282810, 790492677, 342161720, 71423738, 478478542, 50409222, 902368694, 918069297, 920034303, 145089539, 126033346, 529278431, 932139488, 355824151, 933479339, 480755724, 70198314, 825637095, 908230780, 140499361, 9570456, 143643704, 340054220, 232228008, 937879782, 67180595, 998077274, 552901442, 952536768, 694240261, 939703353, 184699708, 585130065, 75828753, 743626832, 103609939, 254136417, 749828499, 263066966, 632274128, 224275633, 463173364, 350356676, 845010428, 10521895, 265715112, 225186635, 561407716, 118902647, 146081192, 292488168, 570725360, 151343503, 338159711, 708494501, 379149233, 693256603, 526972612, 31625702, 291567746, 122119191, 124899224, 874552159, 165540257, 998657171, 781475407, 639638165, 28859353, 65822434, 316339452, 213870521, 200339372, 637766983, 23033812, 782892983, 809247938, 491568161, 864209313, 914021687, 537014019, 911821812, 462625794, 75772152, 211621219, 322115700, 812300186, 575222268, 636588172, 274537349, 186948406, 777235906, 662439113, 954728073, 86891404, 144191687, 711562793, 812227861, 619381686, 856043584, 861397158, 776821658, 90657283, 423511013, 114339858, 276960728, 647460259, 697514513, 42904933, 49570369, 593893077, 142817477, 15406672, 60944888, 520116232, 115141595, 692156193, 236199465, 349455669, 615328463, 596811728, 572767898, 71643130, 285686308, 318641425, 232976431, 924972415, 106247546, 266388986, 688732827, 535560201, 402269357, 359258808, 360825673, 863822179, 135719158, 156687568, 99626703, 586732226, 572561465, 918980791, 974002436, 171968715, 44245174, 932920027, 651996859, 238651756, 160328472, 158857596, 511001709, 75569268, 849847749, 662925729, 881644998, 70822311, 701258390, 439362170, 254798150, 185801380, 794533249, 259951853, 976746346, 515176267, 303934321, 10261124, 152517895, 390894470, 996210359, 228996903, 921053277, 508940237, 436486155, 651574265, 275642095, 592878592, 715781991, 213463555, 648605425, 318016532, 163798593, 169610788, 152768198, 405996438, 885737481, 564240449, 609861703, 573019468, 581528062, 932974969, 20354494, 392979155, 80578433, 195702448, 698028499, 553832507, 830176273, 782985295, 973358643, 874592201, 448681674, 59722110, 708678460, 973027322, 980377906, 730827303, 371092681, 559296841, 154659352, 537209230, 75729288, 622376418, 855507018, 397004727, 757406578, 22878047, 553360736, 991206225, 192738126, 318144353, 905038962, 214442260, 622002487, 892369277, 478367301, 299283324, 521033702, 910532357, 158848371, 446703903, 979663385, 114605291, 12564307, 797300326, 691174799, 377170031, 463853401, 819093425, 161228907, 41423564, 494139077, 901240115, 514891135, 285227059, 68721240, 227184570, 210778145, 467604637, 746587428, 269242525, 994819222, 568305943, 414223935, 532587439, 725017502, 203447502, 892547706, 334797100, 143082420, 653993228, 283197524, 149354060, 548887217, 174825615, 508067084, 789105327, 422479171, 476484687, 103860739, 669045589, 114759269, 60548837, 595066798, 370434767, 858717946, 171346574, 139129653, 747697279, 683930903, 195907165, 678241336, 197234093, 601505550, 1070118, 936788162, 988718870, 759728473, 12658185, 886330435, 844215628, 483131910, 11244512, 538820245, 376473518, 264494351, 539518467, 109122945, 390315026, 425020307, 97155183, 539095550, 744832743, 544949496, 289953688, 768099663, 321793187, 797867601, 95033208, 680434226, 203756305, 736082817, 888532343, 60506117, 777685413, 572373872, 157851614, 24016672, 596907654, 240753367, 995548182, 525601758, 885550978, 754805814, 154137019, 258253962, 759139002, 944811870, 494472695, 149790892, 793714610, 850027945, 595044858, 45174734, 219968269, 106692188, 511470099, 899976793, 898318388, 844381066, 539755818, 138643715, 837475425, 707055424, 58989330, 784628624, 147716898, 786021151, 372740506, 463010174, 496042770, 986733918, 197142498, 324810752, 829140373, 504703650, 146281383, 220172674, 599427766, 408659419, 711426715, 596835639, 606939961, 875516982, 803966328, 963158679, 317437896, 767884666, 651487035, 800090084, 71712871, 643663981, 313100119, 783017563, 529877658, 810580050, 954510029, 707725610, 583570188, 897694189, 393031473, 237409869, 57101164, 283847367, 854623851, 797102792, 845715419, 605387756, 398765086, 538604240, 530088711, 965228121, 904087254, 45912657, 520714650, 590687949, 173843245, 678819470, 16932965, 980916472, 928441868, 368654039, 195328700, 105950163, 717277721, 545855296, 764399855, 934647156, 640962040, 265200607, 282640977, 636418313, 684132808, 3237088, 26311812, 999930548, 418439877, 120286205, 737675752, 308150631, 360341018, 536152187, 66418322, 359638395, 723230451, 733742541, 493621047, 278865040, 183327482, 991775198, 184669521, 607655459, 83597954, 839577729, 639965456, 489124201, 203813382, 273681438, 924771138, 617047069, 388387556, 967801539, 155392187, 82258214, 146731880, 219117434, 619214741, 615058826, 766590871, 25531026, 156139848, 228591790, 86965250, 7730442, 2396416, 696642987, 386051145, 164369627, 362528336, 418856617, 220817631, 194327519, 111224317, 572799997, 723927952, 950675918, 455176849, 197350866, 488075202, 750307542, 65309705, 879835, 19874557, 747377191, 105408330, 116290838, 927943333, 376334076, 13230221, 734152655, 853499777, 42851811, 432448835, 587542960, 127141087, 451838713, 492006052, 496592752, 604626554, 689679350, 98319435, 631963087, 263492992, 59959096, 33121404, 308533060, 983020493, 27865427, 910603783, 828908156, 178528160, 990774476, 755588071, 511606365, 354719011, 533630265, 243988714, 642134462, 482518305, 476151683, 340609964, 696264685, 192565721, 425802761, 880642989, 968774360, 149213432, 9440274, 769552289, 156548852, 850158996, 366264213, 729078542, 343124996, 197463517, 564201889, 736614884, 404340304, 238475285, 132844021, 863148880, 594069664, 360685584, 904965960, 674016531, 316652486, 763700311, 687439488, 451154703, 231579050, 272044893, 769895301, 746715012, 19357870, 622031823, 21958410, 205573997, 5226938, 970408198, 640137328, 147355213, 6043757, 536960054, 978770364, 902108524, 20462274, 277792534, 475550486, 967951845, 962111242, 226958618, 511857211, 262103607, 743842595, 358747482, 654071699, 393224087, 210362291, 149717158, 750490089, 138834262, 916436517, 102610691, 581112035, 465486934, 361922210, 96271820, 482551367, 99404968, 669326636, 15234456, 582688630, 278614920, 66954491, 757798449, 580830661, 703196084, 494196138, 781201173, 246840705, 279774040, 715721761, 506869462, 253439092, 245321368, 744965593, 29157995, 358268203, 261085220, 101893510, 253688670, 184815859, 529509753, 430579187, 192184298, 384871705, 309791256, 611851775, 981701643, 736488307, 334415193, 557804414, 139871351, 873579142, 401902712, 578398506, 155453350, 540490326, 878093334, 408271056, 583210865, 33922586, 745874873, 661244162, 190717754, 867412970, 488544384, 998101447, 163421476, 812819659, 715654544, 936055603, 246635073, 484884576, 80155008, 641303538, 983957584, 477495021, 447148183, 764271829, 430301849, 303549267, 814924866, 784541385, 169001035, 560011121, 907718346, 967631239, 297550812, 573163685, 321862775, 735600072, 755954206, 329344511, 41593521, 891849952, 742138968, 118744670, 503730930, 166165572, 608366785, 581465114, 505773408, 773978379, 428374585, 177480750, 900446884, 403091684, 958239219, 252204076, 465133351, 454913517, 658719070, 986478160, 153677185, 31412506, 313620159, 847899963, 220408455, 784285767, 72219073, 882224054, 247060850, 237775980, 693755865, 104496240, 958619206, 97437719, 220894250, 645999660, 605309857, 545360075, 916825228, 975564078, 118014542, 897756889, 533150687, 453868465, 113064451, 175562108, 440130085, 264181, 950573472, 875150393, 796461151, 49304256, 361556100, 366720645, 239459647, 133646056, 739080589, 513693836, 459133374, 866865361, 955280855, 789884320, 1416408, 7639651, 508495362, 557402903, 132083011, 371710169, 728785022, 132637686, 640144237, 65091948, 579596452, 195770382, 635302326, 603579656, 100272174, 977296215, 820499683, 486579244, 698918714, 272881832, 613539521, 923896811, 944475243, 144754467, 797740591, 735981373, 698566937, 290228499, 923339953, 537448881, 279273130, 564132642, 144078032, 821308587, 34263482, 454245101, 456444183, 431771370, 935800472, 141442960, 65674232, 384172964, 421341769, 746263501, 399976244, 769610884, 446421397, 832738700, 441020863, 973934077, 106747837, 893650433, 868259338, 902394424, 669727467, 147753168, 60796384, 469519309, 708040449, 871854611, 825950426, 752199492, 423385928, 586686855, 263194174, 53986904, 670809067, 538712939, 111747573, 860267989, 936973755, 961250384, 555722743, 920769862, 163163317, 977231032, 890884665, 66640478, 957314070, 438373221, 149421972, 261665375, 843321, 131324701, 780882994, 971183466, 179479714, 563428122, 537488545, 496279577, 604596998, 403885013, 815756704, 142477424, 499841788, 219060676, 596515743, 171929431, 131743982, 800896463, 707661453, 719186217, 775573240, 463227869, 958265772, 156108416, 904549969, 425605556, 6833915, 160819313, 546732794, 642888688, 134237803, 567976798, 970037204, 938225903, 166157545, 458229408, 60658684, 455693020, 273560090, 930592517, 797172531, 630391303, 606523679, 130311811, 342144591, 879890129, 879924871, 701828695, 500656253, 30686185, 398825913, 794997857, 878553064, 123319607, 942052788, 948497893, 19666185, 481237090, 673376120, 314034191, 551203664, 687950837, 789425167, 952222382, 807877599, 315381676, 233514197, 694939993, 277446334, 347845556, 66116427, 381986116, 127864425, 411105317, 466660794, 946730220, 466197164, 39623743, 875474635, 430153517, 966304256, 740990185, 109119854, 250191171, 376961540, 503871550, 895693173, 381244517, 283393873, 178998268, 778547075, 921564121, 118265253, 569155429, 496321081, 928260182, 451925055, 697712972, 512317298, 307633750, 197276033, 848911873, 482744817, 361752536, 758616620, 928781230, 905674557, 988545383, 343518778, 784839969, 316463229, 14249135, 942506742, 987060911, 956554306, 395058871, 952918548, 769281804, 129999208, 161140350, 121690483, 494110351, 555510002, 589802462, 190093112, 94991627, 321730768, 601439217, 628145327, 402189280, 961566682, 243834226, 467596475, 606764730, 329628828, 926875048, 451315692, 539779806, 230805687, 164726295, 899556638, 329254596, 880107867, 831371432, 190792599, 743312390, 813143789, 818202977, 438674953, 201750934, 735034405, 751032984, 887574106, 116603597, 304087669, 932305222, 758998192, 918525271, 355368112, 624748830, 62359895, 252806799, 90875013, 633946090, 377481986, 6447029, 614387520, 129164019, 11309120, 342264220, 70181958, 793021248, 572152707, 314183186, 61851748, 964704357, 553127140, 478529783, 481795920, 942621626, 575303859, 571700745, 143058682, 74357868, 540560462, 593399197, 328077616, 968072080, 250130624, 389836795, 249457541, 575947532, 482582377, 379722792, 403235016, 836985484, 664868899, 776368096, 848167726, 358204409, 902957746, 79667326, 535305175, 285996312, 695779201, 425586691, 137466433, 380251458, 817871023, 527012124, 862904102, 689702600, 899886838, 98590747, 735290823, 718629468, 87082655, 394104517, 565281074, 802835275, 400682312, 737447298, 342918328, 13686750, 924136471, 567406518, 884006513, 624682332, 191706254, 976616528, 410107771, 526381440, 126850024, 656819780, 103715927, 931178221, 849861829, 972723600, 25010832, 830341140, 603159205, 61100478, 858299259, 182983855, 486616358, 449059647, 460007790, 988650838, 773385291, 450335177, 623415050, 92213267, 787377617, 941152401, 792066008, 478357882, 463336472, 923172858, 239149522, 419322900, 236116358, 926151797, 931782981, 205289658, 252668924, 738470379, 972871904, 457465534, 723176358, 799913255, 372196093, 689535018, 539975403, 962163112, 90360716, 394509191, 688004835, 641137031, 436908815, 5036664, 724027211, 335650472, 343098186, 235317598, 48824648, 298155430, 470907676, 482820905, 874778216, 170489979, 913556800, 701930877, 436910314, 374575767, 541836631, 47068890, 794068563, 574660457, 395590857, 130146633, 311797283, 275676953, 639667325, 112013061, 10624153, 488479337, 435553381, 544958003, 924338120, 365212252, 906062715, 137247229, 674664444, 609251479, 974508887, 864001926, 876914079, 31858218, 366381393, 415071813, 718345639, 20034971, 344977511, 23167021, 493657375, 79137863, 998524264, 649197769, 203867231, 406849777, 437701559, 100706365, 592983468, 6612687, 537694888, 177240933, 230079995, 410877717, 145543186, 894587752, 27563725, 229444624, 678295798, 955249887, 760902927, 926746371, 454490861, 810859808, 570170498, 944579162, 441490845, 743166258, 369599477, 384695821, 169766796, 951666710, 902836779, 213872438, 950017320, 895090197, 211722442, 470583326, 409083402, 431776685, 363866026, 923741600, 215831812, 289616568, 12996177, 369581463, 594940975, 386350563, 701502183, 651105474, 156793934, 484772423, 455811952, 691782705, 805002102, 236697852, 14170742, 285999561, 448677686, 821780545, 235629595, 155067586, 189041483, 102323231, 705015767, 705533394, 706002676, 449602635, 385106527, 619885372, 606815835, 517617786, 366000174, 480928412, 783323627, 460608886, 391438759, 596243005, 406399483, 873591239, 880851671, 305308757, 526761735, 264782185, 353349500, 730952123, 173702064, 302376710, 542301988, 296397367, 537757665, 704289178, 466399346, 717903811, 892512796, 830214029, 201858499, 72582075, 232514098, 597059787, 530657518, 104504076, 168280276, 786940439, 208721289, 666804493, 714214448, 551952583, 632495141, 317402464, 753875038, 147071846, 506022377, 218567865, 34030749, 668655891, 101242699, 42823282, 938306170, 832591969, 761155863, 639443970, 630738900, 335979844, 475330888, 57205568, 165340398, 475172514, 424349589, 161870238, 618942245, 933847575, 387687276, 358970278, 573613475, 152911796, 397583945, 903105493, 565937061, 857302894, 18564437, 768479381, 243362110, 11902254, 828999590, 306327694, 21963952, 700356003, 37065052, 585658272, 712067000, 571102565, 633698864, 388152326, 282994890, 528984213, 80129035, 54577862, 703252933, 834783121, 181692454, 897147506, 752193426, 982145169, 483767605, 622992826, 974403738, 74567955, 253385860, 463765354, 251841987, 268797586, 188652065, 182050755, 214599237, 494768674, 413320715, 393212266, 821898087, 816950804, 87866364, 258327861, 450412889, 461152637, 312770642, 167940420, 366807891, 133979650, 640701357, 996436649, 765042286, 273103662, 558355423, 339061809, 739824055, 114480089, 120582844, 867410646, 2634543, 638937740, 653413100, 783562081, 523193806, 780234515, 405826, 85449553, 249789488, 256288642, 829209321, 132199548, 120694322, 664900164, 235461806, 668569692, 846655131, 507616402, 225090159, 923141125, 271783869, 455963657, 280244005, 970370143, 220623387, 756985403, 33178306, 558454614, 239304917, 548074389, 78443375, 229389870, 795175201, 876202520, 654071340, 939438149, 367783981, 906447891, 325760792, 511125109, 93735352, 707320619, 218702985, 671333151, 816163625, 424420134, 449171816, 584535206, 894491891, 789280447, 322855702, 979127537, 39606304, 590790706, 744671803, 601934084, 544953816, 605612608, 359769505, 547147949, 868432751, 816736759, 413901602, 143023138, 921069690, 61303432, 856255185, 869207218, 30014539, 14049572, 230332322, 688971018, 809405869, 886702904, 184870310, 920664552, 484923822, 460552187, 818067512, 815160857, 4969705, 353621333, 363824294, 947288202, 19470632, 905890676, 402186380, 895101646, 792887983, 97752529, 342935957, 521543294, 233744623, 983334720, 582230161, 508438585, 734648101, 195631308, 231229378, 748688863, 80635067, 704946473, 476754570, 234188804, 219737965, 119694994, 867900551, 398864252, 653435843, 918572914, 138329927, 968234527, 298675950, 165701836, 935053465, 85836140, 687031734, 953867067, 396007570, 981358918, 762503381, 842929121, 537044576, 162296640, 19756655, 436464114, 767372633, 339624801, 38323680, 506066997, 506011150, 111009662, 652402958, 4280404, 768511121, 750787274, 837614828, 351240734, 954296550, 279709466, 406090610, 869617742, 316474760, 932619165, 758173900, 214353741, 279554166, 692422108, 637366879, 910033584, 593346837, 316195833, 720811974, 348277175, 454769159, 975421355, 257179186, 737606716, 984850179, 16776178, 752100729, 493125618, 98587201, 450489386, 140250575, 404543781, 844706483, 392799774, 804921808, 494424758, 905101108, 83137133, 53855463, 792852143, 924999131, 163153760, 730684223, 276781887, 783001762, 158705642, 310867070, 43618084, 651831009, 770153277, 107568795, 375318919, 56105331, 58978391, 299672877, 512732695, 30273749, 45183950, 894807038, 129586722, 809578971, 163265540, 801563186, 510440900, 511471834, 203159408, 954490528, 491673279, 638165196, 978073162, 293127942, 56787879, 202991156, 504172598, 962136332, 13648795, 390067521, 744183777, 43860982, 142629951, 899152563, 212004325, 530786566, 735077587, 562857326, 741213322, 435547546, 578188349, 386142538, 429969476, 177873042, 55877489, 506523645, 97420416, 925891073, 977354927, 113388672, 922651368, 27975217, 155074089, 90122020, 436235374, 40873464, 314746702, 73621264, 39254220, 889607534, 31068481, 67659462, 882433128, 958746095, 929933578, 521932953, 690946504, 507417217, 64743097, 621856125, 967527580, 96335807, 104084489, 833896655, 154381747, 965131331, 454364902, 47214806, 987881969, 808117158, 181396510, 204436003, 376813170, 865084081, 551104985, 417348956, 682128099, 331281413, 306263903, 526898195, 924554890, 500928573, 421335107, 219853307, 918092348, 577679430, 754407377, 646896899, 928921359, 26670398, 282163060, 880540915, 653012588, 572966112, 796323662, 212094139, 972424242, 437031096, 723513316, 115356229, 673379122, 953537443, 585848208, 655240287, 774302667, 509938910, 174401326, 785746619, 108282527, 955512671, 543791429, 569392304, 74364386, 235204804, 291174147, 871474725, 196646441, 328659152, 794458217, 219140567, 983109918, 410771658, 212100872, 928428542, 930768154, 777841853, 451832217, 176482226, 855078956, 3954215, 109944306, 996594490, 682760068, 254709805, 500187548, 323244810, 852320391, 112777963, 268477690, 974538797, 939719613, 827816371, 630524203, 441245407, 268692390, 752434949, 667402365, 238271108, 719766357, 645335182, 684786740, 711433750, 983676346, 289554557, 574069203, 962169970, 374899260, 389968330, 122270374, 456636600, 597501586, 777938243, 87748871, 577784429, 292687394, 168654178, 936461044, 468774045, 640478400, 943659391, 138510994, 613934875, 980092588, 243859514, 574527397, 220078021, 967045565, 119146521, 773505951, 415921428, 820012442, 225526306, 145106329, 425413928, 353327825, 915406838, 836691784, 639509689, 948156297, 336892641, 501040790, 43779021, 994332563, 648736587, 562990801, 164445012, 962633852, 343642848, 59742542, 952262199, 193818999, 93176183, 823706694, 550704140, 935674484, 907752455, 135197166, 503924267, 675447761, 870206801, 545819644, 319642967, 359134571, 336264092, 253651348, 34774154, 81533860, 750765141, 200919331, 380655858, 682321194, 335388078, 538776645, 18960648, 637511255, 970649710, 761806918, 13543669, 147130239, 785817937, 987671586, 160873517, 760885892, 129231632, 760804437, 488982448, 584648918, 718530340, 576579998, 162744759, 731920109, 219101495, 701003079, 313713158, 63967031, 709064228, 840363259, 255686957, 953327682, 342412496, 642717972, 302551861, 468554750, 843587914, 383342833, 16638098, 13720349, 297642464, 86387039, 411993144, 993156471, 979735955, 494236693, 554003789, 713670897, 407274318, 4909725, 496081717, 475898855, 507393247, 241094519, 194789698, 806630919, 590958805, 395245657, 838836784, 15808322, 404783993, 189560603, 278165389, 718099002, 210011740, 65711379, 17649439, 580059065, 767355506, 586853065, 238831449, 931753061, 484807068, 983036512, 741016708, 44168722, 357346042, 5493394, 592630055, 148060147, 515227151, 663826108, 149563376, 544597248, 621623945, 312779433, 934542371, 219337851, 210741171, 360799385, 722883930, 199874654, 424171100, 971256864, 243560316, 940919307, 502221683, 268366815, 187371470, 552065634, 429424198, 119145268, 477290557, 543634369, 715934174, 206890005, 206297506, 101157100, 320426209, 548208348, 45567647, 825411117, 759830360, 445812320, 228491437, 90223171, 443739698, 718564554, 165735827, 197499849, 6946378, 886538169, 48044791, 836604267, 821990822, 55642674, 169484649, 944243900, 329779562, 573079742, 26507372, 248987491, 598331203, 166676307, 528951841, 229972449, 616615150, 787684581, 900773012, 337967721, 373047524, 768535295, 14636282, 991628613, 675804915, 298834930, 287104318, 870071015, 262170500, 398404992, 388502955, 891678918, 521092805, 915066787, 317773049, 83036089, 197798544, 500775386, 969772379, 594075174, 500493366, 95317387, 130966044, 676839221, 745830824, 256243594, 911832856, 28528393, 435100848, 140327747, 538373878, 321818811, 667073840, 87489906, 33889714, 97779085, 583719546, 108386266, 7012425, 561137572, 69687600, 52581962, 348408101, 58566351, 521940777, 279578987, 723989997, 591938809, 484677665, 81041331, 443773722, 106960545, 450154250, 78099560, 43839926, 210485823, 915755583, 193014886, 503630872, 683636492, 150303007, 609918491, 623024643, 365085016, 783787995, 956599355, 959798564, 396926969, 927061716, 302661158, 991283206, 438699038, 325676097, 700658186, 625204732, 957268501, 884024971, 556217361, 572329285, 813450417, 144116678, 273177465, 711250679, 721974733, 55037, 560425810, 765003744, 831122474, 437349197, 670084959, 681532916, 253124511, 266409886, 184660562, 230886205, 307545490, 832712428, 511840237, 896280253, 403087023, 508295630, 331961317, 115964865, 362208856, 316663585, 104646139, 626269402, 260487749, 779514470, 857654112, 85187108, 146829624, 751618215, 66280598, 120977466, 598179879, 256577577, 268432399, 350497732, 901693172, 793391669, 928007027, 698144708, 924167099, 959730954, 207911388, 678528331, 849546822, 673978798, 405589092, 603190121, 245080815, 384840092, 306192708, 822594857, 857623359, 90564352, 481595696, 153837389, 546755033, 728276799, 645740100, 954392113, 692731746, 781718409, 474849682, 832725653, 931675198, 469718881, 80935350, 475658021, 557085632, 266956198, 52541098, 44977883, 610583345, 878184398, 403883047, 694500349, 59740074, 269243970, 354950522, 948437771, 991228431, 80311702, 318219133, 733978304, 823841202, 855088970, 158260704, 60017533, 85616045, 787342924, 942472662, 883019902, 280394166, 101962880, 853836800, 330887254, 242155089, 542435291, 132953883, 933166643, 888287848, 399856476, 624714572, 860172382, 453175851, 696647419, 35788158, 718467458, 980287509, 428927816, 86795901, 104157656, 462847903, 646294971, 489935189, 4589707, 21179357, 115451622, 231883767, 463588646, 460141608, 291929764, 538446449, 204992908, 85952026, 820808704, 344321437, 265275427, 448080289, 311849417, 222830649, 943507118, 304878139, 307887446, 147375574, 123238714, 896105989, 605696221, 465899946, 408625445, 618541532, 345305317, 938253385, 997619550, 515877704, 605309094, 27545229, 916155623, 626532512, 137409524, 738587283, 911567294, 478402880, 263143116, 264780980, 758505833, 774041221, 748671352, 765359025, 385530698, 133453986, 710625131, 900862276, 460352360, 37260738, 344173958, 908711875, 969838342, 619009339, 36909880, 927784992, 856592927, 814509125, 234732489, 90423671, 231719638, 780094449, 206357621, 575298470, 853837060, 133617879, 502314748, 734516098, 28928374, 655548102, 756965208, 825151023, 840475351, 907225371, 578481429, 740220619, 140003319, 834669712, 329970110, 843252136, 82706543, 648645372, 18053831, 211634105, 349614072, 790542424, 857010188, 741607248, 199534566, 961826689, 98848117, 214108095, 573859655, 940139985, 918025471, 883054936, 148103209, 419250230, 524802159, 321424711, 427549076, 487333998, 768791231, 139538294, 130508058, 177784294, 783063344, 369881724, 562428625, 388540770, 417687453, 948152912, 293656884, 199945031, 75681112, 229911882, 876995397, 381147918, 114435562, 369844943, 352696420, 323113439, 385283489, 168307375, 241710232, 384419639, 427591777, 377000091, 986235792, 145592139, 293049688, 968450186, 220971613, 986038855, 80358596, 441228721, 195586318, 205944371, 696340117, 302264153, 261155225, 610932349, 458056072, 241915485, 471439784, 745907479, 509654962, 352949282, 480217807, 243989334, 741530008, 805548794, 360360460, 381597484, 263500177, 391965886, 80581700, 629928982, 4662690, 886115978, 824724532, 500117977, 855244874, 989165362, 77910409, 246374387, 562813613, 673717413, 547139715, 948491318, 513659571, 721499644, 461642014, 100226827, 79317807, 675262078, 320907959, 200233494, 646313386, 188165496, 520703305, 232881796, 325561543, 387007700, 789559418, 925627643, 798511207, 30427613, 600564848, 508910299, 212197616, 72268154, 244522234, 648643460, 12381399, 950309173, 108156964, 27227019, 716756931, 768715788, 867636011, 753603699, 318262591, 790501508, 595085679, 368422547, 293655662, 3653458, 386264311, 837399085, 530783884, 445095311, 513293857, 44272413, 850711191, 84003452, 149206403, 948018892, 103430639, 882789238, 93635897, 197920230, 183156049, 478784916, 807731513, 261146787, 240062518, 464975835, 720314862, 339996154, 532009419, 276630781, 707639883, 947573766, 964676397, 64360679, 132535474, 922747407, 382019728, 4158639, 453554764, 824017149, 373402904, 468539241, 953241253, 503004611, 79573619, 823799250, 752051720, 353042331, 764258967, 323706548, 538963018, 914600413, 294907980, 829853138, 109459572, 944308035, 710088462, 744251712, 549731775, 655124640, 490089228, 93282694, 95910649, 653053899, 139824374, 781308866, 484316251, 165856283, 301764915, 311042789, 541316652, 544821085, 411488380, 441114081, 419679537, 532736238, 8417421, 857038589, 336917060, 532768139, 767272857, 841599110, 416720080, 119011821, 583692629, 680977954, 846677127, 434427299, 958326906, 10355391, 958711423, 972852230, 969321173, 960784448, 45096185, 804297361, 594301739, 940923204, 40883460, 179064851, 186669334, 933191551, 724649622, 819273363, 513892754, 455866297, 709693937, 51291409, 155181773, 554326553, 859513992, 335708435, 283544451, 311082736, 216714873, 203028285, 465205169, 418992058, 902879683, 326001075, 700030276, 708236554, 97434567, 604659104, 59428210, 640520962, 110971826, 466255660, 61327164, 49723677, 209360970, 934634064, 68641701, 838265571, 811395181, 555424082, 996220619, 807430207, 914377937, 859483573, 808038, 58373877, 541831349, 314507287, 433915093, 98670912, 275591845, 844821722, 228463151, 98110359, 738773690, 559917287, 929140371, 761069793, 177969785, 850988069, 548777573, 777188576, 556696342, 124788625, 444606955, 536852177, 627484472, 276046213, 460494594, 631556027, 711923941, 568368559, 309407348, 263891612, 63472609, 984605712, 534201066, 902122596, 32504966, 314258977, 521082780, 881409384, 93677311, 469198712, 838414175, 744599058, 281971605, 908326504, 577362339, 983285655, 34056791, 448782991, 689648808, 972369885, 892052156, 8204437, 144074358, 431829462, 986338249, 416696091, 382219672, 417708002, 16533252, 403766466, 850986675, 355475304, 71886947, 925511395, 400563458, 782476639, 792735568, 199051161, 459197410, 512072775, 449320771, 687727756, 793774837, 13089277, 162816024, 45403030, 184437037, 309631688, 93010271, 840010969, 944455884, 537805058, 16221505, 727231833, 364222866, 125800660, 123133007, 809832475, 281824672, 56263789, 695221072, 409219543, 353860238, 404500306, 222600486, 765497219, 976495174, 876836668, 600332982, 199834678, 678209539, 780772421, 52805773, 187669726, 970132079, 297064500, 708923583, 480432351, 894960250, 361072827, 849685047, 408855852, 241957730, 747106440, 749358558, 738195232, 261710143, 904877415, 361532832, 784471776, 803166110, 271467535, 251648826, 904148389, 825353293, 698393720, 28368791, 513838731, 837638674, 98495461, 662750811, 985243145, 473975577, 574267690, 631177856, 280576507, 576932878, 812081291, 583860818, 956986056, 769520494, 57357581, 861202827, 271091117, 210637295, 381753748, 248494436, 669761177, 477154533, 372320734, 104282900, 458624037, 85056851, 740601157, 228405574, 795241401, 210602983, 896699939, 820408334, 89393630, 711710016, 442731887, 213889562, 539249479, 416634408, 16549310, 59975115, 206251845, 891119968, 846489636, 366042797, 90107387, 423074900, 289322318, 600497659, 81564140, 362674270, 651261524, 744374899, 889349048, 752708868, 304069712, 856272391, 139740294, 77396740, 129132043, 81764345, 557298631, 87536252, 543583379, 99660708, 514818316, 442715551, 352875343, 301006617, 788393120, 969835295, 204563056, 855567606, 844374805, 500386279, 579577869, 13909189, 129350605, 46226570, 843264732, 598870146, 973370453, 351387933, 33026696, 230456549, 548926136, 721132345, 512529017, 267751239, 348508272, 928951252, 787943627, 599339489, 10403558, 595022849, 53265472, 725534955, 935549422, 446113458, 842677618, 343079407, 951464783, 425363366, 72959860, 208740958, 492555949, 390772075, 638246312, 565348504, 942151115, 305911046, 418801880, 46303523, 715049660, 632222235, 418399574, 784766048, 182775974, 282449254, 478193572, 359395814, 15060519, 467381860, 726460706, 494653739, 808798049, 836069017, 943892027, 424671215, 685235744, 459446177, 147303095, 932056714, 963414050, 914326872, 704268290, 274439332, 365427230, 714557959, 977030340, 953662526, 28559195, 796557677, 336184469, 481488133, 387629258, 420046740, 511980847, 648212627, 168356034, 935326079, 383553015, 41673701, 875757836, 98400962, 877102664, 844751057, 871595430, 995649282, 609278500, 127012737, 800042999, 239185519, 32801558, 786623400, 110721410, 341191607, 745934130, 32895144, 308299999, 162103632, 624717535, 861593700, 32360386, 71417875, 816190877, 246651270, 254016597, 861377095, 832350297, 998075221, 942864102, 354413290, 378886233, 12014078, 432457688, 689204491, 209402328, 563724841, 16142351, 298207130, 268082136, 129361704, 767762209, 467867042, 123960545, 250086437, 193752987, 606847199, 606843955, 763107042, 716180998, 441171523, 854692531, 984890636, 110119178, 116809882, 130940412, 92811649, 705497129, 831350167, 69742479, 485001877, 391730579, 886901526, 426310585, 704366734, 496942142, 861743010, 632495817, 329577983, 728613313, 62575999, 982381760, 247675388, 876153322, 503571392, 151116885, 945478597, 951531648, 786005294, 400317860, 483400281, 378719988, 750758304, 542125797, 552361704, 863910817, 54871094, 247950829, 779082537, 523813233, 865513573, 110886630, 381381289, 700203104, 617850513, 751799684, 895342094, 5089824, 900510310, 161266790, 865651884, 888896197, 428252889, 577956816, 955434790, 737990548, 768960710, 361100604, 656314791, 525672201, 558709107, 468775188, 719928859, 871286857, 25745368, 895672328, 188334869, 472852782, 198041854, 458949807, 906826230, 733086455, 178490707, 32434452, 928775302, 97496413, 336625062, 294095431, 150799941, 225112841, 959855486, 677542804, 371754896, 97193901, 105157270, 770170519, 715951811, 900169438, 310607009, 168876515, 530983456, 852756338, 764493512, 558965616, 335987029, 218518205, 125570171, 864744884, 142030080, 55896813, 584496733, 835955312, 360638546, 142211588, 622434277, 905933284, 839885329, 303630648, 489728855, 905482527, 404892137, 492154089, 514697640, 44801417, 869850438, 137144859, 892652423, 690742505, 322826783, 755220610, 958707655, 114148952, 883972277, 557075452, 53022442, 384661055, 621569060, 113257619, 153607698, 463591774, 648394085, 713913366, 770664750, 739444011, 223946219, 451350179, 50993595, 350095102, 234091414, 933223368, 632770175, 505585308, 111889541, 167632120, 532156117, 832045339, 228501123, 580829943, 250468819, 977347888, 62279235, 775251556, 935918997, 131677597, 106443939, 804187392, 322792199, 975403532, 290401832, 147439427, 432092689, 91848580, 827559099, 146362026, 268904369, 793541634, 12375208, 805019857, 777526320, 972203636, 623618988, 842540159, 826242727, 837047296, 913417423, 834344423, 691339714, 947197403, 91011554, 782871234, 261516888, 749700310, 849953303, 189352005, 927612481, 587840362, 281845380, 72279736, 334948505, 89384012, 518335088, 868839682, 283729253, 946501565, 673336873, 32584124, 361824791, 627396470, 445296617, 175188607, 784424043, 855124391, 90239879, 88147633, 576978576, 327340861, 881628692, 597177022, 640584627, 764793931, 817156691, 946219631, 408440068, 592180837, 760408893, 579248212, 569242453, 147217163, 354723619, 523562077, 82549636, 309156815, 860766734, 167918199, 948335870, 258608818, 511549867, 303952799, 527153844, 385868446, 712087958, 615944940, 533384535, 686012996, 235863891, 206701712, 112005299, 243806868, 985529698, 655042428, 168140216, 237405962, 437025093, 74271522, 535091336, 619451829, 312247065, 812699805, 735887301, 376642905, 579227400, 473016082, 277194769, 414743460, 388689742, 116625584, 626277667, 535348948, 668806827, 723482003, 714283550, 178982984, 265771624, 774405706, 886738151, 627998744, 705865014, 73916256, 29167977, 42859548, 843552176, 706636446, 156908685, 485552165, 626633699, 622269284, 16542431, 330087495, 272823429, 860580175, 770809617, 254174259, 112973419, 102056743, 434733159, 444024277, 938586799, 993730061, 828410634, 153988922, 272488844, 501123519, 73331424, 773306210, 665906414, 140518235, 388885764, 487820861, 461528165, 14432187, 474473328, 631328984, 553238195, 968726655, 695990473, 186347049, 659772661, 234409157, 113240650, 856927851, 664760881, 576788821, 214072345, 548407003, 79275790, 573863897, 482996552, 736856149, 701482043, 35571944, 618023690, 125413714, 737904207, 9545332, 943468619, 732811271, 285012267, 811730951, 967935685, 161538635, 115415134, 935598751, 757283007, 155951474, 980195075, 672789823, 59608319, 145215945, 543637188, 140079538, 427023744, 987471845, 627597622, 741691191, 231712115, 782337120, 483034853, 553056267, 23048608, 951365276, 358340854, 752055490, 24436714, 287858266, 387787188, 100124790, 198427440, 750189213, 479634149, 702035191, 452242205, 677267618, 293381142, 320132227, 671327755, 752457936, 256700208, 698970036, 399808067, 383153331, 797190351, 479016342, 381643933, 596046359, 204892493, 970073139, 685776621, 225072213, 705679549, 292556437, 734878876, 783700416, 167980971, 91030645, 550919725, 984196694, 888558342, 77259451, 843389745, 148510001, 810561667, 352385419, 264017696, 541673725, 854373294, 523735315, 909893137, 425665666, 642444432, 133370654, 942190481, 275836365, 467218788, 984501774, 287965542, 716432354, 642733913, 681781974, 230296992, 798908150, 405767795, 369361652, 633690669, 928473618, 703943565, 284726161, 261385427, 581326725, 530814415, 707701731, 47045297, 923796790, 783961096, 797548195, 659103126, 586544010, 86867767, 501461072, 940790354, 366452883, 823529163, 662371752, 638493052, 93976492, 920741895, 807477380, 755726501, 755103113, 739106680, 569113669, 856156431, 101620912, 277573324, 317144497, 19184998, 944691150, 724884778, 670083794, 523375474, 985222209, 536563090, 15739990, 512418623, 372750620, 181661387, 170059476, 349945128, 289480921, 738107659, 395554758, 797448065, 309046342, 189040315, 969231351, 633683793, 363235899, 106198065, 444246752, 10167872, 602744951, 876607397, 307557855, 489392577, 30542642, 470613687, 855609874, 295986835, 298704463, 670390225, 129706562, 164713893, 829056586, 490198171, 953946998, 485035503, 172319069, 55017193, 163209007, 194217984, 816626849, 111569648, 725663891, 584642480, 896757976, 321281699, 533379087, 908599850, 393449777, 544834782, 644050990, 277340307, 497685075, 85210401, 66402209, 581621940, 176423685, 924865200, 34059182, 681174295, 32831922, 407527180, 632742228, 936649505, 459039848, 952376672, 69640530, 408844044, 432432953, 880548096, 210333580, 12877735, 45520988, 116371359, 897870965, 689974380, 845576638, 62616220, 24922123, 909424217, 413537952, 761696669, 675052655, 251612807, 932920284, 384695044, 999580610, 298445210, 70981498, 224027125, 989337455, 402892397, 155907885, 576429237, 567961208, 948009940, 228985444, 282187497, 108453580, 430145299, 490902728, 450089398, 960094780, 595781672, 876152259, 23081925, 311657041, 79356886, 970117842, 870271732, 294943948, 502873153, 846816634, 435336550, 633944495, 351252423, 446284012, 609282338, 123137096, 63767390, 923523956, 744050575, 694996603, 833869229, 530201745, 285952893, 414672316, 968128283, 675772288, 278838747, 9591888, 732795090, 856403288, 954297130, 432562705, 167190754, 181190980, 650133482, 252250295, 518065341, 986614535, 324842774, 378565390, 121260217, 292509033, 252044798, 712676489, 717488985, 280193848, 324083506, 178518639, 646075772, 456486588, 790070083, 416710164, 976775954, 776119938, 324264786, 578927720, 296488932, 145213821, 995771308, 989489942, 48847422, 158021905, 562325311, 850771193, 487297772, 378343528, 400040170, 372408700, 191092547, 934360016, 775573227, 460897371, 307245658, 707450617, 570977044, 35183798, 159362702, 440395753, 123263704, 733948084, 205535179, 492323221, 633637214, 978888679, 775084964, 411151161, 321291991, 758429186, 773207327, 811879996, 906198593, 298274757, 18765069, 181228865, 293806856, 793093466, 642976204, 261657098, 667793191, 489517081, 544384856, 658049532, 903857937, 878871346, 436406562, 325636406, 153118748, 377998296, 328312332, 539038174, 228216800, 120496672, 662657508, 273730805, 65154624, 627070384, 218115981, 367810728, 429069879, 490099152, 305915462, 980668356, 112044564, 683613254, 627509267, 413726424, 401948651, 504595246, 150220646, 867540749, 594001988, 40534424, 590910250, 487616951, 996148673, 115165730, 669571913, 662474080, 404690563, 849410011, 744262635, 999741158, 266435430, 282889175, 873866149, 768530557, 835224214, 710817994, 709568644, 654335666, 228167294, 114579060, 297783723, 572680194, 758731322, 825619182, 388040712, 415586593, 348539424, 617190225, 236225053, 225232211, 246834930, 246610129, 284090912, 140061547, 514527810, 995202047, 714908424, 274171267, 998200584, 672712062, 20811673, 221324657, 833697338, 29328136, 171223113, 666803216, 940415419, 660754483, 810899401, 144910113, 291797161, 711068011, 931595736, 915145571, 243856052, 914778223, 661961531, 504571032, 252187672, 862948203, 306035347, 57502512, 445690104, 42992221, 464407845, 880068679, 713323302, 740163053, 680284942, 325805923, 253320458, 968814299, 419556736, 518052949, 124573430, 131502129, 360318128, 451266533, 158053823, 438817686, 286619456, 586759653, 342810445, 652783885, 557141792, 785044721, 467896136, 68148241, 824319785, 145473269, 618606584, 347022947, 501312734, 585681224, 387762849, 225685076, 77889869, 952815465, 395904948, 387906598, 564851627, 921302912, 825997997, 825608716, 818662076, 245511717, 406744479, 827568578, 372537801, 580276131, 774592737, 14249417, 853143475, 42862655, 599372268, 814733011, 878510043, 407542108, 739460972, 880510370, 606667687, 651130034, 688723711, 876149076, 317350783, 707298940, 288668717, 560058000, 992341611, 760370573, 115863573, 119209796, 587896336, 854870360, 836376688, 988556618, 426514265, 201288412, 646255418, 669142241, 544436042, 978431667, 165309312, 59415075, 78972054, 706027151, 909292539, 66344835, 569995010, 71131980, 228195810, 15388327, 982058690, 277690889, 952786608, 39248652, 263556040, 497221962, 341422366, 717987899, 995720030, 573716470, 646853559, 822511606, 316853491, 973443117, 992097401, 820699969, 130835156, 985540141, 763091205, 432085572, 737492438, 917157444, 191965149, 511515754, 795172126, 50357409, 967289196, 614238672, 800000152, 600156021, 697803609, 262682861, 240250482, 208478661, 478419010, 462834072, 197747174, 784868907, 965096906, 960238158, 23706463, 256220126, 248394328, 476590957, 224374033, 937971394, 46023718, 247444920, 357395029, 542433270, 689642803, 98318593, 284385586, 638352062, 163442987, 129690411, 427405030, 121424371, 953415415, 125600241, 954582571, 94578720, 99949010, 458280821, 931271578, 698771446, 40697530, 263930680, 97556118, 675687004, 743752096, 97903618, 971683566, 348916609, 78023079, 944718380, 877349262, 867900896, 419391353, 964512253, 839230219, 530259032, 595597385, 976582459, 357757219, 966150278, 333954106, 441587737, 9633202, 774242643, 256475150, 715768176, 781645409, 234851506, 821329961, 474461634, 174758327, 510200202, 236124549, 418007866, 328105861, 580348196, 725738291, 809677150, 614039806, 335393666, 983100359, 139989895, 475044743, 692657365, 520835083, 342573917, 654269732, 299721366, 694209414, 464424211, 836501159, 922617536, 569928885, 290031296, 810238617, 80694227, 486347178, 571921885, 140967871, 952834802, 898304442, 942060205, 140757940, 4396762, 343505304, 891129786, 468947952, 751782426, 351272163, 86759978, 237062393, 19731432, 43322749, 583107661, 284280065, 124354840, 172866087, 366024315, 198867104, 407720565, 973053843, 611157336, 650720627, 862872152, 712932864, 858771270, 482813488, 346369107, 214348714, 977933244, 145832539, 441342088, 394807965, 445604723, 369906734, 651116861, 273530640, 447222482, 925405966, 506201626, 678176113, 386279889, 114844337, 14940655, 897842130, 84271100, 942005801, 236107831, 85970939, 372062415, 846527570, 885580419, 708851587, 979093625, 70251215, 98042589, 871404009, 653310657, 209712690, 916027020, 96730215, 458967636, 898556875, 778103747, 628874881, 928174846, 821519135, 234626098, 434557166, 645563435, 788935124, 350203709, 851215072, 460255709, 593889212, 949212633, 377557987, 823282845, 782568341, 577121922, 278255262, 177764150, 4812924, 80184798, 412332489, 65150293, 877430578, 531388606, 141750824, 990205093, 176392502, 683826285, 664025508, 329845677, 446724269, 229905310, 257498111, 549125840, 263672792, 764556863, 595460040, 285184984, 564815935, 803085865, 732711567, 57922022, 192079352, 520464172, 328349142, 415804902, 744670255, 178682715, 760630010, 534962483, 189138633, 109080092, 21065403, 821871380, 521338913, 533489965, 568170088, 948324832, 663535699, 276353164, 26361810, 665682108, 196204676, 876431449, 743403818, 243573841, 642088557, 655003385, 752225004, 892029880, 281429157, 163914211, 7947986, 161373021, 948461072, 145977161, 878496221, 284390198, 23889544, 461172068, 309401612, 529850745, 539242679, 790979179, 747938635, 445462133, 191293434, 224038240, 206523791, 219817113, 161212593, 195173858, 474105691, 936511699, 638162569, 24954454, 292498389, 71693064, 568206636, 800462886, 591376719, 619359815, 734386811, 58900354, 509824595, 531704805, 758979354, 769386007, 223150089, 714453580, 69490434, 559269503, 148210413, 474038469, 880847902, 586007874, 99366844, 325799240, 417528363, 118240736, 660371201, 193169020, 417154883, 384790597, 482950262, 159096272, 456593945, 407348294, 509132312, 167957812, 520457347, 919168607, 879958581, 262747769, 358710461, 572357563, 914498113, 520178348, 848996228, 331079154, 599051506, 223413789, 348028363, 589267756, 864654318, 147918258, 754894247, 977673563, 187562306, 469500508, 553788294, 887941210, 384266625, 408874245, 870639593, 109581570, 845073637, 187670164, 265106047, 120944107, 550175034, 702894613, 763661370, 481405445, 432237895, 185732460, 717181288, 627966180, 956924053, 661285244, 735537525, 217994754, 999184516, 324294197, 556542352, 674438125, 327490178, 374202779, 445822574, 474268684, 35672818, 991367097, 222569863, 395687724, 815097772, 624779928, 25991784, 94906234, 968611538, 609390447, 616378975, 988301874, 539420313, 15495959, 442835325, 876906421, 865102677, 70064784, 682695663, 211299829, 840434483, 171276167, 96713128, 453643639, 168310887, 649361970, 955243680, 398167830, 507700870, 557123932, 611907088, 943547971, 852331015, 154784685, 807369960, 341222989, 87711037, 655584642, 604256770, 145272845, 416721241, 902675182, 377194146, 339582581, 65876896, 431852465, 49559003, 221183219, 115350205, 104077462, 108267555, 155648646, 263125911, 451473218, 798125035, 687890402, 215474206, 175969311, 262206424, 464879657, 766144965, 888053398, 560720181, 880476425, 600434222, 939692665, 217374780, 495950657, 424508428, 292906643, 705142473, 256842293, 118570217, 423041321, 115684420, 650092344, 478687, 81422716, 415987811, 707877633, 114873587, 469495586, 794616738, 227978793, 544585563, 721260284, 549615655, 841397626, 393816062, 340569946, 379963210, 942356782, 321255093, 760114700, 332190896, 202859290, 878142067, 482873794, 450089935, 739892879, 816361032, 554417209, 143917780, 133983688, 84880823, 683007104, 790547066, 408287895, 16874088, 355975316, 153364262, 785632860, 748362072, 859815802, 966630581, 619179294, 878965892, 598197903, 381858407, 353375976, 157652334, 648438114, 284716242, 776400674, 852245335, 223891426, 538196640, 602935833, 534588093, 784065106, 821973409, 314305913, 658164349, 107835520, 477719140, 254876757, 927418749, 85546438, 100884338, 549251270, 447780474, 311567295, 913033239, 692119892, 803780163, 894817357, 28816769, 65062021, 444163897, 777227807, 116580817, 599285337, 60151638, 420700855, 9523766, 312222150, 45561148, 282660813, 807298151, 704682972, 337432521, 824770658, 75861957, 189739997, 145321642, 112267731, 651538085, 544226612, 887943974, 344859412, 233348303, 135598968, 252415401, 312565046, 186139132, 424734387, 653400494, 587458979, 503032037, 866360168, 465773200, 461529342, 765839254, 201294086, 875276206, 654881965, 607997676, 170352775, 95128957, 113331549, 764434794, 546729678, 526932889, 100039741, 308176626, 554688545, 144117961, 870654372, 169223197, 201370731, 481634042, 752590966, 320683042, 365601366, 821074986, 646752120, 47930933, 986023279, 805400638, 832049012, 136996525, 348430656, 608888548, 326666096, 669753769, 106429026, 278144186, 884763652, 529966378, 650821924, 905512594, 634031621, 847646987, 87528386, 243729420, 561629169, 772369038, 292561750, 141968994, 914785124, 551092004, 973321174, 764724280, 801147370, 540007584, 883113707, 244616069, 123316565, 768515461, 371106787, 830955850, 636770889, 990088853, 263953464, 590981093, 186542372, 253407805, 547742174, 454192608, 671854935, 636459568, 677472160, 78906982, 634541200, 335314598, 261952568, 512948809, 419128998, 972891026, 779079432, 215578411, 822610446, 670409799, 618972546, 879959460, 358588319, 302907942, 158146136, 138141859, 63094968, 399675839, 946104936, 710577542, 230367758, 260027637, 832535707, 548516239, 70073, 143161632, 367223617, 199165337, 58152904, 390890991, 411616450, 53703083, 181086911, 956757942, 676854948, 891463250, 577797844, 726929059, 455580067, 496609229, 507613274, 53667014, 246604097, 298130774, 993433111, 2041514, 579960565, 189486631, 965569019, 289705944, 379738587, 925665876, 803732073, 413769331, 754564516, 785485660, 531770395, 687539535, 752866220, 602097646, 999088784, 950078368, 64985076, 819094741, 150907660, 702440255, 5914298, 81998126, 742438503, 448305997, 129628802, 757105286, 804447027, 360646567, 944271255, 163828671, 428814193, 848325446, 167341294, 452944515, 565095710, 657350312, 8700915, 848031595, 760194469, 767320595, 246424076, 480017206, 772185995, 602732851, 92201472, 131044367, 431288657, 548879000, 362561915, 267325593, 762735120, 314351269, 781325563, 329229161, 89254101, 323422317, 876553106, 254131897, 134342312, 883796673, 863199224, 564342237, 141519358, 560645897, 165755583, 129949333, 567625691, 86872084, 466881773, 25581048, 286580131, 332993687, 234384300, 643874061, 473666082, 923384424, 474070295, 686161955, 987429690, 661282969, 541679648, 953822416, 694789498, 889375458, 880988419, 736566950, 928425764, 520234333, 984318597, 779043482, 568689481, 537378689, 540614354, 998312876, 53950410, 77751610, 23976604, 136617974, 418922334, 587082027, 102219392, 980307587, 963210844, 179391647, 969264645, 3537189, 108292180, 460407992, 417225901, 107854758, 117459153, 546742090, 291619681, 296343212, 90994037, 167649434, 153170702, 19123246, 630195512, 674273379, 553955290, 98394680, 420776427, 841817365, 268888308, 309993011, 85281870, 804839893, 461717205, 417579239, 639581259, 259839340, 858581526, 468781549, 368497366, 634075790, 348678508, 253079204, 653263179, 217145130, 537418375, 447825447, 772061536, 184670494, 876609997, 403529855, 694685276, 522974423, 570892066, 739531051, 873396109, 347929759, 697131149, 211618102, 84772256, 586315600, 690618333, 676390688, 727036410, 281115495, 365336359, 626650208, 579105739, 379248204, 132823662, 68020651, 276726685, 652257609, 462961917, 445003881, 484481113, 637858883, 941160872, 359661280, 102407702, 853437586, 744020082, 284780704, 842700628, 936219422, 785467906, 616864699, 234249350, 875040613, 921355863, 330516105, 183347039, 875325023, 66158510, 341748671, 390908692, 16179889, 211744459, 419989983, 863824685, 406975339, 772762833, 130937711, 165103091, 621875261, 503076607, 832607736, 636864382, 217081699, 693401482, 278116485, 800814465, 968888080, 982183281, 290536285, 55765895, 526026007, 670234838, 740155704, 64347297, 856498398, 939926516, 225113410, 58497164, 466617692, 66502001, 682973865, 495254600, 645889211, 866164714, 871290849, 677804892, 185123987, 89114926, 780532420, 34795321, 168815849, 376541319, 698240733, 158412775, 617692212, 470293840, 505856026, 51850336, 716170613, 147368617, 147101198, 70269559, 90961766, 939716974, 699692610, 539337367, 647356853, 650276517, 796001890, 700452090, 558969383, 81372980, 158759398, 929822156, 205165543, 28450833, 294960826, 813861405, 965731730, 202594924, 111358493, 393326440, 7185994, 385073903, 512067275, 666302587, 657729161, 502854822, 429520197, 588867876, 28695666, 841969640, 327783792, 167746135, 873970721, 403850063, 939179718, 350583132, 8629474, 486267944, 165301276, 308148350, 948704043, 466150177, 879220459, 509605995, 428041356, 539386724, 830887766, 616363214, 37915730, 945019554, 367315247, 536631246, 805419893, 773682948, 284720657, 172526844, 698660463, 730506631, 700493587, 830773550, 644221350, 627570580, 717322290, 200120174, 388350489, 711780258, 370453246, 400759927, 419398067, 783305292, 883991004, 375681099, 650553570, 465296680, 373381527, 110022605, 143723485, 45861137, 775081484, 699965359, 691624739, 396526411, 382468976, 93591119, 112285612, 963718797, 529129098, 921123853, 190343769, 336188576, 895782612, 437573838, 910650446, 634531879, 309099821, 949862018, 282410732, 318520479, 637763520, 768360643, 760841865, 44698153, 19282334, 376067380, 513554179, 150091284, 728871481, 993174542, 829896713, 64348515, 713035672, 823844371, 824475122, 283368408, 670114663, 689500507, 17406217, 615173336, 806126800, 517126629, 901733763, 804614924, 493018895, 153616093, 901896154, 595016871, 666923121, 89075217, 857270093, 527172346, 34988878, 592210126, 921522151, 74701732, 538329392, 51164318, 16163457, 631053666, 671955383, 49307346, 539219927, 636449054, 618507392, 649051313, 996473574, 828145062, 491485744, 806558238, 305601820, 850263451, 250743131, 942937528, 652957440, 865661549, 386894555, 616819551, 68548652, 717388706, 726736593, 678492848, 607923578, 749324837, 529780451, 170378015, 443063544, 565175347, 939015666, 646418357, 208155580, 5395807, 975006489, 444464701, 204904203, 789950415, 721100881, 867507122, 559808789, 199233123, 284910081, 894897982, 599243896, 464401418, 394367024, 812090438, 924866832, 176322088, 107643780, 229624777, 985471644, 322547001, 105550243, 729222007, 198216437, 93052971, 234930359, 80069631, 424936830, 298875956, 622463395, 636153905, 751545351, 854551109, 189789074, 247921293, 253632433, 348905386, 676171666, 851136159, 864957547, 895368017, 383357428, 530528849, 755310263, 922552184, 177340700, 515144470, 647795756, 691751072, 744542700, 8325814, 729123985, 899362873, 755473046, 670211992, 774339609, 217359827, 954320292, 42654099, 701442380, 705203281, 69723130, 965660386, 695111753, 11543815, 297882276, 409818290, 297614073, 865001725, 663825756, 193010110, 846789283, 226845521, 993617094, 728021265, 506285535, 341524701, 274176920, 684817769, 136846014, 966358821, 852611477, 712473288, 438485542, 732378049, 464627266, 334581695, 271649184, 166076673, 124665054, 176135245, 700986035, 674831270, 574937859, 671122788, 866867779, 359577133, 375561133, 372959555, 976091493, 293083865, 867107389, 801146661, 472095460, 73784027, 781816385, 417702060, 728455985, 948986205, 917826324, 601161138, 638594944, 670261364, 975819711, 421135317, 754412364, 356599263, 504183330, 154950044, 229047465, 789753100, 162141517, 781169357, 715615520, 410125909, 891892307, 899733982, 814526530, 280982670, 253729319, 734309455, 644592142, 246349658, 651233948, 743739621, 196396379, 61126450, 926959544, 824227415, 971890373, 553123689, 769771820, 215801445, 802636033, 453802478, 412030076, 867737018, 150873651, 717435226, 17899950, 104223870, 58064677, 831089341, 617250650, 532048888, 991822598, 392609392, 200479213, 148154721, 620493803, 658479535, 767292432, 724035561, 552004325, 309211077, 788909022, 216335767, 169596399, 478108606, 227811016, 361504031, 705163902, 973310810, 537101912, 666213359, 629187055, 17034872, 753103420, 367183497, 455796636, 857155911, 771365949, 565414050, 495644373, 106993070, 313708082, 626262567, 375885722, 344270872, 466407776, 929127914, 341773476, 293611856, 707641972, 410186709, 580936628, 842214877, 952939427, 765729257, 982438844, 79087356, 889424733, 548807415, 942713014, 197646645, 157216701, 988243884, 6658601, 687499237, 388356047, 25956727, 663695463, 258435260, 136771014, 788427198, 792033617, 664457599, 805998590, 537267187, 703666324, 887665170, 259575245, 97167602, 775000992, 407164959, 621949859, 21531615, 788223387, 22050049, 833967320, 451079008, 381438220, 269822334, 38892302, 274044285, 292781704, 669298610, 69655694, 928730016, 212717927, 740965042, 937215890, 965607815, 301160247, 440632089, 453702982, 742016466, 877849727, 680670760, 300177201, 759908472, 244801623, 734136579, 843549512, 416774216, 705754261, 822043809, 524314274, 661960079, 116690293, 31456493, 231812490, 183332269, 547657161, 247299342, 866718641, 731780924, 977192700, 883803699, 606372260, 243674951, 326431587, 900802779, 733433385, 493777812, 480044155, 262813524, 112113099, 778510805, 812248169, 929283942, 183640760, 879289515, 923311505, 670480046, 411348416, 431646525, 406539682, 224921039, 548792157, 96619452, 550002894, 559719070, 541550460, 696682192, 665836168, 944012478, 564146945, 965544783, 886138235, 221825410, 818232054, 148078289, 309624465, 799078717, 118966389, 445042186, 107069427, 512920322, 652525061, 873343976, 778708725, 160207625, 641374309, 990969728, 778586346, 383774391, 433435144, 754974216, 628614983, 794596427, 413435697, 209739781, 93743773, 754762897, 711347597, 287170475, 352575564, 241468421, 81457984, 112780698, 713274307, 427532908, 781972962, 869491542, 132528058, 42069396, 167587690, 820016127, 608128319, 761919078, 212730485, 195662091, 145925389, 9619831, 973409620, 290829216, 463967874, 905202829, 547799235, 957403708, 702539648, 120070812, 402720886, 229537898, 271629650, 832528678, 667399260, 789639932, 893064444, 267121203, 918096836, 843461311, 904234995, 718286385, 532003724, 816929249, 231474092, 173211118, 527289646, 822203489, 702347456, 718896434, 579890359, 640001659, 992640774, 618599300, 990528324, 319737857, 843169027, 198604803, 247117681, 32796683, 26250709, 394814788, 321227484, 538740392, 224263971, 967546836, 670176087, 609684100, 844590076, 869867052, 139919763, 356186615, 973517129, 5935616, 497550043, 823020008, 222225402, 475459449, 263068301, 558682791, 72498002, 865235819, 327218464, 682527376, 252096908, 335141455, 590329388, 433920803, 993890305, 215499212, 725196738, 693087688, 665381554, 235701806, 964025764, 426173808, 721983259, 629106928, 90970155, 198364723, 336425338, 94927875, 609780647, 738918065, 294126189, 943330015, 876336855, 903523405, 486092767, 851836850, 266324640, 76425524, 95390821, 232698339, 850776374, 81652541, 523917050, 115453653, 478790546, 471534988, 67127527, 518195099, 80143322, 940272339, 5570953, 46867873, 665230528, 144861123, 922412156, 848146734, 843396257, 715354162, 94627188, 330602637, 638834678, 209680566, 884449389, 730794484, 537308952, 921537860, 455991439, 728270331, 98002515, 36721525, 951921200, 425805932, 295405649, 822746738, 394913043, 374039960, 824707932, 293998625, 30510692, 760642252, 99599713, 373005559, 425603755, 749813846, 865472678, 375196563, 400233444, 169359547, 751885915, 279466416, 543847871, 746081041, 195207486, 194817839, 225903551, 664395554, 617270189, 323063064, 903197200, 400553190, 741906344, 993272937, 790827957, 180231221, 774629993, 335381038, 205433661, 543385511, 456383563, 752807646, 712990918, 118794494, 540760145, 837467864, 330691924, 260358847, 534693748, 475662793, 368995343, 748998893, 27284041, 338262652, 120287305, 947906682, 513435132, 491993062, 148146822, 280428823, 797296597, 753546686, 579370355, 464994663, 994121519, 86023253, 733418867, 835626267, 995550769, 975760171, 932223239, 663452360, 302579023, 308126213, 135207507, 424817292, 523826107, 40415624, 980446263, 595060497, 117891420, 450638368, 834275208, 144927043, 553778272, 625861066, 454392580, 442615962, 688277727, 943883859, 196560995, 831952370, 554850407, 528239868, 735019192, 183345709, 966498877, 69608795, 242298871, 637005666, 256646520, 983355439, 394078933, 637614573, 745596386, 195172316, 711909399, 970696639, 508703053, 430778211, 401175207, 497841106, 383075367, 555463272, 116593923, 529734547, 961374336, 990915564, 759247062, 695889662, 507529886, 325200507, 317591954, 717110872, 578601856, 497140933, 353904339, 615463664, 299744732, 537512347, 152576611, 389649435, 763687651, 632832188, 808416219, 998830633, 64093807, 433875813, 327499062, 905671613, 22866802, 318555082, 272689315, 793622792, 933050357, 146654617, 793473262, 903923589, 751898187, 816718091, 702073814, 156354311, 604622401, 843226716, 541766040, 778566633, 105440129, 731867315, 83721929, 92479158, 110372375, 977192522, 4591734, 998098553, 427280241, 941491174, 691160114, 23072657, 115846431, 732496556, 991270523, 845738292, 821484251, 528069290, 564743858, 966854811, 896797595, 219803779, 858970115, 576131070, 416032181, 785929444, 351023767, 69100651, 556880069, 795773729, 210311208, 905875488, 597288188, 456255768, 677959261, 501401143, 706021378, 116209032, 837033617, 866167585, 751333756, 352324335, 427145108, 600961617, 213113869, 773812302, 691318182, 152454808, 818533112, 156116467, 979191515, 811918079, 696735992, 429031520, 191564655, 993058325, 702671909, 300644987, 15751287, 358546898, 38574144, 498623188, 675186699, 696345441, 573296600, 461328802, 301995482, 812537332, 826628263, 997165299, 11057682, 681336315, 492494101, 602688421, 48539586, 244960304, 482375858, 516245844, 620204746, 856467376, 515370776, 419339621, 564669287, 41185746, 25812419, 59985781, 146453652, 961115594, 216486367, 346942837, 227371970, 894546769, 571755777, 563798942, 40324082, 964294872, 494668866, 567553832, 837765986, 414558775, 435339695, 120881271, 215659142, 514566177, 273053756, 553545396, 695990540, 35954761, 592886543, 337340174, 334695879, 952535505, 776383285, 686709747, 209971097, 221333473, 568240112, 388909859, 399379262, 291570743, 932217182, 730107368, 62107208, 373004615, 703786733, 318648571, 688380638, 543071994, 973866563, 54364610, 362513289, 560483610, 520551969, 622575651, 533846559, 6079495, 473156281, 264814450, 645801833, 794515524, 305268021, 631641602, 667524937, 187879289, 285297148, 599520081, 764693529, 722034569, 326546785, 580637192, 610535973, 37392922, 457108170, 488536762, 480870810, 292562430, 86493042, 875697262, 837535417, 783155006, 160978282, 341754118, 485254729, 158111180, 557449573, 980594636, 482877233, 334229666, 480820379, 583855760, 836580052, 387374366, 516896635, 66257272, 748076965, 391026439, 817877743, 526387875, 887750829, 253499290, 306111005, 596373242, 519763371, 483449087, 783859277, 870911995, 225546739, 295008743, 187363260, 481790628, 967099014, 210579646, 745749386, 693131111, 546239220, 123707541, 54099823, 572538871, 14168699, 304711902, 823091400, 618298560, 963918305, 485015406, 702273247, 53368897, 159147653, 40876410, 722449677, 472314118, 944338347, 836594812, 385915714, 903127710, 436167139, 520599005, 463996943, 868687677, 79286782, 865961310, 54915025, 875811931, 572383846, 858473385, 67642675, 337025590, 374986018, 222338628, 523180733, 753029607, 503778087, 521553686, 8640225, 988811424, 298725835, 6223990, 586249968, 531599662, 780772712, 34822785, 540787441, 92866504, 913993722, 832515893, 30908981, 733098576, 941234096, 576479002, 707191240, 956824541, 650135819, 752140334, 467418518, 953581091, 649249890, 556878442, 59637850, 594784873, 906876077, 224538932, 955961332, 590419036, 111491780, 329709043, 240483692, 105976550, 199654807, 59363364, 643856132, 490040008, 968717062, 782608511, 328624295, 31215198, 544806131, 150531539, 966393012, 883552358, 419578128, 214875069, 981664863, 491379730, 301635643, 332888306, 211448738, 54442483, 264351569, 606875754, 457973272, 921572383, 837255707, 978582213, 699367273, 958032328, 102301158, 20700561, 615646989, 304914171, 460838300, 56034977, 599038231, 418273449, 45274034, 70591030, 233593511, 597118893, 972140975, 718176975, 500480961, 846732717, 109428732, 761070488, 146044557, 773549372, 369059834, 697823568, 749690997, 235922007, 448081134, 997500545, 434794468, 403631653, 746361264, 545476854, 326447737, 548043116, 591676177, 847174328, 706072581, 494187819, 831965307, 811354773, 425422393, 993249762, 948723316, 845702072, 260565046, 917703038, 657939144, 409549246, 651405577, 882790375, 981009197, 662653042, 353771039, 314406851, 16664127, 336208194, 529997330, 264802377, 246480781, 155278588, 481349902, 324657205, 422678765, 160371064, 905657759, 656792866, 17701598, 501686092, 990933788, 962553906, 668149063, 13057403, 119581961, 394166962, 933836645, 688283401, 386480197, 665044157, 734784715, 349457953, 968205314, 776015393, 687895288, 296215394, 180087762, 337448405, 492897154, 34625821, 653416526, 941045669, 852248227, 940514308, 467919371, 890224130, 716342065, 389570134, 607201783, 847686029, 139111608, 29524407, 844523868, 270328163, 274002471, 549421727, 133414783, 378556603, 969721717, 722731219, 48483536, 209171720, 892978887, 986581759, 432490637, 500638167, 28182100, 690874389, 206737968, 81396413, 621390662, 929175349, 276960970, 351054951, 809898922, 346146029, 253108777, 558784184, 746818707, 39825326, 373833411, 278037013, 234009068, 695690384, 944078447, 29194691, 396345780, 407763984, 13568138, 765882299, 491870419, 872457784, 258277694, 388244671, 993824150, 260254747, 676088085, 839010285, 860227388, 295938965, 486095793, 140561755, 673829721, 545287104, 218825824, 454006594, 295777557, 852269623, 79853713, 625777611, 188627939, 156780071, 568233357, 589942511, 425644029, 725918829, 263073860, 340227384, 405909578, 496455801, 467997158, 633583251, 157216954, 27767788, 169259057, 525390918, 944401071, 156969530, 614588702, 165700519, 843631547, 822456025, 264943113, 814532149, 700176777, 891503625, 27830172, 321808743, 624230745, 547237327, 62504266, 982559605, 454996576, 983241308, 695468545, 579707861, 678195137, 498578732, 115496836, 265188239, 999097126, 180496920, 150972992, 138906384, 507506312, 297019081, 756909257, 523244243, 99852241, 938773172, 459453054, 814709261, 973384398, 876666549, 328527419, 607498207, 622717378, 716530693, 807663804, 326262044, 826595253, 798016393, 883254664, 546001811, 848110153, 361224532, 624590081, 51870433, 21979170, 459069175, 571247428, 6720197, 183991736, 75509909, 620403275, 790171424, 156367711, 420794079, 136603660, 968826130, 816533808, 65273696, 526597130, 214028862, 776818352, 815617263, 894147754, 151521157, 27947468, 610819311, 448921421, 351567760, 902209161, 888536781, 985851506, 509949360, 594483081, 942956375, 648459983, 64040435, 942654098, 875606674, 51223886, 828891702, 326188635, 832309987, 282849041, 405591341, 634502323, 599905032, 907287427, 319263460, 342280521, 932694164, 275266423, 312059743, 893083667, 299386352, 571407683, 363286540, 828418065, 371741405, 416922526, 833886641, 350688254, 853416701, 249714894, 673322891, 17860074, 719641829, 395734145, 216201850, 466208001, 230740994, 459276956, 161497014, 331632782, 81825164, 86500741, 411007995, 579374340, 540830139, 152595452, 79185251, 385506266, 993006789, 598161839, 500673016, 48980906, 816749877, 569495563, 171773129, 571200359, 104676909, 338522662, 685256980, 539555996, 625246298, 279591621, 760636770, 589941057, 339056413, 869994733, 842302473, 951250599, 800687227, 171714416, 596916540, 343190908, 287769140, 144473463, 600553408, 627360552, 765808155, 460296417, 983573205, 739386234, 781354719, 374544088, 741755977, 766942318, 660516925, 981344062, 532609008, 246921494, 867342506, 901603722, 777049561, 228369364, 781371046, 925659803, 555843865, 462296173, 184524441, 885995971, 272739703, 664156348, 583686903, 126042056, 171638785, 920111076, 591502244, 461333694, 710671153, 461643929, 965305482, 753770332, 612656142, 453588958, 703019682, 595308198, 303484521, 892516978, 204812531, 828829242, 162522036, 413052969, 65520099, 167042998, 789528244, 505917080, 711699579, 822122932, 784314995, 480211840, 77032347, 841359566, 473748930, 802772279, 171296095, 389833892, 209826179, 544552930, 167007142, 704121707, 551912024, 313330395, 368195320, 461999279, 351866253, 676137134, 32123663, 304524696, 696913702, 806116859, 692573093, 37670014, 159630058, 778587006, 816197102, 532802622, 680466152, 470853702, 156130880, 235938765, 993670667, 459154469, 486479048, 462127324, 27683772, 303253850, 945532855, 24289800, 376578763, 454388562, 525598472, 915836500, 466399317, 866395129, 940781771, 676826184, 434540157, 682896475, 837930408, 573525630, 13520188, 42283084, 831526049, 956463802, 669450590, 181573577, 161027903, 234645776, 275709085, 948030331, 852089346, 1124685, 208340320, 979205697, 714577393, 449389701, 262021342, 157862897, 734821901, 901896243, 197129141, 434837395, 919603836, 888378491, 421608870, 88498471, 956517993, 967077480, 832031345, 499513506, 495535087, 810807291, 173874361, 679393349, 300606329, 862189494, 115017763, 506122468, 345767179, 842469335, 118187469, 401116482, 7527076, 307818357, 705950884, 200645968, 917605307, 577160733, 683429925, 947510498, 758465321, 4831317, 547908363, 160844903, 918242519, 526461794, 261199409, 217827145, 142974459, 997422642, 372333000, 313971247, 844090816, 919351272, 345081878, 563289841, 739944178, 657502849, 166517442, 978136361, 532352762, 196604303, 282334782, 639893354, 900541507, 473494280, 352545790, 44433263, 781640156, 306369638, 595551132, 814730496, 933873194, 177316677, 194738324, 288877298, 871194084, 946539189, 889392496, 751666928, 33836527, 970393897, 48922138, 17021804, 958894674, 278949089, 404640641, 779106300, 240307213, 563818023, 818232330, 628166357, 31086509, 478505175, 253651696, 723551134, 959817548, 328940836, 39982867, 986327644, 971639750, 154717599, 291069129, 504562408, 881778325, 865523329, 613967146, 744691708, 263114205, 527402710, 521307283, 688724137, 544925740, 337551911, 244190510, 44443988, 611123012, 287273662, 475631411, 707344240, 184468457, 879203900, 997155938, 15571864, 483291271, 330151874, 783439822, 235986219, 402748397, 207850760, 737390404, 652645111, 761688530, 888520955, 983648309, 203810455, 153545897, 462223962, 838268881, 627758865, 17090260, 517392389, 400580455, 915901717, 952003108, 514603383, 217179709, 803923109, 135690252, 302956785, 616355453, 985521873, 752685526, 241778079, 718308292, 513390675, 808484794, 574012068, 469552071, 356009206, 352108717, 200310760, 299088062, 897314940, 843240072, 226497173, 149250087, 386115041, 708103757, 600751286, 552265975, 845802991, 835799570, 527464081, 566122799, 361107675, 652396651, 449296991, 657174294, 871652136, 860963006, 112576760, 343898461, 168751891, 734121142, 248325151, 538540753, 348840649, 521445902, 612524412, 717772590, 52305767, 37239004, 833608552, 880969718, 913345491, 899105668, 950633768, 134079243, 492250124, 190780182, 359797311, 998379044, 857059134, 719125663, 3498356, 77774139, 62773755, 669910537, 588332426, 785139648, 702946312, 519250261, 927825143, 641792179, 529185610, 337189513, 620487402, 247380921, 359995205, 517720769, 714751449, 40892365, 509233568, 115092166, 395682679, 758007451, 921351929, 568619731, 819802624, 843823276, 687005139, 160674043, 668320614, 546821043, 763118239, 489365905, 98614058, 957068670, 531397158, 225117277, 626506831, 108337906, 769342254, 809572886, 379710389, 376268264, 384322112, 917462934, 217747130, 478237985, 413027049, 960263533, 801691206, 805776225, 759398859, 439644647, 401827922, 988753766, 945710202, 909862770, 317072383, 783027483, 225103759, 691336429, 261033883, 392861871, 771588786, 691424590, 567661248, 335875622, 657003294, 943288527, 317161656, 439490638, 676515665, 704651793, 680634480, 56460267, 662060363, 337608932, 649388763, 771971398, 56145349, 758301571, 283769643, 551421355, 712209042, 736414605, 344601487, 631023047, 388787797, 465623881, 736866161, 240782148, 523326089, 206006800, 895426253, 413164446, 851446135, 535852918, 992392934, 933258749, 683114031, 869022723, 300907387, 3834871, 809733668, 324659234, 556032932, 225167151, 728929183, 228979951, 777650781, 402436754, 137660618, 670752808, 235578387, 990608487, 969797841, 567338818, 348183884, 484601933, 769072794, 434809268, 473518523, 910672817, 687651990, 91052409, 79661071, 605525872, 265247542, 502800686, 483737248, 975720467, 139739595, 662621972, 791553791, 525525832, 860836476, 855462164, 10808026, 232032972, 359710107, 406016184, 861765336, 84939232, 166289010, 287297597, 720511755, 388350463, 667379632, 372366252, 193521346, 325975835, 615605021, 330896503, 314310341, 846851633, 303583694, 429608712, 190790341, 657377136, 824484041, 896413601, 698056749, 302859804, 385575916, 975033875, 754760833, 516003242, 162458766, 541061997, 617092526, 966259808, 138028059, 960087217, 175154042, 942195718, 732194766, 738983926, 797751631, 906706203, 958465206, 910803809, 109054261, 218454590, 485914166, 789462089, 949175710, 23950163, 750499576, 953209477, 835534354, 852163149, 634578107, 599370401, 757182372, 471306374, 727146584, 252881290, 283898031, 836743349, 266549965, 108887854, 199943860, 883896773, 497826558, 498168077, 345754402, 347665688, 812890267, 747854857, 785501491, 167942524, 659273999, 926600198, 530934053, 621800013, 12148735, 747376838, 779519476, 224811105, 301275508, 788477124, 682649682, 187879438, 189547688, 882535770, 830039500, 855967829, 480811640, 567706364, 33046937, 194893967, 223057809, 701688965, 58143248, 463330960, 169349114, 14706884, 75524518, 972201751, 460210095, 722396462, 46358353, 347407269, 471712537, 846153441, 784715218, 800097907, 341735493, 940246162, 73330154, 167495833, 278683410, 300873595, 357331846, 405163387, 915626216, 900888099, 48125931, 402437501, 127938966, 871002747, 915109371, 305677576, 93165338, 51913162, 161146235, 878066823, 848050359, 242592352, 521587286, 317610531, 518006034, 196912876, 561024332, 231497095, 158495594, 163130356, 17516100, 608597987, 145183161, 961584452, 91084527, 781965767, 389312076, 839457077, 194238894, 330482815, 213937155, 374343071, 617862282, 617641896, 824996140, 794559217, 118119514, 863406493, 778744650, 371226010, 665865268, 959974666, 238256848, 206644667, 318750255, 223108025, 92112674, 63273964, 729144937, 53255188, 682538246, 277583474, 812778378, 712817855, 931657692, 500674177, 387503984, 593329993, 596782990, 325728394, 277531806, 655518603, 302123400, 910172595, 377428519, 714831448, 707022555, 493278621, 281861497, 452770950, 468501717, 946223190, 113904265, 145856321, 265454826, 639438801, 865497337, 665567261, 380980301, 150303988, 810066760, 53054618, 537899596, 931210960, 77107542, 282418802, 362782313, 812736618, 316556529, 132749078, 155403995, 37587693, 832126620, 370788845, 892564952, 653482598, 739557199, 342821666, 467150903, 884967619, 952848397, 359359905, 897506363, 795079913, 847992776, 818593200, 485582946, 633093910, 217263752, 902497174, 659960097, 800254150, 166475981, 442407317, 775609716, 752401790, 829345786, 913044355, 586864585, 213446415, 175770212, 284608287, 23539338, 843667100, 74948173, 15828013, 991103584, 196835332, 902912482, 347195759, 57699247, 478149078, 957919668, 808698926, 456381933, 171714757, 182385254, 956062178, 568266585, 846231010, 719380621, 352294347, 828424534, 643716455, 409989975, 811044889, 848699078, 3985829, 948161201, 433603423, 314101270, 693797460, 849660112, 105205603, 536500776, 322728599, 421363031, 273557440, 515248292, 6523204, 428842109, 516285208, 897791763, 769085550, 320646790, 711104474, 567918473, 11800879, 983977342, 433114117, 391292352, 387229670, 155295384, 812047280, 908560123, 714303269, 452351618, 754031892, 526771029, 604026041, 568107253, 974477245, 136815167, 561821707, 234884410, 866734437, 502809857, 662953231, 859285195, 257923331, 47975521, 873989249, 349273517, 497665598, 115711502, 436305952, 229248882, 661994774, 549374271, 309311524, 543543465, 532172438, 341925237, 151686681, 522700632, 633312294, 551017056, 886625819, 874149570, 486596998, 668514995, 165145169, 565169129, 968517979, 540259846, 236949638, 702261488, 70592117, 797717148, 956878847, 117552378, 39793706, 71414038, 350423663, 226959006, 859567674, 581895460, 372389304, 68375193, 868002751, 671895977, 849187311, 624330680, 748961764, 879290806, 472872243, 77876507, 814471845, 210694124, 215259044, 982553529, 613200483, 854848410, 344313678, 930440362, 177497545, 10263955, 957433135, 177747460, 627166124, 278602112, 338774358, 963429336, 882842309, 194120345, 699330867, 71300958, 44471250, 62776644, 173550344, 60703470, 659741332, 753172351, 25820170, 675631978, 999865019, 777239505, 98585630, 189025064, 104318231, 16346558, 477766282, 551862639, 61651107, 829674694, 296991634, 391279949, 638671821, 824690086, 281456515, 634465816, 151253739, 371046537, 870274593, 607855241, 935348413, 107789495, 160480897, 815223593, 977932778, 517854890, 105134643, 916729711, 76889242, 985211173, 391721626, 376842276, 573812413, 348297665, 22448754, 264667741, 77549785, 928863902, 721103101, 723415836, 792334649, 556495689, 808489046, 75625490, 392635024, 161460564, 126557206, 332892472, 222383856, 360637018, 263262025, 611683089, 27834201, 550303680, 641960297, 454650564, 182288621, 688543205, 955551215, 827407561, 128217184, 771038413, 808773973, 196486047, 883166291, 925014670, 67362579, 678093467, 422475288, 40248030, 118349463, 838135304, 90653354, 810833357, 596041828, 580205861, 329599113, 500223440, 647566138, 218244660, 546753822, 850407111, 721769996, 787604583, 162401709, 342436691, 96298831, 744884386, 313923199, 665494960, 643988931, 795246407, 621713460, 203198528, 965273398, 18592416, 488154211, 283179874, 96858259, 336011463, 123457666, 530542343, 684724104, 562949565, 75519018, 446161326, 341646449, 212594578, 700455609, 191504040, 981236284, 650559132, 123246363, 44767260, 95245431, 152933822, 395077852, 435426451, 588800113, 740970518, 949696557, 859800357, 215277368, 922739958, 244402769, 488859891, 121476394, 586904518, 789196038, 466049935, 419690207, 763895304, 449901771, 685637884, 946422855, 867843553, 912624326, 548092173, 350932570, 197591718, 291157796, 152003405, 699325906, 993342820, 998898677, 171044752, 866707221, 268551832, 696088623, 558702546, 239550331, 574009679, 590510049, 236905057, 842394524, 216953299, 972350460, 977561461, 12754508, 961677303, 321581797, 10000044, 290730692, 407562171, 32900721, 2112780, 37481552, 986635209, 531948005, 937896306, 928049714, 23759935, 63508946, 439980054, 496741695, 186565558, 238554378, 527022254, 378529389, 314426665, 447628940, 747958996, 594001975, 48203011, 723720965, 919082645, 899723853, 98765918, 20710061, 744566892, 179661240, 118403382, 894749111, 147222123, 939387902, 548379717, 667509129, 369624668, 62307853, 435009650, 273375760, 883251732, 580450851, 585476905, 655962481, 991430132, 734483789, 358124601, 971616065, 218026264, 919641072, 599090276, 218857999, 290402825, 208479721, 19391419, 156986984, 117311796, 361505351, 909467271, 728883227, 632102098, 845262399, 256167602, 58430795, 17643360, 582014418, 57875974, 105344062, 198044746, 52800801, 304343016, 37173167, 340806858, 688055730, 592863355, 669563307, 382319577, 900486599, 516491477, 786411372, 927346952, 717579256, 647622944, 975650972, 163457770, 903277692, 412544602, 30637451, 400142455, 372667463, 719983576, 558606902, 444647903, 692713271, 285841940, 417826940, 836139371, 360039821, 11642324, 469862329, 999023824, 966285866, 108991998, 111414944, 1472256, 874399458, 580630481, 428453024, 78692780, 81727834, 867831391, 268350911, 369722184, 242564900, 23836678, 383532604, 274290170, 147736787, 91766266, 156608074, 725366294, 476339708, 356455162, 460104550, 947738760, 839865950, 543637633, 430110396, 879234668, 173728131, 645371838, 894896716, 931137674, 440221776, 188030237, 607849888, 639206228, 918353090, 478591494, 701132897, 45858175, 244304731, 382079159, 422921036, 448112166, 568058444, 293996288, 242649256, 665300420, 649814268, 760709436, 503355033, 446427621, 510177665, 538181438, 574333926, 751223231, 953963758, 46156708, 669390794, 14229316, 740834164, 537781309, 223216344, 972503952, 540759174, 307854498, 783254018, 405633891, 179332674, 584899695, 79310742, 401859535, 803728100, 28405605, 766644135, 3677902, 269856298, 367756286, 316837127, 757982441, 109157135, 554702515, 640760997, 149281119, 811501185, 200115725, 812985088, 217986163, 140057240, 262426223, 386522651, 35882518, 594007915, 681226403, 70638011, 506302268, 200279080, 108078914, 335874422, 933999398, 443484654, 400094871, 790534533, 88239109, 975608255, 49554417, 872378506, 391971844, 298556717, 606391273, 739382419, 158352218, 43468902, 256153409, 757813348, 582477284, 260274000, 170265681, 494293319, 248833211, 2736545, 101767926, 19600238, 903931544, 451028830, 219082438, 554794832, 478483328, 57319233, 443397731, 877837536, 589557965, 828445107, 864420751, 571837217, 490407705, 195033816, 382053122, 756555229, 513540311, 60646715, 146842847, 560772588, 868839615, 477084735, 90733879, 553790997, 926478851, 126136416, 738234766, 126346547, 343322417, 282140902, 463100549, 120859368, 299040999, 209667810, 13185011, 18045917, 688423864, 819003478, 420550081, 425033398, 282129395, 396252625, 864898444, 971475221, 576548575, 141023320, 913837738, 267564168, 306999449, 550089839, 710328028, 251692420, 890457919, 828086209, 181040671, 674937872, 95235133, 691597681, 565957368, 504033836, 421227963, 508696174, 588831690, 358078323, 998478589, 624558563, 779312843, 22261368, 363815114, 730808458, 444794998, 211241086, 609292321, 52527309, 73639011, 955042212, 164570909, 504587998, 980404383, 577421638, 186133077, 703543048, 634156834, 727267916, 522717645, 587905200, 846414896, 9566581, 789869240, 175414646, 295289573, 575015335, 587693859, 870542515, 355434301, 473779793, 336098313, 634870251, 185418188, 885897017, 79990146, 170791512, 625988462, 853879981, 666124764, 879232106, 289006230, 262892870, 639287418, 464918470, 616911556, 139132769, 890899661, 816691280, 513684849, 365016562, 724149341, 287091743, 54172364, 67432223, 582621236, 363158436, 952088456, 434245403, 481902504, 224965278, 826787156, 23906151, 670615865, 71537409, 419294153, 550791120, 139130931, 158404540, 793525437, 431241414, 857770034, 214211568, 933578081, 266812925, 954577304, 746783546, 738672946, 821587704, 817238849, 488050779, 174136593, 521394792, 511174090, 590459922, 760836745, 540904375, 705081256, 410226180, 542764652, 433739561, 443584351, 31390885, 118664962, 210034725, 608320125, 941967653, 750926960, 367782950, 510941619, 279279552, 355986874, 880420124, 855652830, 152363143, 961035766, 282372649, 196025782, 785263496, 576603018, 982154336, 577150859, 825980482, 372577483, 839030206, 724881944, 690457395, 827666418, 596973309, 717583330, 365864170, 436407480, 890524234, 726638891, 434840628, 86463910, 326375736, 65386009, 606335017, 399124586, 361980696, 497924624, 951232186, 507024433, 415219612, 665403198, 8527551, 169245583, 808359647, 188810888, 643558487, 120734496, 752329380, 296995823, 636399030, 630993577, 439238, 774938083, 388178287, 510516156, 294678154, 125588180, 109383616, 829657147, 666673914, 840114482, 721084043, 542756683, 898375481, 966715031, 167686825, 4211787, 952499255, 33861051, 13647746, 77831815, 589739776, 252545073, 607957813, 447854600, 431300889, 170843802, 581295135, 442476940, 130020673, 729015164, 868091024, 495616604, 510885144, 570162598, 744166218, 752501034, 895397318, 387603513, 175004888, 667676997, 128423639, 893962395, 580292376, 83696855, 831584897, 566746257, 571873431, 575165201, 672243651, 21901209, 569373690, 650390392, 111882021, 432540245, 578434547, 867915970, 332149754, 520007380, 926114576, 353865373, 67460843, 721651104, 20645960, 665974632, 659276036, 207182049, 536653620, 410318526, 367169266, 619175979, 350238645, 358368005, 337035034, 644778349, 753586111, 916244891, 593432368, 45899766, 196088860, 377528483, 948686514, 983500559, 67364132, 166991660, 136516277, 969760980, 283142172, 82618269, 253988165, 200277908, 345641031, 654558026, 269041254, 141447488, 111830580, 653516121, 284214227, 606375526, 388422579, 984844740, 141057992, 529436475, 462720486, 815210523, 709482369, 186253214, 203417388, 461590860, 910745767, 503253348, 630258873, 995290365, 213662403, 447599699, 859254279, 815068354, 245151660, 795947071, 178586237, 7605989, 802456222, 405328364, 228675094, 900597012, 918856976, 861425855, 922811541, 535256018, 884682976, 91239815, 277291323, 781092693, 214374909, 682728643, 57856472, 767237042, 741726132, 368467835, 57786600, 807713176, 892718864, 252901082, 463978816, 237699203, 742971387, 846606375, 24935617, 186737271, 514225461, 866812448, 561305904, 140569882, 59388954, 156047525, 110693786, 269327362, 531616054, 294236526, 240348712, 258197021, 512657301, 381485355, 315478582, 724055180, 734138098, 582173547, 190173388, 118530163, 749514569, 930984411, 212273965, 655007847, 683516586, 987411116, 119654770, 37788510, 970720660, 108301666, 302819200, 312946466, 235583299, 785733530, 542419770, 138299387, 656669587, 422427785, 844254691, 990357550, 996220995, 9264930, 108841600, 44926841, 989748517, 604425139, 748368884, 506714797, 146036727, 746921782, 242560049, 422923226, 584373170, 231419962, 290644953, 795038729, 427388722, 770783890, 181005849, 438720563, 89197831, 538077233, 915629194, 358015672, 431113490, 665768664, 958241656, 856724294, 610668316, 269686390, 283607796, 869728933, 882079624, 672982551, 20448697, 619280436, 319433167, 917037994, 735725670, 718520372, 962135157, 206825287, 164016706, 793774368, 817106744, 438379253, 505891460, 291880218, 290451652, 7332497, 195602060, 432939968, 610003068, 73870912, 91281556, 335183777, 76300734, 762756588, 883318469, 429460451, 197117053, 94864464, 346151708, 766007079, 564095970, 719862694, 830766701, 406338685, 564082749, 605822673, 697182423, 253969439, 665870806, 214553585, 75592631, 317045262, 307661115, 329177599, 943102225, 520630422, 197402349, 885035131, 255909319, 985989637, 445274580, 726453704, 114302228, 154371171, 949841740, 719973751, 456986531, 858445736, 896128778, 643669490, 262567649, 179022013, 324133781, 32371075, 174627078, 982094593, 838809934, 184476202, 356075301, 273730359, 96903247, 132046440, 42721374, 944921849, 243440053, 152982635, 204363976, 128193522, 922529387, 822564373, 841949897, 875980021, 298596467, 659701335, 933885152, 604704310, 230635673, 238107076, 661151742, 214914232, 148126515, 934543854, 576736950, 339115086, 916666281, 435085289, 610509882, 414530505, 763550925, 152231615, 807061283, 639371536, 621697732, 170869207, 48855192, 359974748, 291327226, 484632922, 417525494, 397666047, 259234960, 926721553, 224958421, 803062738, 979776787, 848118415, 686149568, 267253788, 370124917, 499058885, 397404651, 641846371, 792030784, 409878358, 283028243, 313339754, 271149143, 815786108, 523403102, 292100725, 968453261, 178527919, 298992136, 70649108, 781306213, 653160971, 755336139, 140187338, 766877157, 29919398, 427501992, 743335681, 71279335, 860759163, 942985854, 898732757, 970699548, 273443208, 196101968, 426690365, 176269660, 936718701, 700018641, 548223491, 786694410, 14963904, 615694382, 850759942, 647152064, 46663269, 686944705, 145937801, 958913979, 160564071, 538530137, 144796434, 826734006, 455598178, 286036871, 112014214, 980829336, 610764047, 3575943, 174527277, 794269361, 598737992, 817758090, 791232880, 642372145, 788815689, 362620219, 221119123, 247177939, 495398133, 23965930, 836122589, 740013497, 831865909, 996081570, 106856349, 884343860, 637548128, 3311372, 967289495, 785313652, 110977859, 998799828, 354163653, 610102911, 411759874, 584163353, 749487587, 448844006, 992472610, 917192019, 177831913, 167232833, 288015451, 776381749, 763923857, 387137825, 180196670, 577047345, 945490755, 821649400, 453878195, 522472066, 899468299, 541494038, 422953974, 244173652, 592303000, 900220152, 557509702, 874381975, 417792878, 539686241, 345878709, 73161201, 547003198, 767157156, 336234134, 43896147, 738223648, 35701570, 701598692, 359155323, 254363683, 306805188, 654196314, 283729370, 901111396, 924180942, 390340066, 240755584, 60965734, 267794697, 141009892, 805888915, 184522424, 237505227, 69050617, 24203023, 802096024, 172749625, 766830759, 291067272, 302100544, 68028260, 622354520, 296743447, 677154481, 427317364, 769316644, 319722162, 689136075, 908280281, 569807887, 301722457, 208814479, 496854736, 697207556, 112792112, 469504936, 419947939, 198895020, 613608950, 74215698, 687126185, 834236300, 870322718, 905595549, 251073293, 608212379, 714081078, 844432663, 876372172, 811285779, 647957374, 882665926, 773619414, 749930323, 15367946, 41610087, 226872362, 567038073, 934259300, 128778609, 872192458, 113094816, 324307967, 893423658, 177760113, 523315702, 31424165, 772852652, 311018769, 205634471, 23310654, 487288477, 626551359, 337985219, 959060778, 65282728, 631220704, 974192875, 757863542, 248294158, 972512310, 930785454, 35980961, 759972114, 798290828, 403550671, 177348307, 614953734, 175595712, 796810236, 178674759, 109735979, 398677689, 796979419, 619794125, 430512131, 786582336, 264424895, 75485948, 426997304, 20959415, 402579769, 358404328, 121977864, 197056434, 794005490, 599480525, 620012322, 102081423, 167446333, 739958499, 498040531, 739052976, 368510530, 204441583, 529229254, 879941613, 433075211, 929658825, 217533526, 488204084, 586392810, 614691992, 387299030, 675055839, 347132909, 883303023, 151670688, 730685887, 881696225, 940316284, 412343328, 931758013, 645179303, 310972615, 476439838, 135451017, 684984721, 332588926, 86278846, 948511725, 801627501, 367916082, 858688589, 723681321, 264735320, 631559209, 700175409, 659127563, 158981793, 850751643, 215650230, 880599816, 927266895, 307842867, 970879604, 81383027, 349114490, 256364816, 282439769, 484552984, 526941838, 211918798, 685554227, 780627182, 850961689, 580805070, 147034882, 46339909, 875797289, 799216201, 460416036, 988668334, 27182109, 426116871, 279070783, 496825348, 5421116, 913270795, 26080329, 238879705, 464708868, 377076648, 410084442, 192862748, 885818281, 243102782, 590539757, 446156481, 364462638, 242751742, 44657640, 45620555, 819258580, 632869971, 347380359, 281964264, 875644613, 626679693, 653705822, 638273194, 170303650, 666411896, 435545931, 963257510, 591398657, 485155805, 429554344, 320046464, 360174597, 947167391, 404683831, 367268706, 477330068, 695127760, 261838753, 977929515, 291693862, 590738435, 542414026, 699316367, 128678566, 688118261, 614735339, 643088261, 229395463, 322344082, 859006010, 168349912, 338605846, 940416732, 332995161, 55175680, 304175936, 995950047, 223465291, 703947793, 268971218, 546724810, 861603210, 998001026, 720814790, 811934230, 67645122, 356640475, 354199708, 43921985, 158484067, 322496463, 838517025, 24354336, 532090893, 672936358, 305871039, 967089845, 333776982, 34573609, 467447756, 347045258, 792571544, 685553835, 295439626, 926279690, 334963091, 500595253, 310103267, 608430517, 177622635, 323469057, 386064956, 194184472, 448852228, 360631484, 231496293, 101434574, 815720330, 578776928, 365466439, 63886802, 972256741, 515568114, 808407721, 655324710, 93385314, 303126970, 60231043, 311300994, 612516175, 547188222, 799494246, 865645863, 797834152, 646498054, 84054924, 677962821, 954546314, 323136746, 816405021, 715466962, 456963692, 203802313, 59193337, 407526893, 636372297, 661983940, 862908061, 578119933, 301985784, 609375787, 504945416, 13663946, 953434663, 922732213, 374827150, 626742253, 358990084, 412640171, 863203961, 594517279, 383410487, 820517042, 611624595, 234473639, 983774396, 654619631, 32116690, 678225979, 766568659, 18513087, 638030961, 139118178, 292634031, 6836399, 970741209, 908907325, 646250288, 253956307, 101328741, 109751975, 639337314, 5141654, 305622667, 311560571, 560557361, 636919307, 74222340, 478090843, 450099180, 524781686, 50122816, 582717897, 326984274, 759937381, 106091059, 3084514, 765196365, 157384316, 300426605, 76704596, 209709546, 685473512, 703571119, 648027485, 216363349, 20942575, 809929605, 298209978, 750115797, 576660244, 974682149, 743065590, 65533721, 425177491, 30227768, 21880699, 723404944, 95961857, 744737847, 310902386, 998294714, 443835603, 964718320, 719139240, 864391240, 172804936, 661124610, 890102643, 449843196, 17892037, 135350838, 884350399, 28241015, 410615100, 703589769, 168576488, 64119239, 472384631, 477679342, 917880256, 571300303, 755091989, 888594245, 438427837, 920924735, 173031885, 129567012, 906707849, 29452810, 430880487, 979132414, 254017446, 85768059, 419156190, 184616776, 680453825, 219890515, 998114337, 127831064, 219499410, 640468464, 890850528, 869491978, 749956260, 849077059, 292656879, 121827656, 455445773, 479607296, 874666225, 868578894, 381009355, 455944623, 53934724, 357551386, 874365347, 926956482, 301459392, 568477990, 518037907, 130974033, 70912682, 373579774, 263014105, 646480333, 558900940, 630830632, 54363068, 120007030, 686872383, 513853494, 530076108, 867672168, 585178279, 259790485, 876779355, 957151756, 673927265, 645137008, 717470854, 176705449, 476707626, 130519786, 55284602, 510703572, 929762586, 580738412, 667227194, 470919171, 744226335, 998671506, 876374812, 21651302, 267860564, 571414256, 20987791, 129463487, 290716993, 804148345, 19825792, 335222864, 148568923, 829604669, 278543156, 388607338, 265830919, 933116469, 437579173, 531727899, 889073556, 595773441, 635126123, 400661568, 938710267, 713018000, 845982626, 942981920, 204894373, 886005306, 813940047, 545558966, 208441992, 897775321, 541672285, 996432199, 878057008, 44297259, 192967184, 975233078, 480934463, 923871936, 234443651, 147588752, 556791329, 38641724, 161933281, 456644218, 146464617, 817206440, 731923590, 320614634, 385571739, 552364312, 667676313, 775364467, 211643634, 434876524, 359477644, 945116271, 967506882, 115290890, 776338936, 516535977, 481413716, 183191346, 240634043, 968688878, 918864756, 132031294, 689352782, 510002062, 156687786, 404383580, 586740042, 945484200, 59090097, 985505723, 457586562, 462033407, 445708840, 998507900, 59988199, 155728819, 559416243, 653196875, 550217244, 981147153, 760218116, 895165108, 591386360, 19297237, 362312448, 314997168, 147790678, 541764259, 304720567, 245044093, 202285196, 852480544, 832148829, 374117688, 597799421, 515368212, 305199474, 127698837, 261889262, 67689189, 459956386, 452404901, 793378300, 140904728, 643045766, 98393348, 872964209, 115738595, 839822543, 579297193, 486816711, 71387613, 453509676, 693941294, 142487644, 223179704, 177611371, 29927960, 694679163, 836694443, 980249062, 248711797, 289973771, 822051131, 409328546, 215835161, 715198352, 768613763, 149494644, 901284127, 949031796, 350284682, 900215686, 508513253, 682723193, 845560992, 801576220, 710308099, 542960499, 25219950, 268085029, 445138432, 955026281, 574561144, 618743926, 838293196, 521517424, 121339549, 912930449, 542092597, 967096361, 146461084, 98214711, 360849, 116322441, 790541651, 410205751, 747270662, 322955098, 208655153, 534542696, 547010715, 509595339, 306765985, 823553295, 834593367, 797785645, 812666739, 480494040, 558027713, 752806565, 175762423, 765703870, 544281807, 244140772, 980278565, 894909487, 242881424, 391366904, 773479697, 977592800, 527595930, 148386726, 613382523, 826537125, 132438125, 751480210, 116064135, 935471881, 680910008, 565376938, 951049332, 452338, 291428170, 901530679, 522438616, 679148569, 307470779, 82413381, 908279257, 607357611, 15577763, 798601981, 261211266, 879520580, 789846259, 708996925, 193323742, 766828575, 955946014, 240788548, 754623343, 927996218, 178458884, 341031102, 4445305, 723411047, 147907129, 952884993, 516044163, 74330938, 917257655, 144564561, 678457351, 771799567, 67889873, 793328574, 173179518, 464383042, 941467193, 647822388, 104156142, 364004133, 341761044, 211524753, 380072702, 857854011, 867515954, 259915660, 337985413, 772758868, 126452593, 33692661, 925741025, 934562454, 149830333, 721305830, 903930979, 448856286, 97073186, 486036078, 947451719, 116224917, 861160380, 113251757, 411197606, 244939808, 66446525, 707871147, 388030537, 21278869, 721662697, 722538542, 466993495, 950032414, 98945374, 63695853, 675434387, 153758710, 903984729, 779276098, 242689416, 90677107, 895132149, 647126663, 374611929, 335736069, 386462377, 252888609, 703847743, 651052635, 281116697, 254104, 304000699, 647193636, 547473655, 769939245, 973305226, 711056347, 663754072, 270596116, 66112810, 674931167, 98749076, 752002809, 355578016, 494776898, 725643660, 904056085, 274764798, 382306178, 678611671, 824328178, 705251539, 754786209, 165005258, 965377521, 691906783, 715326134, 859587622, 982788168, 949788309, 199256758, 830569057, 14233502, 349298363, 225743368, 887663720, 971947569, 27240704, 706922410, 844661507, 60505749, 232711513, 821391112, 508168743, 153729329, 393268036, 424828181, 514562142, 306882351, 238400942, 363446648, 634061558, 10371623, 707919503, 614880636, 278953947, 435827147, 607060002, 276501509, 717312026, 193251378, 436015333, 234400060, 654379116, 737277360, 917236821, 722937993, 572063560, 168276660, 595811491, 38883902, 144738500, 552668474, 561975551, 219216076, 35051949, 757794992, 604889026, 99959025, 641578178, 294518231, 557940199, 422148522, 884633243, 736768767, 612162392, 366982705, 855544027, 147629120, 666602253, 299146785, 401480353, 629227929, 680943944, 828538148, 230533160, 878339311, 555819285, 173387681, 465716278, 954925832, 463925255, 617156234, 285969470, 412459986, 894204257, 222677263, 249146429, 532241867, 289445333, 655074882, 932318667, 239529814, 770002223, 203801906, 450671415, 828289343, 422946572, 819190644, 888793461, 117276649, 791511722, 235823778, 448870327, 404036643, 171379049, 138323716, 377579864, 4015658, 37653844, 877697773, 606189463, 199705513, 333826851, 670087263, 837125101, 413641337, 586272057, 459452959, 925965585, 521090377, 955187835, 760190269, 725835676, 474497672, 187678328, 844403373, 146692360, 4707250, 673368387, 184239616, 420793804, 998594917, 270512776, 126783510, 177612570, 767864759, 556667227, 120096506, 587988160, 450647489, 758624943, 581661750, 248733924, 426253482, 575058765, 175236920, 102786755, 216675940, 609829017, 75287450, 508362502, 145906428, 976841734, 389292499, 917646822, 824009008, 452901680, 812740354, 452326006, 358790264, 592245799, 333087289, 818222052, 594802664, 377046179, 281936828, 523621759, 102188016, 779510445, 783488744, 225452761, 173232876, 393105103, 505453785, 65003146, 628313754, 818628462, 324598363, 572119276, 261954883, 617363079, 46103451, 244821440, 428404238, 322058053, 891990353, 709440658, 246398910, 521701038, 489461263, 990757330, 623626453, 922829968, 865743863, 876351554, 312121782, 119633749, 465190716, 363097923, 454733522, 887000021, 883062014, 141577258, 286016728, 239585159, 534100356, 328256538, 457761901, 404565019, 318218523, 326327691, 866834339, 87255479, 770958465, 405708732, 131150130, 718094473, 585559402, 262338342, 798312026, 492884980, 936317629, 41575777, 239352551, 918791866, 399387707, 948637251, 71537828, 582362237, 94177183, 570821152, 727246542, 673671510, 232248288, 182262887, 968770321, 548443364, 607814935, 68878931, 128258254, 665816609, 690666572, 363791830, 169034328, 835758237, 431970313, 25529405, 644972781, 846173920, 138578394, 197594533, 464592791, 83040186, 297493145, 50788978, 51435131, 905602892, 123152989, 349889710, 582115706, 330438566, 647109778, 400323052, 403963157, 323538003, 724352465, 513950278, 893933621, 494656619, 81303940, 98301777, 11606883, 260709602, 764845523, 142860620, 763898110, 34463284, 194751315, 997271762, 360407371, 359621192, 610958425, 945049227, 905542503, 677477913, 169439932, 134143838, 84258274, 414237249, 942741397, 683177231, 592075080, 556018254, 271830179, 521346206, 837004150, 324704417, 663156223, 562912972, 399677158, 789236602, 475431557, 611865929, 975542612, 708528472, 796332533, 896685215, 79075175, 112285047, 657421367, 503284875, 578488898, 965871200, 342449265, 733411584, 289223234, 366831952, 503573620, 797573588, 767234142, 392830729, 903644762, 587041144, 340291763, 312221069, 491799988, 791058365, 530164910, 89937420, 220840387, 75797974, 687353016, 607248346, 451548182, 651552148, 772455965, 923373131, 540182243, 157663216, 468272440, 747853433, 33061137, 217569176, 525713684, 650828912, 992614846, 63892735, 75812012, 55773107, 915596491, 968435579, 910306762, 512501924, 192679442, 787719859, 450733155, 971234844, 353313543, 380733166, 349609106, 127409827, 620517237, 855835303, 500021221, 822069495, 52837586, 937167054, 220581391, 947467817, 234536110, 981824161, 183481520, 415583728, 866406412, 266158912, 518951549, 22378414, 913550029, 637697146, 403343839, 812991633, 224269537, 68160972, 293697407, 645075801, 785283421, 268872273, 68681579, 44338604, 34111392, 640367521, 751840111, 28321406, 151262750, 882424207, 327648393, 654827114, 952023481, 214749509, 682758724, 153656086, 984480588, 743826530, 964322234, 222649569, 770144340, 294652670, 6322610, 852870419, 718402988, 519491770, 916132145, 167753836, 918635385, 117715240, 894176756, 665088136, 322455582, 701842948, 434476496, 830901568, 522064979, 346941290, 703037298, 953568958, 70167511, 543758691, 453573079, 974911077, 197455688, 920256534, 941551945, 158695011, 956699810, 44276447, 164950929, 907820631, 577229217, 929275486, 632083139, 113464731, 126392069, 74698376, 265780393, 512624311, 491801363, 380217129, 745287621, 911086984, 453857248, 36191756, 698766765, 766429240, 775971754, 263659914, 765731623, 192391291, 11715974, 213625617, 505949841, 33678729, 764484112, 30823335, 945095463, 627609951, 210657555, 112681400, 975812989, 4063611, 173308227, 5472096, 598508475, 543575421, 316413278, 762388149, 935053470, 755230412, 191335968, 614940847, 595053972, 278580399, 393059003, 888297707, 514955727, 30725307, 839519139, 709234839, 823556098, 90727931, 812244291, 630312283, 790130818, 138928086, 321477927, 642242335, 85792, 908103905, 802570738, 216379340, 893719034, 858037758, 594648095, 623839008, 674126720, 649795566, 91691279, 686938158, 408157278, 10688422, 182295837, 853179608, 370782658, 973493233, 219828408, 13078993, 703699026, 877863015, 557368577, 533655889, 587956209, 322142425, 565342881, 437873462, 149704589, 772870134, 158928299, 588403894, 698543754, 835984465, 312450088, 603701166, 85567773, 29262033, 778147971, 332365708, 532865140, 624328001, 261794931, 473886130, 960528205, 12056682, 134030190, 451855954, 125448666, 841718238, 114264479, 776471499, 3924264, 236458277, 10318290, 928230529, 463915800, 405947592, 946541431, 28722074, 566465428, 406634221, 573576497, 74910339, 505699812, 191651346, 843110018, 956080177, 689216466, 202732951, 960446034, 553136671, 454797282, 826652460, 59039532, 99473717, 294220743, 172696875, 315317959, 668003007, 23562494, 649615059, 550382558, 378673465, 521547312, 188351182, 778876074, 546446562, 803663135, 444446975, 405843113, 568376019, 745140237, 277684337, 765946442, 806557113, 167405250, 953852705, 95494483, 759207139, 854681731, 94826195, 711826731, 479628480, 103245886, 548701620, 104563023, 841676639, 738892683, 267311205, 127941000, 381682389, 847973492, 420723142, 419913468, 281633758, 497515058, 912317478, 460824686, 120797341, 499142449, 721024850, 619688140, 568909107, 117725013, 242338757, 642392406, 566425661, 239080448, 650753246, 63382576, 315542751, 472494546, 867593082, 824697865, 557662375, 164560459, 568467341, 405780627, 766103125, 250280822, 205031609, 786799564, 728534502, 240492279, 832029240, 50516997, 255711829, 744280825, 693345960, 890010756, 24196143, 774734321, 281174723, 528879288, 303142566, 876299303, 65245273, 944911407, 957441612, 614739305, 138230143, 479130849, 222425520, 615121259, 138848362, 415000732, 484547609, 308124380, 29366322, 807803116, 109701654, 989509377, 689101338, 486183222, 501965663, 718963612, 658088316, 683640876, 669619700, 85745247, 305909273, 913273237, 40409935, 472600478, 985492202, 350522376, 254210043, 603092011, 521600512, 279365007, 741748534, 199996640, 586524944, 115692511, 932572335, 631809675, 314455481, 466954647, 543651127, 841634333, 313786596, 249604286, 406993775, 178058098, 148104782, 631439478, 796975062, 893042746, 36664850, 557577292, 579849806, 530204796, 873679441, 949717, 195742039, 38520736, 914514398, 987919150, 432709068, 590682552, 597746852, 963877115, 23669742, 377361759, 938525847, 169079261, 127634938, 392860917, 518102849, 67126168, 414910444, 759103784, 630261670, 125402342, 428873796, 782743332, 875872805, 169721412, 594915005, 469308996, 590921371, 988284831, 385292597, 282673363, 403824454, 365075507, 754702079, 109520302, 532032836, 204753685, 346356393, 386687124, 635223301, 346932384, 337112761, 598872980, 204247326, 828917996, 342638632, 495893612, 687307454, 729741504, 207632398, 581460111, 860923838, 274080050, 323623015, 722718051, 165843157, 555102543, 607228876, 72944260, 601971559, 642961554, 728508508, 930020703, 300415248, 168672351, 12782177, 846996002, 610439990, 211885890, 332939879, 326542918, 536261519, 97205971, 331921603, 587613987, 411003871, 209201513, 615628851, 697483930, 322512184, 549580950, 745955989, 615295282, 339134913, 979652406, 435221047, 741415956, 286756338, 692712026, 949647388, 182060360, 28944458, 32402995, 234289525, 80264353, 820763489, 325547899, 260386153, 342230200, 652207334, 769215461, 135453447, 198877367, 221129247, 374183154, 752728361, 467956968, 928459687, 487310456, 144463627, 667910175, 23967697, 590247476, 462763836, 929468541, 242523313, 982156344, 97188941, 960764535, 408013605, 924149854, 538398238, 99298755, 441307025, 153460665, 869434076, 416315992, 747466453, 255003247, 443246504, 501076859, 561236081, 828733062, 583207516, 718328039, 293724877, 431279708, 888692504, 520713118, 847520887, 534583450, 259672137, 531547920, 908240342, 758168727, 119884816, 526441572, 761635685, 245752262, 477103624, 376130508, 875600337, 805809443, 787647682, 899107316, 503187942, 860557905, 271727718, 375874465, 831982507, 474227474, 429876966, 855360689, 924573949, 72508861, 153122314, 909985156, 337994847, 503091522, 732079038, 334048685, 961365533, 928806060, 347353225, 982814486, 261937650, 775186230, 410232141, 22408439, 60861452, 156695513, 465359456, 920001680, 465851975, 147826464, 429926811, 656695734, 239817414, 488737971, 495754751, 573554374, 84231607, 776684638, 204298877, 703492449, 773066377, 108501590, 659613059, 626813989, 277686236, 182677056, 651588159, 767494811, 223775839, 784236168, 834163898, 327247498, 882693072, 51095421, 940887051, 29555180, 533051232, 180938060, 439234697, 965333463, 524228537, 666416214, 372843824, 626873206, 168393039, 285108007, 31374665, 866456089, 642547128, 243325002, 353133775, 540664042, 659807927, 41617367, 242834559, 105783428, 535431577, 281981588, 181586112, 811335348, 65403298, 320645135, 751089619, 623489337, 486635413, 380832749, 21294108, 507844518, 316345044, 29116438, 454104112, 163896468, 340490021, 193008274, 376690392, 649775183, 150818958, 363861079, 372121147, 572617468, 650168850, 232948507, 558531177, 681644580, 835281041, 629676310, 487569199, 23574873, 707404307, 800913677, 329633107, 827438323, 77781104, 709869601, 836801962, 836386333, 681594279, 397644600, 939845817, 517631853, 448117443, 486081514, 632413139, 255886445, 12639277, 999483975, 804254167, 272077711, 381011877, 409463955, 672750260, 966578225, 95303000, 530849266, 415277235, 204751028, 38338179, 508967348, 382178404, 102540380, 710538175, 831378014, 651924664, 417374309, 560303327, 114564984, 261694793, 393009218, 986077312, 887308758, 664816579, 458171756, 946863203, 982859714, 109200959, 307840183, 915377784, 674562121, 114555571, 523586145, 419679447, 918164719, 372482025, 139874913, 455264811, 239975699, 518642381, 318250771, 938100479, 358070935, 844393767, 423296696, 781986185, 806577925, 34793914, 386974774, 555279116, 930645930, 813677188, 784070084, 539114659, 76764717, 131187450, 653292998, 644427539, 670546887, 292174045, 999727917, 392436640, 795572980, 779535163, 80906799, 304907611, 877229339, 296429673, 504688795, 915864282, 71010276, 981256426, 333571667, 745898035, 428070509, 447936828, 314480971, 459842665, 4691534, 983739875, 467785684, 31247173, 760521166, 697030314, 165590619, 207235238, 657334584, 390478796, 154575368, 579061922, 213759918, 814000711, 751632108, 697605078, 934282977, 388420270, 197611048, 65130270, 12351930, 221883980, 618692493, 303212906, 267186103, 998694662, 780293171, 497850600, 310352421, 575692640, 372648869, 401176396, 804859672, 146980112, 529497486, 96694225, 37376449, 98197449, 212909962, 596560736, 1030515, 365233724, 799827865, 316859999, 903740025, 257862618, 625033331, 435034211, 827370476, 604910252, 283410582, 920192121, 837460383, 736369178, 629343853, 296596467, 603639876, 663510635, 221891051, 131951572, 415020528, 924024665, 847300262, 854779289, 304724208, 796038289, 567665987, 15288244, 572340101, 982955590, 960891863, 393438213, 962260334, 101300746, 950335096, 534401519, 907203154, 783856546, 688757268, 620705236, 781465054, 719590983, 438424133, 395391524, 868593766, 536617410, 379500603, 301249243, 742929336, 19389841, 641551254, 196101546, 273745202, 636499361, 453748892, 674644785, 143696598, 68201684, 823308444, 346456471, 942850946, 739976360, 768716251, 468138102, 932793962, 370818679, 868196474, 363466589, 813909457, 711820227, 140595888, 484772159, 45371355, 922231727, 144327361, 993632422, 493196982, 782870390, 351850542, 75193284, 85857064, 18695281, 767821450, 888967265, 67488877, 808745131, 534676229, 918706921, 998338375, 705571972, 65970523, 849583524, 566737662, 222073290, 561287885, 971166995, 891122420, 484424016, 473015033, 963999152, 919836701, 133902053, 134974270, 288846805, 50470863, 765997364, 830362038, 346849151, 280669751, 417666128, 581784904, 213423606, 576258440, 229013556, 740548380, 40171140, 643268054, 544023043, 524685941, 997892632, 67794645, 784814627, 964542588, 950609385, 950807470, 47941697, 713018377, 344290124, 603312192, 906655808, 492148012, 359862879, 464643408, 230327775, 243909601, 100823153, 792418225, 326670789, 149506095, 899655755, 236682086, 213242314, 784709087, 990989161, 890727956, 337194952, 623765564, 888286130, 345217672, 298722558, 245000530, 724441552, 975626213, 250582368, 390393358, 30313735, 584303929, 687893232, 201805317, 884190240, 114350716, 324441924, 446912815, 683576424, 653815220, 432865421, 391769930, 324280341, 178546088, 853389650, 7063417, 567203193, 820936058, 697557173, 386137007, 8642729, 168844123, 843208724, 375514596, 989089227, 463964156, 380482174, 625167276, 175267474, 452080855, 738799354, 36484447, 535054007, 306678607, 131719251, 585480650, 557376311, 343071749, 782775994, 708804717, 282654979, 176949974, 571818036, 728799705, 121005320, 115078139, 2763294, 29932558, 932992441, 627883328, 238839982, 194090911, 637267123, 718930660, 691693618, 426535254, 266171920, 695552739, 669826019, 467796042, 544713040, 823523330, 51618758, 394053675, 544685748, 954779191, 849160542, 874253007, 621856188, 450264229, 989786426, 439752208, 246503101, 791376445, 733752232, 119227566, 309317768, 981457082, 184440404, 361406457, 528137537, 875526509, 834703258, 754590453, 496648955, 266269249, 372481412, 168125775, 674867323, 515406745, 942156517, 15487623, 783323247, 51288902, 245907202, 949353579, 361517477, 820957284, 514031619, 857151782, 605620634, 705971798, 316456901, 294358935, 856781769, 865822790, 80961541, 356198652, 756350532, 152244857, 480202519, 134514747, 929643871, 725179206, 260097402, 537616933, 892185110, 184756414, 522937427, 800508980, 147368741, 652385842, 626311507, 589184692, 131378544, 761415073, 430916370, 575471790, 507512187, 676276996, 909587521, 700025368, 939393117, 101821362, 459826495, 43790793, 753196842, 107799916, 122387135, 213501508, 268078281, 481752776, 715879722, 780152970, 919791003, 306402152, 143808292, 691606586, 337745174, 402620388, 72979861, 157720160, 799869001, 463108480, 353703418, 116366075, 983372738, 243769213, 213519406, 311591605, 559892763, 145958385, 324329360, 905896230, 533309429, 898570767, 866138543, 255550708, 678487603, 444490004, 843534134, 342231586, 779454905, 603295162, 433701684, 961992441, 167326712, 51531662, 167629711, 805737106, 778894898, 170525318, 886430115, 40186849, 310539459, 558456603, 673039130, 916146385, 881587753, 995670284, 39960849, 393082273, 909990869, 617068470, 135390913, 609885602, 936468575, 464251987, 397280053, 343802482, 93901029, 907241977, 255263129, 806499360, 613545134, 262872792, 415747812, 642614352, 252602609, 62382717, 62969824, 832484970, 123740479, 156966995, 582707398, 406589568, 907157408, 969547364, 19134431, 549256271, 772860795, 496116067, 909555514, 895882443, 822116659, 276083269, 899332922, 443512832, 465114915, 301180654, 639219244, 557618783, 747996354, 600881234, 166403313, 160996746, 854548222, 557485172, 251665548, 117703373, 73893215, 618374341, 52419617, 83549081, 285015962, 68445370, 516518810, 533642244, 942762026, 115031553, 993202707, 335467353, 435232161, 137967184, 613394570, 379200422, 61411379, 97093703, 668073154, 190312593, 701493090, 145640680, 315111131, 410795846, 485180073, 17324888, 869914601, 746734910, 758500961, 495819270, 97426948, 132121077, 336304267, 155555693, 985463165, 493197966, 82771113, 708578503, 576079990, 41591095, 756652755, 570754197, 497116207, 605926202, 711075630, 426211551, 687905369, 257681962, 85263161, 255479723, 517008234, 196939911, 67266667, 155151324, 715743035, 472108169, 59017572, 390611687, 822343843, 695624952, 618586446, 882332603, 901409158, 382703089, 769962908, 31785960, 619963180, 561374930, 289195290, 884148635, 24654766, 561597141, 886166791, 468561061, 285330385, 518285549, 485230133, 981948583, 714683327, 381779037, 581910236, 257682415, 275129563, 619393149, 4426685, 194142375, 309528792, 564149706, 154027664, 160303019, 981821247, 657757882, 817399286, 874557767, 781936550, 893984884, 864161871, 348628636, 712882258, 959944997, 488299341, 483628953, 140991216, 983428608, 308798730, 140583029, 408730786, 51722269, 806331464, 458827981, 461186610, 728657214, 245904417, 204027042, 196628126, 588641438, 259570290, 428172095, 966617876, 231016805, 402588123, 829399956, 845078439, 77060722, 907737387, 57483779, 651240476, 134016141, 949903877, 475865033, 4365032, 298845313, 83734816, 741021487, 268810097, 712665925, 827591550, 942222928, 882989343, 273099539, 802431149, 639060273, 621443883, 646734978, 541234230, 204313534, 123918522, 356255279, 70485251, 398811058, 590600399, 666864887, 225984564, 544267461, 970476743, 409127426, 722422228, 972187318, 626034188, 686977291, 343648212, 352150820, 156577994, 923366022, 978212568, 335034917, 156883706, 453192068, 955016905, 22342740, 995517621, 2172916, 9821084, 726411455, 806090568, 29304285, 13926743, 614401385, 343975846, 202072028, 868594461, 850148255, 951735939, 382710199, 62568053, 508308413, 345611102, 793416966, 584689967, 911755558, 24313131, 429524886, 527924060, 260743208, 281973107, 753507275, 780959278, 831298257, 37451492, 943369810, 970628950, 613637087, 170256187, 844938864, 225909827, 237839310, 753292195, 266184520, 416780783, 959263551, 101323410, 922255238, 729245623, 604169492, 983104856, 205727606, 310638777, 866615514, 683437798, 702698708, 73286597, 969851733, 699997190, 910741049, 645723580, 939793687, 56797392, 540549157, 804774224, 36112304, 588198120, 913554449, 361641353, 840181474, 317014304, 41171406, 235169419, 289491925, 335500116, 33606992, 470579979, 645384642, 854258666, 496406141, 927781058, 495898521, 401806525, 283051888, 346612757, 294922609, 873126263, 375525727, 557485807, 25081572, 816211194, 574148937, 414687734, 879270890, 978286777, 914459538, 250765121, 484569934, 691293731, 550008405, 786297127, 226142002, 615532627, 528885227, 238325158, 549602864, 953016350, 217586046, 101521014, 409940133, 624781937, 128719059, 286655132, 644367393, 984879047, 820282273, 811168523, 206911433, 725689153, 185905370, 383062806, 400738220, 843289345, 62203118, 625303252, 732288449, 195567029, 626944305, 429105680, 356075035, 324314872, 381207827, 808774752, 687978826, 764491978, 386648743, 365130414, 523233299, 842710322, 488998348, 45615511, 501100958, 700084878, 266111947, 504675417, 808838891, 532763286, 480611952, 143483981, 81619009, 974138356, 586421934, 51957623, 148984504, 11494139, 319712046, 162374469, 640792732, 296636948, 653143299, 371837883, 640598736, 353340076, 298702673, 361404696, 293669596, 150295960, 130647175, 139192309, 679033838, 646095542, 849365407, 11615670, 489213099, 382304826, 792980662, 229651524, 235106859, 257961023, 945956719, 896748603, 63828361, 854823131, 986344417, 765270348, 454862929, 994797439, 430511065, 222211782, 515348128, 957294643, 333114005, 377359531, 264802514, 561294133, 35526691, 494800312, 708736751, 806276855, 724185016, 984106685, 399641577, 734883922, 109192826, 675330633, 24134369, 827271159, 666324558, 334930109, 328176979, 474539003, 424805171, 615088470, 195673743, 260468110, 717880238, 635354699, 598074759, 736620718, 480245905, 827209743, 146172963, 38101952, 973512222, 837904083, 183184707, 775931883, 430890579, 874650219, 491340376, 857926823, 397913228, 722508078, 549208831, 719024321, 404085410, 350479920, 900702956, 262766096, 385529319, 996838546, 732762777, 678334893, 489551633, 912753339, 464104085, 559702480, 22842139, 334917470, 129225018, 396889183, 562598902, 270619494, 181729099, 445439577, 872620906, 282650382, 65438222, 318682639, 231411518, 414924530, 240578141, 926757187, 929450586, 853534380, 107903102, 87537335, 167766084, 546857481, 787925153, 770705875, 249075265, 300830526, 316381076, 485854531, 563467772, 237623208, 697030367, 145375545, 440341028, 910040365, 793234710, 936127534, 888030861, 462474549, 883828955, 201940826, 590293326, 125491772, 83964950, 118714996, 758508861, 722767189, 238468379, 513618741, 700733932, 437587497, 855768194, 233543688, 971679774, 561294686, 63543627, 678488336, 917914253, 255622884, 525974435, 135603269, 828503084, 73149476, 141720008, 899493629, 893335020, 216266106, 579104703, 721671558, 419323600, 93289390, 332994896, 318015337, 766462902, 741995160, 72390912, 542349582, 521169725, 848656545, 252547702, 401151178, 40754895, 848873514, 714077561, 663600220, 592872355, 765129509, 775018436, 939831331, 824190811, 646633668, 929756612, 911659034, 626632026, 303517396, 995376619, 110113078, 488417456, 279393204, 932491534, 360835783, 87364706, 319002315, 648407482, 93088249, 738886526, 202107761, 838183221, 275127845, 370146759, 559172016, 82473160, 381390178, 15982533, 987708437, 548997164, 772879361, 845506633, 496788895, 938355054, 121758289, 871389288, 479659668, 749442998, 102289703, 718586709, 712609315, 66722729, 939449754, 58231013, 692774208, 67787458, 934535926, 147738051, 13232494, 534575446, 324437645, 555270110, 945392498, 800691320, 929282184, 902110309, 832095038, 565885678, 12303103, 113305785, 247872598, 809225998, 649320387, 343000649, 102837445, 415251131, 774034612, 311968799, 606873615, 499335276, 818663831, 793188013, 493848745, 702843568, 379380985, 728991066, 537796643, 134779263, 41801864, 666537401, 98476616, 235673326, 380222849, 820062900, 112938169, 956998080, 851586988, 92828742, 778802957, 871737151, 758076362, 498161250, 776458032, 923863740, 487694796, 884805503, 916018747, 243422002, 241380520, 589421852, 344363909, 773582011, 152506181, 895004627, 696652926, 373832462, 332839804, 288322649, 129607554, 289204100, 913771786, 278739597, 45450841, 964169788, 253797950, 472642933, 144777052, 385850266, 703920759, 783935806, 371106149, 303422270, 780385298, 992689060, 148712067, 813013212, 287288982, 703747297, 67233129, 550142665, 369778589, 608246263, 857019781, 174956986, 482243801, 111209874, 839894695, 463789914, 992855582, 678136608, 593868443, 71019826, 979759259, 815248866, 157969568, 303957530, 318145725, 425235239, 865144544, 931572736, 473765398, 301397359, 970501100, 921645724, 364047315, 874580013, 294578455, 927130161, 619971352, 141083646, 758202914, 767068505, 782372020, 785609718, 793528415, 533275548, 463954688, 266936596, 359882362, 744855517, 632529481, 301149097, 624545321, 905129232, 136187523, 992145589, 822924627, 569112311, 220307220, 937455963, 599006960, 824530745, 531581076, 744298498, 413340413, 165270685, 572063414, 566936629, 488413954, 830414720, 481827531, 185960746, 401369935, 478490417, 534149645, 58475856, 236201565, 614557331, 941016493, 354113037, 737071399, 481098406, 922209715, 798426554, 156143260, 639897358, 177718398, 604201494, 324750902, 749696482, 535706683, 754623479, 989746969, 104386268, 631869479, 684129158, 332606295, 555750016, 812800817, 48963288, 774676924, 359129437, 510016214, 827073208, 47794164, 651114795, 226959518, 443121242, 833085965, 400445074, 610376433, 317198790, 849623432, 988641028, 38056175, 360668241, 164296032, 592449027, 507172924, 643752347, 308909190, 592946558, 391560832, 778272592, 881983709, 889929992, 727468322, 349002782, 77906013, 360455184, 810140187, 671357355, 366684764, 172698975, 624312644, 521209829, 414787547, 29961474, 463379613, 300745504, 209644728, 391794746, 273651135, 386845296, 949803406, 38900259, 347462318, 756226625, 746750526, 192026273, 184542923, 646492653, 951315800, 784626619, 461376549, 902058581, 284367625, 382776503, 517088408, 322926932, 32632885, 796090091, 990120285, 7689095, 980268939, 769682719, 685379768, 492690764, 661145453, 873439507, 528258093, 24136551, 36891476, 992944527, 441058052, 798467613, 683070069, 654434578, 17805502, 596732736, 308920047, 260833128, 124330840, 222937763, 985189370, 74570093, 856480678, 836940530, 591375704, 360516996, 67268821, 884837694, 911585424, 313099260, 8035076, 385873835, 470962958, 992847572, 211823720, 863346690, 51677209, 895467568, 173389159, 770133139, 813683788, 935929217, 663672144, 45045321, 793606911, 308746549, 38995887, 150656859, 242361287, 143000934, 182893245, 414939143, 999618274, 225662987, 95867596, 81773593, 353729358, 702738751, 451039760, 204514131, 166746108, 753036567, 290455004, 225193237, 545337975, 777781660, 597045901, 33312175, 499375772, 646335653, 423394145, 672166953, 72189711, 198309976, 781233801, 940039508, 990283344, 36207228, 324870463, 890813127, 223818226, 898304444, 661269790, 458185420, 803732193, 540487768, 575604935, 91112001, 768953491, 419496286, 488950996, 379580466, 153333764, 235371852, 213062988, 747652138, 492503657, 298424717, 901455269, 46236456, 442661861, 952760024, 854192230, 543352667, 551334034, 815229717, 297477273, 342718887, 478286376, 465388794, 704463803, 972977449, 1365549, 182931591, 352909541, 281185112, 395018353, 955102833, 133508530, 42718966, 783793040, 940517864, 770938106, 716255967, 864824237, 926306518, 778693221, 844948708, 80790722, 905978594, 907549941, 53900634, 426215428, 781446549, 777317022, 234388235, 346512445, 490389903, 538855132, 606788892, 885299319, 144152290, 554239835, 809923797, 992147242, 999963387, 74815496, 575559144, 862160789, 923143155, 426149287, 118361123, 697676854, 576031487, 847818969, 37134769, 983719822, 338071976, 894256892, 576244063, 523114706, 25742858, 208957187, 623555463, 534607629, 598603350, 167144063, 192830196, 197812935, 41486427, 763550170, 724589479, 410752218, 513494529, 267835004, 648194234, 807014118, 53664830, 273414235, 9486234, 673408905, 517190807, 994566969, 114909581, 441824617, 27300241, 59496951, 273176989, 729234729, 158949371, 656239829, 894402800, 74972380, 268042140, 440417011, 158560352, 585085276, 229995000, 383979750, 554788164, 762573368, 409714601, 231385861, 407353015, 306261736, 320536493, 160432642, 13327896, 321674797, 96484001, 468095709, 346172128, 650762805, 7384968, 748760509, 230436897, 438773517, 994330112, 618297378, 665169763, 442443032, 899939960, 616796554, 576811047, 314696341, 513197025, 116103473, 919943389, 247319542, 119948994, 222629660, 794554411, 418739566, 710445387, 724159457, 966971333, 630916680, 690897767, 938576265, 62689971, 697281477, 454806938, 109261820, 770108737, 198310725, 408561372, 995826590, 471314267, 601531334, 763128634, 725928740, 132628096, 301026764, 53043160, 722791806, 501439006, 158011528, 566614299, 703324541, 822229687, 780162598, 649008122, 608140408, 486403233, 364425110, 373820556, 127761257, 876593798, 282204106, 382921447, 551648468, 147517389, 7653699, 304530564, 383101913, 685458748, 635702100, 245173658, 347546264, 890305667, 537579317, 261627897, 743999068, 675623556, 562521798, 636248770, 190446119, 761419900, 744619916, 85497060, 776923499, 430064127, 3321481, 468714153, 95054343, 130479943, 802398244, 941801351, 393825067, 600952182, 448606773, 2097012, 527192544, 601215835, 107292236, 855295723, 126555320, 964448916, 87222266, 941315283, 625921712, 538206386, 628112038, 816335394, 283340271, 151428581, 647914558, 836210945, 395341767, 647190586, 901194161, 422367556, 719196116, 299429918, 402685912, 794116985, 104134443, 384064710, 753116658, 291320438, 921665669, 486800459, 504110852, 918260086, 556067164, 901955311, 7068604, 228710129, 275878041, 12201907, 945251042, 374349811, 721633660, 189973601, 242251969, 238360279, 678028711, 180907606, 527191816, 804920933, 49979934, 390922022, 710104420, 740236006, 339023676, 502540709, 315882773, 1732624, 366717579, 224081822, 669803441, 29206402, 471291845, 976269294, 364041954, 147812283, 744779406, 240927858, 184613869, 348327328, 411920750, 739590605, 290573777, 519427721, 273561400, 981769384, 822502718, 367843491, 779732971, 497480927, 992667201, 380055507, 236038879, 145922094, 558391927, 557519052, 561856048, 877660051, 269542313, 768638505, 630790220, 712842537, 214677823, 520542412, 673431327, 956289165, 552548853, 976033472, 787996956, 790595116, 877938621, 936804431, 121093763, 2317812, 887456175, 777713176, 356076038, 245751054, 732694769, 57940343, 668233062, 463548598, 414215330, 908357536, 168205497, 787026094, 334920526, 522294956, 19537933, 547317700, 575857196, 77240296, 690386167, 191371036, 555519999, 638109539, 220952461, 859146343, 682646851, 928777665, 95940241, 361928953, 734328898, 157129089, 946753945, 686128783, 915761732, 780088778, 96534662, 740231456, 402608520, 65818846, 759480879, 582375279, 957789361, 469765912, 275377096, 251174978, 756645726, 770410808, 516694845, 164645481, 338285233, 967308654, 848041256, 541011452, 28593219, 193642022, 353137563, 611496820, 888152891, 161797373, 851511056, 771127254, 640723778, 757962328, 833098073, 454616506, 327843079, 617695694, 883737332, 223543065, 105476705, 322923800, 907317150, 950335517, 913767308, 623580701, 894729550, 399701273, 550741986, 633555567, 775845662, 574157265, 368722900, 991148941, 169011743, 288251060, 225985025, 514970213, 973745965, 56731475, 967851147, 895274151, 827799576, 582599827, 754635323, 870484432, 61667520, 688395198, 96222701, 38482537, 36493046, 965050165, 43299839, 155896888, 932374632, 33871037, 941027900, 550629234, 771310128, 622271667, 14052137, 234455084, 202291148, 245129558, 485967391, 739126008, 150061300, 574742791, 74500935, 155458038, 934064531, 629248360, 413622530, 725514572, 284837879, 528667477, 919023189, 177784842, 789988352, 940939317, 309976282, 602073676, 720352101, 689576089, 895910350, 326477203, 58091224, 223600529, 741230210, 253064186, 122693056, 462122596, 743901022, 809082950, 802300073, 954159188, 782037226, 93928102, 154735716, 389822672, 287431233, 313178636, 641033914, 866809948, 500911129, 54399527, 287316252, 198970687, 102243498, 481500464, 42378412, 127598010, 463213902, 591014890, 73199226, 825554472, 214794195, 518566174, 388190765, 318753633, 209702356, 458303888, 706243144, 206536562, 228602578, 704626798, 842245543, 856807886, 501849085, 277175264, 814043950, 715975226, 439246184, 299152780, 561813751, 965198763, 392424978, 535785574, 43613070, 972171721, 871267307, 875653946, 917696513, 13576718, 732956687, 22382888, 675981249, 645916570, 450488196, 734195669, 868230089, 158663052, 83096166, 321127550, 825214179, 812054138, 599098221, 140505081, 706130053, 744457441, 405292619, 616349875, 411456117, 217457926, 7474575, 961113677, 110793773, 120064297, 16193500, 650905316, 2185833, 921986460, 732328958, 737061757, 870000926, 140189281, 975694348, 420350481, 886674314, 547561678, 571937142, 911541917, 593425513, 395306342, 551897815, 179133962, 489805238, 33260596, 510393943, 754381658, 901322681, 641631197, 465349983, 348029693, 580044249, 16086798, 655685860, 118895942, 473447488, 907203896, 20613206, 573004597, 446202195, 340699601, 254351889, 73372693, 313401475, 138061538, 621180067, 635282540, 730854456, 357321114, 236152287, 414566432, 821847475, 997718125, 73742721, 542255483, 180125713, 420101216, 798101363, 648570731, 492853778, 371119916, 926535342, 963959712, 259727469, 260822103, 746380619, 582684971, 256531958, 510816035, 928386845, 195658304, 169890900, 837089767, 981511036, 933295175, 262754543, 796334034, 213421516, 645714887, 605498347, 643177109, 433236416, 777396522, 370409753, 666179630, 517147658, 195741033, 468929242, 571663414, 911889792, 622521280, 160658050, 485164068, 685747565, 638398401, 539814288, 483405661, 384811465, 182367847, 233686979, 60932222, 199822757, 305966823, 393977766, 481424507, 209501041, 316175166, 360915401, 369800851, 573791410, 266995710, 810007314, 123533719, 367754500, 976348278, 702929239, 275083349, 723267951, 233153070, 476923664, 470173182, 508000572, 765432268, 631236003, 383754512, 581675567, 918237293, 734339868, 196842790, 55628261, 273751664, 834931426, 534413143, 16706898, 871075758, 224961549, 398388455, 763038407, 662289460, 59194772, 939229178, 573424126, 216082878, 478579107, 829917118, 732859747, 526049458, 383636639, 773098745, 151448194, 916256453, 802241345, 777107350, 173819145, 880453826, 144959187, 603557977, 549187297, 570670169, 960796007, 955164960, 69387312, 390617536, 920435106, 243012778, 677017780, 686178564, 204645353, 568936989, 451188095, 806533292, 822060727, 183647422, 764093329, 526244285, 362589721, 431211556, 75878273, 666738450, 74263375, 108432372, 712709624, 4908353, 613949627, 23398163, 560943342, 37945409, 61653136, 436512326, 800176878, 533943015, 9977215, 187028203, 658792422, 484776527, 109664147, 104635331, 278148095, 90045365, 464144949, 370392273, 325562422, 360065311, 389834328, 835278169, 853030502, 746567203, 685184771, 889520405, 945967419, 178178489, 440574887, 134184090, 948806033, 555295530, 585286424, 805271503, 748592730, 370009994, 742459073, 78966834, 733092, 205391497, 374333230, 650904829, 384452005, 51985947, 129440864, 990340329, 204839353, 864066447, 283365824, 518721338, 926995347, 937454214, 626178441, 540051496, 62283910, 288676777, 193491348, 748547261, 782734392, 745222306, 294083552, 362793221, 695099582, 428577392, 519303213, 261383146, 561146643, 955541087, 873381712, 901106163, 870949804, 897107301, 293450591, 581782507, 810628872, 87558968, 33443979, 845392300, 289595915, 4567639, 69051808, 347747284, 704408328, 306253620, 298385324, 678948175, 432860970, 761306533, 537218999, 859010955, 429327619, 872204262, 582682959, 534228618, 834205649, 744901890, 857264957, 150117868, 844611613, 606984626, 129941085, 741442883, 47849995, 443871172, 785756761, 936985195, 390883013, 460190306, 524061541, 127957754, 959600123, 301327999, 741947609, 34579445, 710858966, 339227007, 637307324, 79550244, 470512952, 924086683, 201657841, 565147282, 939518918, 336207124, 687290405, 667646078, 311807135, 970936217, 16503757, 441119078, 396149168, 75981341, 557400669, 261088020, 656697935, 11252815, 276476570, 990568123, 655345800, 290220051, 474522806, 819972134, 109880501, 779334427, 573735142, 252568011, 600535420, 667453756, 546765093, 869277540, 611961839, 794784591, 645900001, 106881103, 849635883, 142625643, 993528209, 534751912, 858055985, 17451334, 361950425, 27335788, 311905261, 512029703, 944264516, 692929466, 985998472, 14636333, 537145802, 943830230, 238992031, 28540912, 794617664, 96933217, 536201206, 816435709, 205429874, 575130944, 786231736, 98394302, 204829008, 209720065, 128015054, 804829631, 842881238, 272504921, 430448072, 79614322, 141311557, 759166507, 270504253, 51483564, 542569291, 336796952, 40812490, 908411012, 892626534, 894354032, 626784677, 983316099, 377797511, 831130339, 611698167, 297875245, 436767155, 38328894, 662185774, 468240040, 556568812, 280684456, 497587641, 397163453, 545339368, 335633615, 961937701, 595965375, 427090205, 98254362, 420447333, 826521467, 223968941, 774294720, 389239052, 750916699, 837617294, 346565396, 491694777, 986433225, 95515558, 197849638, 137981575, 238563790, 568381511, 667794901, 512312543, 857958282, 627943226, 37710091, 343407081, 756623069, 640307841, 812295696, 476719710, 491998716, 825273507, 585969619, 661970820, 495023605, 130365796, 152250221, 713271785, 346026588, 630931570, 995034883, 366730557, 711791007, 578076660, 401451231, 840310859, 900176239, 408160, 222243398, 638623508, 982569581, 919880824, 498497675, 675801478, 917598369, 356850209, 988612504, 738645751, 686774137, 618675990, 675366506, 459390875, 642622096, 448022904, 256013906, 505777820, 999290238, 139301114, 383132562, 114123746, 587198976, 140719128, 616121361, 665011189, 55367179, 560820398, 505311790, 553164569, 818709583, 381092766, 581054803, 738017345, 152924517, 247151328, 832666107, 390708056, 321365820, 394398307, 528029197, 718951216, 506416310, 481922918, 787254319, 269404022, 892140288, 349028358, 95743410, 882197856, 515625887, 92050968, 20235488, 456334619, 271066811, 982710535, 617989889, 185641976, 74348043, 996411709, 308068573, 769401896, 411498668, 736862869, 952778624, 93266321, 657434206, 446837381, 677681454, 145247793, 767205640, 924785894, 132654672, 477940347, 455042544, 604859783, 924314093, 639668298, 741249850, 19672830, 70576145, 490656108, 395896124, 697293323, 601189157, 183608687, 483782638, 640676177, 832749882, 664228517, 500719570, 738112983, 732300350, 71458271, 877058801, 809339377, 4010059, 58483141, 65648144, 959370285, 936766518, 715728191, 188264846, 765986522, 801391544, 968787335, 265206972, 439085347, 497108970, 180989431, 200581828, 506764413, 825852055, 403517184, 179228486, 772772749, 692345787, 274086838, 398285328, 467449010, 482783161, 259300548, 197588532, 138706857, 189573913, 286542478, 643138081, 107561233, 137898625, 844544072, 169919815, 843015729, 794033861, 776202502, 444150471, 788137283, 571334253, 63437618, 195576288, 159803913, 628266655, 572510630, 742936059, 662632656, 544952558, 295544606, 484701496, 439628440, 27382925, 671055694, 143533118, 570556708, 28483311, 301187662, 34005030, 374506030, 619880612, 905437942, 277343461, 248999650, 833948807, 121257013, 896238720, 997192178, 191147232, 990044174, 511811150, 646389425, 971066803, 795778519, 985358456, 577638462, 250803278, 313362778, 672049661, 400578175, 579120291, 193459224, 232368144, 445207375, 743353535, 78321708, 884082778, 355514292, 756270973, 336467829, 75614609, 443151184, 339329104, 235525666, 632857045, 279523323, 923310051, 399408914, 631429365, 82367361, 526566899, 272110497, 957162513, 766179889, 356093687, 191472044, 431570527, 9677504, 565443555, 369808407, 463869319, 532370322, 827977750, 90637846, 137822609, 790749056, 952728192, 607096612, 792816354, 619074728, 12556873, 677996663, 427793799, 321199022, 924840459, 95499731, 982602006, 425529194, 309772852, 893648934, 353527383, 783454383, 85015969, 332078447, 546993261, 838103680, 557663154, 65286940, 259196308, 923547198, 665899298, 981548382, 251170159, 801490330, 760142663, 606595781, 251478116, 742152958, 320595501, 960875798, 660764814, 117166622, 249198077, 835905193, 660620941, 307225356, 747105998, 339716405, 66883653, 721754106, 253111269, 243520147, 401356420, 908950810, 38564266, 347221019, 594936921, 905094575, 61435947, 571024221, 168585639, 457517332, 253555220, 418178330, 365733249, 646545662, 866286907, 332552207, 387791312, 336042319, 954268067, 641526054, 155464352, 182247222, 320770245, 458739916, 925000190, 662365672, 145739309, 211129339, 781045188, 580066115, 31394956, 788873496, 5129424, 55080576, 993016331, 437041877, 394624800, 481584525, 531595258, 211540689, 612732004, 664003430, 122461360, 24082650, 854189225, 667956217, 610524030, 339618509, 827335191, 31892500, 784514380, 244425831, 393857214, 508675191, 15642567, 608795223, 777356522, 535723515, 473998282, 506551581, 696114855, 698477168, 571756072, 398641141, 563162584, 334280816, 677399479, 196402081, 274151533, 482188823, 558541421, 818015094, 490539517, 129677434, 219030210, 4056017, 671772261, 215900383, 641368554, 607470339, 151942862, 41851651, 235929787, 274230654, 575646502, 868128068, 25723179, 554882153, 369827795, 299085114, 585202841, 420850223, 383050036, 784192139, 190875696, 5523944, 838423956, 445719875, 768913998, 239938102, 450931496, 419330455, 997046369, 849516174, 260738394, 195308646, 144938213, 964933579, 288279664, 741230967, 214748771, 874896498, 410302155, 672145838, 882316018, 89357725, 655667987, 131872377, 367596967, 312226593, 72957060, 350892768, 116724263, 314983556, 950553179, 704238955, 933432594, 460177864, 319546238, 523985057, 3985945, 276903629, 263155482, 519638691, 611191160, 915131591, 205041761, 985476529, 484263904, 950507279, 901113912, 449102197, 782524698, 154131077, 111342607, 536404898, 184621934, 74545785, 264725937, 229099448, 36479203, 11449115, 118684227, 703580660, 319100715, 900221448, 341036235, 445744167, 840688301, 761619351, 608357360, 734523445, 463663594, 449072559, 90947106, 295715609, 953227948, 161524237, 667654385, 425750139, 144288838, 934566223, 13737289, 381004133, 641163795, 174530757, 526043559, 311895917, 624835234, 694170126, 368268855, 617019663, 693843875, 79603820, 961083397, 313977846, 165913218, 400865824, 657238463, 122222496, 822997656, 724736801, 381289765, 541680884, 73294152, 827341181, 517605870, 652385322, 716612269, 301046096, 438527070, 196626999, 783805623, 821494876, 249647958, 983397390, 335448132, 592585330, 867563535, 767097194, 244090762, 930643572, 311353230, 699260143, 191249550, 371000848, 490781514, 83621935, 233186610, 405277281, 150176851, 885291907, 54059224, 939651499, 700903180, 977198552, 614036134, 268509808, 258914728, 343474441, 583457119, 61124044, 741442018, 33782167, 901571403, 654514925, 182269548, 547087237, 937408414, 490100819, 309317142, 957791064, 713501959, 422581737, 143970326, 247733969, 833199350, 905624387, 840113916, 167969317, 420482607, 166385310, 573156542, 100732558, 450063184, 593024805, 136604790, 733580630, 971627544, 124314723, 290968253, 543255508, 580554758, 200721825, 206555401, 444454809, 388418227, 19906194, 923935063, 836534340, 656093657, 649433259, 643226855, 342444368, 690702086, 4920810, 830054816, 516261977, 268693441, 671830517, 455118209, 649319420, 304158053, 850138112, 980156050, 55497198, 446065994, 922956837, 551830717, 332992641, 29662040, 578922829, 767364852, 231744376, 324390570, 133458645, 691666914, 228763141, 645267431, 656192553, 48492587, 309485988, 18044818, 24937220, 565443601, 40448898, 435411617, 794972113, 591608161, 384226861, 290402403, 764106054, 16974290, 731892584, 834697727, 204284289, 362645510, 698465160, 187878292, 235395477, 91910785, 609004099, 618147054, 453432576, 448629473, 857386595, 634125179, 219920407, 682580333, 106222262, 690859978, 492605878, 802076329, 703308621, 601444607, 280256595, 836061957, 721684112, 763815452, 801400568, 281063469, 566924188, 876462424, 667380018, 770744429, 859303010, 212136454, 380852263, 872805362, 918628790, 542773641, 400790764, 535502092, 927660434, 52032787, 238407300, 259708498, 912081961, 133655622, 19452489, 319132489, 562129053, 563925299, 898381197, 323646594, 896629050, 183053571, 196204647, 231630604, 474773488, 235419416, 325792160, 41317606, 820508923, 498203552, 109345124, 854724706, 276310716, 767045161, 817212350, 809577307, 280947570, 89290265, 322407735, 867987032, 410284781, 603874346, 908260564, 630955022, 216230103, 399451563, 679678231, 488674276, 801190208, 585629646, 209066822, 401419416, 611353809, 593172187, 566075130, 81118408, 240837263, 328997995, 985837015, 279152023, 503334055, 187669287, 867589054, 41621365, 723104892, 971363438, 217743793, 540697598, 494064933, 946693252, 40204279, 985217813, 173635719, 90091005, 924419331, 935691157, 217632280, 394913075, 808140980, 760120, 268856670, 927926855, 440961402, 401089933, 39066088, 820001249, 407257291, 527886805, 245340266, 553536486, 795148447, 165747344, 153149569, 396340752, 50360774, 961417531, 636221258, 563792919, 31755467, 845566514, 248173622, 323883487, 391332643, 256825528, 173672351, 863047150, 791199392, 396851529, 585878141, 215721935, 732871075, 978946400, 461747034, 395476293, 175312464, 91514967, 750916549, 667293188, 530233857, 878485484, 236797722, 567769410, 142457813, 717659826, 675963120, 376142330, 949598129, 864249850, 377459904, 323215171, 317259115, 560790866, 204344924, 644164445, 836461670, 494975320, 578546347, 266818452, 251315148, 283692282, 115281876, 596192678, 195510932, 676301809, 450785345, 913854622, 836690448, 575134700, 721652363, 822609259, 54689517, 901806625, 783180490, 782372033, 526014012, 615555897, 960429190, 955730687, 640040754, 411296239, 41993144, 959183870, 580324525, 548626441, 653369444, 565761257, 448627103, 622776929, 704447193, 385440925, 263165933, 139747784, 799215539, 740169481, 972016379, 468214316, 670145399, 537697009, 10591006, 729927339, 174554860, 864660241, 729968220, 804812281, 576833204, 991995410, 960369289, 955351822, 605884017, 45971797, 67766647, 37959237, 68427596, 166935478, 795172837, 239133587, 271760274, 887979261, 19236120, 702965567, 529469474, 235927660, 510019130, 438885036, 151974435, 411976133, 249004851, 887638243, 238311081, 945369788, 459987971, 517738627, 808659884, 840329924, 910089117, 817029517, 889407479, 711885158, 88162033, 946111882, 727052625, 910785985, 667774247, 334020279, 156755642, 995339685, 613001446, 673210158, 98130085, 445832165, 559429859, 536320688, 105322550, 940902133, 401993053, 398445094, 151274187, 148559709, 732557283, 590647009, 876557511, 783537343, 442905000, 891656800, 916644418, 232361053, 122951991, 690126005, 199915923, 798559397, 807829866, 702259148, 579252516, 328414695, 587077820, 250900990, 665189736, 361482833, 92869246, 543246246, 765428987, 589727657, 246408824, 963579576, 386907867, 290879142, 243869367, 856975611, 134292763, 360228073, 120692401, 420207206, 618511071, 60105921, 226724518, 756727689, 40510435, 322229853, 672369841, 21620586, 25801233, 568590367, 529780228, 73813501, 363214922, 144671124, 723613220, 717072762, 696588639, 625751744, 726551876, 137033119, 759851206, 236183460, 716352970, 821387412, 820962324, 114759649, 703261794, 444963172, 26777039, 517527804, 763779785, 49852024, 949908729, 226167112, 397878632, 507401658, 765289018, 976296280, 659252066, 250635800, 815923453, 891046759, 835001564, 650531176, 391782215, 574427557, 336560889, 723560296, 842634773, 23932615, 687584924, 353009246, 561375194, 26970886, 237485539, 821884464, 221823767, 371106126, 150183795, 242824612, 885251667, 158074220, 849804871, 1840233, 196084896, 894739416, 835218149, 113957572, 503402895, 263238756, 306584951, 102096742, 867684056, 146110062, 337555200, 946276127, 978525592, 210649075, 290407053, 144593266, 286134045, 451938590, 293652740, 332849372, 232388573, 967811132, 47956732, 671988173, 218809283, 821975343, 759720648, 974870440, 63193042, 137948155, 268066753, 521994106, 20986792, 388336066, 546313524, 999641157, 161891581, 217159662, 740006421, 596452785, 253036529, 102707788, 604490409, 804316438, 513585416, 538691784, 469481250, 595203002, 220011517, 783069940, 245084147, 749592242, 854817732, 195874408, 972920201, 452459662, 253333653, 668097107, 776486481, 574343537, 216761528, 84941462, 803137324, 38902166, 291408162, 993074217, 472572258, 719978945, 497042150, 603408732, 819641379, 889385750, 266611127, 660420480, 265734300, 124057009, 298580386, 960890083, 955895878, 385555511, 996062908, 248329623, 212101889, 872430503, 672821903, 152632442, 143133289, 767277169, 217636384, 257598049, 756296105, 49822669, 965783571, 186270246, 993631859, 148902305, 365731448, 369873417, 229605588, 338197936, 806078966, 300577263, 302751119, 779010222, 961335238, 609634762, 467969038, 555280964, 103384355, 314486974, 228476337, 549930434, 349810067, 425079610, 492526633, 111020990, 851536803, 498762376, 268490984, 203697284, 451429843, 415791204, 338263322, 659688158, 257483122, 955315955, 288814221, 851258408, 33663019, 799882579, 632225453, 80496567, 762614362, 329861616, 571836211, 976001259, 138887268, 545328927, 649972172, 320324720, 538235183, 296519343, 189918730, 187025628, 119866366, 392292586, 360777066, 319547749, 64988561, 467112230, 269519818, 357544257, 62103212, 234777975, 491330433, 140253276, 911343743, 351077353, 32520278, 27460717, 573934870, 260499868, 23446906, 660761222, 477231474, 199510387, 489456584, 131110602, 117819610, 555540763, 572271413, 453058238, 432924910, 937039567, 808924087, 25870714, 782669244, 291069024, 387912363, 327510109, 994548264, 692455410, 697704309, 275185579, 34229470, 960238717, 495125962, 123181595, 105349892, 484889718, 158214706, 368986047, 331247595, 875003159, 168631964, 164223311, 847442483, 707088122, 974888190, 874907043, 794533458, 300410390, 627532703, 60052850, 533772959, 45963033, 968980905, 984926992, 477128288, 409886222, 39702641, 983293958, 973121810, 514947723, 12744142, 323434746, 120405388, 13113456, 254155980, 563466987, 760622422, 719761986, 298211510, 100690528, 836817241, 833374781, 671239325, 373876558, 829369466, 473164909, 929832059, 330095753, 627945841, 837249025, 354494107, 14240317, 834904, 107544739, 581605319, 44400330, 388193417, 177514298, 493949026, 32016967, 676762087, 593425028, 358266224, 284298968, 428980599, 309537329, 306220141, 292578953, 600760636, 604307507, 522411264, 865082697, 827546423, 155047965, 433459031, 964495692, 520938383, 19734142, 132422776, 742298003, 707521791, 742859984, 965708873, 232494628, 662486690, 482211490, 981013523, 763455735, 160648716, 465254692, 462503994, 261801405, 333666446, 83541895, 149344051, 264961626, 768493388, 377726122, 187570778, 721720140, 441149172, 83188110, 855043209, 823907011, 209125514, 667690934, 686540518, 37757715, 917954883, 491127913, 890199549, 42957463, 521423752, 882321532, 872612444, 187778254, 75451641, 503030980, 344318882, 569961578, 744428376, 947363325, 990711582, 669733117, 78869725, 788563233, 682864174, 529936839, 657700728, 703246171, 889524587, 121217515, 277229121, 579135752, 791193607, 822574852, 236452011, 720662042, 851718474, 44406963, 153019853, 216655141, 82662529, 963399695, 57178361, 528183245, 125620693, 355478170, 44693159, 878718383, 460125115, 407773908, 582617721, 898570333, 307001598, 687395402, 271194076, 150000783, 621199508, 370860465, 258289274, 240743191, 755855619, 511287398, 837697988, 379912694, 269238615, 571028624, 195576245, 862991733, 530580016, 753384877, 484297906, 837830138, 117106563, 859410277, 633163446, 166317297, 493692210, 288878680, 715852284, 368086088, 752716672, 566150471, 338793262, 913852068, 757102152, 545525211, 592547948, 876187112, 556109784, 888103591, 41176336, 162417622, 593945629, 535492898, 378731905, 196625087, 24749982, 484679343, 435215930, 360194724, 953703260, 252042043, 171673459, 99781385, 371788602, 329364203, 249655813, 660885762, 995654445, 943156894, 493787286, 57070606, 329757553, 953984027, 145336124, 264289439, 232265809, 532719371, 813435198, 541958584, 47419809, 635890715, 170685805, 481445430, 259572985, 894309528, 324471652, 503439877, 298304118, 977562453, 45488503, 310148277, 621938846, 26501167, 529534953, 740300362, 770147315, 941417172, 141047089, 410706131, 289108330, 822361359, 186291376, 652893727, 865376905, 717591424, 346682174, 566057070, 786432459, 914884214, 461694919, 101086985, 869487965, 923687542, 641798264, 955429402, 847389045, 303167596, 440882098, 471541668, 682457748, 236123642, 804464182, 172778592, 733526511, 756071017, 824682252, 138960036, 953688762, 866439803, 759832543, 61427248, 741932869, 63472484, 422075939, 487660150, 888762810, 396234378, 824032139, 99995401, 69672939, 751199421, 75836464, 450363584, 9583966, 239848584, 77852523, 649483563, 572997523, 219750220, 109055422, 549805757, 899656044, 78756771, 101727033, 972761033, 742674640, 163320861, 326162421, 228569438, 10242845, 536428995, 477376335, 918836230, 305905599, 390106659, 424284144, 96471307, 83803604, 453035421, 274036726, 746584174, 812673464, 984475734, 359245678, 4080571, 160812969, 46626674, 526970673, 475828950, 404999077, 146523047, 447423095, 433643237, 625829019, 656386569, 353491942, 501566075, 904363717, 386031872, 238652915, 168921555, 624578623, 700578870, 459897007, 20883616, 872496260, 533958115, 768547009, 240705757, 332866852, 211805755, 247430318, 643847566, 741417633, 969040787, 678540794, 735280920, 410091280, 876401644, 561605412, 364491211, 682775568, 40208796, 560009211, 171256491, 405381126, 594510855, 888292974, 114456276, 19482814, 215325492, 358968620, 606626932, 728188310, 10592184, 635727617, 680421503, 738488057, 170198728, 289717707, 396864531, 620038855, 781936749, 373922964, 654779488, 544833968, 501123652, 690582697, 960615075, 124299874, 446198884, 781801088, 567858356, 315702766, 644036320, 578684417, 35406648, 259018281, 488277578, 841481077, 237983390, 662931011, 184316657, 555154168, 22835050, 373768102, 691574331, 797138157, 444448032, 953034581, 273373583, 926946026, 662911967, 274844553, 52244085, 266620205, 226836055, 243120778, 192918331, 793967855, 848025471, 62596596, 348682411, 412028681, 124482347, 253157885, 866140824, 853344919, 727058770, 687409735, 841830226, 833268552, 870245392, 324666047, 937433855, 922796167, 197540965, 722308846, 875544891, 367779528, 412196761, 991545411, 712411378, 667781067, 86985856, 482430845, 947355743, 982218019, 402002958, 662128768, 881915328, 759802789, 422061354, 61939669, 866595988, 543863309, 268060844, 881154867, 5315000, 437024526, 700259791, 242248483, 707894638, 512510349, 73434045, 984006714, 206216686, 740590854, 401016713, 641657332, 979000921, 520729313, 273705277, 514433033, 385282033, 859307159, 65666837, 512246142, 197037536, 926432639, 31520595, 778210239, 17260470, 744935689, 925708944, 534975325, 464793245, 385079589, 992360409, 570203641, 106063895, 220253183, 936098452, 751738437, 391336200, 33061421, 139486521, 8098983, 960371774, 970076788, 855588354, 11662438, 691301937, 616806570, 361804244, 957566496, 687305380, 897196437, 944020785, 529278210, 307002742, 170668521, 492921038, 820516949, 417091843, 243593015, 240045861, 885036623, 443317590, 128445263, 823190980, 342083918, 629375137, 926527013, 30123441, 947567545, 930017276, 60250286, 565331818, 910359621, 328809987, 471692409, 391516515, 760141842, 485685476, 471807901, 279835425, 836833341, 179578227, 131871654, 173863166, 300239938, 116601850, 207049166, 289807797, 553001331, 787390305, 320195956, 77152497, 872964160, 349630139, 525716469, 718269911, 817853954, 634986413, 599997682, 737050127, 667277233, 394913329, 539203628, 400754697, 567206720, 15186855, 49576839, 32087792, 918687421, 977891691, 645077567, 904076559, 34358527, 740779078, 560215102, 397833485, 998730594, 560415918, 317974325, 124912689, 571731339, 137755799, 439711020, 671195378, 954809621, 345019208, 557397592, 704906, 382749484, 166351225, 782917617, 696397916, 373583781, 911386170, 188049009, 466429395, 866564383, 939575029, 277459376, 963022423, 153955154, 75882026, 451115693, 688684290, 97329903, 697029784, 776281067, 585147929, 974283850, 220693019, 873606415, 546749918, 147064702, 123349105, 664545281, 543314864, 314423240, 943601043, 450384267, 149677543, 230777970, 932165269, 895712030, 101165781, 292408528, 389626053, 523658364, 977092254, 59145887, 73941095, 581132565, 580690342, 567630625, 342973077, 663043292, 120966605, 391557931, 118063618, 534487716, 953364378, 304314033, 413847704, 964118749, 643681041, 956010532, 622767858, 801463368, 717436976, 566278353, 52203854, 450591922, 68815100, 822351301, 837536151, 130715678, 483299425, 581674571, 687002989, 332081789, 425226021, 883840024, 112781938, 945336159, 584001789, 42633941, 813534581, 352018461, 826033586, 655323095, 712109525, 53980775, 421017783, 927438498, 506810084, 775154971, 380343816, 522183986, 381754063, 309132288, 909792993, 240796461, 441158225, 17436492, 894907070, 990741983, 793845382, 712417562, 925080773, 986745175, 89215226, 333860826, 614056808, 671901885, 217844486, 367695689, 285775019, 353317458, 88796983, 512532992, 976136172, 175869174, 714739649, 834658922, 81203049, 763673684, 728239611, 883561779, 725010417, 281719171, 562203578, 856612387, 416857694, 705561854, 570328392, 226910117, 525708350, 430859285, 229265884, 22592348, 257413081, 12425110, 630225916, 14525444, 914479869, 234152947, 630111795, 151645649, 922551739, 96991429, 942164015, 18229965, 51417538, 810751246, 99036035, 826734307, 668930014, 31792005, 306681968, 415387284, 331080320, 741634521, 17336845, 596875987, 241454747, 973313576, 231476614, 719304785, 568132748, 347421886, 348907308, 186984623, 830090991, 181175634, 227308079, 575557752, 649899294, 537277054, 689966947, 298757669, 956913976, 204159492, 56106630, 445884680, 215381021, 84060929, 43728441, 890171607, 159078399, 704871702, 817070637, 35432699, 301791442, 763237120, 740481671, 266522116, 576123643, 99994984, 206598992, 607094835, 423527879, 88287750, 223440556, 413167881, 7932093, 122623522, 77076380, 396908229, 547310214, 764091338, 267513296, 186282553, 416931617, 181535469, 248530108, 256416882, 121047824, 880274057, 835448166, 475175298, 640684440, 578817996, 302414871, 426923526, 990870770, 283172062, 173667649, 570638208, 930730167, 20510395, 696570951, 714388352, 938300705, 344300613, 41715099, 596073590, 900023028, 441190352, 245183606, 844168797, 180339412, 206101392, 464545085, 805795397, 817236875, 646983299, 802832388, 451462126, 733408025, 130042937, 123013206, 82807955, 447714303, 11016416, 481586234, 209179408, 810463230, 856662109, 12680867, 427833572, 971556513, 203021119, 247346564, 129577099, 967658525, 592154783, 475375933, 12467197, 988094075, 236387912, 832392077, 145237822, 409401590, 544142390, 955870037, 425775888, 276634348, 455241456, 689090570, 329129278, 404226237, 743901309, 936201665, 519388738, 298343096, 128146340, 863590635, 84223926, 209309639, 520998636, 247093611, 589408683, 51295003, 197846585, 582381494, 592174264, 262056159, 865712687, 578298513, 132793477, 663036666, 549818790, 507913867, 276979252, 956912789, 632786205, 19353993, 427689855, 659548195, 902812626, 452756576, 141673557, 16190609, 828886362, 313581038, 812134952, 905650269, 248155039, 459119473, 466316835, 322188723, 252718740, 719728303, 556639812, 166201952, 388396380, 518436201, 883558093, 550941640, 661653984, 852541042, 962228496, 745426047, 131707231, 581346861, 199123413, 913551724, 263055473, 857517156, 583366558, 109544611, 868754764, 861760262, 592547983, 855208553, 521745490, 667710019, 240901793, 342690166, 809539393, 544557105, 917405763, 316148386, 5837979, 629416883, 981275720, 904981714, 312921363, 614570303, 901646273, 201904946, 795448792, 546860614, 355113166, 706424462, 358124449, 63968343, 517717775, 570145066, 187373284, 389600357, 290937899, 607531760, 258907164, 930081754, 254499177, 370961420, 666255211, 711263264, 192556472, 818463035, 17185103, 668924881, 488117666, 272840125, 46982142, 18866222, 251806122, 518970599, 413559769, 226941165, 747384245, 176407579, 315246658, 8784537, 598592652, 73863408, 293684739, 304494538, 812661722, 701078799, 424331863, 93146989, 660288901, 867718537, 332080809, 704195910, 849235304, 473612139, 979209374, 297820203, 493472620, 866724623, 970167160, 574302160, 878662475, 189887554, 12899664, 175317265, 444846079, 149880469, 218922535, 920915359, 905788286, 650627932, 584382938, 930468869, 26578818, 385049104, 63648152, 72339210, 171304616, 939993783, 400203056, 472030848, 511163830, 997407538, 723223266, 853691621, 370074639, 655944581, 888739469, 302023592, 748966291, 907535968, 882493075, 667183408, 304607692, 107112579, 700494589, 928458667, 690231879, 265385213, 204761943, 178735858, 499263444, 539367207, 776505751, 814562715, 901815275, 869175553, 753660497, 141420780, 210588392, 702622027, 372284863, 160458648, 874006396, 403215560, 33426413, 176086112, 727445709, 419713081, 769032864, 73258822, 631680891, 85844203, 438011373, 576819876, 168624081, 855463744, 979317467, 521016801, 679093051, 5093522, 763693930, 769162816, 212006402, 359455996, 515850402, 185226352, 96858320, 993646316, 373229765, 46618033, 600616102, 800830792, 850872686, 858276106, 391107182, 93065595, 495792500, 302651516, 594788864, 292232243, 144327745, 19096979, 442087714, 327857321, 623202465, 989310540, 462912343, 93284836, 373225199, 427693390, 390330795, 375990200, 611490613, 470292556, 508227855, 770993910, 290264419, 235817855, 411904239, 223035937, 21525193, 936239718, 210340229, 510546084, 846443182, 577928328, 950790704, 534546022, 933728640, 635530354, 212271073, 331614242, 612635468, 989747898, 267618319, 266195232, 355864414, 904385432, 485847674, 636021444, 996692034, 276850315, 813248177, 959694009, 887801293, 564480315, 97088026, 781856264, 333313710, 762868493, 731569960, 690618605, 89575039, 419069988, 175728050, 107814459, 3785772, 355353186, 358705796, 593066932, 371187689, 556370660, 5304663, 107753169, 444395367, 346964629, 870160562, 468041690, 343278536, 25019690, 342798978, 934468780, 230778164, 104965876, 349723195, 72531456, 681226436, 534902870, 916564620, 918454693, 702532501, 137351050, 382931383, 881779627, 616463030, 937951678, 81128264, 422120472, 443776960, 162345916, 94193308, 37351280, 1625704, 48457629, 984483743, 778513970, 909198549, 31224621, 674937790, 464740638, 566623816, 671689167, 758093637, 990060467, 978055270, 386782163, 980812879, 984097663, 55592034, 108238616, 701746677, 970324340, 32137873, 240111734, 781714179, 705150305, 531422647, 559417926, 916903793, 203078706, 477501568, 753983360, 903071350, 657275395, 722673158, 260196649, 867056224, 878390493, 403881491, 995676673, 718320715, 316389898, 33298725, 525139702, 464173981, 285719740, 249130958, 552245692, 7073359, 114274977, 4264338, 348402338, 750925616, 210680081, 236284650, 803408846, 753198758, 209120149, 454694549, 562176738, 747617799, 911093310, 404082097, 385026791, 268963961, 928390526, 313240506, 795804785, 313582259, 20734235, 418060537, 871770178, 439084603, 526792401, 929019465, 681547421, 123949739, 202327131, 793721849, 661428961, 467109269, 294187193, 852118889, 922341453, 423433564, 232254326, 567739082, 584846917, 887583457, 597838469, 506265435, 372951664, 983237926, 962845366, 688420632, 125161445, 35457676, 732075122, 460808437, 869337455, 714813683, 722645776, 760941111, 574627294, 15145977, 2158227, 457746770, 796429003, 454853036, 717825498, 205052666, 987457055, 428735742, 180215545, 493555401, 10898336, 821477087, 192718617, 712556239, 968075284, 512941467, 73727050, 995743351, 46796683, 658411293, 185056276, 651259704, 121174918, 876007005, 608919273, 565814085, 236522446, 452977931, 738941911, 986229927, 620223917, 215740001, 652547035, 389025549, 115483852, 18659480, 918157137, 428453810, 930737040, 422585311, 67044518, 770934881, 216163296, 246257439, 594610634, 688364339, 999243120, 247682442, 522337221, 909729166, 448086754, 235812050, 895454689, 87422520, 338748977, 195089417, 699196282, 556987399, 329230019, 576841286, 271429532, 433549753, 693378951, 600826567, 886998853, 731936469, 881621067, 281250164, 358881058, 659165828, 47165266, 279763070, 215245307, 527063181, 309601502, 779273357, 932973913, 303132410, 213014506, 472027192, 816053808, 753039074, 969341348, 122063707, 389229058, 300908528, 746420464, 760630392, 294152453, 224498272, 565145246, 720809090, 631040215, 737783929, 888445173, 88368506, 444201317, 220045967, 350461178, 969261813, 464835456, 948673916, 18972940, 339102008, 979370571, 879745391, 919231375, 97270695, 45708451, 586439354, 64317313, 809615206, 776746336, 634745309, 815656861, 798406828, 676533999, 899359076, 844793504, 185733579, 789711980, 124299176, 698889775, 853385045, 40562670, 270127665, 700804209, 275056945, 411574749, 152589417, 83927861, 722831046, 699736679, 392660623, 986430508, 306002512, 411726787, 348818304, 928490108, 547263938, 954509336, 388443381, 86485671, 812264573, 941254301, 241265461, 782641242, 842602896, 651531489, 412762436, 602641124, 232778339, 188261734, 851208404, 188109663, 131890729, 94330011, 717604649, 11395607, 813141826, 527396035, 434955917, 212727524, 384676342, 979748021, 270387522, 792934629, 565373137, 974785422, 188347573, 248359451, 688596980, 836656169, 563141893, 550346290, 301619521, 533888058, 834038676, 451461340, 561661392, 576615898, 162409683, 888162971, 377232784, 38238569, 900329280, 822146955, 134976540, 971420181, 877155104, 448265101, 165353005, 521375661, 252579440, 13929873, 849895119, 905149714, 173720605, 872893454, 276942145, 872945670, 747024069, 341151639, 949389674, 381465528, 877087790, 425701429, 971400645, 124737196, 36230065, 39095598, 788191239, 239713770, 367274800, 156972821, 485130124, 877466185, 214052777, 944693165, 954215197, 643581744, 950576001, 536834503, 641042269, 291120196, 598017700, 49012258, 234296417, 150619235, 306220598, 909514599, 17844671, 916797163, 385306773, 769766974, 680487711, 573874982, 819973402, 976014554, 623103568, 36981109, 499885020, 3878227, 115068203, 663266854, 242519736, 439959285, 696266611, 388005917, 838923552, 53907480, 305188064, 31445020, 216083609, 20468500, 493684633, 5228286, 269918329, 461858934, 297817346, 405234617, 793363815, 603225681, 158816502, 817974247, 230510677, 190985149, 668679072, 880187632, 733196805, 251202406, 346061862, 448689551, 378694814, 33350081, 375854829, 552329757, 483011569, 683121899, 53840280, 445765738, 974645466, 882840634, 616954634, 41101144, 995157979, 180487678, 360178140, 666113439, 258996949, 194876126, 843908831, 484109211, 789243028, 117870029, 701429576, 935662984, 202737476, 511764521, 476844910, 493209769, 676129344, 352947784, 768416836, 216401530, 414061228, 818693635, 314624448, 699202005, 682013221, 683318474, 395354459, 900279954, 277268573, 31015044, 163030051, 246145036, 226404124, 730568339, 779092720, 96104407, 602097344, 575052656, 209599130, 104145183, 867440554, 175800816, 388862411, 944893439, 237251493, 677927772, 544651672, 295476159, 310137511, 266215961, 408664385, 252095955, 736614749, 159600328, 383824908, 748950292, 858168577, 711092533, 671570081, 760182155, 154657911, 932016577, 403948763, 351492468, 689876556, 282537723, 553048320, 266273149, 389173028, 967545787, 52657614, 200370389, 265663307, 398729360, 924404277, 451977835, 173427713, 21789697, 521879598, 86073479, 575415803, 824443391, 685549673, 399249837, 923438530, 441109439, 549858782, 517476447, 886120549, 808926613, 91535826, 772675354, 720574813, 409089678, 633594848, 477452735, 129109588, 69156765, 940606859, 248576997, 309735140, 503055304, 322854911, 256023615, 931178393, 407161881, 458770997, 780346250, 86865770, 347493145, 132731889, 53250449, 705459384, 113633195, 8713824, 306434040, 411944878, 167543564, 486027847, 899658057, 153494276, 589837490, 846692031, 495455346, 990428538, 632377369, 275317828, 654009624, 903217927, 362937713, 595523673, 104561799, 619540257, 591972737, 713953295, 55898207, 250286411, 515134144, 951273221, 868351317, 215827101, 644048895, 32125177, 731343351, 294823418, 581511177, 928184293, 860261292, 97501170, 727556976, 15315341, 50411493, 263025153, 460508404, 828732842, 133165683, 973754126, 781473956, 167136935, 265364217, 146575610, 733661977, 818469270, 48013968, 162488214, 698199033, 588646243, 790108992, 283073588, 866485810, 17566942, 62434769, 335240234, 411242410, 518421754, 373566323, 540597311, 689706688, 817892792, 567951018, 119625718, 746804265, 798838520, 685365084, 729754804, 841932556, 790763543, 159395987, 626108138, 375859531, 913012594, 334353084, 119902132, 162696086, 277250598, 591200277, 579543513, 938727603, 378817185, 1564382, 836538556, 627930364, 925338591, 368468020, 234021773, 477669020, 538705707, 5218860, 507902792, 639879341, 70568219, 507185951, 836125861, 965602921, 78158054, 121856696, 625835, 703096539, 354225273, 650025510, 32159850, 365416951, 438655987, 480408243, 428927115, 448885581, 227548748, 579714709, 315346683, 41047903, 229968247, 992395672, 120441081, 115048669, 358905775, 460176899, 715312801, 404726294, 264291683, 777863985, 190321905, 486741272, 318291773, 337439922, 582102153, 383963702, 472429757, 629071645, 281425806, 369507837, 429366864, 955633460, 585915952, 335982604, 948039142, 637208068, 158817341, 27201413, 63859840, 368231965, 908904810, 975324133, 801617936, 162891342, 851334564, 263679928, 112872152, 469792828, 758231599, 270462895, 305009353, 34821851, 602041758, 905860174, 938546061, 806844804, 602016927, 851904009, 260370158, 613744725, 574072348, 699817866, 294049486, 162931624, 483695348, 821103891, 775802045, 415843379, 17037854, 97294843, 287429939, 425886659, 872069424, 517867451, 495176846, 612112751, 522068645, 248842392, 113064769, 444287752, 166451178, 996424329, 517914091, 485562552, 885681657, 608233488, 734339031, 798250058, 843869453, 180255748, 625450582, 931661529, 578784802, 58706070, 691485338, 113836240, 429049366, 122242002, 479910305, 206521384, 218165690, 126920623, 850274447, 621744986, 498146765, 985772567, 915659096, 283951384, 812331917, 632455684, 951447260, 296616013, 838772394, 269381657, 155407914, 240400256, 893142533, 310517783, 535569221, 359473739, 588154866, 195924134, 458769667, 401434910, 497223721, 864069378, 95760268, 12878467, 450423580, 189009171, 25825541, 99647650, 577844781, 254480465, 987876113, 635749596, 802019838, 80683764, 260581509, 444990659, 193623629, 580948916, 316217687, 277088835, 53809658, 363618308, 348204770, 838045315, 155647002, 182605984, 745440905, 411858287, 189604391, 9781686, 4068047, 925184859, 58556713, 322080971, 323391941, 921244333, 476451133, 759570680, 120252499, 235236237, 236640934, 692572817, 796065791, 304961913, 299489192, 10958238, 808071446, 141202885, 986232154, 360879919, 610698077, 696368865, 17804476, 665536235, 295940277, 934828486, 160778087, 275006794, 750541274, 967718689, 945734214, 564012417, 246105493, 62437636, 52724114, 470332551, 622281403, 166222069, 189109612, 784548254, 937606155, 491254339, 792971537, 305603149, 946639335, 33845258, 592001975, 288806396, 851159782, 806803358, 770936840, 878816626, 92335865, 18359498, 708597624, 416431194, 442218028, 513760782, 798672990, 906273529, 641772457, 964721881, 51061242, 496480508, 83595869, 211491489, 660799395, 595066367, 123633571, 509479718, 587810184, 802545077, 505819492, 57236183, 491812925, 876751217, 574869343, 580945750, 164693487, 746471716, 287198590, 728952261, 745301003, 670718190, 837144477, 118487929, 849930212, 554537657, 586424428, 292311842, 362079815, 788452249, 939883329, 463414865, 189475821, 390605392, 247382886, 154965526, 664036631, 468802437, 618452123, 656332081, 318973218, 912545558, 42179997, 635148333, 439414046, 457833022, 845838015, 191462665, 895861283, 199615672, 678596511, 564401436, 391988477, 820606220, 274912126, 756702549, 987845871, 267163733, 113127542, 109722704, 413648140, 114029597, 533558882, 304825641, 855248513, 600982992, 860730421, 58362697, 163155126, 449726973, 912472622, 814669106, 628773364, 11417543, 278072956, 199315311, 427766838, 102411294, 674734109, 479906401, 160808789, 718493291, 471831087, 825114832, 486292443, 556297172, 29406794, 56903438, 905998129, 944992849, 155385696, 402951023, 531975449, 195257236, 576624050, 359508400, 102983614, 712195849, 2488445, 718898779, 634338180, 322954221, 591908588, 858109277, 644996981, 334036037, 781283581, 818200795, 669431175, 11346939, 875455230, 901607385, 558922567, 529846342, 833210984, 822421725, 79322686, 407114091, 667400762, 715217941, 777877536, 107127188, 479688577, 548910834, 651966013, 936559023, 815297166, 330907328, 616054486, 358645640, 884167569, 121247778, 483890732, 532394161, 350712356, 641442746, 18413863, 657745729, 272611564, 891563184, 597975717, 660104768, 718136710, 646160055, 976679909, 627191783, 888450122, 854569205, 396109012, 994415044, 66160498, 229552831, 997018911, 754571769, 326682211, 334926991, 11170407, 108785964, 722738858, 443445662, 330767125, 920869694, 954207147, 702721362, 515426048, 954479086, 760759342, 329053394, 506209363, 109614210, 275983040, 915603810, 869824148, 167773316, 725785574, 754810707, 619071506, 984588665, 369031399, 771584382, 328470121, 13573845, 565510381, 664996770, 378691840, 24338001, 325025539, 921435073, 286710657, 697446871, 845848983, 356145418, 495422373, 848622733, 109982186, 222027111, 790401479, 416946069, 374512896, 994840274, 565938326, 501105182, 770782643, 842681824, 274682733, 778823911, 614487778, 205245804, 512388534, 817922250, 552820553, 593278813, 200947145, 898150306, 933045476, 174869159, 140270569, 403895637, 717393300, 817868852, 615958283, 592177097, 61191435, 658989803, 533389927, 808814449, 116779079, 563738875, 134896596, 697835131, 477689377, 199846213, 73030168, 635178825, 507217986, 403368708, 681964644, 553453588, 232318713, 741333826, 821190814, 504530780, 285142645, 899342965, 316563507, 684066523, 887631664, 406640607, 100583715, 866586421, 999692635, 698417073, 20077760, 488133936, 880856472, 135122398, 6252860, 486660855, 514872281, 410828481, 978843641, 538146269, 211589618, 276984734, 761551352, 950811753, 858101220, 779907593, 996493910, 148305325, 106733255, 30326908, 836737978, 484574289, 825463327, 756894881, 131974875, 625460770, 516976090, 352017896, 492135597, 15467972, 745280573, 393834194, 392861989, 467831234, 886278455, 370159074, 823916422, 692082078, 556022165, 485594720, 160591424, 141650345, 198395604, 570647379, 871848348, 920746192, 928241656, 968252299, 812142468, 309538287, 600652874, 997452776, 382350033, 433765417, 845812398, 922826948, 640460005, 288171468, 114517980, 935891865, 843312730, 754665188, 514150265, 476207964, 560816417, 54555551, 638143596, 410623262, 312118064, 166801646, 343154323, 549849401, 704710250, 46244414, 980139349, 927382174, 106816705, 369221041, 798780365, 218295020, 12638682, 473675480, 916415907, 316579267, 185594529, 413199343, 914753682, 684218492, 975434118, 611901805, 287665528, 275443911, 177282061, 306403870, 979814615, 730458641, 857610957, 640608852, 965228974, 902727325, 565530368, 238525346, 586082198, 703313973, 693318478, 78722538, 993168294, 636100111, 836130969, 832192527, 101995868, 356249001, 374788829, 183893229, 93287768, 834223062, 184359188, 693592334, 217199258, 843555468, 525116073, 755010463, 289070151, 118311258, 391269590, 392926361, 679209012, 714065002, 25063400, 795955775, 971156389, 144352675, 16351175, 446598273, 712169501, 72687082, 654865131, 836155376, 149689222, 805457348, 456056378, 167305545, 340065500, 816303913, 260965707, 396514992, 218998264, 302344371, 26515472, 143282824, 81396433, 356355737, 942395485, 115734536, 341522187, 208542744, 921802825, 205994689, 931506117, 934412035, 167047139, 131563978, 764388740, 259552285, 403701368, 488696659, 805425479, 317138355, 78248022, 893812672, 941563558, 61342767, 782891976, 800440512, 744141981, 930896137, 271308387, 307572079, 688085298, 321284042, 984799975, 682104439, 792247747, 381015834, 293349156, 70430703, 518672148, 735164248, 166937940, 490363711 ], 24812 ], "output": 9514031892537 }, { "input": [ [ 754809389, 588630704, 975553006, 418303935, 14822617, 126276303, 328959241, 983373194, 44679538, 401517827, 441687932, 964647009, 760582598, 593764989, 994715798, 59711119, 674074180, 430922246, 396556804, 147654318, 814001174, 523995366, 996282187, 729312001, 959027482, 976921196, 358750840, 168961728, 956831927, 113252302, 191984978, 496907162, 604634991, 763033975, 860820727, 268665308, 537742587, 595195329, 969705034, 643326420, 687325708, 424398500, 948355653, 566035245, 149480127, 302570528, 490780883, 745690503, 705291331, 522534824, 217661131, 827491259, 321904013, 584205172, 371461713, 30342254, 86791800, 549783080, 57238866, 19064688, 884960572, 941662688, 162933173, 541453207, 814549330, 267899809, 421369913, 532453992, 835677831, 19398758, 772875768, 798995217, 473292621, 404741435, 973500515, 533392370, 140966992, 345850975, 783888115, 931094814, 745990992, 561830803, 652697286, 248932347, 362491232, 815336826, 154288207, 446799908, 364473873, 509790441, 392568864, 134687870, 217476837, 66025527, 967671948, 422863828, 909527211, 828472257, 112236909, 783348913, 964157732, 107293246, 347481108, 106949608, 320186908, 859278967, 516061009, 378358663, 134163773, 295083728, 731142277, 719121108, 539580091, 401148358, 593133290, 31776371, 87254376, 713100867, 501044119, 288506452, 907919519, 258072455, 593351198, 594186866, 995546532, 507639228, 14438237, 539121310, 25222224, 714066380, 758704532, 850172606, 466467261, 738977194, 191777461, 371016013, 114171225, 808731453, 862160480, 878632896, 400722753, 796869066, 428165577, 750700518, 664396780, 226312034, 977972868, 567144636, 691560236, 433945085, 54252789, 897086812, 724729323, 630819439, 437855238, 582543002, 306368352, 452858257, 921190894, 727676984, 780806265, 684543703, 331710303, 624346886, 172390698, 894218438, 44116569, 992237843, 891377597, 93272585, 770633916, 656555536, 446717234, 664546090, 713046275, 315230640, 837389729, 532759703, 519390982, 856737161, 81890306, 387298969, 336631112, 208643569, 112081703, 661929826, 305723516, 93241696, 747025579, 856242206, 996571140, 420558474, 716899777, 265502355, 577446710, 180197278, 976027738, 108206546, 177585715, 715889622, 983988335, 790349952, 145563843, 590417367, 519757565, 251124009, 837258209, 638843610, 829486509, 718923124, 292037779, 592826649, 65904099, 45989239, 762638238, 415653229, 331393610, 143500432, 357671979, 896282879, 236313075, 194647236, 335988162, 28841773, 655542023, 366766897, 65954431, 526982184, 516343379, 744190419, 435941470, 108585998, 144531001, 618911197, 795300394, 801727311, 605644495, 129923593, 832375350, 387738200, 820026473, 733475634, 56106885, 748696612, 133102269, 649372019, 405853295, 688929463, 283067553, 760976847, 831172916, 973221273, 258362191, 9583037, 901312024, 564811984, 150519341, 346244708, 577744406, 776466043, 625455611, 296324068, 335516881, 539718435, 815654338, 92605964, 558600619, 330678799, 28090502, 547230645, 878888149, 561227017, 55506848, 78837963, 207706346, 284890616, 101114822, 346231631, 118043676, 113186826, 95233819, 977235902, 560961233, 415576994, 719270447, 805072410, 283936573, 372433958, 222659990, 437534656, 986656996, 292453601, 3165924, 798828127, 100572454, 964676773, 837424376, 354600426, 886618752, 775490617, 646197046, 181115106, 798254111, 375281035, 30686921, 140071660, 863768670, 256795884, 388487016, 327329905, 549223570, 450238656, 11028712, 719232090, 693761522, 312186880, 887603898, 499635471, 436136958, 520646896, 281223761, 148043711, 939728165, 853388564, 121448289, 393890817, 603598071, 735822175, 566279571, 624804100, 84658385, 129156838, 754610814, 79258357, 57351138, 985636999, 478438396, 265294276, 985912979, 556727752, 592763117, 460676494, 895131646, 302407545, 398694726, 264775559, 829825660, 476915247, 146088938, 534863971, 125686787, 908077582, 126221114, 383829077, 439852225, 179480216, 560442014, 244355282, 300007761, 726253030, 541815359, 261141843, 443135046, 347122204, 730835193, 198651540, 730941246, 627206065, 885986974, 761728140, 63701183, 778536130, 113886932, 670039983, 722087520, 487833844, 57764306, 913999279, 464210166, 836804825, 953538882, 204792893, 181587405, 409602692, 972295003, 585833370, 279610989, 330006101, 500931706, 750112297, 301626021, 251366599, 639347795, 893495850, 406365147, 181756589, 246912494, 846386497, 707729272, 217451474, 826979374, 266748592, 410735957, 425100992, 638731426, 886769475, 178607261, 997779777, 484042093, 181599155, 49094311, 371219674, 906555103, 483863660, 467516367, 19426910, 479055856, 403943567, 177679220, 83602510, 570532555, 210964174, 816199723, 739531149, 588765941, 26230317, 553163179, 976627420, 480449397, 886479252, 738063122, 138669970, 548957440, 37870733, 466754921, 247267334, 247814644, 229851423, 941342446, 845556386, 6806164, 69661308, 737086687, 274438198, 672677493, 635503012, 886552521, 957391830, 873729932, 270310304, 277342769, 844675253, 628313124, 546756036, 995579654, 955799110, 929616506, 935311514, 104537138, 879123719, 870142732, 827519673, 806091521, 955976275, 430525129, 628444307, 541143862, 877820155, 117597353, 613652274, 402046311, 82681673, 517750778, 100670828, 309794482, 848432601, 459385815, 704619654, 958760439, 680997840, 240372439, 373967498, 239345215, 612014987, 925961884, 435739120, 554900181, 911201060, 587190874, 886699107, 801945662, 97362345, 205541490, 78506138, 851293117, 250206029, 970559145, 951772757, 544133035, 268792886, 691824050, 31252769, 997293797, 201715062, 520029413, 459634467, 544666715, 35729501, 175324754, 400024522, 483878319, 57580623, 8399799, 2530101, 877323341, 958383300, 504461323, 934961976, 583871583, 580116876, 626862502, 916352455, 348321559, 155135463, 202152013, 524664904, 819356806, 820894312, 142141657, 173981614, 703254266, 272833158, 560310584, 510484203, 459276171, 623287780, 468642393, 540862716, 839761029, 770763569, 73546136, 181837566, 941045528, 422601958, 861136211, 901801053, 51912800, 42405340, 850491668, 353529683, 150997396, 347504007, 509445366, 145459689, 532924437, 258159175, 41310604, 581038825, 930644030, 158223842, 607691965, 79417582, 932834289, 898110305, 116861753, 646059183, 934074039, 739576518, 152604404, 35050591, 384318525, 832451578, 589533249, 342058779, 939860991, 12185434, 733381497, 539206387, 968413040, 881285540, 634981247, 369151121, 148885515, 632578669, 351804090, 536402157, 684528282, 530582671, 622014597, 692667512, 916853494, 783333907, 120871998, 85759756, 245172708, 57440827, 645089052, 582653769, 123136784, 221093675, 670201045, 940478813, 5637343, 487256322, 101598110, 642230476, 521156154, 26901901, 294390474, 604078464, 908569296, 921731500, 296613410, 667653015, 557861405, 715179068, 656614487, 843430699, 505384932, 517878405, 523798895, 598896, 444236974, 465971675, 974918390, 688110613, 285274732, 442246817, 681345419, 273500554, 576638044, 463320714, 800989748, 754680052, 253151957, 271858266, 366882321, 389451938, 121463403, 585540338, 455264150, 809404998, 229691620, 52479164, 143630378, 653040458, 78243150, 863702470, 742836132, 414017794, 376834236, 496299589, 701613939, 375424707, 143181965, 332627156, 265677340, 405279713, 715882260, 133146671, 724601457, 794109918, 78445556, 218924365, 703853351, 189056072, 69271549, 346438202, 926525034, 868822267, 987322741, 67920866, 796531253, 213931553, 313408793, 324438521, 285398815, 251333960, 154685778, 242758279, 748130525, 322755804, 558402260, 390210050, 53379147, 414558509, 946931790, 304577702, 631556578, 242033546, 410238853, 805555371, 42639603, 995248836, 544852908, 78032817, 451986410, 990732454, 434147237, 381923958, 88221590, 882292961, 653198080, 804626751, 68482145, 961947517, 638068103, 372402988, 228243869, 272229262, 959081851, 471426531, 177719193, 933514415, 157450724, 242267572, 706961826, 704525352, 493588344, 722290129, 698226583, 814016065, 473890440, 905979607, 983053812, 923468526, 197517874, 198632008, 718665604, 565427511, 832222513, 275559697, 673485211, 261953613, 745564209, 100641749, 866680956, 133288951, 417839083, 267262424, 545922405, 107933550, 376561025, 476735018, 909460916, 227243070, 809088051, 220310399, 503163828, 138857271, 587343582, 205715234, 9821953, 623814579, 763663401, 580965647, 458483980, 168646842, 826717898, 863967846, 732125184, 209976823, 818506205, 911618833, 294565988, 209556611, 791325978, 187950753, 920907438, 952634618, 207263734, 665293802, 765846959, 772932053, 556786693, 963483699, 801651723, 526595769, 777681902, 666780136, 434832422, 886392802, 287832356, 663333257, 236318540, 360237631, 729616651, 719441962, 383207166, 357524758, 87779030, 204732232, 356969629, 589154394, 665860369, 462135775, 674034151, 840269435, 834590402, 251139823, 902797564, 961242104, 413714604, 51336648, 906947310, 380378090, 78605403, 138197026, 162909707, 135248666, 488461790, 77044932, 926134981, 484695764, 720648602, 288590690, 911744629, 861686141, 21503557, 191184990, 926459803, 834839632, 870407108, 170164714, 208875463, 55467695, 388733349, 917943948, 495151791, 82554188, 726443679, 974398840, 508468492, 519083332, 266396763, 992903902, 383648020, 999061952, 697573909, 636968762, 317164712, 945363350, 443900100, 576759286, 730141922, 717195713, 498634936, 847360903, 825577433, 868418653, 420531606, 991755897, 934601363, 47806539, 251647923, 312905937, 24649598, 125190270, 350087238, 214854003, 75736253, 177077232, 139177259, 479771185, 914150953, 340092132, 972412790, 250816238, 851343281, 159739073, 83347953, 782288607, 817113514, 271096531, 609404559, 249426654, 940408958, 401111133, 150758720, 476065206, 736761252, 756699945, 570718985, 430887262, 817323423, 629003778, 335705790, 338231891, 606275013, 303757805, 440771274, 397136725, 71471599, 201403861, 364966234, 142938409, 467270311, 917907401, 643400200, 59187800, 718991672, 353327616, 133927282, 957683113, 312563815, 131507900, 71112413, 128563916, 502258022, 42930143, 149184224, 646529034, 648953545, 959229163, 519829621, 904099031, 181624082, 556289705, 773814855, 300414575, 44438822, 414311311, 230902295, 707094049, 459337672, 607584145, 576768688, 747560008, 28142623, 849669715, 858918962, 27364239, 104223539, 449107869, 828677901, 967741608, 697827609, 184635001, 1329884, 899212679, 445901072, 650322551, 318165205, 680063276, 735587656, 371434404, 833916935, 686416857, 836443681, 352231088, 658109300, 78083630, 78066073, 7947151, 777004291, 976406017, 900874862, 991162452, 15715508, 818068441, 907555522, 57933483, 799725997, 248650140, 132683792, 526450440, 42164940, 429515597, 597175101, 459339153, 225573772, 843567378, 101012861, 232451967, 734526249, 197562061, 37372659, 748894936, 269560940, 176556543, 448494678, 713943677, 851013217, 95703941, 661463516, 180834997, 520648990, 900232812, 949182343, 469663530, 641345196, 21531357, 401389909, 601045737, 6034404, 876195820, 690522939, 189844110, 258483907, 706744486, 581442646, 656860188, 504746553, 652756821, 167529502, 875225341, 865553536, 754189531, 609372770, 233997787, 867194884, 892862411, 741725544, 154729618, 315416191, 562178793, 831187178, 101557434, 403914272, 121786540, 975127751, 82826896, 378913215, 966667480, 815066381, 493177487, 396782911, 960733142, 93679681, 942091080, 918101276, 819146395, 110683718, 607323476, 181171387, 427909829, 782019349, 188798650, 995505022, 26776794, 165919803, 889994006, 913921534, 711723286, 454020928, 299702883, 697160360, 253090773, 992912498, 845265446, 302464750, 836285482, 650282650, 17124296, 398551465, 253054069, 882689697, 403913061, 538590046, 460108611, 97335666, 352259137, 738382959, 803321569, 116269711, 941743966, 333937533, 467395639, 309794551, 611083593, 793477162, 300785235, 601061302, 864309514, 65162303, 268971901, 234191175, 246745941, 106604598, 473496865, 647436456, 786221711, 302642533, 467045356, 497648130, 523875534, 528857176, 78988924, 321577103, 936847295, 516591136, 940834457, 194407829, 325622147, 360710075, 775837399, 169256287, 453098536, 620296286, 944150437, 387408304, 954612341, 981394631, 306541924, 11988992, 948943008, 20815648, 402821633, 54994886, 810996257, 716357326, 923637946, 307469587, 272425119, 58916719, 769522247, 216169270, 697130891, 629902471, 445063288, 409491420, 713629218, 218922186, 849783763, 898971304, 339513812, 286204619, 716831870, 212587858, 566295287, 821351254, 269632249, 351050798, 679936437, 255090687, 678490255, 789461608, 66755800, 749696348, 819570252, 407777693, 730252638, 274546336, 350567503, 578270067, 671600113, 553170173, 244703626, 984959561, 859587228, 391633575, 594659273, 644035563, 534984989, 411063654, 971366608, 698297112, 521250150, 404471895, 210261742, 737726104, 750874380, 404487459, 986091807, 540120596, 859696682, 88097625, 242479737, 316882803, 188387264, 5682083, 422602194, 182585438, 668179672, 219925425, 932960789, 166852993, 470687020, 915738723, 112179721, 972522596, 502855002, 224667343, 827698599, 182800477, 658234855, 328230503, 134933729, 454904327, 95706980, 72838336, 763558626, 512498838, 456300862, 443130023, 171319144, 248976740, 657975962, 398921899, 225065411, 193570845, 274731821, 246806226, 871278748, 733752676, 771664569, 874981900, 46917905, 471945523, 602979387, 530747903, 116492768, 229528259, 162951895, 313409848, 54986468, 790339271, 34764844, 78546590, 905127695, 253680329, 623992742, 749089539, 658111460, 561291624, 212266926, 185107998, 376949038, 32081995, 655728481, 99329611, 205680607, 958079737, 156404104, 412336994, 698412173, 737658395, 13625644, 252402849, 306274307, 203131495, 497514371, 202005125, 784312615, 299446956, 778947146, 790141233, 641800753, 49964431, 586190435, 830947147, 496909008, 751524349, 729897181, 400626380, 559600056, 138316199, 815384621, 676208604, 433681117, 161363098, 557402411, 671524625, 345744147, 262918088, 925846875, 270684079, 204699797, 749671411, 633514263, 461855986, 965645381, 373760661, 564246622, 969753349, 583363650, 608285466, 981393457, 3559836, 11226183, 990700409, 369618284, 931947011, 428502090, 114189274, 234381262, 328792761, 318594908, 964875070, 387757202, 233882983, 61532564, 889465456, 833859761, 846086404, 522683601, 670622150, 531561845, 470273274, 216646443, 377129508, 251820820, 541051864, 523590178, 396434510, 552017371, 569260629, 586422580, 395068025, 202294718, 398597940, 404581386, 365029263, 134273716, 338570148, 889035678, 843395815, 159162986, 135308222, 676042571, 884805481, 278572956, 359161210, 160649445, 640584681, 18985241, 728042839, 885422869, 651842489, 896405930, 994276678, 111826278, 194439494, 75728993, 904281319, 421087141, 633438410, 736540680, 479069740, 129529612, 429301590, 126591035, 487270041, 250958825, 873548759, 269171956, 24368620, 877467046, 886892406, 725476362, 150073857, 683257969, 424384338, 169414794, 441508459, 811422372, 452172148, 292236410, 801191364, 526534826, 713841780, 729834869, 907300021, 397542817, 729188770, 73544399, 755304017, 534040785, 537148456, 990574672, 923156238, 5631876, 229572810, 133283418, 417277558, 469278593, 232341708, 340112190, 286387582, 700346365, 675158677, 820365779, 342919638, 776835995, 73636, 564975740, 177912402, 456278778, 914407726, 507545447, 108831547, 160315258, 342613412, 222976876, 666685094, 893805822, 716614147, 365931217, 647524311, 771970640, 518434041, 17386924, 141921158, 120054129, 221103580, 762873750, 386381283, 637411663, 69833314, 494769555, 359826182, 166280786, 387936882, 509832805, 126425779, 144108950, 677556586, 527405884, 512127961, 37811072, 556470852, 4257804, 767117799, 145547515, 967302602, 977430216, 789116070, 223457646, 678594490, 805068135, 715232695, 951528288, 113749075, 822148555, 311100970, 452447682, 772675279, 868517972, 666698043, 196778900, 97971989, 658927403, 19020159, 701522995, 628086266, 241345317, 579701955, 593966989, 395870708, 246603666, 129630623, 111996703, 224338694, 657519400, 383610896, 943082826, 991419054, 513187433, 134763126, 670411230, 355353392, 628531998, 970132041, 155503694, 756302419, 356692950, 857316889, 104453044, 942446623, 179293387, 432495533, 832905424, 267622192, 46175718, 199891577, 891084337, 656772379, 161461548, 361717113, 438380038, 126755507, 419431159, 569037401, 119806762, 382342989, 943412906, 132315254, 403301622, 737289811, 636141130, 340621293, 207588095, 488996645, 290138391, 712773143, 465887179, 755155270, 672703815, 719310970, 558232007, 118621, 12593125, 449929431, 160427943, 482392091, 538645191, 365884257, 401321275, 820573848, 479948144, 963453029, 612782137, 692184666, 489221543, 48418780, 700993242, 39803514, 245735605, 67033527, 822346694, 998455792, 840115764, 873606557, 223136616, 961819378, 849098363, 515601870, 32449064, 585589064, 246126622, 781296751, 445195696, 907476148, 861172031, 446744132, 227733074, 431146635, 165703036, 123443757, 197930401, 840841762, 988164222, 360137339, 181692505, 685172954, 371085261, 315261528, 693330536, 674549605, 841880736, 793007912, 603564115, 869316828, 734726506, 465291354, 225415281, 833345716, 917099782, 830607390, 401158628, 927689602, 114695365, 85977165, 179204694, 533220711, 956068304, 654350115, 624515049, 83707180, 344296040, 285271114, 151166739, 354441015, 269087828, 359171800, 128709363, 460338987, 756666437, 923542532, 103046949, 218816015, 177490147, 230212301, 824374147, 360773904, 133663504, 701644025, 720122306, 388286859, 321014339, 352260420, 487978523, 99161100, 603901198, 387181055, 237844921, 645904717, 185244909, 212525758, 383382065, 95889306, 590640097, 694873045, 886781474, 682822131, 640944120, 939354821, 363670192, 209504630, 970836541, 795636658, 480156540, 279447425, 37055956, 1859330, 872523479, 183563219, 715429333, 889072817, 266953945, 718599065, 59088610, 384275481, 597797356, 219900622, 871874240, 979243169, 519733258, 605703618, 78322436, 380930348, 121692149, 926440313, 613355655, 662774910, 24910015, 491640040, 480249937, 638411904, 201790717, 743291485, 350906546, 543805775, 964611287, 590426192, 133454214, 358133834, 886235900, 345213478, 53558611, 84688698, 246858899, 893299368, 141093276, 671560972, 138742280, 472446147, 777805761, 287572553, 643896666, 161287402, 514766080, 51313440, 110923965, 673638133, 430905835, 230364253, 25713319, 360663304, 418336692, 483321134, 597242158, 803289297, 467365210, 932446796, 998337598, 409535275, 182122367, 551251447, 751121196, 324512771, 498517575, 744731985, 848849044, 337354608, 989523707, 998668054, 797447167, 932179401, 787020764, 517313582, 113927221, 98768481, 682916907, 812448750, 646606488, 344006382, 986050838, 738789731, 499745627, 53203132, 943749697, 350105272, 912908797, 735135829, 384484015, 236867908, 103715402, 785263121, 2325438, 439850146, 237649634, 292450154, 19079258, 353363659, 592373507, 816750752, 532668027, 827454173, 982073896, 491784572, 8183387, 312293410, 497456451, 998381295, 708074625, 604241303, 777948851, 979886758, 507033855, 113232035, 596103030, 34458253, 120326644, 535079198, 764733403, 335729486, 166257762, 165018189, 324937227, 774458018, 881340180, 654195829, 373094318, 338638278, 277138081, 193253105, 390406606, 432897066, 263500389, 630455620, 598089144, 684190917, 850213162, 347346021, 464458927, 142545094, 472578030, 167633349, 145890020, 908717615, 681783398, 942099496, 25617241, 115094907, 190312715, 191458101, 179564929, 184563116, 370593746, 416963281, 8550055, 611425743, 710664641, 469429559, 747543909, 667224012, 604861641, 966341707, 190818578, 118675117, 473350677, 97163908, 520782413, 776267438, 518557093, 39130463, 880664479, 350745735, 515316340, 90708526, 868408007, 711172543, 851019130, 516218417, 488917797, 493746338, 823739366, 562117612, 203585074, 894956226, 390968181, 91163779, 274213675, 865708816, 261381572, 884743129, 840475833, 432997825, 24211548, 627411357, 555016650, 425768722, 133338188, 945952366, 947228541, 623776145, 683382882, 40848487, 852433982, 5644646, 219850890, 848397948, 969473773, 685747155, 92670404, 433836004, 490346486, 691250716, 529485087, 176809049, 857494013, 706855437, 380529805, 570993092, 760717578, 762186643, 771976247, 303251707, 63091230, 948861851, 378012682, 591624088, 150744007, 198364056, 146377269, 948773629, 452447547, 313602449, 239482057, 656459209, 478386668, 40783768, 887484772, 960051513, 714027141, 734332867, 512500479, 641526321, 358956308, 189599279, 441356076, 130362263, 514208638, 483183894, 775494243, 283961112, 713438381, 83781041, 365406732, 530306247, 316356878, 303526095, 677397500, 275245579, 347762510, 571084394, 99384123, 139952205, 805624908, 623833318, 836798547, 715092437, 481965928, 866268917, 119791486, 89160679, 585617927, 258320962, 593469179, 553986275, 330891545, 531824405, 856132579, 604962000, 991482226, 167876903, 621100312, 481759179, 765557296, 404928442, 893382091, 247802472, 491475597, 201063856, 791492213, 731023434, 870880827, 419820580, 390399976, 506049568, 683495022, 838121035, 704744045, 43598578, 869081925, 651925445, 319722170, 701791532, 309231864, 845499745, 543388351, 624333496, 706092144, 837992386, 310692949, 723665835, 338201370, 100508747, 826610879, 322838295, 151891574, 909955758, 379491921, 420060624, 458101852, 777716147, 723294299, 908077276, 589443646, 324922232, 554589129, 955030431, 409500547, 490235010, 583193640, 182548642, 802520282, 872688749, 961150064, 172138927, 131877138, 954039549, 702811341, 558440298, 762614324, 487030638, 747837521, 726550812, 308186536, 477406981, 299555892, 141224569, 911579419, 916975742, 310330507, 973764694, 235395021, 250460415, 421533814, 263797166, 759428093, 998438109, 263538498, 252983630, 389848120, 985177382, 152224302, 445333410, 244898885, 316289001, 864199576, 448039681, 760928459, 512721029, 768670245, 530676045, 98547256, 446641783, 676079957, 419221738, 91400879, 989794791, 1046431, 639184544, 660627155, 630539349, 807090858, 794104797, 933708795, 507275834, 587248590, 91620679, 988097152, 785993117, 51956143, 641246197, 492373021, 501249220, 713355420, 683640700, 671815784, 321554499, 37334158, 641313831, 847227178, 712528165, 883628377, 336097664, 318786921, 10875908, 916681822, 581284433, 994489083, 55045594, 786358798, 698635921, 425194434, 736664430, 567355386, 827562041, 287631819, 687914399, 106787832, 525598678, 327656686, 825744650, 434289186, 491450567, 994322048, 288678649, 107360634, 661474673, 382468213, 349126110, 382943300, 926776987, 267890786, 40283053, 496462892, 862504891, 910660711, 732838561, 474242214, 837006069, 857487608, 531271753, 262353930, 687620168, 335750671, 619729409, 792008585, 301782131, 110928783, 218180676, 490090079, 913199541, 324658652, 391075903, 609855597, 109351463, 351810120, 988911588, 610105674, 391193541, 688323338, 36800154, 737215723, 882333697, 155949505, 548124894, 826690528, 878377133, 224983182, 669111362, 292108843, 400323895, 97756212, 99421277, 175725611, 488172202, 260912607, 300366438, 349355562, 520036083, 467582626, 164048103, 382661690, 307734929, 309973946, 179275808, 752042387, 804323738, 68012977, 490313464, 427790147, 375238391, 226631778, 425486584, 298678576, 726212385, 965250519, 575919052, 503086244, 436153043, 764742598, 241146024, 401099919, 69109846, 204198727, 88723493, 160655887, 276604237, 154705319, 406277758, 702825151, 760582205, 295262123, 633763622, 589318798, 855414289, 868981314, 389034254, 681461550, 900037009, 826545280, 354548020, 217163769, 11302846, 65975481, 896572603, 741119903, 112148594, 412731540, 625298772, 81506239, 612759950, 34956516, 442882910, 971573081, 113565514, 503371377, 669769892, 697195531, 371820299, 93120173, 993777186, 809264213, 239628620, 774545814, 813575177, 973698497, 928624441, 223652300, 726431981, 255059070, 851754911, 406275407, 258659597, 939336497, 452953389, 727428171, 591861935, 689700376, 284272818, 877212797, 855982916, 882381219, 173882996, 720210363, 535684897, 893696408, 392275392, 555279510, 991307303, 420066374, 385323672, 681415660, 392790181, 692772887, 643136012, 575348500, 295372211, 140232513, 89370976, 751918226, 209798710, 377783576, 233796763, 852600692, 403062807, 342222795, 55563746, 595100811, 661694645, 411888416, 540000306, 720198907, 526242397, 96247507, 522830607, 773706865, 910014653, 161179573, 57578816, 92340935, 165902264, 469695620, 166132876, 828383753, 176932087, 365904334, 500759356, 885537302, 775790305, 53401409, 968957558, 745259959, 794309362, 293382932, 274121816, 11210487, 45325934, 15767446, 436392055, 147824347, 93124206, 646128753, 663717862, 169972279, 828248010, 872706370, 182490221, 746789247, 863504770, 987918119, 106782527, 407998513, 739894726, 168098138, 780793338, 671497241, 391957478, 422239177, 372888946, 810551215, 283678953, 468521828, 593167404, 775598815, 935922473, 132429810, 194742785, 518216012, 277029667, 299306674, 696428337, 758289550, 981557801, 408956072, 650127267, 197674309, 605918411, 413748468, 688660861, 32523637, 470439042, 824343068, 132926447, 971697093, 501693193, 485938966, 85103786, 631881535, 860918823, 679604967, 670703541, 403569875, 304411265, 427379294, 294835898, 223929692, 387018095, 630970256, 191694343, 432043525, 256695618, 319622671, 488573024, 874475580, 19190118, 196773084, 875902511, 493017995, 228648903, 140029211, 905695628, 854554402, 295335947, 350772684, 432562010, 281798046, 171413785, 642364352, 802092704, 883562076, 894657346, 526661020, 205377780, 77962555, 783613921, 300720864, 217682501, 756944773, 930537705, 67050490, 167780428, 600107472, 330566399, 290988590, 536394531, 585939274, 367908811, 882764375, 810663384, 201828629, 893155464, 745850534, 332077042, 939287181, 250486126, 284413074, 548651984, 384074571, 191789381, 24339822, 426212520, 811241223, 280635292, 77876198, 536422064, 364892509, 246535678, 873482743, 563960941, 771930927, 416047909, 736232433, 85570719, 24660995, 923616551, 341158468, 423445510, 369744807, 548835026, 723912035, 528926991, 603942848, 645197850, 360032128, 181646291, 841641999, 787540294, 280917764, 698120213, 791189790, 446769433, 727748508, 215723096, 976667446, 519972524, 964824077, 484302505, 688797281, 436650762, 63103346, 551275194, 858024723, 436405075, 717533767, 847495304, 666868459, 453518534, 219920091, 870040215, 578352321, 101393332, 351466784, 881488593, 807038371, 995196400, 386695123, 47393424, 543767101, 507288037, 415782391, 300040114, 996806435, 815390176, 764927342, 209860613, 220592571, 13554952, 509388320, 597469142, 512400797, 440102453, 4184247, 643784235, 98443013, 236222631, 828880254, 450361627, 942647883, 59566091, 380850504, 824759822, 377021904, 319109986, 796147330, 272780385, 77147942, 523900365, 672332834, 347271395, 625157300, 480287567, 324822966, 336993448, 927299099, 223076430, 815448879, 935531134, 105247205, 918155885, 541855888, 490226848, 111019343, 191823767, 101609457, 788009700, 940652260, 459956890, 415937682, 530451852, 398650018, 520363131, 104800450, 349950776, 93357647, 490847965, 311650530, 707665577, 15759176, 519492113, 509610231, 364961516, 54068200, 649560844, 515113090, 530786877, 98641905, 512866512, 902351124, 560767181, 633126528, 775303176, 522564640, 148427760, 264498558, 850248656, 706825415, 806494185, 542575257, 305286032, 940882123, 498109980, 248516127, 988823691, 680238189, 757387748, 589486403, 166531912, 198521431, 757163733, 375093755, 760976758, 427325724, 39239401, 823422407, 374698036, 54998633, 695191764, 746205479, 799718320, 91964101, 883735175, 452198044, 718986561, 341875406, 440288407, 683279958, 995852249, 243828735, 946777212, 211127527, 905801878, 107897954, 879896969, 39245914, 534627798, 117553187, 393068462, 138979618, 266930036, 892634071, 361551119, 426003378, 128315240, 411942619, 683255142, 744143495, 932970935, 29175316, 184280982, 624337615, 903848876, 578639, 398496385, 413287678, 139932391, 563108291, 6445010, 824744672, 317790814, 717111955, 219837180, 293987126, 275418805, 536331546, 885962567, 218828312, 432556665, 225609582, 206893517, 617210739, 492220369, 76015264, 867172748, 286160776, 367183908, 565032247, 590957864, 399317713, 611489006, 203849378, 328557920, 692798648, 94847818, 837403836, 240194243, 418743230, 213443430, 602342971, 301474435, 873282048, 575613707, 526306825, 335782039, 839232857, 555279898, 285985542, 733981197, 634426682, 94456876, 429306921, 978286144, 987393885, 587988201, 778927884, 22528339, 885571905, 962337564, 74907635, 153136074, 37206618, 161305355, 464328934, 756412292, 332214231, 610635933, 808461236, 155775749, 863777688, 106731531, 648731461, 80420171, 386472629, 152225980, 864098157, 449503122, 701088209, 958577867, 643005418, 875310217, 339467534, 366292277, 326066016, 202830542, 494178902, 875134680, 85947467, 599972898, 479416555, 963881570, 884918375, 411327002, 26359550, 237428013, 62005780, 948374987, 197266108, 256525923, 554110904, 643908892, 363415342, 365525930, 14660806, 799525103, 834379947, 708337668, 901177479, 306363031, 425035278, 284290620, 291174005, 545796251, 55670154, 785913596, 418056580, 191481512, 154537192, 21752960, 617681188, 288475504, 187890049, 970268147, 319280486, 846889750, 435861014, 746696563, 928228696, 948674060, 740061803, 150359148, 781559846, 149658356, 310886319, 586941211, 498711791, 560269743, 409986445, 36432745, 995719238, 319988767, 529439253, 368300852, 812219780, 314242573, 826862933, 248582063, 407730084, 287232274, 143443982, 388865555, 68521799, 625412201, 875026835, 336589428, 140146254, 259619018, 275462050, 982037717, 698353071, 661466014, 805551071, 499716329, 317081937, 991594329, 554675197, 213008836, 845891345, 954428555, 755216330, 240840749, 633208425, 302762789, 750511721, 585461958, 525134957, 765842841, 981314287, 314695174, 580044044, 68857525, 45082082, 527339316, 871435659, 164302199, 37256170, 703620066, 41546827, 348990307, 679205138, 341842499, 805665079, 652422750, 86074044, 357145583, 333346323, 1124107, 713208130, 438270626, 322945510, 502407143, 809733957, 989975908, 322111337, 484291722, 793055862, 63163108, 561849003, 970440097, 431517381, 977335311, 171605899, 878622619, 35994449, 911166555, 438342211, 472013553, 240849936, 918211027, 579635362, 55424399, 686035927, 666936342, 92636220, 936665425, 428646353, 805063219, 132590380, 435771180, 377032276, 328592441, 60028545, 734390966, 927926397, 592272181, 653972395, 437453015, 258032646, 409201966, 968557971, 445213534, 461802143, 108224179, 901346893, 21770009, 852423771, 701092585, 224452643, 352608377, 963531688, 320319147, 833087922, 846925316, 629069766, 379891543, 185630122, 633851265, 56146457, 404129181, 835740991, 367024100, 358460909, 587697414, 628725123, 279498275, 57358904, 331104608, 828921777, 350513882, 924422006, 594900944, 238875720, 722999708, 932551099, 488191869, 511492122, 576156648, 120706958, 749272019, 312136651, 862646809, 45252219, 841109900, 100488946, 807068975, 933417155, 710620986, 256348502, 405883111, 202707593, 494995841, 218147742, 54979552, 133516465, 833116346, 532898707, 574977230, 607132579, 507822007, 997859193, 368235414, 361526200, 548710384, 426072939, 644203268, 293710952, 204551315, 832142897, 382699696, 867694591, 439532794, 650382891, 201679175, 864449252, 421861600, 603663588, 12097742, 908884325, 299740680, 604611511, 116653106, 478592314, 709414695, 771467932, 822274467, 319796306, 122320641, 11079928, 505147179, 70357016, 29960368, 895753558, 416715514, 139589633, 466280754, 525093636, 511820643, 454723840, 617676248, 215910415, 787521674, 591066667, 114275409, 575055363, 75628576, 734909359, 247405044, 463987535, 522507512, 276643927, 915511037, 165842163, 426147733, 966440134, 497073524, 866591150, 104957454, 871983693, 716739409, 270048932, 372071165, 621025954, 62107335, 590347155, 211875836, 746755944, 106888294, 921278239, 309281034, 705892691, 688907217, 289225907, 921537940, 603551176, 918116516, 683536170, 289530904, 191156607, 842829063, 727345892, 515672336, 33691263, 44263035, 878113767, 937097176, 19875778, 753895515, 786181779, 79656602, 87414418, 227190697, 336494044, 561237140, 327283157, 972079029, 253611006, 401902877, 673313287, 818298043, 757260800, 857769883, 914435754, 386322254, 959881601, 792994169, 601436411, 378106057, 976625545, 346301451, 242903967, 800492078, 722345724, 439005364, 489298299, 544127899, 474888639, 903836672, 979589507, 380497664, 853390117, 785672132, 128608155, 137750860, 418281455, 874693263, 426359585, 14009016, 272084652, 436382019, 19572538, 157222720, 532788620, 51777725, 990749284, 721196840, 844178400, 404242709, 799147279, 486717862, 80524522, 754694367, 184710895, 234900897, 820424707, 612127074, 948019855, 785127151, 20697916, 9619677, 455706888, 463090751, 41519059, 170510796, 596971940, 265956468, 224692747, 451176285, 605825880, 959953939, 898231078, 794454286, 510793907, 312530734, 967233015, 283524539, 916489006, 128233690, 865534381, 80695478, 708512833, 836825514, 225649402, 618663133, 593494988, 994925772, 557482006, 381305232, 822481662, 8327506, 722025849, 724043340, 467242023, 21464356, 899249930, 142585960, 196649576, 178415031, 597485601, 366520446, 824282351, 275062429, 445650501, 696624539, 841382501, 555224888, 113907954, 375940679, 995146975, 844848235, 298092916, 297322543, 22282355, 598978571, 215607092, 972137931, 949054454, 839995137, 742110207, 182417292, 423753908, 208651994, 73797152, 835378135, 361310516, 818298754, 19085967, 144828455, 205761027, 427932595, 666555356, 610434540, 460375414, 640473673, 597930048, 185793747, 115637191, 901517697, 420156722, 347411281, 793018236, 119319201, 902314184, 627238712, 405654811, 133790355, 220313711, 540840446, 348551734, 151260568, 406951716, 84842938, 664602067, 499184, 317962726, 771651783, 480548857, 493055798, 823619047, 970619771, 511061139, 604238467, 457138997, 220061023, 788434379, 122157732, 275120023, 514887814, 101039795, 467986566, 32194419, 92357353, 345377118, 205743748, 16965907, 27303061, 350561450, 78383168, 22409025, 558392621, 923258759, 390969537, 213681905, 999324710, 299329842, 714683711, 273960384, 214422309, 758404903, 659451353, 541938324, 863253761, 417998507, 890645873, 782348865, 525854513, 638047419, 125731938, 591268123, 94435926, 93870581, 422337173, 212897990, 945351240, 1418336, 353693570, 128540228, 267788704, 77133778, 265994855, 705418980, 706495709, 94568801, 427377275, 588407386, 763362984, 483729868, 687170227, 176866497, 629396432, 561618241, 193661665, 632749801, 118814313, 67403228, 601383593, 708154766, 483285271, 364525749, 714536059, 260236134, 731193723, 724502620, 854641879, 512612090, 914435619, 436547332, 879716750, 961057453, 542014035, 195890288, 944244373, 440806201, 348557324, 493087913, 62824882, 623653399, 995482465, 456524396, 493477291, 512405852, 635650493, 247928434, 238782106, 263758331, 906382308, 727650656, 707368377, 505592479, 155438766, 995805312, 540936024, 697567768, 145114554, 292815028, 395025262, 984604476, 674177684, 914829659, 861990746, 467085272, 362457329, 373646758, 956920792, 213549749, 704843843, 800883259, 139592099, 254180589, 435811480, 793803046, 832051785, 530501811, 301744727, 839659611, 16408485, 358705971, 30673542, 285934201, 546001310, 519720078, 545384985, 812176446, 382241081, 7495075, 67749791, 483082951, 995929573, 199390761, 511086910, 639282055, 476165503, 310275459, 50768645, 610649058, 584865751, 969324820, 382503387, 670132820, 891321331, 375210456, 581837166, 683892251, 32610999, 186056095, 432979464, 276750969, 113786708, 656116691, 707810666, 784853545, 39467126, 921032026, 8026335, 305053209, 316861433, 179868276, 188024400, 814299265, 445064390, 590729211, 992059884, 165651668, 434157986, 908911993, 597007320, 817438210, 277109413, 212495298, 375575964, 753901091, 804020946, 576219119, 504403147, 976998090, 734339156, 357380422, 400527039, 679922839, 918578885, 303140294, 922677730, 732805262, 178980289, 189574557, 461737204, 525251626, 590207353, 645238755, 788204704, 532508889, 819968637, 16225524, 206967306, 289717978, 165051495, 484147878, 965909705, 687520189, 612168873, 225088763, 599020462, 657592852, 472358012, 502469454, 856343064, 663514438, 9876809, 295661934, 387785521, 590827314, 714709823, 480965778, 543449430, 401005547, 743961790, 46828003, 838309554, 737636732, 369979244, 264756545, 164004252, 919792458, 538956426, 359684065, 333645048, 933600631, 409353888, 874773082, 189388966, 599318468, 265391996, 517890943, 652734645, 967329560, 122615129, 490432370, 695582528, 827314916, 549444138, 553171507, 988713289, 663440386, 758440356, 889064937, 286432566, 152820772, 400383206, 793518664, 345656616, 192436982, 502654207, 331996107, 966151590, 152185807, 15152597, 300370150, 926757333, 929672831, 504047926, 435835445, 759578819, 405457358, 572557984, 673154042, 497076280, 175137420, 308445066, 507753496, 5530546, 565380354, 844492137, 986061316, 110497438, 413443097, 557239922, 254359718, 302500950, 406676356, 397359175, 34270732, 840268990, 594817495, 529349187, 584185547, 772707783, 285280398, 146159983, 761062345, 17302666, 912101714, 348822836, 383646343, 616582755, 382567822, 131420978, 186989262, 888273428, 966645775, 771610628, 940842056, 721567481, 627468104, 928467280, 352304389, 253848040, 721502699, 830776166, 633069603, 776033538, 495391527, 762353695, 146309129, 770470197, 319915633, 397286653, 727431748, 931525008, 705190507, 220079579, 664769967, 754465899, 672681437, 352944288, 449184308, 981706508, 223005673, 588278090, 365128524, 38312681, 177545524, 384571704, 397803790, 538220583, 91706065, 587397670, 849325552, 712084149, 903114133, 426186772, 310171701, 663653497, 415848003, 65350505, 60041221, 972512894, 82786448, 344084951, 336872274, 765810961, 544120608, 525637178, 257863163, 48774535, 363284640, 33295575, 526027490, 493562388, 723094097, 392272592, 337106648, 35106727, 404162108, 442716727, 896698256, 771113247, 327363520, 788517296, 796420616, 897392739, 715697051, 585600630, 563027188, 19799771, 337219977, 630141528, 925936816, 285286081, 86440340, 561066498, 834517246, 39925082, 509203121, 142797745, 558467736, 860109839, 300705972, 883113997, 462457797, 593719963, 289515170, 531337549, 157197197, 308031160, 417324138, 66126113, 84356008, 851856685, 927982696, 637524715, 600398233, 895999618, 975887365, 923429592, 285613381, 722716311, 428711595, 12491389, 184171748, 780565604, 596143757, 634846925, 404644947, 919156598, 784027192, 917816881, 817871566, 818986178, 43743236, 714139161, 808976889, 294863293, 920722507, 90161979, 333421461, 427239477, 912512886, 174227687, 57368139, 929669481, 115472666, 380222997, 301884095, 161280357, 370019449, 674071035, 194205333, 529853384, 703432794, 569268425, 127361924, 719278341, 695858081, 616443014, 373868692, 446488943, 188951808, 278318998, 547652156, 60122579, 412065377, 620926829, 931694044, 944869706, 579015023, 396203253, 858049170, 412443541, 291662544, 483661753, 118165759, 260078692, 752804460, 841550723, 816520792, 146390927, 801719055, 610676901, 974417063, 470857956, 217571891, 746984189, 52627457, 713100054, 545721179, 915688720, 602882317, 404024390, 534348414, 351273118, 733410573, 450081191, 787243818, 320564690, 538502073, 149593726, 179621299, 449061417, 94098793, 198383102, 996975906, 612818867, 720164552, 655330061, 930182188, 673739312, 25921882, 226435101, 950164756, 83389864, 39120621, 98031557, 649544030, 851998028, 433248361, 464400694, 299112043, 956605780, 441590525, 215243830, 45248157, 116201476, 32192970, 682911585, 164882285, 704645181, 868326285, 830990050, 327144940, 241380265, 614718406, 526947118, 271276831, 759288352, 12435891, 62548489, 120713730, 873410075, 446906246, 170959344, 167402929, 918703642, 321191716, 475910973, 451765754, 334147212, 973158918, 748948252, 584591169, 297386195, 631479120, 363949450, 579925584, 80121392, 802418733, 460525360, 840979469, 344620615, 238534448, 418757941, 32311371, 365318959, 572125480, 529628301, 831483763, 342937576, 988003270, 778634498, 673479270, 647595545, 588468140, 813097072, 289712307, 222289690, 191124780, 150074885, 62700623, 80345757, 4393014, 740166876, 27541667, 669334018, 792518306, 53578007, 964905240, 465869151, 87598044, 778367569, 847983597, 995203461, 413990295, 147571729, 399267884, 701973266, 728405954, 48939719, 693918697, 194356025, 781956955, 202294772, 788785017, 927307807, 904896518, 130038794, 482632441, 422206044, 340681093, 929933903, 206867767, 472717174, 798358114, 474882850, 791681441, 183308735, 944850772, 708964536, 867333184, 554845253, 848198143, 903858844, 23455611, 50803744, 168579163, 685804512, 972224724, 836523633, 767347475, 347071109, 476001911, 910828684, 755379363, 53183458, 389113838, 135329737, 801402872, 116464973, 35093986, 15814561, 597361831, 672988983, 578200856, 685029861, 423082330, 204316834, 441969369, 424254259, 707117, 400592283, 476284959, 334438527, 127620058, 234742320, 951263604, 670246165, 752329050, 720495128, 250512953, 359945327, 981748582, 292604628, 206096188, 683091925, 873501802, 756787297, 686433476, 836022285, 586388466, 464607165, 62042610, 557045341, 593806170, 851298394, 351817917, 450508450, 761825341, 229824814, 539049764, 327086623, 315104139, 212929271, 748525038, 303760433, 896278007, 789129876, 625363628, 137894200, 227214295, 52182931, 455944758, 677535213, 126810455, 889679126, 376699783, 449522692, 920264328, 878983383, 425987079, 295833453, 734119800, 51065147, 800448028, 239086300, 593571459, 504668009, 583109129, 558694247, 816779827, 524816194, 365134662, 36993273, 392174750, 259783462, 773513721, 777626940, 772919075, 899288734, 979831569, 490906158, 369142108, 556377923, 907605916, 661564910, 792196673, 194067536, 316596073, 793875504, 182079469, 714143034, 808557581, 317668378, 73439497, 163435800, 194516976, 874461013, 354112530, 995931449, 853370796, 992002073, 829665556, 762105084, 629092815, 835186614, 703188784, 201839229, 218044684, 376409583, 751720415, 456546603, 358481346, 854946454, 16772923, 73594261, 203890418, 720061943, 731626664, 309928484, 345438824, 996889095, 190057159, 775064354, 117804728, 152761769, 167515699, 428464678, 677665116, 178594999, 132064834, 50413788, 11986393, 598906752, 556546111, 88208225, 719009817, 914159434, 971388626, 648538386, 173161545, 219847183, 611515772, 394044104, 501059267, 99169775, 943728645, 613907464, 80941980, 212571945, 922850957, 304131776, 434161702, 800669501, 875087096, 500975211, 542139924, 117457335, 814641355, 672325493, 11696254, 12016318, 498448518, 609309070, 527432987, 701996245, 514229292, 268998324, 175127434, 246633206, 901509824, 760648878, 969091234, 613105409, 706391827, 567152108, 182432424, 304615703, 197945293, 112004361, 586354928, 304743430, 116112478, 260444579, 422365245, 886262399, 360472027, 462625315, 100183679, 298475021, 673226562, 92507745, 949521271, 8428088, 659226428, 870754877, 265464894, 3072113, 106478492, 345640158, 500974915, 457993151, 847055002, 497452347, 686412555, 416513659, 741330675, 121794830, 519067806, 11596084, 585130426, 458051375, 260753362, 26464406, 446609869, 594388861, 41283224, 527616774, 347589266, 295058785, 331310923, 287478307, 255353277, 652978896, 623661518, 798098528, 179924497, 839717076, 696497183, 224240951, 644742077, 431675112, 640134167, 952177515, 157441353, 998113439, 307347544, 795385267, 760977570, 328751394, 601896797, 927285809, 172811458, 283511028, 39456404, 770444172, 758849603, 534163140, 998085014, 834638676, 532931137, 821079011, 761560277, 516142800, 951504906, 847878081, 116662656, 780163632, 689255872, 652162115, 876751217, 807167124, 960621838, 134550327, 492965717, 698868791, 703784908, 967783479, 492545742, 71796165, 732738563, 621128747, 9162458, 443005065, 139829948, 3269053, 78161658, 415244857, 841877082, 36508404, 537358990, 882636935, 402647373, 478365249, 144985483, 218574195, 226857867, 641129809, 405128660, 719072634, 725748693, 348905766, 156174963, 880847472, 878457068, 538589091, 560561594, 528788291, 998724489, 669575733, 549618111, 364219941, 958605103, 922734877, 542385307, 371520162, 58513894, 368323012, 244969004, 10910933, 902564527, 810705652, 214259660, 51768099, 140873652, 181189351, 366834144, 307505356, 406494615, 788295909, 412768091, 84073053, 645687507, 548880314, 405481448, 378316600, 668355112, 860541534, 996908022, 781396109, 784987340, 451494733, 756510657, 530127788, 133889736, 172458662, 418096929, 326648607, 151765582, 903626839, 18365526, 435706987, 348132538, 547377499, 47081490, 606802561, 941062390, 79114814, 301383743, 441932281, 621045627, 250489158, 828109618, 692853613, 365036388, 173107446, 651859231, 147062402, 233202815, 441373126, 137909159, 799397295, 60318614, 164266620, 940072163, 669594159, 601347287, 860678295, 547394403, 601074740, 406166095, 640933466, 626785048, 463369444, 515843653, 324159814, 231305700, 48657560, 809294094, 153135168, 491148220, 682338703, 945023065, 948221682, 527011523, 966799045, 660266393, 967312053, 872687298, 222651132, 794946963, 482841357, 752857723, 894707177, 909598039, 211433564, 164254510, 720340984, 201694880, 240518726, 286624536, 347515727, 771790433, 689049637, 262909701, 208798937, 346383000, 656317246, 185955393, 92697422, 98325132, 378565396, 83241583, 585672443, 815756188, 528820310, 832249366, 357127974, 840571390, 455220029, 417956809, 797512772, 61985880, 568242717, 982132031, 132699534, 914077477, 278147237, 940858399, 996758645, 196236744, 68293117, 173067974, 746013538, 728585651, 691070442, 645738566, 643148019, 77200678, 443199629, 179018685, 317068802, 885175474, 999627361, 658299898, 767799659, 69703677, 67723913, 511223031, 806644292, 264562139, 9664874, 935782547, 325743702, 467362396, 444419216, 16323785, 278724333, 867458732, 178725699, 464725077, 567680362, 517038256, 842706015, 809809957, 88560610, 220662923, 522764772, 228084041, 282482864, 831344553, 648848869, 748892852, 524830940, 371974194, 515955337, 621726740, 92361758, 657804116, 177171470, 820799226, 641676980, 247039297, 809232792, 577163492, 742407973, 8784513, 242865176, 964480547, 673877366, 371572637, 573727445, 865247415, 640711140, 849517572, 385079715, 198714, 201633477, 917559116, 772630562, 146008845, 593148133, 969508234, 860299616, 957774577, 128815476, 558862213, 339526878, 93987167, 25414356, 5331533, 811482718, 129926562, 51070449, 378116619, 660967355, 601481340, 328127631, 107118198, 570141553, 846286109, 566389747, 914358348, 663555681, 510291499, 196502628, 388852812, 612217360, 865787055, 612423062, 404382534, 444101834, 425190643, 338670303, 52484313, 87917081, 709420159, 689033388, 186227147, 171461096, 508434601, 275360145, 916828390, 971436126, 838693023, 287075105, 387996473, 435764340, 675922893, 514450093, 428912125, 438941910, 354241618, 920528182, 335755008, 3060486, 417814365, 298587707, 867447675, 576801644, 821312766, 1809617, 586356791, 341874784, 709713560, 459259580, 921893799, 709817403, 711375945, 23917325, 687717476, 4357116, 566016000, 854866594, 629764902, 272534298, 111381433, 549563985, 687459276, 691144136, 702665925, 199778738, 222808819, 419520311, 496214102, 290319700, 441536768, 895207980, 45164609, 932122901, 583425200, 356511072, 309970727, 300393831, 33955616, 681405394, 626816630, 370773854, 977601381, 429955265, 625299029, 43429299, 812314, 379230329, 835032055, 709480658, 814885744, 532508960, 270134164, 970178325, 394602644, 397187283, 543268922, 647252294, 297653654, 358854185, 917161203, 69117294, 985492478, 430770421, 579212411, 854401973, 549731382, 331673358, 518016388, 781983966, 736708282, 646175133, 236244945, 898446816, 154622533, 162325218, 788026285, 280550113, 85983350, 635030953, 958876485, 750198528, 131472711, 416634802, 407927494, 92872195, 360506529, 504968277, 611136581, 28221835, 605385245, 395269315, 190842482, 336947978, 432353075, 128898580, 379571911, 511368827, 650395252, 86633207, 596128642, 566208906, 978677366, 963525401, 128472709, 261817961, 63635369, 79336727, 894613324, 526130077, 440259021, 313807161, 374234684, 746047390, 700337742, 290805741, 42540725, 240239604, 568020204, 475838142, 42854658, 504306398, 583596801, 848109753, 911944327, 82662148, 850169932, 479358007, 803103417, 551113954, 59412674, 357943094, 242832293, 876341218, 765817045, 892112696, 538349, 11200065, 839807025, 659383939, 409862336, 654322020, 416305777, 264961588, 595781779, 364523567, 920925273, 345861516, 996446966, 273031158, 923903309, 564822820, 842033499, 676283830, 148510172, 300295793, 407385729, 106760805, 708219787, 87072106, 843527121, 988314061, 358349316, 891714550, 174711662, 657159298, 2302157, 27229280, 924604017, 806547156, 288788012, 742193674, 917031094, 747337727, 137156531, 687602656, 547334215, 59521178, 933010816, 377287034, 939612887, 577608471, 79465024, 164114400, 170976488, 748936919, 414911989, 509210723, 853529757, 66765845, 336579402, 795992432, 823951503, 632240875, 862232790, 682796545, 397799040, 464077648, 435099639, 242146353, 850951304, 464753067, 99326310, 456820642, 965488586, 997461735, 387642956, 71347370, 357037004, 860358548, 831608342, 345221310, 872511839, 352432862, 748495565, 953337981, 603676531, 903072914, 136742977, 324007773, 450467343, 300858967, 364233623, 646016249, 132959087, 820707867, 251205944, 721342588, 281805764, 955557105, 147985109, 615424906, 167914917, 514541955, 990119664, 57220498, 653314536, 843864303, 720151251, 153946152, 776864108, 397773974, 685217229, 736659238, 490445325, 212437048, 943412932, 374453623, 495740107, 898035754, 454102719, 534299170, 313375720, 220106619, 247833936, 406425058, 620640441, 236748120, 668393411, 323640972, 947046820, 565411970, 305378861, 348612799, 883239656, 327243585, 471891490, 22580935, 144622351, 163197122, 750820078, 162542124, 453436793, 283111169, 123280141, 989517292, 64114122, 667917202, 663051018, 50221644, 405939796, 414030599, 414436251, 145895331, 30679037, 995866372, 201221623, 85979315, 139905737, 898606020, 248138006, 716629822, 800542764, 478184563, 957358537, 862713443, 328120199, 217418193, 211187826, 217247192, 316068119, 578128777, 744273883, 478500371, 292106855, 853637575, 984276809, 413118913, 475568915, 347484677, 177860462, 183701751, 541749964, 686635027, 312992642, 631512721, 901484251, 530789559, 317596343, 183647784, 645893802, 151110633, 437691525, 747607544, 993950166, 82963235, 742650022, 622148960, 34828984, 488480867, 273406479, 411040256, 55207413, 811286216, 933226866, 855080894, 276222071, 33869733, 927412463, 365135576, 454288729, 218424465, 95692080, 541226494, 85895091, 983830644, 939699397, 290766285, 785356578, 502731181, 330386667, 495286728, 833763065, 782148640, 17842942, 577152602, 612132279, 98229789, 232348338, 653338170, 219568647, 603287684, 519563389, 317117544, 160665316, 887077922, 566885117, 299112238, 232344819, 633108930, 589279433, 727945422, 525518943, 903264874, 739708962, 616399616, 521468056, 942556225, 213957967, 348513667, 360332873, 217190307, 292120341, 312845910, 158203190, 991725912, 143968600, 947311362, 908911060, 286752340, 13982265, 198417547, 390912352, 771382455, 491843318, 515275131, 750032992, 729197592, 482576957, 951674323, 5873106, 616513313, 110577979, 247013834, 255681677, 54279876, 901819047, 551146519, 194368638, 62475553, 732084561, 863491999, 451894206, 213689985, 152329421, 751078871, 569452537, 150447351, 930267678, 142188936, 855416657, 498364340, 347173945, 127802624, 770582696, 744022490, 822402043, 682766599, 414322560, 510733631, 947975364, 381837391, 949745422, 333681772, 72134646, 732360203, 966270421, 236463094, 736904233, 850559370, 387559420, 511799087, 644106660, 693449423, 688785026, 438453096, 979303079, 290414301, 924259256, 876926817, 940995905, 39050336, 582281989, 865698936, 348358204, 642856638, 770228187, 875148349, 697047620, 932184486, 905333041, 198865159, 119436072, 638429143, 404412013, 969620990, 845303259, 341932497, 420292734, 471504478, 231665016, 482869157, 958788004, 519087316, 520035435, 265690180, 566433238, 630774987, 484893299, 66828625, 830049676, 946533736, 9334833, 756997089, 39340402, 342321904, 15485687, 889733203, 290571154, 626742517, 365736044, 248260442, 212100168, 903468764, 661180157, 904451141, 809357759, 225753152, 558060809, 719022674, 269077569, 510871635, 94897188, 582030761, 20639410, 249235068, 525378113, 684878104, 311700266, 725495957, 626230741, 919387443, 692614778, 752212776, 174817073, 400465821, 406645923, 941870205, 253658844, 993567598, 144153955, 603678238, 568580827, 963402907, 423752434, 5107140, 566885155, 825794464, 277962946, 483531813, 884485193, 455501656, 974378024, 942578653, 729966906, 975033360, 735269270, 701712891, 576081990, 234843570, 620847815, 681527498, 441386536, 896041138, 655044469, 773842740, 968835561, 982966084, 398863528, 187450008, 230424345, 250680754, 249043708, 648562509, 270277700, 698385810, 376096882, 462657376, 250190665, 740252540, 141011548, 535396255, 617824612, 402203628, 229752153, 100303744, 193120281, 681722785, 44016894, 826020344, 731854889, 806184005, 778919122, 144629250, 480215191, 892766147, 588935400, 509459600, 284571089, 424791149, 811823002, 100076050, 99664209, 622763113, 358741262, 325958821, 315575774, 25274528, 315967954, 400771391, 945877254, 787215590, 955455124, 557683335, 96887775, 619278468, 204900220, 226073981, 638708328, 731512446, 338717803, 357130105, 512016398, 46964540, 825822989, 76925727, 843186876, 961502842, 148609159, 184737104, 48645146, 748728487, 412803892, 879574607, 598923998, 81900689, 992864632, 233279663, 300424238, 909623937, 610267496, 867334421, 956684076, 918801673, 386044170, 959884054, 404965597, 354609930, 101479779, 887360785, 692615140, 200730763, 568888545, 397024839, 633562178, 994946469, 323581934, 442671475, 750884048, 179723522, 746271288, 234283349, 416776507, 538030334, 182163611, 938272809, 538393147, 526421812, 932243150, 549471322, 180164709, 21651538, 716099160, 52868776, 223984858, 675369820, 413571492, 676196296, 715588359, 570944671, 900479859, 310233258, 964195941, 885766837, 976630053, 911501988, 935186230, 371870160, 130452697, 26376731, 422490230, 435151826, 970934283, 53165884, 332530403, 476582296, 367776515, 409354003, 560589508, 204255584, 214544654, 864672569, 218170443, 439573767, 765823954, 688438141, 924028844, 885483977, 746613414, 686022144, 223559044, 668559905, 578672373, 544985150, 607825936, 199703110, 360332992, 458951326, 409391086, 393883718, 314387396, 342514580, 128855309, 695404449, 542221567, 280854124, 394315302, 628854264, 927018442, 593757162, 312087012, 218849792, 818696866, 264011901, 833675444, 147721924, 598323943, 249067948, 469954986, 334149814, 593633036, 463380934, 320394256, 218388347, 612814588, 387812164, 791515913, 425166978, 162973030, 730208007, 72153029, 826163643, 977290215, 562595899, 85599831, 396139891, 418394297, 732030450, 995019916, 670656745, 919792789, 221419673, 474202134, 648152196, 552479123, 255853843, 9076482, 409554141, 410715265, 863961616, 333728193, 450743379, 671107272, 779630788, 333980066, 257959774, 20122231, 154383147, 771002524, 771774078, 59038475, 832486490, 754184287, 340223831, 576150706, 91154371, 194557014, 848529527, 355538830, 927851763, 348944134, 375905216, 257940827, 249755041, 754516054, 296352890, 857306553, 803261628, 721216828, 4336214, 575627808, 370163142, 346275763, 934225560, 816014897, 457247514, 7186993, 703436350, 58811849, 460346338, 529141734, 999589263, 31598511, 547358547, 370116305, 950136471, 511252124, 812091437, 863752544, 702616444, 765701996, 770656858, 951752557, 720653363, 562980969, 96414552, 67674358, 23267780, 579042590, 229732157, 474502840, 455144308, 60356217, 928698843, 415640752, 121586455, 49093335, 388690341, 424572927, 23243385, 349380521, 567726495, 919513672, 165510562, 513042072, 23067887, 679094501, 146602958, 757156189, 217256887, 341617620, 989523294, 753620466, 528606778, 419894503, 698281111, 3048486, 27303424, 161761061, 836780742, 722933123, 183650230, 233383059, 800196060, 122345677, 700696090, 435832876, 657556916, 37978400, 834915151, 945102305, 504457116, 118656520, 51620349, 763645544, 258023479, 558098497, 880215296, 942475822, 862899837, 737392292, 472791623, 363567879, 177947740, 655598566, 319031288, 337023529, 532449225, 686545024, 270577554, 496492469, 948002895, 94454023, 479428345, 166177221, 501150234, 996720506, 826409416, 851268719, 243933411, 274518645, 163233029, 785704308, 915215375, 705503920, 825465293, 390528757, 269896628, 718870345, 344174517, 152840617, 780557659, 123900631, 737291078, 449480170, 809880111, 927316649, 129572677, 555170297, 545188874, 264571696, 696453501, 982296262, 301789580, 639208823, 691092437, 958766886, 204201786, 697009748, 258631285, 385978017, 502681039, 232518992, 466329221, 108321671, 783893725, 393295030, 226222425, 198328865, 138953175, 324138853, 320089791, 649377106, 107032102, 850783290, 371790330, 497088067, 564822473, 339048759, 789675133, 318451664, 733395075, 464592828, 790266019, 422491091, 191952272, 20585367, 630375702, 53024477, 201102902, 717463650, 695072924, 457490719, 116124143, 556771391, 671949226, 639184930, 599971574, 269018105, 743886070, 23219478, 885519276, 910019182, 354177191, 241652684, 160690776, 955632242, 667210686, 815693735, 638915244, 509472417, 92074203, 847543526, 663582512, 312663749, 475282744, 498136515, 916888113, 549821439, 308113978, 8809039, 856174722, 817543146, 116094190, 272591978, 231946557, 507920084, 636922691, 162886925, 893871017, 334771960, 525217720, 970897896, 877806635, 721249257, 21540413, 381304455, 238337022, 117237315, 765546510, 169944024, 695548779, 899877545, 425296833, 211915533, 350360454, 977390380, 97124277, 92523579, 12548074, 990931658, 286923706, 482670331, 110249479, 89162428, 188256717, 719017655, 945957899, 913475779, 985565226, 490535862, 539065124, 445637297, 54214946, 545912921, 829037883, 386735339, 303725075, 446792443, 249117267, 238082275, 633547503, 370965402, 531766381, 830022315, 134994916, 104740513, 854488541, 953597994, 928209695, 748386173, 300804925, 453428757, 119949068, 508078364, 517836987, 175517010, 64648438, 889965783, 699158993, 493355370, 315951126, 115138738, 454913820, 242679986, 883115916, 651189542, 4681408, 261799605, 650912418, 88090939, 641888603, 91818423, 94329096, 526321303, 186335452, 686393067, 260276023, 68467398, 803543859, 711546515, 379524431, 235703757, 73809595, 9171849, 283610163, 415548359, 949421873, 728765691, 242297079, 230045130, 383476193, 311194731, 117150789, 650855451, 487762699, 590951427, 290674873, 228088267, 601436286, 630403635, 856970078, 808236966, 434270992, 730522431, 851186093, 134766347, 801309398, 943000227, 887826528, 861943617, 709224322, 770400144, 151868680, 501242924, 426071131, 673106103, 776874006, 897937166, 590887779, 96644211, 357190710, 128988385, 875248881, 125563778, 884285639, 690998867, 49504137, 114591718, 828441437, 786134915, 78378728, 365206265, 884484250, 710438064, 40915856, 673753525, 38988857, 206213693, 11742528, 807579714, 936135707, 927906401, 812676297, 672564277, 10908057, 721133689, 831270147, 26169402, 920236428, 866412663, 705514552, 13271262, 443830173, 603146537, 251420025, 974647975, 337538450, 734415509, 829754298, 810263492, 440376001, 983467404, 780320726, 828669543, 728372332, 144551775, 926390134, 312266473, 716091199, 373665725, 467420019, 969485535, 748540615, 490224971, 628630877, 93471655, 365932327, 610840421, 888187249, 378461977, 458900933, 665038690, 923965513, 272891036, 267704513, 836548258, 779239008, 882157861, 849985722, 700734335, 931550217, 258134691, 677690731, 750086854, 979751841, 71339194, 172018195, 775170562, 394702733, 645060559, 744941452, 125263950, 48717947, 640394265, 113170213, 619223859, 25852870, 304447468, 229086906, 855469716, 339450568, 538795659, 710286660, 254568682, 741501849, 232626293, 623068855, 832801087, 720167433, 887035822, 833835109, 193817699, 418117324, 332735497, 782804988, 782500332, 787689065, 278006282, 249585156, 126720387, 455307801, 514698090, 985133089, 600687172, 321261854, 853237565, 455157794, 538833972, 559544336, 839435472, 640203838, 56006607, 966897717, 114552178, 199596525, 796509711, 873353883, 688352715, 241880786, 157681668, 781955682, 272567926, 958305990, 594556966, 480416824, 869701446, 718617139, 377487248, 69137067, 331775749, 426739472, 51911992, 669353414, 129694462, 927636407, 507931306, 848795762, 436070100, 426149592, 396584674, 667762094, 794518397, 725263504, 570838336, 70548730, 535822714, 755356937, 152255070, 256899839, 676822903, 100296730, 610937947, 803069297, 367855574, 197093549, 471643205, 665466258, 3293007, 350479397, 668286374, 307643265, 120672581, 329428255, 564503766, 299747720, 260883077, 179680994, 525644782, 295469803, 35010806, 136669619, 269095084, 665094702, 827841530, 138702836, 755824525, 189053184, 331114483, 637466383, 277771758, 487729909, 226767981, 170824296, 349897373, 615929098, 174283563, 673150905, 824018102, 408643074, 931325798, 777570713, 58983375, 36856139, 441104247, 83225244, 874406771, 891897643, 922930197, 784560216, 233459948, 388867720, 61656857, 764103085, 893148743, 621984732, 173354419, 726712240, 798136309, 815711737, 853883322, 634298463, 704784158, 380932813, 67911545, 483056536, 799572836, 449399091, 605634233, 638397201, 93017580, 943124192, 124350466, 490853463, 428924775, 106305526, 881523071, 811123867, 804253278, 26295704, 380448450, 188702753, 46397974, 963689470, 39461210, 749588544, 172807188, 819091194, 664388205, 228803487, 41421987, 350868667, 893167632, 730354010, 206263801, 3470357, 467373847, 882375662, 783701629, 203456724, 922052217, 981402587, 182986732, 527970, 16970279, 535742545, 105848813, 488753540, 233854781, 387374923, 687033391, 332569430, 238421067, 557353678, 876310660, 763985976, 657085195, 871926235, 258445866, 567865483, 644853846, 251502753, 622481532, 342353872, 417827677, 622043837, 623950251, 998471703, 405652965, 657921649, 11857299, 787156765, 279577589, 604450526, 812587948, 932921760, 698944552, 422355082, 410803691, 969637727, 484327444, 394568586, 284144031, 646207380, 450960716, 182087536, 621807256, 690308808, 352706902, 182311683, 844730641, 837136496, 583592396, 194065968, 305416250, 952358917, 754772536, 847595727, 820664476, 521947880, 175113574, 161652153, 795608440, 809028763, 511924521, 522296697, 307187109, 319520972, 265154994, 589617536, 856005175, 832972429, 899278473, 357526545, 734049806, 585171795, 504350655, 172705349, 276442396, 756595340, 195423733, 122212110, 3062127, 750946859, 929794844, 278179490, 975278710, 376465689, 917431933, 357139892, 792048838, 851237211, 333736675, 680138735, 915578815, 772171990, 1032925, 269807077, 870163352, 756152222, 732209659, 842903637, 251338447, 256072243, 866257813, 711875744, 826234930, 569780761, 507966824, 527914131, 138454031, 463961251, 583609307, 413376369, 493553679, 119718224, 463364033, 402991283, 807861044, 347734629, 574366578, 905221187, 845609950, 709766925, 575008621, 683303496, 952111944, 969491721, 817003231, 349805151, 938688800, 492465807, 466521639, 48082220, 486567243, 713191432, 423391396, 576388665, 704253813, 306730380, 690680903, 805102205, 381495604, 68835350, 977319047, 210191128, 197690887, 933443784, 856215856, 90320191, 776764175, 691436096, 37118367, 549114456, 814938112, 476567525, 371997917, 242169355, 354285716, 267061623, 720953730, 132863056, 865015973, 913321292, 399297018, 270355095, 539634465, 225136439, 20962243, 356137935, 960595032, 491870916, 474280706, 593026526, 806567118, 299186722, 491608063, 820302434, 943661238, 923337228, 941095843, 318220387, 426885099, 875374129, 274019471, 67984239, 160056413, 192685833, 907964234, 95052112, 609460696, 84739467, 154379874, 840840814, 564337710, 241718629, 787696439, 85237160, 685030071, 661671982, 252248992, 662718357, 144311708, 28892957, 676480561, 600277182, 426235884, 170943387, 566326820, 333703954, 803319970, 573192001, 933139465, 657075869, 712640297, 870799337, 523775825, 412754599, 939885874, 886040438, 896869318, 252073709, 836734929, 356875328, 56808526, 685351285, 689548178, 20374198, 247783106, 198620834, 996657415, 227084498, 537407420, 376044436, 764370049, 6768357, 334589512, 159571018, 757383893, 42313917, 621717339, 823313054, 982760906, 932712466, 794647241, 373433492, 848848540, 44972604, 570566230, 139259512, 75617533, 244224076, 66838619, 898752893, 750172558, 753281432, 4769767, 281232011, 799929254, 492001463, 823488645, 531903185, 886457088, 410349638, 954288095, 486670781, 154173296, 493855900, 434875145, 508841221, 900658491, 631141948, 807600406, 269481289, 601251944, 946630541, 982892128, 731075138, 133034478, 590329531, 19916121, 570887815, 304144811, 894852280, 932368802, 333469988, 677853384, 817429796, 739332476, 782884936, 94519914, 163218736, 146916531, 527109835, 931596718, 507169116, 517825971, 759401124, 235170454, 17643626, 765146727, 215748992, 421565805, 568609511, 645999853, 185948649, 413312703, 63220881, 830577057, 145138340, 809177054, 52664682, 282020114, 430475018, 952933735, 608676710, 492095907, 676038969, 983452519, 693965713, 865448799, 384880654, 65492222, 42463069, 517356194, 925685112, 26399498, 369396655, 936813520, 444727081, 431443840, 743571581, 257681573, 486523324, 634445197, 535420950, 115214262, 21601018, 794961943, 495304944, 778456232, 695071600, 317714729, 166957704, 405400763, 111675542, 662183236, 970335424, 736244529, 63824584, 376934858, 455966184, 375933024, 993255099, 750980343, 210977609, 178579009, 411615094, 397341581, 362330346, 776556512, 313117574, 201392762, 770526985, 318984076, 667528186, 763517382, 522565471, 95132339, 141022, 411247644, 860625043, 39152530, 689955873, 131055568, 135825498, 59329383, 232171124, 706469738, 367851565, 946468096, 887386189, 911664209, 592628334, 556894809, 711934024, 307160866, 532896015, 588846503, 12816139, 26269987, 169348385, 927178925, 718699474, 942047510, 868939676, 893197334, 2437047, 412629677, 503104562, 339518886, 793288788, 218208936, 223407227, 234153878, 185496616, 776365373, 700569667, 642605340, 321510740, 544148026, 642035907, 450470973, 74326517, 505244753, 119089045, 428302934, 540568270, 676756300, 150895313, 151524974, 116607588, 796178630, 107550845, 977923262, 878726595, 784253707, 171186056, 866691314, 578600209, 588728212, 742552762, 484292048, 594153214, 194165313, 360889707, 112901188, 545145302, 539132475, 597731109, 8524329, 944963214, 782649779, 802868871, 896827066, 55710842, 602087674, 353727592, 634942291, 749166286, 652689224, 226748287, 431041750, 967098662, 501688630, 36012360, 341004381, 626601179, 195827050, 447914445, 70323631, 710962579, 508660449, 28068072, 775507725, 340071429, 190487579, 231160636, 324607644, 550799922, 628905280, 880328623, 826427852, 587140713, 246796321, 853664478, 346147034, 743779306, 892644490, 982040990, 656158875, 951470498, 25210501, 248843402, 866694815, 31744255, 403749590, 870213218, 299685014, 84320330, 409537903, 69570288, 662854094, 552610590, 816437924, 735105336, 154020638, 776563555, 793506810, 185313509, 386499866, 317518811, 569859603, 653481105, 604729355, 833284273, 712588812, 461392485, 858431845, 952821938, 974441641, 902432676, 403086986, 511700585, 572065294, 456768122, 733575823, 30214679, 975477389, 992434322, 54356178, 829266177, 865628415, 291646240, 122175906, 889360085, 841463863, 695835407, 91099533, 147222326, 5987784, 752426710, 771151858, 18249322, 4203999, 187985286, 234384267, 671530586, 54376532, 890673057, 718186067, 724260674, 439489602, 615870708, 248189336, 969324160, 137558430, 44853400, 599263901, 202365249, 898680963, 652238239, 543814820, 439566368, 142288954, 613559951, 744852925, 403835249, 569697054, 114482758, 668260131, 294371614, 933412724, 140081563, 268901781, 919144169, 213657593, 846012645, 555485819, 929092397, 343541373, 747988425, 508170828, 433895280, 31097269, 110734883, 145753444, 443960803, 201680345, 786693890, 218008027, 730240590, 155661221, 739352530, 465944231, 217155109, 780314249, 305020474, 178015715, 298565331, 801641217, 1437908, 569741315, 693343654, 959731816, 745016993, 226769164, 943824069, 390583968, 858597225, 360225416, 735276416, 283281124, 90406010, 597003001, 211646645, 254907131, 891691331, 843982689, 477850885, 514097087, 213091413, 987404930, 342086165, 95407352, 144895395, 255788038, 96992999, 360514904, 127791507, 226147775, 589397796, 813039798, 790674051, 284568903, 554141573, 114445703, 376762329, 180914972, 195477541, 187448139, 699566756, 135928988, 352089648, 236764162, 432057935, 705025295, 742297286, 47605550, 368290094, 497433032, 863017700, 217080719, 976811997, 624273450, 956942317, 84875011, 510408959, 944780902, 117759964, 418353254, 329107642, 735733448, 890813910, 217489660, 494940404, 762129437, 915152221, 548879475, 986800845, 412021743, 764528219, 492745953, 439356369, 513769809, 709551679, 793181792, 211676276, 161415158, 300682784, 316632283, 963620452, 238266332, 746433244, 602015701, 511319651, 28936355, 635300581, 944986533, 166322563, 455804411, 855378705, 954895332, 961417630, 220175019, 630037954, 497019884, 25017013, 108353200, 622649751, 288237485, 978610235, 94713629, 429961008, 380155682, 388756681, 806171198, 111892141, 570172961, 143895862, 229894827, 38525692, 649365597, 17346646, 992444138, 358291563, 282230602, 632867161, 1047420, 682134257, 894930481, 847926696, 542358787, 666348434, 933820577, 782268326, 757805169, 575786399, 174761378, 131023876, 866688502, 686327942, 107503117, 490986907, 133022011, 95600626, 434098460, 671124274, 550457362, 572455044, 780272180, 854460752, 813596287, 350884350, 871358383, 602791791, 346854755, 791740183, 610882599, 854590763, 338528964, 771702324, 716642514, 217315702, 387317609, 618869296, 432424891, 404354821, 122163186, 526121963, 262432946, 170549115, 897626993, 599680043, 74012722, 867204010, 761524667, 290537038, 874226758, 907237092, 705089839, 693075037, 985135224, 725783788, 390079923, 828298086, 312693775, 827095410, 484813972, 569377481, 583456706, 605584145, 13324423, 343014860, 864387204, 348986846, 878727760, 956901429, 890701026, 450573200, 51270829, 245954748, 261209060, 274996836, 396951652, 348085461, 153372385, 787877872, 722175554, 861082414, 778925290, 335020142, 190329151, 136409959, 115964825, 958173018, 945032740, 43395600, 736196896, 592977088, 539014221, 705930387, 249424851, 969816492, 974371828, 628613596, 329940088, 385362237, 228179077, 994183206, 628764530, 783611934, 341185600, 727510017, 655005230, 651898394, 494118066, 588965103, 569250587, 167168195, 534617128, 938721777, 674483606, 129600408, 960370768, 51666633, 29838622, 671758961, 932131230, 554044316, 460521848, 947071543, 261983530, 930610705, 208956899, 342450357, 277952366, 208819271, 968848107, 442352086, 301229380, 77553314, 168171351, 149861896, 865370583, 668382962, 214106568, 579163098, 361501292, 791912319, 563970160, 933776668, 579528692, 119106539, 522640502, 657023743, 720671766, 800715048, 942400742, 379075510, 791933973, 436318515, 247861273, 696625998, 881733143, 650395347, 599611177, 256755984, 75861074, 443633530, 572027657, 24486399, 721754996, 217601012, 40567079, 40600854, 362306802, 986156205, 932406272, 454694562, 709984383, 244980393, 793106774, 903406490, 886340502, 289931994, 928512167, 532699302, 408517939, 142254646, 638892211, 851839230, 353615125, 123648997, 459035768, 497727090, 598033652, 414447974, 404332164, 378566122, 451471890, 436304173, 737079697, 982861325, 433268608, 403356705, 317422833, 526802531, 870144016, 660062745, 706758294, 340909690, 806563864, 176531084, 189364565, 295158728, 336600532, 896908511, 707818778, 91066749, 294190529, 56148061, 62201079, 48845153, 441359878, 122748066, 502524797, 577177160, 174051855, 181161755, 755794096, 953010937, 279545595, 576267990, 898199537, 590634630, 161077551, 933863469, 956792976, 349437500, 977667968, 459108132, 670041679, 449235125, 734019663, 368589706, 298842961, 947101865, 221201732, 203615558, 12832287, 596150482, 536945658, 179461841, 500534774, 509439416, 244242068, 176986633, 710925082, 584333700, 627029435, 378167821, 705907054, 732408626, 77476831, 186096490, 909832763, 192315101, 672317010, 583622784, 912268938, 90910180, 874024964, 960772711, 758176700, 402322000, 448360309, 225700862, 435050839, 435116882, 961469976, 833462474, 335255857, 483967091, 386812612, 815487585, 702863781, 446467548, 744900950, 728016810, 85858478, 367953502, 891075857, 991038891, 162938747, 695539087, 889900773, 195692400, 867268188, 976100463, 335155366, 232834312, 104357702, 1195523, 933882936, 239799801, 523985836, 777120835, 40941309, 436324749, 734624819, 948419179, 619651229, 966406801, 467848020, 809485662, 41389462, 939476617, 837601776, 828331733, 650600670, 921862137, 553353970, 757834813, 278900836, 349676151, 952730158, 671061617, 972716452, 984191403, 503594159, 234125393, 531513167, 256643081, 665115988, 563253153, 142229748, 730740732, 876902826, 603875363, 432558887, 990062346, 558838208, 909990026, 899666969, 900190953, 532938898, 577872625, 970296476, 801409002, 703796522, 636202704, 775055257, 192656002, 787013565, 650786304, 723042609, 269556082, 815983309, 922884056, 793024354, 56576598, 320627516, 338782620, 539562539, 493146623, 922627114, 995128239, 977440773, 900318913, 90703768, 450654735, 147205649, 910436117, 905195512, 489497208, 482598645, 386930384, 148951316, 855474707, 85238843, 946288070, 911320803, 160683915, 857223603, 63063973, 42611496, 149395338, 544776256, 297338730, 275543166, 788697958, 196508549, 417612809, 595799134, 664940290, 988778041, 949083954, 394079759, 620481713, 997820481, 828273633, 732500560, 238193266, 544092916, 319159886, 21491037, 135919382, 581435048, 839821240, 122891484, 892424952, 258819813, 812901375, 36674453, 552716812, 841179074, 263895580, 891971726, 239361933, 300216006, 212186534, 427495657, 634082448, 543548305, 122333675, 170195571, 640089497, 674460839, 419425602, 737909902, 531762445, 983015474, 422135583, 196920845, 969778540, 505919263, 25859090, 766483105, 198330965, 431747706, 827397842, 641175543, 958791418, 434284549, 456352568, 115020762, 562913399, 319164801, 719256122, 718025818, 682160143, 540439139, 120423076, 721280937, 308985797, 17810310, 101270988, 546530894, 514555415, 493760037, 811444420, 368577774, 60184741, 479392444, 457297319, 150266343, 723147851, 472254880, 141760187, 268563778, 837548617, 767132509, 640596528, 442275889, 157965396, 644019646, 180999212, 838500935, 876174382, 176767749, 476025252, 42495654, 646301679, 705458698, 881482650, 234487303, 13491196, 820100814, 896907165, 273487896, 474622630, 501136742, 56060938, 989960016, 437639231, 566471029, 510678260, 885245132, 700331844, 104569793, 292707891, 191379818, 356753590, 915575427, 579212852, 421106229, 337788790, 444154315, 28450791, 500367723, 112298599, 865834716, 3991558, 618541019, 950478259, 24905442, 813079867, 776829309, 323062540, 98003083, 562637036, 418684842, 832143450, 950896511, 498453249, 957931500, 632188490, 540822425, 957036278, 256977783, 147494234, 436397979, 204565385, 713241846, 406211943, 262118822, 20635550, 384931321, 35237896, 842243059, 863127471, 731120315, 691460100, 808604667, 82383839, 750414539, 35412123, 965116946, 735039606, 263910746, 608760744, 455447352, 158901643, 781431984, 688100053, 441945400, 479147809, 66673642, 47926720, 251864450, 166497867, 964172300, 19529294, 302584979, 441293993, 678598720, 525103619, 109583959, 405960642, 80439588, 835212964, 89161228, 433975717, 700978916, 948424996, 639093984, 721938570, 800511948, 88697509, 760930578, 970033531, 96746263, 873840400, 263057741, 95133345, 160423651, 399469503, 88737798, 785376642, 923460408, 650526083, 984209026, 286625299, 746110046, 22401528, 812962632, 591938546, 986685388, 43058309, 814710295, 408865691, 955023701, 301885717, 525737672, 467987421, 117198953, 422437035, 619951851, 134621997, 624873890, 123697107, 351059010, 724183550, 624661942, 133969471, 758006227, 954702185, 933529025, 494082785, 757281067, 650834913, 62127399, 931894772, 22517331, 595233606, 528153500, 367609728, 802676291, 510669221, 138354165, 278654257, 884199601, 423354167, 247030824, 632500176, 584147486, 478717885, 771099486, 985203707, 250328790, 217398310, 537091751, 879655447, 2657593, 141448527, 416365838, 488746132, 763945793, 469645069, 252358734, 142592200, 187407300, 961602401, 3333470, 648057793, 896936511, 801210997, 655254550, 510544573, 478471420, 551206617, 204363892, 739609902, 695886418, 143445303, 343723438, 165317670, 505797974, 804924109, 704145198, 7149172, 25391591, 669720505, 795096547, 227617481, 551705082, 66397139, 249367062, 812503575, 528683373, 214596328, 730347300, 907376173, 360955584, 281217703, 80718953, 84352485, 758911031, 257293823, 723245972, 93350090, 298024915, 261272878, 501340796, 409209074, 678710659, 769703621, 252630051, 36780919, 809620559, 490625743, 16102816, 708974984, 250656933, 78149803, 614622805, 270003910, 225317084, 718746717, 963789010, 858215515, 32142584, 765464290, 18180345, 741553791, 20301829, 576322614, 814301585, 987402140, 674834131, 136278034, 529147889, 280189328, 429665174, 650830364, 979826501, 733233284, 560468858, 240235461, 898027046, 957419580, 675627044, 573220110, 771538106, 926859042, 943216800, 169129776, 787271327, 66153436, 961937840, 37589055, 754839024, 209697413, 127088235, 186843252, 54849607, 563764155, 657836283, 40376861, 151809993, 879254529, 26483519, 364510306, 419109699, 951234057, 105333722, 906113642, 928476130, 146675890, 413362679, 777912396, 64306284, 298040682, 569567769, 5720104, 990510353, 540929971, 772394626, 61916015, 872882022, 644723069, 650099248, 823058707, 172601595, 252395461, 723124801, 918980011, 287653019, 123904558, 519355207, 835594714, 386479125, 592903243, 271890671, 711943065, 737356913, 410525176, 751963578, 524266144, 903839489, 522988519, 441001878, 819960286, 960906215, 419677605, 490608232, 680542763, 735411687, 775807339, 518877110, 751051101, 42791074, 702408333, 102341275, 473052076, 438456372, 895833391, 128626779, 255583329, 168073738, 882362805, 204773879, 895634992, 162661543, 516172636, 914465992, 58793501, 906328680, 788507085, 639885799, 740574250, 311925784, 444234468, 986548343, 529410225, 70992198, 672692531, 891864176, 575934769, 353037620, 261135630, 124312671, 585568377, 862106862, 673739420, 261935609, 683887193, 378477827, 446957754, 328249715, 73080215, 969849335, 496772631, 327547257, 214696357, 439799541, 925941553, 815460087, 638154697, 806241042, 94644100, 249123879, 123589315, 397928630, 805270996, 808774640, 841978569, 288452739, 335313082, 804040020, 773603329, 881231319, 809855957, 145961915, 800634812, 798352160, 520834975, 679770973, 921441700, 757548449, 155305979, 78589289, 991970485, 807408777, 451271832, 661155674, 383965616, 981269968, 297973143, 427322062, 143042484, 828370684, 32817225, 983109370, 599737602, 276845129, 357841689, 751071648, 814814561, 850169788, 734344508, 641188538, 346525976, 783731672, 161986923, 411545667, 912022646, 978104531, 425130912, 678405988, 496074502, 723990236, 990355530, 557881427, 334307433, 573836719, 292958436, 823839925, 716936738, 539242456, 699475698, 153714647, 7932699, 246402917, 317401056, 883511320, 926160021, 368913665, 154934523, 360391573, 954062658, 780118463, 720667129, 782699970, 831700529, 536569149, 420558670, 464332735, 223257248, 76542417, 747108369, 693606597, 163517061, 330835217, 509769406, 721438456, 214425697, 682939571, 520530651, 145713317, 451570024, 796339885, 586981126, 216390871, 935596922, 770352047, 68485839, 155250793, 693520855, 407033448, 924117738, 269762730, 838208193, 993653639, 18895211, 189759022, 338236218, 52597692, 842818109, 283973338, 441470716, 423112384, 111273208, 172335725, 116553178, 65621937, 863676546, 333083385, 507430944, 609542317, 46969934, 214103707, 330678456, 777604137, 115410979, 475077906, 617830309, 857944897, 346753963, 889256441, 45728384, 933705054, 744861389, 206208783, 242467300, 751309549, 800906943, 688974803, 828663499, 967028565, 722646209, 39649655, 320358117, 950598416, 752560405, 644478102, 515828868, 913756528, 462638460, 892428292, 376109722, 34631459, 417331449, 102400710, 958199856, 441536597, 862553360, 628951741, 950173104, 765632846, 811930409, 901920981, 951896330, 892366794, 287126327, 92780071, 546763601, 406376835, 298961003, 50361576, 702418077, 873899690, 65375549, 617794704, 839099144, 500979200, 699509636, 266067575, 480709101, 118975567, 141684912, 401190618, 907998925, 840833044, 571674073, 179400913, 900931011, 577424705, 56525704, 804366238, 768911679, 376352294, 376613198, 392261032, 386765873, 300119185, 322850590, 603641795, 887458307, 167130381, 949774488, 275472297, 403162255, 45732888, 126856882, 569381042, 855362602, 131273172, 774338682, 427238583, 640677266, 134076775, 165516499, 723917564, 527962012, 358849481, 558064933, 300719651, 228454436, 180030192, 251554932, 695217142, 967622506, 394311275, 507121357, 176605649, 373356043, 761001499, 407956782, 782288083, 233387930, 894934739, 13729919, 739266008, 663352217, 927168689, 420016594, 125505561, 624288268, 283844961, 130327877, 231038439, 195664214, 659786450, 61367647, 586239216, 745583109, 382403647, 484059376, 519419147, 294202611, 751477657, 206068621, 879688215, 13718359, 51541671, 383157053, 545893065, 178688132, 700965221, 982765236, 177616652, 909160567, 504632806, 717948026, 780915073, 168399797, 344531928, 7606153, 80790223, 908509445, 476933956, 847760183, 237839856, 610976725, 156957276, 674632944, 346421686, 825484506, 7161646, 349431299, 440554162, 331542881, 49010918, 931848381, 834595728, 262057378, 261909829, 680044993, 544612784, 857694628, 270376727, 491917395, 319564040, 920650581, 45189023, 131858573, 62030590, 72794947, 782641022, 627405831, 540519670, 896810184, 773566128, 631622226, 177616206, 67147571, 166001619, 300333914, 858672873, 74676913, 830254899, 881418630, 348910902, 858930997, 610774773, 468183899, 162053740, 605158930, 451023840, 585594174, 759782401, 800520677, 616029079, 803336419, 766645247, 421492072, 31583000, 843797583, 26217340, 908550855, 285331688, 307994664, 288544754, 749960636, 352189774, 501980025, 318675826, 435504255, 781608316, 36646979, 190876739, 291678643, 418543894, 62214683, 19544073, 332602193, 16438584, 628935406, 378872239, 17529168, 672664176, 945361452, 120678419, 274125643, 133819617, 264251621, 442948024, 543925427, 790113598, 490937250, 257497703, 86027327, 918284371, 142271768, 173386490, 467049506, 415654725, 670826041, 778626175, 623411388, 545343819, 234191683, 720307729, 698934149, 180731479, 875721714, 950862684, 111393016, 40203561, 990273462, 687404281, 812047815, 136222505, 937707007, 513597944, 126042616, 134366606, 327225640, 585676260, 243716685, 991134465, 585983724, 611480484, 3307279, 556506094, 974239746, 37682296, 666138069, 323643890, 938642851, 133873954, 982244765, 410649963, 303161355, 160085992, 723745399, 944122954, 906191231, 963376870, 492101260, 268934509, 376351025, 762950751, 871831367, 64015794, 808079451, 716229038, 946622776, 386869378, 299614813, 26096375, 699029304, 739033801, 970481612, 401307103, 231862175, 513096122, 515692876, 631278506, 800285531, 501132385, 558174007, 771131072, 144054546, 371758283, 106083960, 588008256, 397614215, 877071906, 994621583, 820844328, 328587207, 555512596, 700068711, 390380734, 209467661, 996517570, 448339135, 753297666, 129702048, 75123905, 848606372, 264928349, 861635883, 956836129, 309160807, 507842109, 111758180, 549920636, 486968493, 574478478, 591267177, 489060047, 958600101, 296968336, 606778640, 762949309, 380425176, 243264680, 166310835, 184327530, 805544089, 575751233, 397572212, 384626422, 586506433, 475310857, 540044662, 542222971, 525943485, 564096621, 955810702, 297081795, 880471047, 130715746, 184394894, 338994227, 839985491, 717606620, 940167358, 901103637, 796802421, 834456193, 486579918, 242630959, 937896855, 657411213, 574786218, 42100523, 690669065, 600029106, 845952316, 356456555, 474953857, 464284288, 442780482, 62593248, 698583573, 551158377, 57843891, 684277282, 116448674, 614718601, 645267355, 853393421, 476873312, 805610312, 551327153, 727335417, 591817627, 165370156, 291739701, 438657080, 953710649, 26329169, 282254239, 615352045, 543629259, 300439274, 443493889, 857332430, 913937729, 667303070, 371955836, 460726403, 47751544, 159451536, 27923243, 353932131, 811631704, 973350838, 580162909, 63806212, 145101522, 786625140, 900726796, 600609657, 487899302, 382565172, 516810956, 939361805, 325301112, 110963837, 837116854, 263694228, 646974515, 142795187, 885442997, 469590845, 119498516, 542309898, 242218960, 23210852, 293186049, 938739145, 861889022, 121740347, 43822437, 155431993, 255237166, 865980002, 41003417, 97804017, 263481243, 541218299, 327832220, 535685176, 842450557, 489235747, 744490541, 627664889, 771514251, 484107042, 669196659, 886878068, 234133396, 118444199, 178741672, 743008099, 490620721, 3060525, 14197771, 188701219, 821948842, 135481722, 777255676, 319455947, 393598791, 938492030, 949600577, 608449567, 548389954, 234730937, 323656609, 81322237, 480999036, 806242702, 760434778, 471420768, 248776118, 387480813, 13358726, 5722063, 432994360, 629286922, 163797770, 388234300, 458537518, 221747043, 898298927, 56309234, 694102847, 748031873, 816943307, 558811503, 550241882, 670287817, 50626052, 214233314, 5130661, 420217030, 372749822, 958445414, 322087501, 804326368, 952378178, 112482309, 99346800, 836330786, 209418904, 399637357, 165539831, 367940405, 577406930, 17612491, 172723155, 440489410, 217655247, 805707042, 737879434, 725040822, 59525817, 336250722, 714466612, 81949823, 33220207, 320375740, 132761887, 609768327, 655666705, 305797180, 645366852, 148336820, 339714981, 87277632, 16015424, 292647988, 660742235, 755642865, 564116571, 946965364, 475339392, 874381270, 470545009, 587161543, 325743923, 240349092, 363703042, 296987167, 982990741, 972073115, 577414640, 102308638, 863665286, 566769449, 693609991, 195054146, 16535016, 323023540, 628283888, 403936039, 415668980, 651192685, 563134811, 772659198, 182370523, 967906864, 329527455, 802825576, 844234210, 977110288, 70655272, 411613357, 51511877, 634244826, 828129103, 820855034, 948972273, 177386166, 627814901, 368234516, 937143088, 773145764, 428102652, 957712561, 909898515, 142227695, 73859581, 17401124, 343908619, 317449992, 452493596, 243271470, 757563369, 721864453, 342939815, 144121972, 835878839, 971386405, 148307262, 300703713, 257677133, 90247589, 661764536, 455806168, 137403687, 562382434, 663622594, 810337011, 696108951, 438205691, 926168546, 780281084, 559283261, 719000798, 217446723, 903864337, 224330184, 129431253, 771309938, 591922874, 282744474, 385777166, 702712418, 644967725, 64651972, 590358528, 711957690, 232908401, 218311138, 514586073, 442200485, 157392896, 789691309, 94417188, 272291474, 744353447, 817886930, 692812850, 195042042, 777624673, 275490633, 450650408, 637226895, 89913821, 642864693, 952968338, 711165571, 973500349, 956446141, 969469168, 547159543, 257767386, 666015094, 789280868, 23865032, 383749188, 999347330, 836591134, 347627951, 335585471, 754168442, 935566145, 656405868, 954206635, 33678834, 634782458, 178168387, 612221322, 152049808, 679797160, 783318086, 356891728, 676482683, 92913123, 204794519, 292670715, 330879659, 372342607, 121314199, 663146465, 694690499, 551688576, 947136215, 282429807, 30938501, 602130940, 639875310, 245901769, 885585136, 505643779, 683611665, 538592455, 552556930, 729190953, 799993396, 853024775, 580073357, 407513428, 330595455, 610865651, 805938087, 801130211, 516376457, 333429899, 205124430, 131614671, 420193676, 84489612, 697695854, 190356817, 657791435, 764270432, 76243466, 85176864, 117519293, 269934265, 528907087, 51727101, 84367401, 420336460, 476567355, 746394063, 763274088, 466568109, 186196783, 727025562, 381153255, 337768994, 97594355, 489389099, 981836413, 400919279, 269581882, 579240874, 901197039, 491967396, 949625978, 245760035, 249814550, 274741367, 885465153, 725112764, 422869997, 366464771, 240571053, 213376429, 646480345, 792488072, 240949816, 227534526, 342370646, 392571153, 488631701, 997943059, 78984423, 615399359, 427591319, 281174508, 340568737, 449959803, 844474535, 979194782, 603671362, 401910670, 700125595, 895551876, 56577607, 225935664, 417861093, 416555546, 654477296, 514545259, 703743244, 841144095, 445288464, 567061947, 402885696, 113620861, 729269021, 92215789, 119878180, 338806555, 651600817, 859671751, 853021304, 33174969, 5836514, 431918322, 618874205, 932664635, 712657869, 364662370, 999163419, 436123662, 810785640, 544038662, 983440147, 179938887, 546304942, 339956585, 840381740, 479176684, 5749664, 483727371, 993481887, 228355604, 576908412, 106947651, 53933016, 907505268, 704387242, 529010912, 555095018, 33540298, 975316076, 260742783, 69212087, 865296424, 181671563, 598934025, 114421875, 966373839, 759208196, 918202123, 249518658, 119780392, 219346120, 492119189, 329519350, 611488412, 741935178, 557213526, 65949887, 817954634, 17479559, 45650827, 579120730, 362452057, 488947451, 558692531, 611198741, 179974621, 354166956, 336891847, 218168874, 191824483, 375929069, 173524032, 998735364, 4577952, 565340496, 523232547, 414456330, 25194871, 701426445, 855644431, 855370530, 155927000, 237621944, 456242089, 649499059, 990151635, 504370220, 769381316, 235252435, 235105883, 681373022, 923541352, 384890651, 772799386, 376760670, 438842207, 524355780, 18080187, 826104192, 649558642, 926682914, 542458446, 102137991, 319469078, 563659244, 709801930, 782910400, 783611087, 326624612, 375245401, 977276143, 643075034, 257354990, 173439722, 518252989, 779663725, 559143106, 955214086, 113428895, 356450217, 747474801, 837658262, 591782985, 921204803, 336296564, 557598054, 819113507, 906782576, 631844117, 371551992, 156705421, 936871094, 812747281, 333891673, 835943664, 758489294, 449388166, 168234299, 453135173, 259750272, 836322612, 72403142, 891369456, 86008026, 551582654, 158633423, 860232065, 566945388, 124583788, 453233889, 833456989, 833498767, 33131848, 451063363, 942983736, 386940601, 640984896, 656052298, 24555235, 695999496, 356583204, 219260039, 740074773, 212763425, 173721795, 691452123, 669710970, 318714555, 53650360, 860120816, 396703652, 372342822, 586720866, 841915596, 125787522, 501891456, 456516805, 756477049, 900505567, 658287962, 945200457, 330806467, 285786781, 690814631, 191240333, 123742632, 230048901, 464286709, 419624500, 451558866, 820716009, 304727420, 299978570, 582577562, 457263243, 332228284, 231470853, 325861057, 832319481, 142705165, 959213996, 347532825, 356323044, 179760020, 191779578, 900121388, 532548646, 541612142, 286402304, 90835788, 307592831, 554713607, 314207300, 454278210, 638349793, 379519675, 239037541, 905145703, 689194939, 604394035, 93453018, 237510374, 186081859, 505534331, 895450815, 522464889, 598365361, 333257610, 545034807, 890402048, 620395832, 663127437, 869270711, 228549462, 354690881, 663239198, 517637741, 384474698, 104478058, 827558325, 893731476, 351429964, 965890389, 827334526, 666228749, 988559038, 436202780, 41662933, 895671521, 344587254, 294270565, 277086429, 974191320, 675272113, 294700181, 697559725, 507033286, 407939301, 747672900, 170997556, 412720328, 280987368, 165821503, 457401778, 741760540, 385241111, 957698780, 203651750, 6566583, 522480505, 766908060, 947191184, 145832034, 156539549, 801568326, 991044606, 761838511, 561778656, 188080647, 356368149, 831935517, 334582459, 153915877, 118752867, 886092643, 638187934, 648716818, 212772873, 218986801, 569157751, 464002369, 470033373, 937775545, 503410300, 959609656, 583296422, 233307440, 818234206, 666496480, 91099518, 854818940, 852718449, 162444163, 541582216, 770870670, 982357589, 482004179, 772348221, 388285196, 594479165, 793777601, 995016758, 982135159, 56617923, 891466117, 594611666, 1576034, 645804102, 87606471, 319934953, 813666443, 52918065, 293377788, 187146593, 333254186, 459982462, 406108782, 968222571, 747184589, 408572228, 837431586, 383493277, 435337124, 289749848, 608920380, 830635378, 473364938, 246835647, 618644120, 436707376, 733577926, 724416985, 563618610, 579764363, 943471160, 526639780, 696050768, 415280645, 301064275, 205899225, 251196673, 888438635, 352362307, 392460610, 610864491, 727350605, 899581000, 784056008, 462965315, 457406444, 775792818, 748584450, 891522824, 740800019, 492051237, 58189703, 32189971, 38979925, 331618705, 562171120, 193990518, 183285097, 390928766, 929729920, 72943401, 522514192, 359105146, 832192069, 586673239, 714173244, 288444950, 163803574, 401711795, 951824488, 743392604, 834396179, 965377874, 298328692, 623532623, 96120402, 975647688, 87501542, 283874212, 57639663, 476136939, 716526059, 89362040, 641907525, 106177627, 162101150, 889276168, 941229274, 543310896, 327956715, 830008141, 476685847, 853327970, 579402997, 200892497, 564993953, 660723615, 945926890, 109642716, 338440342, 125839185, 787645980, 703646803, 85514806, 709409924, 668287054, 287711765, 360408628, 899869976, 544184485, 516785197, 570201926, 694742474, 51304584, 52547833, 550778224, 292346565, 691749626, 824961686, 51707548, 708389959, 47904767, 367844406, 390278669, 454178328, 33771578, 867337088, 136422182, 944085503, 251588590, 592332406, 230392048, 721317917, 408312146, 773684257, 245141410, 323127736, 192080202, 364773520, 116292885, 687919468, 137231635, 837232293, 276130918, 765593644, 779080591, 315478681, 149539999, 20075307, 693490526, 191897786, 354360806, 920126620, 9130864, 951608123, 203679585, 196501064, 364474947, 136539115, 515912059, 965886796, 786508644, 609451659, 102019099, 741540833, 241952318, 787327742, 812626156, 951611608, 92240196, 980997526, 789070271, 666582312, 949931410, 194038732, 218573086, 418211025, 18951680, 206243707, 183293295, 516889624, 451014199, 970170539, 785568849, 285325219, 61011568, 233432150, 15038446, 473591733, 146289269, 670982940, 739664693, 818226670, 343589447, 748420341, 249085638, 548189041, 931103939, 301614008, 977671101, 456819556, 745887484, 138842807, 271842100, 828546817, 58118410, 751053980, 756396345, 513614902, 116623900, 755391862, 285406126, 127076151, 824684895, 176819625, 911438338, 850704568, 651737720, 461920891, 445780822, 751853405, 39801018, 294759498, 600717493, 793334827, 706890636, 655776090, 979152328, 426366071, 291551380, 312717844, 705258666, 247260918, 146698378, 834274863, 967741517, 150035899, 922941812, 826788831, 500467202, 705115790, 949021360, 291914796, 104098347, 464169022, 551643466, 791048852, 986427770, 489240306, 711140910, 797879264, 139962370, 465014737, 595804985, 413596984, 191111806, 458068979, 648673030, 972351837, 271643564, 527766365, 889314712, 859710028, 160599497, 740335548, 808224347, 421728327, 880088544, 349500839, 245807028, 102005762, 312987286, 385630249, 889452968, 480265766, 139657229, 678404210, 979604001, 285571331, 588577255, 217647970, 354385716, 180849700, 97527207, 794989809, 751037624, 623434003, 704867274, 611009666, 662653643, 568638246, 332490902, 432102154, 15757017, 140207262, 710643281, 623547543, 355835491, 785574444, 409551182, 300859513, 677177255, 412096871, 228554279, 18949883, 339554386, 586474093, 547948189, 414067247, 543898434, 315675690, 898823042, 570500824, 287790282, 682712967, 605865552, 410879790, 151217342, 779682375, 99496728, 315568594, 687602001, 202858240, 357973914, 741375531, 401783876, 363411215, 619307750, 829336844, 11442640, 458970104, 812670465, 854856906, 541422192, 370702833, 538296574, 827268544, 157672698, 429362284, 93543318, 397051379, 490725452, 464376533, 400321663, 645190203, 531387885, 665864226, 345287849, 879617692, 987310802, 179311871, 981310972, 371141492, 750743699, 28187530, 991019165, 835759586, 342329560, 661149750, 543546702, 227598525, 233041302, 841407690, 609790875, 339034113, 145026698, 628565793, 416574977, 44820366, 791689527, 135497633, 702993665, 996092545, 383184419, 142930295, 935782409, 622818999, 450758283, 929337608, 381122080, 163952782, 532729031, 37296633, 847673420, 179784269, 309593332, 733042534, 459858098, 505855241, 262574223, 144379024, 277315196, 854988290, 201833920, 105839467, 64552810, 53889345, 941821696, 326779510, 573062700, 759423551, 803885014, 133883312, 599772286, 786570213, 691139694, 271380494, 429272328, 217056044, 259366535, 421408580, 469224142, 752258132, 115085651, 639109964, 242133116, 993364779, 334342844, 163334305, 271997301, 5690715, 867966694, 861145185, 19877606, 564736561, 667025082, 582483707, 163503508, 743824644, 127482429, 572368443, 566935602, 464045336, 370117480, 754960303, 598128334, 524986181, 306824844, 384499364, 277580909, 73975647, 252972866, 581998833, 634021053, 879361940, 85676807, 480499027, 678576811, 705594497, 173734555, 249979087, 837651325, 45952713, 824397578, 949705903, 308523438, 398765298, 339278251, 589875446, 24793381, 122187974, 627834829, 978062466, 626695057, 396109787, 514436023, 695345830, 614859012, 313515284, 832622151, 463071318, 360352779, 363173693, 361952427, 872009652, 629337748, 461123785, 305943365, 259390972, 531746845, 339261867, 259534310, 676653390, 19908161, 103668222, 578415931, 827375113, 12480976, 959801507, 808065848, 487209200, 587021981, 911141664, 488784375, 813776322, 409498509, 575427338, 926298582, 201989599, 171192225, 313229899, 161122357, 844392737, 879357332, 979030827, 779832262, 370614950, 399630653, 125874019, 670314766, 38451009, 269438955, 882448893, 407632041, 318219199, 942746495, 392654830, 955536299, 904790014, 424568966, 444301446, 24819654, 15765166, 343859961, 966944224, 626323123, 651094592, 587872380, 924318704, 792566657, 539852077, 159897840, 737044279, 123269860, 243005425, 344743608, 18992173, 813445273, 481640375, 101965407, 711495085, 617731139, 421556914, 527975255, 156184644, 28189638, 118057957, 342408039, 825020665, 283509092, 526263173, 732609178, 662449104, 964301497, 991026773, 177241257, 677418205, 251111953, 172067092, 78246680, 935342147, 603190453, 177643788, 371139346, 680601298, 848939503, 716130734, 370382893, 614232220, 406393487, 766138091, 763373, 93097440, 258146361, 682205699, 343488713, 875918982, 294433558, 298935246, 676664848, 582302789, 883906989, 282045920, 765633814, 461237882, 665421062, 822229226, 848704107, 750942848, 836510494, 755162275, 200775858, 119860734, 920947995, 494068165, 566213324, 62310278, 322897213, 996203791, 507116051, 124618092, 946643209, 149789523, 130142815, 698738180, 408452000, 64538866, 593894191, 772292899, 334452635, 338146353, 926628599, 196414984, 558625098, 804838711, 837749117, 881004633, 948273583, 128372121, 459308430, 239872175, 416666463, 185606848, 24527403, 141568662, 133098133, 754269961, 408037537, 661482599, 808473339, 714765317, 513006464, 824316555, 816841282, 839716950, 535435374, 906037920, 327906088, 718441385, 325480107, 935689364, 700654453, 877641016, 794083989, 905721840, 214373845, 214137204, 827119157, 153548681, 538719650, 449281447, 399642731, 499678452, 374667544, 789685933, 611356141, 444107007, 471961145, 711424082, 338501681, 472796508, 606498221, 344848564, 141454615, 236995733, 758143465, 31474937, 79796195, 572983626, 112507461, 879726061, 620868472, 508000679, 580917973, 821575100, 365754639, 178269791, 130959339, 311778788, 774976986, 847178564, 647081338, 31412927, 197506966, 955269810, 385903642, 152002368, 778102548, 871926553, 149786579, 698104496, 100730540, 783401956, 351674647, 489250742, 915948256, 732622173, 257842999, 901855535, 726265836, 760682807, 623808945, 343847598, 421394806, 882438013, 455617922, 124536928, 985866113, 96665270, 76674876, 335489105, 251601864, 19220318, 724623134, 894729190, 236742226, 328686319, 689024380, 776996061, 518834715, 162704205, 300960535, 956506280, 283024147, 231045150, 627423168, 304871696, 712214149, 300974271, 985863879, 866588924, 135090588, 922897338, 869057116, 948162376, 951622464, 507554528, 515178575, 729690181, 48297446, 590849893, 854909126, 555281877, 342694297, 445274017, 640281857, 755932442, 431690556, 23064787, 19920549, 839786615, 718707476, 367013292, 279551489, 763773647, 806136929, 390418644, 390151679, 269241529, 60471628, 513223134, 975922340, 858386433, 18207602, 646978461, 362350617, 541665667, 318594748, 201502198, 672195172, 367615373, 641314072, 561227757, 984082516, 361788568, 229389848, 829514432, 696694, 877810974, 399221466, 939902896, 439416111, 715366039, 839794575, 600238097, 298213663, 678135083, 817170474, 849767391, 213212170, 225389413, 461669545, 980935316, 529546666, 997193931, 512338049, 595513838, 174838269, 154338671, 292513150, 242853662, 554929136, 73465594, 884382388, 647517566, 84393549, 46504923, 45016758, 523566433, 120507042, 632441928, 197471661, 203609019, 360369716, 121497668, 421701836, 145256010, 143049649, 526466508, 153149457, 535898366, 254651320, 664771675, 539526908, 121402203, 724013284, 990754332, 455480202, 461821304, 332671691, 770560210, 358730507, 122823736, 588601011, 194135372, 44384257, 420946598, 434553425, 660120430, 510692511, 74095188, 695785851, 371708309, 393310593, 102021460, 14655853, 191737703, 736685345, 972042195, 262763580, 414334041, 487832286, 720201627, 286384473, 106288873, 42267767, 172984768, 758353984, 160594445, 961030611, 941440736, 458839200, 469265059, 195101715, 626389320, 345837180, 570035668, 438114530, 749094605, 528292488, 189839209, 522150056, 812153725, 28802679, 58246890, 229555390, 820198738, 400306965, 224835553, 378748896, 317017417, 688835674, 8004695, 184049818, 502685522, 157661128, 53974799, 233346008, 315927380, 286973866, 934404598, 233315778, 373312591, 516745526, 495517164, 461837169, 170739393, 934368751, 865680773, 986253705, 356936653, 579536326, 543682424, 767325721, 124094613, 407727675, 135063802, 322129837, 348998265, 251671468, 205724506, 977540409, 295808204, 867044099, 428558158, 778862393, 42490683, 208027419, 869195205, 654629796, 467102870, 810109075, 762279071, 180784551, 611940909, 661301942, 237466621, 743912118, 553946194, 771988836, 258007291, 541177072, 554291886, 77084768, 539122337, 914489697, 610836498, 606142111, 732336926, 242781736, 76635963, 54208685, 910887144, 329468996, 244271627, 375626709, 825456526, 633392183, 766124275, 329441013, 727825888, 50386368, 314429595, 454376406, 230771653, 101990187, 9298741, 776494764, 557272408, 543850743, 118584197, 475865970, 6271312, 483445337, 844973413, 423739967, 702740264, 465894150, 523002354, 394543415, 947130153, 538663035, 249879506, 355333485, 110092773, 989486922, 66165522, 751155734, 712720942, 435467578, 551913239, 444904500, 148257123, 576211622, 186923606, 481461957, 318632287, 714808082, 129912701, 242659489, 926475917, 610876589, 628747416, 764995374, 504567031, 908358544, 862785592, 58739826, 271207938, 834293423, 837690397, 701193780, 167533245, 494881156, 747540843, 445943473, 361278449, 407078214, 258136536, 991035701, 472306435, 701338524, 344273612, 364015721, 365947549, 241446837, 211774366, 111935545, 662555879, 816267280, 470035391, 736138458, 774922748, 366647800, 829945515, 9096256, 687935997, 39450924, 286674402, 683345386, 850027694, 362336625, 726047596, 403448111, 922718968, 514686958, 557372424, 79248709, 789093766, 524513337, 485326192, 788091636, 364053708, 355795169, 748203597, 471976590, 479578806, 865071169, 802874612, 105285479, 494680836, 533751803, 22100381, 612092503, 995969411, 10412396, 72367376, 432702048, 43839118, 56416416, 992608759, 219258357, 786553465, 187699695, 813012682, 996708086, 607792277, 295528648, 590973358, 380773565, 869517468, 902831485, 295947077, 788880898, 869332146, 965812961, 270881813, 722787743, 383078694, 990631973, 964591924, 90849982, 73004553, 652550954, 366747709, 169153948, 109167085, 977112547, 830055970, 610091988, 380599089, 1561099, 724433941, 963778360, 287431995, 367370376, 451879172, 109763844, 32080695, 608708686, 531424287, 397704718, 819163413, 903256336, 769201586, 271228525, 12348405, 101718575, 509978369, 916677388, 156368793, 667367777, 861242838, 24742150, 303988562, 916520968, 333885324, 674078813, 620436430, 837536532, 640042740, 898942162, 904733048, 547864956, 159075753, 417996438, 136344037, 508112522, 646726244, 501617739, 689086523, 377656908, 976736196, 467552029, 669670303, 627183944, 772438380, 863150016, 16347814, 122987412, 614571720, 438615699, 578418731, 700950539, 960809390, 424300988, 795428550, 14296392, 661816900, 309805599, 549039749, 120258876, 985190192, 979208321, 307482478, 688998283, 755347784, 581799076, 958841156, 237283085, 743866005, 838279066, 132537635, 562841613, 14256311, 163895262, 639315288, 979412454, 223925068, 485407438, 524434009, 452560799, 767200084, 164583835, 234894005, 944358608, 665758387, 331642734, 243636473, 364028569, 768469637, 290845925, 480868014, 592894213, 889978232, 533908698, 78940146, 198258822, 544928037, 159820291, 468633535, 787453325, 352232426, 896397276, 700006634, 630991099, 640625852, 499640239, 929448662, 605282808, 6909961, 502869232, 697298327, 432823425, 445776251, 464780990, 21679014, 821056250, 650888332, 645799003, 261614627, 628381813, 55120296, 983087882, 738636077, 52386891, 234611191, 25496735, 885447176, 471275586, 370900851, 490872687, 447210336, 493140245, 677952676, 453103799, 236003414, 702884543, 623180903, 446869377, 965187915, 129881563, 564686309, 38646835, 141393824, 769713923, 685634848, 126207279, 794860408, 823575567, 965876121, 259906329, 251838556, 69383962, 641594423, 305582414, 16966978, 238460274, 980998727, 484216415, 618207037, 205078355, 406002759, 786563883, 988267232, 945939079, 90475470, 378615505, 442984429, 227351546, 882164735, 867966257, 329425725, 133312548, 899229879, 577234314, 413811943, 166464178, 504484006, 42238818, 372866426, 365727191, 479377165, 485017266, 138432253, 376178900, 174052851, 942513631, 116154433, 427718589, 971581562, 395960885, 807510507, 390465982, 450194988, 906325486, 277541702, 587982150, 432985465, 656807554, 797698196, 246516530, 901469886, 880542336, 33262736, 912802780, 659073785, 621448344, 131302837, 89518021, 952654599, 7541450, 529601679, 386054993, 580135560, 242310024, 165245324, 377273256, 630694784, 263279741, 648509348, 445245267, 777752901, 152950561, 344452163, 547382112, 755750802, 991827855, 614657562, 256719593, 827202245, 554926613, 912256392, 716091350, 2309419, 770715038, 112976276, 786262610, 780408709, 703015747, 258581904, 17465129, 65390065, 245139647, 291739256, 782466133, 978099727, 482243351, 762642141, 954233105, 854950483, 758026047, 401388520, 188754718, 876213450, 516533441, 305272178, 650474495, 329339983, 901498518, 968720347, 995143038, 948311897, 252992558, 876418563, 241366282, 621682675, 260006773, 129628491, 215916627, 985311660, 597745589, 1957344, 569908472, 493115440, 354662728, 520486610, 308802902, 153267180, 788586554, 570481100, 45026392, 554957341, 518006378, 935403112, 877796998, 362975038, 963369324, 842155260, 98871386, 806508987, 830061361, 421749011, 472299429, 419892004, 746013699, 92940196, 993081359, 258838483, 52629031, 684582170, 662927677, 245414078, 155880484, 39367477, 20867930, 154267114, 793697367, 185344717, 266221963, 838267871, 263781576, 83552246, 665176390, 86777826, 508693031, 83290829, 511223709, 227977363, 879172351, 2010574, 231953235, 196665109, 546893586, 362104003, 413759660, 634869602, 477332046, 462832173, 562841915, 944113670, 224317736, 51220104, 33430592, 695977664, 895186315, 655883068, 857965675, 808311278, 146584683, 406262264, 244314684, 350000645, 689072577, 827204107, 650787659, 219700543, 220615035, 14240903, 375542055, 738166595, 354158322, 525714107, 930578565, 328234763, 165592511, 567112306, 583366859, 681437757, 464973582, 429621233, 367039405, 513070339, 653107461, 779993964, 574814501, 225946489, 396506207, 295898718, 216203005, 11256174, 268685225, 952673292, 796795691, 320705527, 276244231, 755336800, 850090092, 358507423, 795249251, 402265026, 294513251, 506793784, 578539261, 571944930, 994978083, 759565942, 827814928, 662585834, 858135202, 353771807, 770926032, 848186401, 745051082, 378427628, 636443905, 944636454, 129854890, 274579684, 24680267, 117925071, 786348734, 509314078, 433813075, 422491475, 439230200, 373900476, 889439227, 448430657, 332429832, 322524333, 660872921, 470630108, 631896875, 86283554, 629774745, 164911023, 933317614, 759438680, 101096421, 593263891, 491415469, 254343302, 965241824, 773685469, 721046276, 607737128, 905500637, 305664161, 482784717, 453235662, 232980950, 637401948, 666532938, 381193254, 563241365, 929518173, 53181828, 531509827, 848374810, 975761869, 62935561, 516522042, 211141214, 730409352, 518556221, 279868996, 709785765, 680526624, 429917662, 99093176, 804428809, 807106496, 869447047, 131654504, 887375270, 725592042, 500499444, 865715530, 423233357, 690987201, 17408817, 99095404, 962379466, 977337351, 208948510, 644670365, 799659339, 212384318, 58479300, 206385778, 482438482, 118095783, 811342987, 752400946, 468960456, 189579919, 883077127, 174340947, 637942621, 843827918, 299470613, 201787810, 320891377, 24189320, 259933185, 172570232, 776110690, 135347227, 134300415, 592486023, 424043204, 883189427, 582880117, 629090983, 224888733, 983340385, 544842865, 511560821, 857924329, 540488422, 357991885, 50317203, 862567010, 150893213, 587382384, 304356353, 776912045, 224463055, 201029026, 727344758, 345131381, 677839201, 285273467, 216966831, 23422785, 41054546, 923078110, 354008769, 488391460, 892079333, 1201481, 108092667, 143150639, 124331526, 888946273, 392993012, 620083893, 726650456, 370775841, 350172999, 442621236, 299397850, 554838899, 888706049, 586879022, 141198625, 984867872, 170135367, 639515815, 961269342, 132132321, 935637912, 820301349, 401972965, 94661836, 295533321, 425291972, 378660321, 363119088, 838139864, 534609336, 1557456, 899341603, 256164574, 395318954, 794550794, 727639955, 784606963, 959793289, 150910104, 96260686, 998957284, 853029396, 982382804, 177245707, 276436722, 367662273, 508199539, 813619805, 140508873, 817469988, 779585837, 676051819, 133128206, 393938949, 277530660, 416121974, 812684429, 68172840, 908109689, 225510025, 211386693, 501027583, 223217183, 619318707, 877864483, 907179232, 152578959, 736020305, 403202775, 757344974, 412484167, 174576353, 97790354, 173230729, 597873296, 738973580, 806278287, 378645766, 423054067, 267420812, 296051880, 501247525, 672969858, 232899841, 790178092, 27352349, 494431982, 671372834, 636311621, 334909808, 79430308, 294324490, 681359079, 842907088, 108084896, 182251035, 637959447, 418878970, 312511137, 667109576, 22757833, 803419470, 600617031, 480494952, 422584089, 548845342, 844288948, 182350170, 750896907, 464568999, 839809844, 335648715, 337931728, 169610200, 734368691, 366183130, 836887500, 767667232, 32541234, 591992329, 659294423, 707321302, 833401397, 213240702, 409085667, 504714004, 383863499, 829616330, 79267617, 641512405, 644297159, 180254855, 552391911, 147016172, 392777735, 781608419, 628972935, 438519760, 633757420, 925643881, 751999142, 92324044, 346457107, 174557384, 621299942, 980105237, 919774394, 280470064, 883334056, 93495370, 334529546, 205653716, 53911263, 642312937, 643514404, 190225224, 833401750, 646629502, 871112672, 97391444, 344277776, 111711710, 651641224, 534514070, 600353033, 984249854, 160568397, 856121965, 32729145, 864554470, 506565262, 331736533, 933575312, 758311300, 378884672, 910170082, 794071489, 148066309, 546482573, 341606289, 571803428, 376998708, 543783046, 395774578, 900558646, 564228208, 148011891, 268551365, 281021916, 829338310, 464865978, 96997156, 75870370, 392810225, 518183829, 982389371, 462100314, 130185051, 250464323, 362772689, 950509393, 247550712, 606174590, 1516919, 991353052, 974948656, 838480440, 691851366, 791304379, 247337784, 161692853, 225330644, 736425477, 331070699, 743059878, 639735308, 453555598, 580858220, 929659709, 59586731, 574236566, 112021712, 909384117, 436888691, 911380521, 761051030, 861559214, 338755320, 276399023, 759387379, 647841098, 987073437, 772067932, 760462222, 36784573, 413230399, 604404407, 485143883, 629215746, 99498710, 804873531, 681046798, 389923090, 975469418, 8745998, 432360744, 876722937, 272005452, 475440284, 768172848, 70170689, 366851304, 301370716, 844650772, 668143823, 665373600, 158754236, 48365972, 278545894, 528325723, 383033812, 785141796, 141736443, 508369296, 126418668, 689265388, 905786536, 387326788, 644517233, 311978290, 460809226, 433264635, 203698895, 977337408, 403844226, 801294096, 969161934, 147530273, 851778837, 309033711, 486131500, 32753924, 764692590, 502825428, 301044577, 208900558, 226762526, 2133418, 350343209, 725769802, 856753653, 307683330, 530424842, 744152341, 212897094, 316672031, 989294484, 486208319, 71678097, 14772210, 467405391, 291164681, 931689181, 928896968, 194511012, 541180046, 71271168, 669023790, 945682110, 25796350, 979088431, 488230601, 952440792, 217773660, 695427928, 636379736, 204711020, 228750008, 424619247, 663021996, 658465404, 593785176, 889153695, 576047166, 460303948, 204238011, 562039073, 903550200, 208082551, 760062718, 120382407, 42867387, 927544613, 786925573, 21479819, 594548049, 611049916, 518129776, 181227078, 899692275, 473493911, 980324802, 841624402, 633211630, 288034016, 944413861, 753513216, 928801237, 160355239, 457456663, 457144266, 287862492, 506258901, 510181379, 193969360, 439802913, 837315411, 130998312, 15614294, 535670880, 497538915, 241809904, 689249341, 121500367, 93036506, 373178974, 940586245, 341961122, 310400360, 734484600, 82910070, 16873298, 643417298, 504954496, 944967239, 15213405, 463188658, 307107800, 441220490, 532785447, 298900865, 513063666, 234964028, 233262187, 709564066, 995020674, 908156932, 730712027, 853875421, 697091756, 550359440, 396301182, 835602367, 323123215, 792295500, 467150972, 761926399, 981258994, 224798051, 884742663, 301594231, 397877528, 963665862, 441584492, 661047507, 135824525, 798695063, 45849388, 804806156, 376942333, 736371834, 607116997, 819703809, 636497128, 597099834, 414410731, 585808667, 291558518, 512944288, 182918532, 482929184, 840213090, 58368414, 222341289, 928800872, 190698687, 37378647, 224197829, 31493293, 515186346, 452693781, 755321775, 25966362, 429677381, 176788185, 109065876, 712865747, 435835976, 485941409, 236027868, 252734828, 502756548, 609289793, 972184006, 980042116, 794914867, 982216247, 884333704, 521837742, 175863178, 253266296, 384034104, 530801572, 476961773, 945066166, 234649521, 936937396, 621210885, 386944375, 317699960, 829268849, 896387794, 12601277, 762383327, 973672569, 918569756, 127666012, 912546804, 854052715, 396160966, 69005526, 934193405, 848555798, 239024908, 824325833, 208477596, 120963485, 689996285, 207864999, 434979027, 510571856, 25041510, 334253604, 869845238, 865364198, 409721203, 480287290, 587213151, 464701446, 318267377, 880953346, 604064854, 63193333, 445134394, 272665641, 430881200, 21230612, 47050764, 364589033, 85160339, 541950869, 808379273, 131051386, 776855120, 673192190, 67155991, 734665887, 570276765, 625087430, 650484260, 646298346, 241188602, 105575481, 808407230, 709274414, 798050585, 979668559, 301816228, 551067761, 756254208, 443037587, 51425998, 626074286, 925325719, 654165217, 956681592, 92154855, 464861060, 587853493, 913303159, 468989324, 182366642, 135258423, 480505493, 602666508, 920352579, 575360148, 219985658, 11979618, 592228760, 126441993, 294087666, 91021098, 823804895, 920008756, 41268141, 440127741, 927647173, 251909455, 535887830, 898033660, 779423079, 537858547, 314819650, 789680706, 494401324, 44218821, 527014990, 106984779, 328752993, 433640930, 989513312, 687966265, 709558451, 534098045, 188689621, 185821968, 367982221, 504894412, 129447227, 463264655, 76188406, 642713029, 628452778, 742693761, 865602730, 535807752, 605879160, 701674260, 410944507, 47718620, 774916813, 609582581, 868094679, 898816483, 657116990, 614326213, 994972745, 112216510, 67333903, 467822713, 562306657, 812115000, 65718246, 292971349, 242843380, 842628075, 827224682, 170505853, 485805567, 529384955, 932930489, 2033263, 944571625, 879462299, 130437494, 337885292, 702659846, 662825953, 450407284, 92146860, 567129951, 540595697, 274611743, 575766517, 750024022, 780513728, 840938693, 309395131, 541076030, 628061172, 697433837, 788711413, 626752371, 901572702, 953031203, 461245248, 226119372, 416221745, 21168109, 992742875, 447493550, 491844312, 477394480, 117619308, 185723096, 706160242, 289295498, 86849363, 128875403, 660604754, 552065172, 997781908, 59433650, 988041359, 742054851, 325626441, 975327934, 783465997, 128808264, 377312732, 316494097, 489662975, 858410594, 278729823, 869768473, 485429076, 738897842, 644642967, 542060737, 431766721, 882945625, 165906342, 55890941, 49648201, 418057512, 735937881, 150059738, 600207833, 110667799, 547252439, 513793193, 350380614, 135076217, 459299896, 102982659, 1982426, 164156247, 726910621, 103971427, 891957683, 322348781, 230826141, 302789924, 493986913, 334717633, 371008448, 503824159, 309110612, 676088653, 714485250, 77059450, 716052162, 223891064, 813603820, 729309512, 483375257, 128612051, 891881543, 932988073, 449894928, 133235808, 739912075, 501241425, 809564537, 671425385, 177907532, 235817361, 666176815, 353466556, 371745161, 404372287, 773275237, 322013850, 991226681, 693909744, 450872598, 750099663, 531889272, 519128917, 210038405, 975083812, 613391476, 569441483, 307213532, 802745466, 882776858, 763383125, 843584137, 549427651, 190016433, 190968224, 485163412, 61488536, 425634207, 402744388, 594410309, 109891828, 208921525, 172973922, 337003398, 882715107, 335379059, 195696111, 319881734, 75864744, 719559944, 879433308, 853909717, 89765657, 701985993, 485343016, 109550511, 771570457, 865649999, 27368277, 904399040, 678548263, 859123710, 944517041, 976937746, 8119576, 416454581, 713289357, 424433816, 756407909, 710428603, 892949469, 163375038, 237189369, 668341335, 726402475, 576409171, 4278491, 687798634, 156259094, 577479263, 299072517, 970320810, 593023696, 524422144, 248131497, 971727124, 700888766, 122488095, 87009937, 509747259, 864972118, 852426395, 902833031, 739566461, 230356731, 220235991, 434908170, 49970177, 273627387, 863894534, 121379995, 923205629, 444779456, 62300732, 191710664, 496989145, 886946427, 660867380, 764287143, 738783385, 765550796, 232894907, 615441875, 784801670, 846280943, 14474016, 377426766, 201317493, 215533414, 568906311, 432802231, 891309589, 395481363, 61658176, 441965168, 26130416, 383711874, 580116400, 417348968, 145169901, 689755357, 466116493, 152561849, 518894033, 369681580, 275416527, 144670977, 895805254, 110859046, 205962580, 449241446, 644821704, 636626726, 186769786, 736533396, 415624679, 290112668, 552093770, 720689657, 255757682, 63618647, 967135994, 798456359, 393901487, 533628674, 722123783, 135176964, 959677281, 629370888, 529019366, 50384758, 652452967, 207793197, 610952245, 66342794, 116728882, 272174539, 816045104, 140302535, 429004069, 995201589, 124598948, 606128263, 630353524, 579627027, 671397667, 354472473, 809786048, 51323991, 848350310, 751972048, 921775678, 749294521, 627532333, 515917304, 76736012, 165579603, 225627669, 250933233, 699638976, 281718062, 505217305, 828473016, 558362856, 450046723, 596036401, 796546013, 238921732, 897290889, 917512731, 272416247, 436154021, 412797692, 610857291, 189434650, 15776744, 711486614, 133155512, 269968214, 80489167, 756123076, 880286242, 98896331, 149182827, 991989381, 53637159, 369093128, 181509012, 32871551, 34655392, 23936011, 478478601, 600077149, 598296565, 61937596, 430516941, 516965178, 293587561, 19084921, 464689787, 501190256, 928129005, 979121066, 626818904, 356436636, 173674666, 27109212, 927959756, 160857830, 489280503, 865539780, 778787184, 63721796, 6880420, 951315930, 816165993, 527651191, 900613992, 726218042, 676341639, 598580807, 22361436, 763323633, 641629421, 205993590, 56299122, 86914103, 845962613, 106954034, 301142822, 459037551, 455262998, 82355731, 372916134, 513874128, 173258073, 37009899, 457973797, 115471720, 174808764, 508568466, 192155746, 607798097, 401366210, 397332489, 863322948, 848386343, 719820626, 940589595, 479166822, 893395505, 513270413, 598709348, 93239490, 647297106, 474110776, 636637917, 220352696, 714871236, 181211309, 510959583, 533209552, 384913051, 597046553, 912842452, 642945330, 935399749, 411239765, 160066500, 748499712, 447509263, 614054345, 642353498, 265982372, 703877223, 931618266, 977510028, 447092973, 819607381, 957130571, 28054028, 907637574, 483284768, 912516950, 817362546, 164081354, 598735724, 307756141, 511483498, 909918819, 964185184, 518490637, 201674758, 604906403, 620288498, 89322878, 161855574, 290146545, 271379637, 3758905, 920432438, 771886994, 826087697, 697965848, 798205941, 556914007, 329042991, 284152229, 922843618, 703064006, 655740449, 353490888, 886387974, 682859712, 176768108, 518630866, 542400834, 152777990, 389112958, 528760814, 822334559, 638388086, 693706839, 34139846, 172097943, 824636631, 426788222, 66472038, 901012548, 932721591, 31461322, 991981506, 164264915, 236853007, 115381922, 552831825, 492450565, 432792397, 624392059, 751759679, 420231713, 361284451, 70690906, 703869799, 427058640, 43048564, 592846753, 517056754, 40245522, 755313850, 535713208, 250572934, 911962816, 628683212, 819526998, 541410009, 737296781, 343929055, 780496185, 789442739, 810517418, 465708640, 19745979, 753255736, 782979861, 644227212, 982569795, 909878149, 809317465, 586372417, 374095477, 342045231, 263043306, 392521360, 826783558, 615923360, 55308925, 207578040, 487158014, 933073808, 823002604, 808442048, 824236562, 891186804, 6343296, 180730184, 615634653, 873841090, 872551777, 31384753, 94288324, 924995772, 162817180, 834002046, 278034343, 340175746, 580243384, 68519713, 9093599, 819429541, 708363825, 79215674, 655771809, 290410411, 376414621, 856473054, 88386345, 675346162, 881308270, 749724271, 372141465, 321279748, 849835894, 26372748, 805654023, 839399775, 207782466, 309303902, 282643740, 461571477, 478673435, 621413880, 725920085, 896923763, 213863197, 296045416, 726199538, 568252682, 388460963, 354468500, 650286941, 463229714, 175750732, 696539901, 955241432, 863136666, 216987939, 954860535, 717729876, 428166035, 12238881, 406584978, 858791409, 758516215, 558494982, 390101841, 665661118, 125212946, 675530223, 870093804, 152981051, 613014252, 194377676, 675162348, 504633767, 289496405, 498696755, 471556507, 79181398, 192144088, 275556690, 265138216, 498819970, 236036885, 320470719, 852551463, 73893607, 465146700, 94115719, 211477110, 842586212, 57716067, 550707488, 339630844, 847427108, 887015234, 849192704, 872598525, 775599656, 787979566, 276321936, 608079510, 207130348, 37948590, 285055845, 532490575, 409218088, 217091544, 144472057, 394240363, 243194920, 473798865, 549071673, 783784743, 136683513, 77579406, 88158393, 26892186, 640646109, 246047867, 710342008, 818312876, 208129744, 620058599, 318494381, 915773398, 176697015, 495182961, 211595165, 279489968, 49235325, 59371463, 934923982, 555732754, 267859373, 974536937, 58283963, 846385627, 679827563, 518423453, 615764053, 89251130, 228475146, 627058210, 755032499, 711025956, 431670587, 176901621, 984668767, 327053919, 465607734, 391099593, 642879090, 348285162, 159208189, 227806933, 873306480, 178117472, 539612153, 597841047, 990393694, 210733669, 41214483, 517265641, 925110398, 983329756, 74498161, 166790694, 514124333, 721789719, 94054577, 77558460, 12768673, 852277054, 375721046, 999354415, 797125447, 202849799, 582731489, 60863223, 731865902, 59079274, 282628679, 724838474, 935533837, 338198689, 327114548, 505819353, 94210263, 404803784, 590682140, 149339670, 875210553, 843249972, 889455748, 802710763, 287775452, 498051967, 437810725, 403158096, 168116190, 311033718, 823271670, 140667560, 408268831, 34285591, 681297123, 934243183, 776828214, 999929255, 385148434, 792949265, 206744006, 37984753, 66751763, 976087936, 597695499, 178742586, 618053331, 556790813, 808998371, 487797859, 965191254, 277162896, 838632612, 103137517, 818525735, 736798163, 586190302, 52486140, 67883620, 293687742, 396266180, 427392190, 103594674, 987080873, 715472955, 401021030, 616509599, 477381704, 957625207, 203848014, 461559805, 973051301, 381825677, 43945865, 851658768, 507164107, 387818919, 387966125, 348123269, 211661648, 722621179, 208002178, 546612033, 889909369, 751727814, 279356738, 945202451, 205134063, 939733405, 412844454, 228174161, 634889424, 313363178, 482622339, 421949584, 474676283, 34086572, 165311527, 984230553, 309406890, 454371521, 103085188, 92370695, 685063943, 721368765, 886899601, 8947557, 989196205, 514640620, 242025170, 643464600, 874755598, 227837896, 535446274, 41141096, 816521215, 184411697, 56236916, 798120714, 916924200, 867950774, 979983843, 985815531, 793529217, 663862521, 932307623, 397362401, 753467424, 858411596, 597130689, 427517089, 404247008, 813616576, 210876301, 677226229, 407324441, 892564747, 41503792, 524602135, 612495961, 641789129, 336709658, 151600943, 718963988, 432770753, 295111333, 916540174, 520523229, 678077826, 590035194, 563461386, 48944530, 556603059, 450234003, 209039526, 869092572, 505597422, 947242542, 896640031, 3966525, 343857926, 528986710, 304040606, 9184772, 924696311, 98409084, 804137852, 955940194, 117808035, 319297788, 835290958, 16339222, 738790887, 412271064, 933268733, 667639918, 740304854, 76627935, 409103586, 712257628, 221527195, 35085373, 57511943, 596450390, 511834953, 949875292, 225054714, 257581438, 408551508, 813671976, 293741159, 281077912, 498611001, 366946414, 89719741, 158131650, 503373747, 242639008, 591312730, 994116899, 665450195, 303506896, 711659425, 261719157, 670541175, 222054962, 515818641, 641696275, 6237123, 759700735, 971671376, 44145162, 16791394, 961733536, 455604624, 861932568, 894569137, 648229436, 954638186, 761417288, 315711961, 887201206, 626649931, 994344115, 702941576, 709997196, 315046692, 739406901, 783489310, 253896326, 434264627, 969640896, 631566684, 351394370, 121545023, 811013161, 216886811, 919479501, 113403652, 835526145, 251033899, 397643937, 227873012, 158386993, 685529014, 16601528, 523643568, 580488687, 716297891, 605260545, 303450052, 914266208, 338997162, 329115824, 602422832, 613913161, 414588548, 880419795, 79842876, 793183179, 835881426, 251281693, 16253569, 593527851, 297758741, 403489691, 797909911, 740163157, 464037804, 800883156, 200734754, 392047263, 363498232, 507211422, 579184913, 548587862, 534299292, 528334105, 655698681, 990410817, 469485384, 408992504, 438616806, 608869594, 171537882, 206284003, 972083363, 319297582, 94487883, 143811413, 682663576, 394852293, 380299048, 966682249, 982640459, 258083291, 470173330, 603638039, 595585437, 591273819, 162028219, 213684778, 749221902, 765922538, 803311095, 28604804, 448977940, 236582507, 620093919, 914384301, 870449039, 385100102, 708627126, 402194926, 74175587, 878332487, 761923704, 446900345, 740993731, 365335160, 679856364, 592733332, 685905420, 856474896, 635760682, 462544440, 835907895, 502519699, 304814368, 299525517, 245203103, 28097151, 718511299, 658327474, 4989581, 274394133, 150394128, 788949222, 566706319, 872143636, 762009836, 357188052, 719595741, 996297357, 807203575, 677449857, 45993900, 224385603, 907103154, 530394084, 266749893, 365166375, 400832473, 19662587, 437520709, 297466196, 936262650, 172048980, 453465284, 164651108, 710458600, 93585919, 122574762, 286558107, 222665149, 532880252, 726758391, 239623020, 87939512, 681619833, 687263684, 530056873, 792237897, 597077604, 447445444, 281264110, 902418310, 626143624, 374629521, 836525011, 847374645, 445296132, 763268217, 470133990, 521486794, 17941141, 560646509, 135509584, 881144574, 183630114, 370181307, 628910498, 814095397, 63591581, 461178099, 791519891, 417388288, 14703618, 632686958, 257606924, 805457784, 353739653, 361495534, 397496925, 627476902, 188781498, 376158954, 422143835, 365748082, 810192467, 815621569, 784291120, 181762599, 434403070, 962858934, 972016971, 857310808, 714482771, 842936497, 661653742, 544015491, 290822594, 598349283, 406185343, 95112696, 297494636, 321431241, 78999800, 691478495, 495899270, 251600385, 381545961, 6431553, 813944003, 264202954, 577454090, 465973171, 457426646, 217987817, 117826887, 264619319, 794465813, 73110239, 16599224, 665950692, 251026836, 492363947, 81379373, 148317306, 970442833, 307429835, 71176734, 849599077, 805865868, 783827947, 568320461, 648839746, 297422358, 967130995, 37009720, 66933267, 950996805, 518478978, 97698905, 479185721, 889648928, 549443600, 659137283, 439646739, 832505994, 191020746, 739718312, 678348741, 867488000, 831825281, 800786268, 63300938, 304854735, 418702298, 132239135, 865067595, 412682358, 506535520, 577474657, 59987197, 707930288, 1304352, 108783627, 611942286, 150701503, 142060139, 932914233, 936494290, 12058587, 288779737, 355965933, 151317210, 59257653, 672411238, 76620251, 323574159, 386627031, 880235898, 512589586, 97451194, 67407217, 951865279, 720185684, 824910959, 189003210, 979696866, 535612289, 355884531, 581016370, 605040425, 328627445, 21756467, 625618754, 314636624, 863741034, 565552511, 556060220, 137836742, 888269679, 80630649, 565065796, 549931308, 122794290, 172688787, 331433686, 111168243, 325244176, 255524184, 249631927, 156897498, 893881643, 776415559, 844955287, 723964923, 125467455, 341390227, 20877809, 351919045, 204974065, 594884188, 901373154, 407265908, 660330822, 739025008, 985151356, 935113285, 198485681, 703153010, 194691449, 990589723, 357751536, 779041880, 654515436, 107714361, 924098323, 49643676, 111394808, 238615272, 124899680, 309900385, 793668111, 108946464, 457709581, 457609106, 126773592, 659678404, 588793053, 33974693, 304689267, 422523999, 29290221, 720918600, 936598373, 448234050, 608770908, 837626057, 439622141, 50068656, 196608168, 83159201, 829418442, 103517192, 501150417, 63790798, 452029116, 304379640, 34226064, 143448161, 769197276, 363348387, 802095940, 819154034, 420170848, 591015856, 681110541, 319595111, 464134370, 819149416, 683180372, 706818670, 697490280, 370063771, 376605087, 403582101, 869345071, 783898579, 546358460, 732933905, 808810365, 153511257, 413419220, 14687775, 473173893, 967929005, 290760188, 937627844, 667080736, 343906859, 786524094, 358865406, 119204590, 516736189, 152514206, 445197646, 721811521, 575024145, 413644886, 13998308, 747350633, 381760982, 162832614, 932937990, 377003021, 618205087, 95056203, 992199349, 938913822, 922836231, 69805057, 71241113, 709663527, 564602175, 827760876, 28142557, 883031292, 989604146, 373005056, 187654411, 319266156, 69428469, 67638580, 223083186, 765506836, 15470123, 219882685, 806100591, 550978526, 89686091, 814726839, 329393115, 91790557, 695078613, 7505077, 449151737, 926424636, 76090213, 577971348, 792623659, 367281327, 418175047, 928037301, 946580483, 294890023, 588073143, 948914408, 334009680, 694718356, 262337271, 159484148, 466409883, 333150612, 918358540, 369636646, 194812962, 392326949, 753375340, 434882323, 803792811, 480222977, 372186221, 317495513, 253497840, 134153125, 638907811, 951893401, 960468357, 250335913, 696552243, 895731647, 126512030, 704117461, 528825370, 673639254, 491658252, 340450816, 117296521, 332946687, 382013599, 589911474, 624529701, 775532746, 526159194, 216304574, 129787301, 841529335, 324839106, 942956915, 320482108, 774697884, 2442812, 136104973, 686147094, 415768195, 480432177, 991214292, 581037139, 261337997, 691981585, 55596425, 251606919, 218508962, 270273468, 556574959, 750379714, 629711733, 791152861, 267114739, 75358258, 368707619, 468979440, 831018023, 472302297, 489412115, 845562613, 339268977, 415132306, 451853405, 734051046, 444338927, 106281015, 51731472, 376593241, 224562015, 424135327, 484698742, 582369088, 416145918, 94079492, 31857247, 168818285, 323461915, 367136931, 906804921, 311695030, 934936244, 762481391, 360675461, 108800684, 954399027, 596025799, 230167344, 214569318, 146388752, 564690487, 98251422, 494407358, 924919331, 804184367, 136088517, 253766216, 626310492, 435292608, 519513144, 477565421, 984125348, 708283883, 165666825, 991539947, 311407347, 302954282, 808234163, 821794523, 737720216, 527985483, 488440231, 399371336, 907030536, 266402945, 224247586, 534393699, 47018647, 698707119, 811451134, 781132688, 316311886, 907441423, 780382440, 943946030, 360194091, 560348137, 436805259, 533585634, 215915872, 861815932, 48512310, 171442716, 34713719, 641992552, 317165190, 880738325, 341821210, 126319791, 410871068, 320670205, 761051844, 885903865, 710977994, 162356180, 498251813, 303721936, 849631489, 170495241, 407939197, 220714111, 553599606, 320519365, 610105223, 846675534, 337892102, 923485880, 558987087, 585780037, 120173148, 593528611, 944158592, 429576945, 475058089, 788246904, 504029836, 220046346, 847786973, 16481342, 274331622, 964751387, 760077853, 882143413, 297268053, 804538434, 944106872, 83006181, 132689167, 322255905, 165982609, 958228892, 935565580, 130815042, 748354704, 232130002, 920617992, 2202300, 960461483, 538478382, 591844375, 151482818, 586532883, 123233169, 124719643, 347433481, 200521898, 396862584, 927766895, 566708984, 56869083, 292703433, 853772388, 498456038, 527037216, 465063118, 461997335, 848648328, 246345486, 474842614, 623457532, 850284400, 49689216, 866416468, 149691747, 775316734, 558371751, 636353961, 610996054, 423081591, 326477998, 628013857, 399027707, 872860410, 509988703, 309941095, 462813074, 477576959, 304230374, 757665764, 556798014, 508747264, 12213628, 755978467, 238500650, 838366947, 731033671, 333989664, 274690340, 966361678, 57890703, 770795420, 865670488, 983341774, 711561464, 782016697, 491723303, 699766480, 161657352, 647813403, 344448317, 563087470, 996319994, 857383379, 985904537, 463020965, 237384541, 85205232, 404547947, 607916600, 717439621, 366348408, 487397120, 414241785, 268167666, 238847018, 486132695, 300412928, 324105064, 826087642, 121627705, 864266449, 901260937, 640197860, 549886228, 805990666, 866513764, 758435106, 169079398, 985993780, 572260974, 107153687, 495813187, 726190099, 269572037, 164935250, 473821409, 980145267, 402512209, 351888528, 3127352, 622206399, 562329449, 68302134, 178834608, 854286369, 456727640, 678195487, 164291083, 106010676, 834961427, 268657051, 808578910, 312524547, 923481500, 15144153, 748649716, 263258252, 40004865, 346999666, 960392777, 648919504, 114236575, 738366336, 636413110, 361197683, 698821746, 42949593, 236524477, 604367402, 417788058, 32222703, 15000107, 634866671, 954433134, 548152847, 958583895, 223708159, 270145082, 832973314, 62709443, 916121080, 180025029, 874415189, 194652380, 292687788, 421405202, 524109480, 985867970, 244093515, 771095867, 580531710, 226852996, 73561827, 839238139, 801918919, 967119763, 453113535, 655975630, 356711599, 676636818, 834652158, 715323623, 873041392, 80399455, 234283323, 891455007, 13323300, 932047985, 939193188, 679492896, 840645820, 295719364, 301953201, 555235109, 305338780, 791300402, 91176564, 939973488, 621230530, 471053771, 393810620, 807662950, 199945578, 574745384, 355519559, 73363159, 192493881, 823725933, 877930790, 871664408, 973951028, 320874986, 470407825, 507185796, 217101027, 584869120, 604955459, 459710494, 712555789, 746914151, 442900782, 866331906, 373249303, 775056771, 211150382, 163681048, 407378616, 50575896, 708168757, 938507737, 396265596, 925256762, 360461544, 44834061, 622207554, 627299245, 208396548, 776247241, 348710289, 912308364, 888343240, 296232129, 79512649, 564793814, 736047598, 282794950, 765367174, 642421423, 754305516, 426033770, 37397611, 910402058, 428366329, 643759572, 144647081, 739209504, 371195643, 318960176, 186980314, 17930999, 195102625, 277095642, 441180512, 410367928, 564408302, 935403398, 673934653, 754122515, 59071764, 400567902, 86403035, 530408853, 399421111, 886721809, 11661917, 707192005, 376945613, 762417341, 533628039, 945703696, 317238998, 340610817, 97804188, 916651597, 222995408, 915788634, 1520966, 799579631, 291501176, 615815155, 46212114, 268034021, 115043354, 805666074, 376471307, 514251056, 255999640, 537578061, 178444708, 577388461, 117742352, 960809593, 919096521, 696468500, 505451755, 179361058, 846093080, 350819262, 97293971, 238156994, 603387854, 206314252, 347328681, 294288289, 672806169, 144729590, 846244530, 286921892, 430167244, 607217395, 963478515, 848769258, 65095431, 218077131, 758454701, 680879007, 71629000, 778605733, 337375559, 773507873, 988935449, 287070655, 224735909, 943755931, 284307758, 972101831, 932427012, 397029149, 711763949, 125315605, 897303377, 734532764, 690535361, 777493711, 535386525, 477046651, 133597927, 828583800, 110781423, 690296176, 44916121, 6091781, 740636605, 471647810, 399040848, 20615800, 815411771, 978816751, 755712090, 265464790, 471560145, 531622325, 285999145, 289746982, 755189891, 537650278, 342717785, 451815054, 150792125, 712019439, 828877273, 753472175, 35310642, 226189626, 743533005, 126061664, 279389899, 494451545, 596032826, 395086519, 883785467, 59617221, 181279638, 688403667, 623284813, 688451096, 88837064, 897862170, 294327685, 880276330, 303452805, 905371037, 941582206, 110234615, 581726857, 785352492, 136046848, 787882063, 360031127, 239585722, 921774810, 895566346, 703145431, 646536738, 10697138, 607974264, 519309929, 712438067, 540786367, 767047323, 38036454, 58574790, 356856146, 596726982, 223192153, 424710023, 151903349, 7382554, 789019741, 188889263, 102444276, 981762063, 350028800, 96777053, 246859885, 601221358, 736993148, 189848996, 640992217, 500691656, 293058413, 202262835, 849861068, 624604727, 699459459, 685488219, 818693939, 363322220, 665784641, 52472560, 662724954, 31969583, 325114322, 681419850, 598605095, 256328846, 326009063, 950200003, 264328032, 454055461, 264816406, 252085427, 883383580, 301337306, 802503993, 68001570, 529472530, 108080939, 85813953, 766558400, 641278418, 377802125, 624054276, 235213626, 243455861, 189679086, 496842705, 49812635, 879026325, 152617748, 141646742, 111609453, 79475227, 760851831, 953669474, 422754114, 352841109, 335055550, 968886857, 706084866, 522762350, 908233214, 516591005, 526319953, 789838181, 7525587, 685564318, 254783089, 69706960, 729526108, 263636043, 902232343, 687071433, 57035733, 399465222, 339505610, 10769628, 159938721, 784102731, 713348886, 625831361, 784815020, 266240410, 386430661, 766019144, 874559239, 724854801, 928327756, 37936371, 219271587, 235333537, 773506545, 768464641, 367795419, 924023877, 62371874, 209947500, 691325488, 900016911, 985534355, 97127212, 32680389, 592830659, 855868291, 29454972, 652585337, 860542620, 747390, 803913620, 65220458, 815862648, 180487596, 787737159, 78071991, 570317011, 683088184, 984459762, 281485469, 35509792, 421202117, 641419013, 583228284, 110657009, 796349503, 681500967, 370840992, 16772668, 928146109, 759546370, 437482227, 381525710, 579541642, 204347708, 762169561, 847437740, 847533930, 328968221, 834897309, 614352326, 259364829, 655916439, 626456903, 493212797, 187096566, 16784083, 930272790, 223862938, 457382426, 834267431, 449480820, 435455420, 278790147, 499856971, 727402284, 164492430, 520433536, 568159123, 927212564, 347590725, 966854928, 198810666, 900840866, 318554194, 603895505, 85332935, 731268548, 782298468, 456317039, 817479248, 14662653, 224233644, 354955634, 405167083, 712480932, 470858300, 46814841, 901253087, 868209060, 78005033, 209451629, 368819292, 657286860, 208531197, 98364745, 54310876, 134642933, 512541525, 73670509, 554273372, 120014086, 929107943, 988435081, 317988966, 531272530, 728939744, 321162508, 96719097, 54358007, 614724806, 197265458, 784158753, 949347905, 617917832, 932810954, 948938472, 172616790, 923903566, 644593384, 520484340, 195559857, 919792588, 343863929, 414342396, 390110586, 210528280, 435249400, 848257991, 184155250, 281929649, 155733210, 385658478, 712178359, 414956792, 901276655, 4263235, 884718186, 244675487, 537648532, 427698278, 169171287, 748445047, 491480491, 197800448, 55562901, 176661181, 958599379, 916145433, 848186769, 620229484, 379391803, 268574585, 723145390, 694756812, 525473445, 119590818, 858911335, 877726305, 530205073, 430518610, 385568634, 907782085, 666126799, 445039820, 53613968, 67853593, 483780139, 212139710, 554623712, 531505784, 385514459, 30523410, 616011266, 854798262, 44535919, 652287412, 966231986, 940299821, 689797208, 974382131, 207032337, 653507401, 304174014, 363162332, 432409299, 984813191, 185086343, 670817978, 758229446, 400787786, 55990083, 692593157, 932167686, 231540664, 471771768, 549652112, 679830485, 597340559, 994595433, 294370206, 218643353, 549321083, 649874205, 838976144, 658354081, 796892094, 234044942, 69570279, 688210532, 563371010, 517691668, 187820066, 194990295, 168239969, 70474112, 671214727, 775823945, 525807503, 942795077, 290351312, 698883263, 52641338, 439874931, 607468064, 818620296, 178311264, 647413414, 357288904, 544935236, 179547903, 972136041, 820061933, 500699985, 891085581, 164305534, 432582759, 620739546, 390726261, 561848425, 31509612, 676770260, 380563379, 112537502, 468076102, 32633841, 999856260, 202680629, 513338610, 945295443, 392634086, 195659173, 814282095, 60451883, 394377963, 292072676, 66688672, 560370327, 671003565, 276488805, 471255845, 80417586, 941300435, 698591770, 173185321, 139068373, 669818013, 302288261, 594498656, 756935395, 388635912, 687094019, 932735696, 202278795, 703354935, 494654334, 363058187, 990643041, 160750704, 368612353, 879634791, 161178119, 469319665, 394722791, 635020997, 193780639, 348900654, 178654098, 558763202, 729166955, 578677450, 183250467, 228590084, 344513906, 394244582, 338071301, 372933043, 552905258, 938646037, 290398384, 401863222, 898495780, 569391356, 839959749, 661049926, 928055773, 549966055, 539357343, 309662601, 196561699, 7282963, 723357843, 647151692, 621603031, 619380168, 22268844, 189436153, 885722621, 959865185, 525562008, 615108353, 164413507, 78068911, 690486724, 257539833, 15516076, 50973493, 730546099, 614305969, 297898468, 555132707, 687769582, 764762386, 418275833, 217665092, 352763009, 141360707, 853817255, 379205777, 64328290, 799343306, 91786109, 183307657, 595995188, 177413525, 712060670, 896108377, 30835921, 617140515, 327221972, 738509195, 166966747, 544282542, 179151866, 553107802, 389569192, 88384429, 721969101, 932338682, 607909577, 293238446, 944871421, 718071569, 571468228, 136500161, 71166504, 355073930, 536152646, 52203448, 548035069, 299244695, 547835744, 696239703, 272873095, 918406959, 812923766, 339532032, 437463000, 884522829, 925303943, 753148058, 54261256, 827814722, 1765849, 256248895, 640180966, 608376600, 748592196, 493009235, 504591806, 477824456, 9035731, 917834635, 20773461, 282965545, 72994863, 111757979, 872373738, 510609383, 957614223, 858618600, 496711963, 785769341, 350759661, 985490201, 425863849, 625440595, 180574602, 403689207, 737444826, 8178424, 172412758, 186327917, 756023876, 358469758, 348672254, 731551188, 860592305, 384503133, 918562662, 707195391, 560534830, 827667002, 226565443, 480745718, 74015364, 738808465, 15361217, 724806676, 221408975, 222668541, 93599393, 161511909, 288135989, 523527264, 848070389, 620141727, 910506695, 130663272, 654182579, 171911992, 374065685, 885428162, 473179980, 978877881, 563940172, 504154871, 22917097, 834861216, 242199270, 687748652, 482876558, 204173960, 828820793, 841708079, 201890464, 916650344, 315030278, 659097836, 406756944, 743134964, 700898511, 710595334, 834539364, 690292564, 709228161, 835892459, 677474952, 71608660, 577023500, 717542682, 934585442, 366382422, 309344045, 566580853, 733975705, 713368905, 784331350, 687952998, 683101711, 297236119, 161255617, 483203750, 527496392, 912490249, 37024863, 705737946, 641061245, 485218373, 535632748, 889715243, 258078975, 10115708, 19583923, 127306435, 87372616, 277460643, 984744157, 399263359, 985286440, 361490447, 898244562, 290060258, 880724539, 787577178, 634730360, 912030422, 848609570, 210559083, 161102884, 890463666, 691695856, 646173011, 577365424, 648879123, 560240643, 153376209, 517599708, 553787762, 499668065, 378463691, 768284358, 456156342, 454186029, 206632165, 897239540, 871825679, 866475341, 320269707, 288635689, 89620559, 559949523, 781294120, 777109491, 477936767, 227763279, 161920047, 677819106, 577716898, 949274224, 641709158, 556034205, 574257965, 84829874, 600134345, 121325188, 657399301, 596498124, 577017193, 367684966, 864075853, 786795260, 478537505, 805766975, 551464584, 641105935, 6868564, 318815640, 731338198, 475531186, 572611726, 451807760, 506551691, 307982580, 862777961, 333702880, 617859926, 948027242, 932550643, 885487712, 514180615, 733273456, 558399385, 182242743, 609349597, 6966104, 489324106, 908946641, 356707263, 380752955, 445059190, 774445318, 200617259, 67280099, 472223614, 113852337, 239437201, 612660220, 18998894, 433791602, 181629899, 997289744, 770290286, 88430684, 526799258, 904021647, 191679304, 813261165, 674619436, 605355290, 237062133, 267617476, 132491861, 533036796, 668548657, 763516803, 405326336, 68806335, 297156817, 996601649, 308254157, 456027501, 373524928, 652603331, 48536550, 5173693, 861413089, 628387088, 315326896, 582277333, 558724968, 248439781, 694174821, 759143964, 89798246, 112282237, 393906082, 87245566, 748148256, 844566106, 769351913, 57794780, 193677150, 572172446, 972170825, 496578672, 799437256, 709318204, 786745792, 957839662, 846786584, 223382054, 664394541, 154388318, 235382572, 568267642, 372466394, 892286921, 360303151, 441330156, 611862718, 164398924, 324422729, 877923251, 597044407, 593133958, 301963313, 710213052, 605924051, 847852051, 173918457, 698350006, 137262376, 766958565, 512643116, 136187777, 833526720, 673484368, 708602771, 226311738, 508469546, 976596883, 466936762, 345436243, 959170690, 774030030, 364444208, 722929828, 562382135, 737781035, 858826995, 257927497, 199557847, 575892081, 104861522, 188333260, 809480228, 531428541, 674828405, 482537533, 536978088, 327563077, 574680112, 600082430, 6782130, 468834943, 393181542, 996375398, 890246334, 330957028, 592688651, 136849747, 139018843, 688237890, 222234837, 908677664, 592788015, 153538228, 516637976, 965563504, 847868411, 65665419, 901135382, 429054474, 123294652, 78770822, 848051669, 118820885, 685068980, 260107824, 724231811, 494778778, 827983271, 277131363, 5880508, 430759503, 61258553, 844757244, 399432447, 189780029, 652453202, 842644284, 207838007, 136895215, 156259193, 60839901, 999000495, 370836672, 379830597, 637796889, 280115686, 552953674, 917422173, 864020296, 633197177, 205991969, 553459677, 325757774, 325682970, 387993825, 521064519, 518498779, 608885794, 413540989, 680108149, 153227726, 234515952, 681529670, 871592085, 411115523, 373811351, 886113501, 818356096, 776887998, 797110456, 814138726, 359676802, 733887410, 877457225, 943318051, 126111062, 326003140, 809686485, 827586434, 707099909, 836440935, 535307211, 322219638, 514906767, 184439031, 211846085, 935003965, 912624456, 408627548, 895931128, 813689743, 342343935, 181341071, 840418884, 510124061, 758661371, 83339697, 682798898, 723845218, 338072765, 966838852, 303040937, 643992339, 713727115, 302712584, 779133909, 415949935, 554697226, 892735799, 858831351, 226000586, 298792251, 314385863, 961748396, 857968386, 697168952, 595353419, 968325, 847832896, 69995917, 872434577, 707588792, 348457827, 258558300, 45766056, 456892580, 217393597, 763036744, 86135861, 590964282, 887705981, 833286225, 619599991, 310642274, 710623447, 651522676, 45898942, 28708044, 162244500, 780307671, 719356932, 621269292, 493389317, 14396793, 960744531, 832735607, 390899274, 367487437, 121534711, 426011991, 360847815, 845628102, 147124980, 768846855, 102983875, 142800543, 815431730, 972188622, 159745526, 788707447, 601929155, 640995571, 720880696, 807738311, 554456584, 873451221, 367111678, 563033214, 905630784, 968960998, 524041291, 565775739, 135944796, 187555188, 108075433, 434643269, 798669561, 480735819, 359412618, 980737659, 658248644, 691239053, 487621744, 191927374, 90281393, 587473454, 71169511, 631636045, 980801719, 444160102, 749561547, 725783614, 788555457, 229245512, 958710149, 780441670, 64565193, 935218561, 236886978, 304216144, 726528153, 492534864, 278510033, 252222959, 249918030, 393131910, 3277625, 623025152, 931772794, 819181224, 403710036, 314700619, 390037423, 171257908, 952786871, 511160502, 993770160, 809439504, 392638405, 783993994, 891178230, 312565490, 957902604, 456649715, 793516770, 425498948, 311258753, 393551138, 878944524, 420258380, 994598627, 798194647, 715398725, 240194505, 40544434, 434905205, 789971346, 54313669, 103343270, 526451430, 205286017, 700457289, 400764409, 74325398, 308840072, 117722865, 215047676, 566496392, 74085749, 234391637, 322898847, 967263740, 924739127, 351005373, 754905612, 406393513, 684282708, 26901786, 862852269, 652925078, 73761575, 810048448, 848880820, 648109059, 921271621, 759936653, 161524869, 248056873, 497635287, 339737514, 816347005, 849878247, 320675720, 694881283, 771324627, 846119719, 365115846, 553038705, 20283883, 380918710, 472883692, 934248943, 303093911, 422943596, 444868642, 784566184, 264171160, 522692713, 123831146, 588496812, 129128492, 896477371, 499585424, 389076288, 467984815, 938971115, 970338864, 38324564, 292878100, 784755916, 812542305, 507045108, 726828565, 216096585, 467808930, 930418127, 321325633, 122622855, 38089825, 903413320, 79303392, 104477355, 676050636, 72427456, 166175415, 750374423, 731287820, 680794973, 84721827, 218983502, 322126807, 831185859, 941368886, 528082178, 283453060, 141116015, 830880224, 525549526, 66829460, 606284764, 361324500, 507864849, 99189386, 553712090, 475728664, 385240020, 122954328, 100668405, 999001912, 444797160, 892707249, 633816445, 530528257, 511932842, 917300474, 55901246, 283962835, 33430210, 848573415, 412956592, 732185947, 830166381, 905273907, 281266344, 822020239, 824514166, 624343119, 43404692, 668360800, 44434352, 801803184, 401680615, 893404656, 594703796, 940734590, 482109441, 651622273, 334844173, 934772084, 944823621, 227881101, 789403296, 893576386, 886157012, 625006149, 382606891, 888219281, 272254316, 112159198, 999213493, 736632314, 632043655, 314982263, 100073795, 65934895, 75951992, 575127857, 347207845, 93516639, 731507505, 571022389, 218896400, 785714104, 105330008, 980262715, 406564323, 553781470, 899040053, 436979149, 217720163, 215628212, 267017005, 913716050, 90575212, 552146361, 136391986, 791672196, 402396265, 293444720, 494178638, 228779324, 825084188, 376519207, 549521411, 801699715, 208425790, 361943567, 102753658, 296556786, 954261478, 556965661, 447284107, 877707497, 137029597, 579250391, 87362354, 508869152, 568999635, 949251340, 877583413, 843166507, 415648394, 662470938, 139971023, 246361278, 649321697, 344925554, 928114023, 370252431, 336835680, 11268829, 744637682, 25571504, 393547600, 294720819, 518459585, 119041404, 333859360, 676075743, 257895141, 166803120, 2644717, 968730834, 802665329, 601868733, 627702374, 333976357, 832930116, 426140357, 950456717, 557000448, 525230145, 857871518, 459023221, 131753583, 371214038, 236990155, 529068770, 845863259, 771975756, 674554630, 480427217, 44147364, 634894985, 865334979, 428793156, 84894696, 59348889, 143890238, 993560844, 783457928, 342413789, 580435920, 334281232, 145166470, 88326834, 292835045, 655582535, 260209962, 667037132, 259786840, 495732141, 97394236, 553997935, 822708760, 522636737, 456235395, 135813710, 93743726, 534472199, 297273982, 5568465, 892777471, 755286532, 427795680, 725914136, 111352566, 543734663, 712530930, 834467819, 534318354, 12521414, 41445931, 847143863, 545707758, 45331954, 315584557, 134949977, 411541506, 102658844, 877369216, 71981736, 445120245, 49418344, 778235665, 108064523, 31645082, 921304674, 688513949, 370818480, 386386403, 754560822, 754983316, 980397264, 38271514, 697354896, 459310519, 890306498, 879256653, 947380423, 20648547, 926044354, 757388908, 650556526, 7332182, 22517851, 417410531, 328692639, 349564472, 679561943, 434662095, 843245885, 782023803, 202378724, 904032129, 483879700, 21696821, 755812783, 912603473, 806138705, 100087429, 462740103, 937552231, 872115510, 554104201, 327585218, 74104922, 656019813, 655769098, 369750419, 965775028, 23327019, 698254781, 649416359, 557741469, 371849474, 622313736, 712575546, 22601054, 492396466, 798613753, 682629129, 698313561, 904810240, 628571188, 243780647, 527102452, 576832071, 682813877, 19580460, 4281283, 116505088, 587542403, 572705588, 324374604, 828174166, 349662834, 57839472, 266755759, 308598209, 298222754, 513606335, 322111071, 76087801, 8480845, 913328837, 485645995, 616231614, 962586257, 339320179, 545844056, 530127827, 632469313, 335084663, 508664748, 974655175, 569820464, 771561322, 329093766, 763998007, 290064866, 679725028, 779260541, 576265737, 569265123, 726971580, 664941790, 994457867, 90347522, 336760241, 17897928, 340185542, 639171347, 899011935, 435630345, 124213770, 452485691, 508800309, 934217378, 433815824, 57239827, 834466441, 615506910, 93427181, 856544946, 740116161, 328566847, 52885610, 118023106, 733230040, 733656933, 373410293, 815034669, 74069806, 716332281, 774585617, 295523972, 389817533, 112037568, 233202747, 783070866, 529401562, 106363818, 664653267, 18609929, 829310140, 413295189, 256049237, 798523019, 895909903, 655575736, 689530387, 669974432, 309397018, 765489527, 316003516, 609646078, 981656063, 614567178, 336144530, 935252917, 937708048, 720474513, 288872270, 886695434, 671834378, 829152819, 1437743, 163103027, 519100860, 592906388, 122023652, 841929222, 42699981, 282589362, 985881532, 366829610, 478208835, 960855838, 37305800, 773577028, 903753940, 720786327, 427582041, 266883409, 245306102, 436152538, 281665766, 898543223, 365449134, 432063153, 481114127, 241048067, 403739334, 687732692, 768719649, 959719536, 535427690, 8629788, 791633096, 889734228, 309237627, 672094864, 886553174, 951723857, 734773279, 79246954, 230225506, 68572245, 989232338, 197719234, 482440417, 801352144, 283901400, 910926114, 725938172, 751934187, 412669834, 43486695, 466819627, 630218936, 255720969, 19533754, 149000975, 716648321, 314789758, 971061019, 156715309, 781313467, 449015117, 872396202, 869308579, 616452764, 901257513, 210122833, 792240966, 780066, 183384461, 198425609, 891698961, 112237627, 606067255, 948613885, 525154236, 111043060, 630714520, 308708767, 633378027, 793418476, 116624700, 405005467, 31863256, 280899640, 851557308, 598533436, 163072847, 512530612, 845311586, 313357697, 384397007, 612845558, 588263976, 127437869, 401822392, 55099134, 888354987, 73461228, 143980363, 448116597, 349460853, 1888914, 440258729, 428609303, 332955655, 71547126, 854926228, 254453931, 800782578, 931689614, 833734791, 101512117, 446812872, 178062950, 429641766, 943985943, 368421585, 579747886, 117008234, 329039106, 382624050, 956330316, 394306832, 669169952, 63373242, 502291842, 539979751, 806007898, 794285746, 723826061, 466424907, 226536224, 300676456, 881908885, 550163528, 69001756, 224138212, 445107060, 559086913, 614877498, 892521833, 833819303, 708612436, 913222028, 966729495, 416161296, 735528282, 216363694, 949692909, 605075940, 119525629, 448850852, 417361102, 637392323, 143595395, 581238285, 775548654, 702070654, 960714990, 145493142, 857327759, 245020865, 163095283, 850195341, 696079161, 770750633, 140421034, 932117242, 546421983, 947643638, 919631742, 921675289, 515795863, 866522136, 347428089, 401380448, 546205316, 214385044, 771752537, 778474627, 429071201, 102608992, 114609163, 480240104, 958471693, 75962476, 795091774, 926487397, 315159447, 902970597, 388004472, 647726055, 44666348, 446902582, 435280656, 203087337, 177817023, 865705422, 501925311, 742858354, 625467123, 730940262, 781724867, 2076938, 438253711, 375678023, 453121219, 217254367, 859454111, 304250513, 563925043, 456273262, 188335824, 786452583, 372855718, 108258665, 268096423, 78418013, 101462962, 956259479, 363221620, 969528968, 683516845, 305740630, 592560649, 890967790, 340935491, 475873112, 913548909, 672441324, 15810388, 358145072, 354613668, 925358637, 398579797, 821992785, 604515661, 20008583, 527149115, 318514107, 504807629, 308463008, 542178141, 126170394, 570530117, 862540458, 993747495, 914355514, 469321045, 945955248, 805017899, 446704434, 887251264, 410058224, 70280402, 423097271, 317998011, 647371678, 62981409, 136770780, 366283098, 549885658, 247622037, 977171190, 969482971, 469502491, 532793355, 122870261, 833112026, 980309572, 545446515, 910522670, 267020910, 983862726, 875063361, 625830628, 884629691, 225535045, 692591619, 124174144, 998962725, 805370203, 39777886, 383014749, 708513702, 214280343, 389377096, 561516194, 381064244, 750095980, 49341357, 277341043, 82614011, 838421458, 467405401, 29272722, 254916997, 461300569, 636818153, 110079115, 49983460, 189938981, 214878364, 628237995, 269737391, 307159873, 483284882, 893532200, 156926438, 691796311, 344042071, 937565537, 573257063, 766987884, 643856026, 416222378, 246454173, 870774718, 216084104, 747413679, 747755338, 308433827, 685131520, 125181842, 819416277, 275637507, 936180337, 544538175, 304592011, 534893677, 281704916, 537425419, 721228335, 650814202, 776148247, 176571044, 144207750, 454508382, 16479997, 74405105, 753267012, 711645796, 488813509, 552058586, 864205687, 360797926, 954153178, 932501382, 473850533, 828404744, 929811233, 79587367, 69438193, 425122367, 671770032, 290028703, 616162529, 355307107, 860817514, 656509073, 349955833, 196488272, 864827215, 47697513, 371490504, 857428426, 475197966, 65266491, 870482707, 695393294, 839681472, 62118724, 473744094, 2661929, 303096055, 445688880, 502216143, 661735923, 554485516, 187687853, 292656938, 681320239, 894215686, 590100637, 977703023, 428858995, 970498283, 356802952, 583693217, 107146093, 89316733, 295238743, 305979675, 134985020, 173940321, 463830620, 668890315, 40160070, 79145647, 454967587, 61065428, 597831281, 558283580, 926631400, 235374899, 330645803, 684377322, 876556295, 403465447, 60245884, 857214396, 870594192, 900437645, 713626350, 395039832, 285074426, 332659297, 112938851, 870938288, 742906458, 307721253, 894995036, 54478570, 639104709, 475706880, 695446113, 582839188, 500239335, 46172391, 135902932, 382847786, 259586349, 193675875, 948999133, 623082154, 72006843, 916246908, 98409911, 660053401, 421565925, 590343397, 215113633, 832356480, 993829444, 82768395, 232012172, 965445789, 473572949, 568244255, 843912480, 828399680, 375883100, 326884057, 820796147, 757961313, 336760916, 289376058, 910924316, 870285148, 360537280, 694561426, 971362944, 357551013, 918839912, 11097208, 687797327, 278057585, 829886758, 832922688, 849772445, 107570990, 79369389, 165915095, 886663460, 32609304, 840290508, 56483705, 872258251, 826033221, 900134999, 342491567, 744797805, 141995870, 383955413, 242159348, 814326438, 603017972, 296737929, 66189808, 327237866, 376213960, 692182197, 587291138, 269129220, 545980536, 856991453, 900382766, 813430296, 44332739, 874084039, 921951729, 816929643, 650329842, 911107079, 717284602, 307412449, 889151425, 180794508, 212533327, 14019837, 236782980, 615919744, 516963862, 168068, 850386336, 743653692, 427605621, 708002368, 519278122, 230432240, 531866263, 314434189, 635368656, 917058707, 357078080, 321272791, 262111570, 381316934, 427232298, 952431807, 548532594, 422657057, 673215490, 665821485, 751751658, 624309274, 248219152, 62671254, 73741819, 129830260, 832443373, 138703911, 214859493, 523397775, 94007161, 246624942, 603496282, 926648339, 88311931, 684558914, 780031602, 905618788, 612270365, 204194321, 355550741, 610686605, 585490126, 357414548, 4594092, 366159656, 61630255, 892134346, 20108031, 107169190, 746692087, 792246526, 853423047, 523595272, 905810231, 895626633, 135305728, 672318399, 542206883, 978744622, 419668386, 509188080, 796427192, 877352718, 205081264, 81481943, 740677745, 928757721, 385740178, 247276039, 460174556, 854760031, 994464646, 856304968, 257181937, 639887307, 499431518, 144481550, 902901628, 301031603, 293151182, 568876624, 189922638, 702429879, 449662360, 596363307, 988004179, 676679593, 431634674, 980478325, 75698668, 783505575, 84976972, 481534470, 509739996, 940920560, 74781252, 915374485, 258583418, 159413304, 559473685, 153463483, 751714682, 238544580, 606893414, 436157903, 315326635, 213643923, 782557943, 227152793, 358527860, 489678216, 990672441, 129518406, 556551405, 703223305, 33934811, 183951295, 164024941, 681712705, 762335184, 803396859, 969102021, 628359778, 411067539, 351372492, 448542920, 979846779, 280881598, 549685712, 36086306, 107776440, 988375679, 301508102, 590880199, 424197138, 958239704, 986411747, 670878487, 252664242, 747680465, 283959290, 400959115, 804852882, 983437878, 77928873, 312245651, 522710384, 383804352, 197910314, 687542233, 695591040, 347006592, 697890814, 56608055, 456868892, 556105912, 762248421, 962485460, 845063653, 363502075, 717293927, 886948727, 865476958, 989422745, 141706164, 128955657, 464850471, 110170436, 637595754, 822420317, 664351628, 118809935, 118305865, 188485873, 155113432, 3816233, 725420877, 57734289, 747314950, 277469054, 978067051, 730948193, 115433991, 910507159, 812110446, 530982380, 249573206, 752685809, 681291027, 648779917, 394976667, 925979541, 464727616, 226491931, 537390015, 811629974, 637216169, 471891391, 601080249, 692509739, 689012152, 339442259, 814393460, 401524039, 859699092, 186114472, 25157426, 85521976, 14797454, 715584281, 556308620, 533861558, 423008775, 229145748, 172898550, 833612186, 36366189, 345375981, 433104369, 58841062, 948579723, 817540801, 333396290, 149244549, 833266309, 480587185, 379199378, 700962700, 137765060, 80269431, 936734688, 706725036, 640174146, 398524572, 501345615, 680346924, 176380019, 824669006, 592846197, 172037331, 286184304, 768644108, 70834899, 748275945, 670869925, 904786359, 534061260, 44929833, 794589066, 638182082, 478043944, 919022895, 333751149, 760891941, 406260560, 532731197, 551602080, 20677999, 349929081, 697303523, 721460532, 762617315, 286999713, 655779104, 461504554, 129565328, 430747666, 239488723, 81209290, 40225158, 269624021, 223050505, 302710402, 939583268, 452428581, 874607659, 67011733, 197584463, 495738291, 257734234, 582047191, 791538454, 587155457, 839694368, 680843111, 349287338, 338516290, 282631956, 328334492, 288057461, 600887758, 690177847, 745836024, 990513330, 236835645, 986450663, 678725176, 80587325, 466444662, 637834518, 766019982, 926456660, 193967467, 468980042, 225165302, 890033723, 163527915, 861697719, 874431752, 312564015, 516322276, 180051491, 665018603, 589311938, 71306792, 823617251, 216007915, 203633905, 731856325, 412544076, 247745684, 598083442, 151329794, 750330424, 197392928, 30265994, 743813251, 740951930, 340118709, 897126153, 928256018, 169399526, 227870962, 959465946, 242626383, 257115398, 577020491, 809026575, 223811099, 836203673, 276050321, 770346210, 652062686, 634961385, 305769502, 655201763, 775479066, 959661122, 117315767, 29239627, 70255935, 780717123, 719544109, 326519736, 594645721, 42262261, 527898712, 378652970, 162369795, 997763993, 772197993, 889206961, 734784017, 454857736, 427044614, 941111752, 203454167, 91197838, 466152177, 542423518, 51656427, 434291656, 650731645, 712569676, 399245051, 320042181, 270691172, 402927670, 843174052, 910928023, 65377495, 720529895, 561451217, 464397645, 5202408, 605359598, 481681981, 506519342, 950043802, 690646116, 271339739, 817762038, 921879724, 621452441, 618488794, 811634079, 779826451, 728303647, 745792084, 545252180, 557719015, 981827956, 525737820, 368268497, 664448460, 423278661, 196128378, 694827956, 918993112, 924337210, 2546514, 953805080, 103148206, 583888416, 977134987, 78555459, 822433529, 508847850, 169560077, 826570327, 809264833, 232282785, 858857050, 813613681, 558471805, 415747810, 20159634, 458766237, 587361231, 442954592, 484740938, 275258996, 589459638, 290034248, 938617056, 610694521, 146261299, 989526483, 155559695, 888705899, 564263268, 714168412, 91989062, 926961832, 232314265, 881238323, 54590085, 370217511, 53984184, 90914443, 541971754, 195667106, 335823379, 978371810, 472714426, 498265069, 275354314, 33331335, 304698253, 37704149, 928553239, 250592196, 816376924, 2838860, 196173704, 637757485, 687431406, 494008509, 77237478, 744400047, 906737270, 62482583, 97320591, 248475604, 416190978, 694580180, 598464431, 86531574, 626918246, 940633230, 352819046, 984563729, 612143340, 463781785, 336398100, 300234623, 316567725, 197824457, 320011564, 866309552, 483033025, 662410161, 568909317, 158547357, 564297306, 668191316, 515274376, 464926539, 89620596, 378044282, 634204727, 871474304, 439880449, 484474792, 718026420, 74977733, 834706294, 344095968, 220472391, 439164896, 636036679, 844687120, 789763453, 125540831, 434196168, 882349400, 355148773, 396168960, 585455680, 165377090, 19285645, 486191138, 488777618, 875450420, 717969783, 382113385, 643496328, 985697045, 388805594, 245345967, 739458257, 311728335, 455611055, 336865242, 334473833, 213128438, 929802139, 144472090, 225079830, 412986817, 561400977, 16292921, 157139880, 322447904, 909435746, 876786983, 86062868, 806168815, 679787293, 8433776, 648862687, 653017146, 489053261, 531903164, 928327007, 920136258, 620175464, 922432851, 516697681, 279622692, 485211524, 941061068, 467078886, 806291774, 253753921, 940246085, 131029858, 330233108, 677241242, 747272196, 885960290, 36811279, 567128902, 824226237, 5458908, 611641213, 413977756, 542697550, 577162986, 227615294, 747842574, 393341736, 813725634, 727331493, 430916167, 765395558, 819375097, 220564065, 223961811, 545940453, 213564571, 723106233, 155833188, 653378982, 598861470, 449196353, 382506382, 322955575, 592490065, 436769804, 270229358, 420748685, 254697157, 565360737, 741169762, 921448834, 348414248, 691798925, 491300303, 365936185, 978526000, 302636612, 133255339, 67848272, 322783237, 948648596, 888545525, 813100342, 527081828, 160551552, 984695935, 279270037, 217166152, 512052666, 492831038, 260548992, 49332764, 940272105, 923213136, 33861325, 440699568, 749134400, 205044589, 719079427, 108344987, 68299558, 75346129, 780874459, 333788186, 229370070, 913941791, 446497591, 362742815, 962472263, 348110016, 179462455, 31757918, 271548800, 164850652, 543019921, 619439784, 221651212, 15611956, 225586821, 528092884, 235715573, 294112961, 857542587, 672252, 506410478, 836439567, 693474978, 591420802, 215302275, 521877397, 9985319, 820972136, 42557675, 272666314, 211924576, 564458940, 181986491, 565196007, 150474619, 237916030, 676348939, 764274247, 988527573, 955580938, 373232341, 462266790, 961823164, 877515540, 914880557, 841006593, 479357880, 848952367, 134787630, 470668794, 665074722, 438496551, 398564223, 643650547, 813772876, 96565904, 752326164, 490901461, 71529490, 526527041, 433431945, 203814872, 765973195, 581113058, 31725589, 511568858, 380147300, 791435599, 804433272, 646892553, 666766875, 853769523, 128624769, 341987877, 691170, 266067153, 885452968, 356597410, 517920520, 106221252, 629593569, 882517692, 454237211, 239356662, 464814152, 639767174, 88720970, 406083788, 180262214, 467591039, 255337316, 85053961, 754719535, 621921105, 881269334, 710346921, 947785152, 710320695, 462021133, 580024062, 286942335, 630064713, 143239372, 367157876, 183357650, 740926307, 544180875, 928804052, 958278390, 542850202, 951743870, 244951679, 467040256, 294713182, 767361477, 370057649, 812050447, 252190239, 246052057, 502618429, 479875261, 255070964, 330935791, 381125438, 782596787, 727188325, 648188177, 523274756, 27245162, 666584343, 8953778, 421067440, 268921416, 37866166, 836006563, 961592196, 663987751, 962250902, 36864686, 764677597, 777289936, 939465333, 302118797, 166044137, 667161978, 115247692, 810334426, 227778397, 831642431, 865852363, 151616103, 394048457, 204491968, 112848837, 140778441, 254084428, 466743312, 672945509, 127266026, 712977972, 109822397, 174779762, 331723918, 996728136, 400170050, 160020839, 921333183, 212588259, 906421174, 982470978, 847774174, 473365644, 134400259, 585027656, 834449221, 60428297, 23846898, 858661928, 380355042, 366295743, 896823729, 265363450, 283106595, 617323224, 735545133, 625622497, 253604360, 821895424, 155497589, 312754944, 658888488, 141202983, 711131432, 990459701, 798441607, 515928115, 455631907, 95447401, 362468397, 116465570, 986294436, 67669790, 791980693, 202056080, 316987998, 210277832, 388382430, 694004458, 100600260, 242085853, 115533933, 416039183, 696497768, 853160313, 418279812, 19276567, 99375974, 725948486, 525935748, 995082087, 669684671, 233501875, 800332965, 613714025, 304790843, 850613173, 40314120, 230055263, 262173921, 939140023, 444089762, 248817627, 396302446, 757888853, 80379599, 667304801, 305809634, 209234909, 599189222, 516916191, 212709998, 693471145, 435230192, 550826020, 692552230, 221497199, 103407945, 211458712, 505363911, 899222583, 839748770, 24058039, 261872991, 762721648, 62316109, 924956691, 744811993, 147090411, 438443690, 494683829, 751895120, 456460219, 181296427, 1599373, 304716115, 586609832, 836932364, 422639573, 966291624, 864730919, 90441116, 985220267, 470266792, 261572275, 435414741, 885508177, 646357910, 931810673, 773748510, 223457948, 279979789, 601697201, 294723286, 292752014, 586945088, 860068822, 875474277, 603683792, 768380060, 843704046, 190819701, 838271196, 263750165, 537012576, 977909040, 344968194, 596422134, 421150279, 703555160, 757426151, 395418001, 775088955, 638555108, 240593861, 199598941, 816764634, 119973096, 157814579, 428830362, 515798637, 69079576, 165890788, 970277763, 935273198, 942026660, 225584772, 273806172, 402683526, 689057555, 897233027, 79909431, 689606362, 683892833, 708055264, 152853304, 163587644, 434165359, 973557020, 46343961, 662218304, 578941740, 963591384, 377530951, 924058813, 999763678, 423986392, 476161619, 846956135, 284101583, 593433463, 13739765, 683127802, 779635671, 713459140, 523502270, 342269354, 14935308, 48498873, 305655991, 606128317, 598856826, 550365887, 291983879, 967442362, 822298763, 349180005, 605384211, 464486060, 305364709, 153412324, 90369653, 137290214, 612136800, 778362547, 128883845, 727137977, 912121910, 941682318, 995964054, 318838698, 76634224, 463626356, 51916945, 43155058, 664910626, 633838906, 968196444, 878713687, 716521632, 900707310, 388108517, 464479701, 235855051, 688400839, 214392335, 470188867, 945117533, 618616274, 680280945, 736577564, 825570980, 509569332, 763507827, 806689738, 718149635, 126297292, 343575328, 788049945, 910413110, 673884530, 607950246, 213729682, 490437131, 538801729, 948366017, 122559127, 455820823, 41801744, 714628897, 207991352, 155921401, 23805418, 824418740, 193245100, 85254331, 572372848, 523314418, 898642366, 595750409, 23725797, 863589297, 876984007, 121070570, 999760088, 85311786, 361330379, 574897980, 923581156, 191432991, 783356369, 934818820, 863141755, 526073693, 680264766, 693513727, 69282870, 940713103, 174726786, 662121430, 667203869, 470046714, 300209824, 815108056, 347685044, 258112516, 660569658, 421019925, 675908490, 675710652, 250021739, 71194047, 611823214, 16329263, 616836765, 49811999, 604216820, 641196217, 322979694, 709204297, 598982197, 613520767, 332265860, 533857338, 902478233, 796710060, 360118980, 132786364, 307585556, 667757946, 260529247, 143419373, 213425785, 179382782, 863375321, 178597585, 623315777, 15588954, 892825005, 435923568, 641235570, 672231869, 115034158, 443408793, 38797167, 844778369, 131643172, 223472401, 445009029, 392922445, 699664219, 47532236, 647056719, 218515329, 917401814, 752917865, 552425320, 813956955, 545043128, 381579160, 223934899, 156367896, 783464361, 416212555, 526864074, 356737941, 747565744, 140509863, 142953093, 553773753, 102488266, 646864295, 997635663, 559872796, 333435335, 662307338, 277667865, 185335844, 779096533, 822370758, 518597270, 702034966, 792752955, 618864150, 518784470, 21029953, 704557467, 257060942, 329852005, 363631860, 722353428, 295627185, 354361506, 165614687, 653920457, 61954143, 84949629, 934340377, 484561463, 841399688, 495705824, 592266028, 565710670, 6351605, 589169779, 219902225, 44662058, 729248355, 9416713, 778929820, 410361794, 89558810, 651112881, 166741626, 173064040, 456480138, 55871486, 158589771, 609457164, 2126223, 922875956, 859862101, 387908065, 903263920, 873768067, 468415568, 442920895, 307913568, 44821847, 722898007, 686510889, 684469695, 761116955, 729231532, 980311855, 220721735, 766223690, 11890443, 469908850, 700660562, 711602261, 177136559, 870948782, 925984710, 200913149, 375553474, 261707400, 596239977, 668229035, 470181169, 570081785, 988165699, 190458825, 318268485, 331564514, 636170454, 309868820, 288221048, 678808401, 748477726, 82646003, 742816636, 965314906, 435810613, 914567776, 34783000, 762436573, 916369530, 219660254, 79065707, 801873275, 340461225, 638229438, 393616480, 423010487, 468637450, 402714692, 489338323, 800809696, 174604493, 359838995, 396278892, 962092980, 29914220, 15445747, 351334454, 969864687, 281633854, 772743167, 930902978, 816999049, 732645239, 199414815, 155062371, 255908141, 393090127, 515246584, 392976673, 402065184, 780294179, 74559326, 3427457, 617025263, 688602281, 462960367, 137733602, 212995687, 370995893, 868587934, 323376722, 347497186, 658380193, 5458282, 433403417, 619728850, 214253488, 509735739, 561060048, 557387893, 227109730, 579940498, 56761498, 527046899, 106764539, 931410265, 320657471, 547155397, 912094135, 595142711, 694191001, 8554865, 14550508, 815411653, 368238397, 686907275, 586491775, 489788495, 65654819, 887201608, 83838644, 608612184, 816250044, 921063334, 923484256, 679594138, 458677088, 472836933, 213983278, 928084454, 616854805, 895826446, 72357440, 786249994, 363604352, 570125353, 718547188, 560808131, 338792143, 373917946, 974457534, 594224689, 942300600, 777202696, 991495758, 175170721, 420313463, 478304773, 842729991, 919325554, 97791141, 864182350, 545067944, 506669159, 62128240, 660774190, 118165150, 457093857, 516793857, 200195206, 181735068, 294855871, 465446979, 976368929, 833197536, 820380907, 818598631, 614262690, 988349737, 548370984, 391058895, 335828446, 680822578, 386924370, 350381305, 612235007, 494956871, 761377711, 123693944, 312918139, 414169416, 415464524, 281911582, 107878184, 446660226, 678303798, 925938010, 563003475, 884546928, 276281486, 931660199, 494644158, 798318908, 420785451, 289372338, 424314495, 909782232, 213496557, 957204639, 337990630, 586671057, 454695585, 298583678, 466086040, 683842715, 600874315, 114980499, 730997630, 888327894, 450021797, 836405650, 935028535, 786403168, 814780301, 30633884, 702889851, 725811527, 63739559, 691073744, 533584944, 307283566, 623499153, 927589329, 526372824, 370674339, 574156628, 541320254, 546419369, 948599835, 363219845, 244611798, 721250464, 613417076, 739077909, 210523683, 387556478, 843060292, 590588454, 282664000, 708626374, 251800939, 982174635, 605875774, 571385208, 329229044, 57370425, 987877047, 600556815, 733904191, 460155664, 60358869, 978215577, 947774339, 946328161, 209996902, 586270065, 474762547, 882463937, 464720921, 881716323, 621381386, 926365531, 233293941, 934298632, 106306965, 843581027, 210955492, 528327868, 623866477, 193436503, 264705082, 501162882, 705588647, 410026086, 760153791, 885261007, 635121148, 699154335, 791901762, 434005310, 90485395, 101184561, 872302433, 72482180, 180283584, 481036229, 470738368, 837675795, 116570242, 222905922, 105029928, 662143057, 966297665, 15785734, 813974398, 828707838, 71734641, 850176542, 681069778, 458466566, 757173661, 286006385, 685417163, 931639395, 281590463, 908670917, 656083082, 547080113, 963490531, 466389134, 139931278, 427176584, 670835097, 212538845, 354963902, 794253144, 475377715, 991773309, 790549997, 644411167, 271976389, 149158661, 59792954, 166486505, 733511746, 229138550, 563832972, 92886666, 810667020, 818838417, 542543719, 988186839, 166202803, 728332914, 552264277, 592408693, 697456992, 196816446, 611273138, 930036291, 395762618, 306255909, 991775098, 772932545, 191501895, 861415882, 308070149, 689775503, 900922000, 418527112, 778407873, 997998345, 327474473, 545467350, 381820015, 791061435, 216940740, 329071829, 561279722, 293048139, 927620411, 157632170, 634811712, 265293761, 486160538, 944132366, 499694421, 833535422, 5420424, 240756869, 656168437, 599516549, 214954190, 950451206, 37017961, 456858625, 509610983, 522461918, 438753109, 934654968, 867866235, 76850845, 269931796, 923150283, 883121264, 385677771, 697644821, 944119674, 789635502, 953524375, 608087376, 867318558, 614849136, 804185814, 920012863, 797367340, 749105341, 617032254, 566409701, 523592043, 599790375, 255345252, 310308995, 100616119, 793681788, 834685427, 453382760, 692001765, 744139316, 991197680, 925349262, 890738307, 775365567, 453007482, 777096993, 664986154, 213319435, 38605472, 522462501, 858767686, 552181296, 134831788, 22519125, 75904648, 838399524, 472119779, 5857118, 513526092, 506939471, 667531721, 600156803, 6324920, 127946769, 88800681, 337560214, 686564713, 295883123, 876425590, 555771982, 213643708, 96335430, 432582112, 443995164, 562444953, 525210351, 990643757, 620404147, 736324085, 431088541, 443013089, 574352229, 117692354, 250158999, 961187955, 220121541, 421507606, 711142151, 144627190, 549504278, 936630500, 814704423, 512615352, 743716622, 17297557, 436426368, 331808411, 467871091, 932793538, 263493926, 878252788, 398307688, 142631382, 61810308, 856551210, 990842340, 308286907, 97291535, 33052351, 749568805, 20454770, 329046777, 728430235, 254733711, 273488996, 562184502, 361240898, 837468714, 209225414, 184177229, 377319744, 149790229, 733301340, 675265307, 534053774, 683463790, 402980666, 943748198, 93691000, 830574460, 264419075, 1115572, 788689780, 569611750, 710096176, 571931059, 470601033, 649339372, 64949439, 885695136, 366299519, 357726291, 574983135, 294449063, 704905021, 401083834, 494255794, 548441511, 627047425, 838692973, 603737224, 412015998, 116182819, 416195011, 29752274, 724759499, 80563914, 96482721, 294002425, 967787498, 486047328, 431482489, 939235948, 803113015, 894878084, 258835127, 193658034, 622201861, 444039213, 977212959, 872733162, 643367482, 415777249, 127981108, 794417806, 273264265, 79868691, 797138971, 430557712, 960861155, 757945158, 337894726, 774593865, 877257662, 489761014, 951527923, 360137965, 220090778, 672601184, 761471716, 430547289, 657872489, 107800980, 899961394, 442647902, 298985557, 464986862, 472034676, 11483561, 636829262, 881832473, 806096895, 259491516, 856404502, 798183412, 293706820, 390602273, 974428989, 273221244, 322591855, 143748605, 225732238, 991468119, 822423876, 544582614, 180999334, 845881429, 552139582, 890225651, 155721527, 722321029, 804046726, 892658475, 390128291, 457221498, 334436152, 518444484, 983925110, 757218225, 438195944, 452133425, 576007287, 592373566, 140829782, 653061114, 654166711, 950136046, 737508084, 590905770, 940529381, 933158100, 178817269, 333003369, 349772889, 84972393, 644260020, 182523728, 106233961, 726435340, 446646457, 13928830, 499397864, 673750713, 106441160, 831565742, 139397128, 826506827, 798254406, 122119731, 522693671, 592309693, 278040800, 132465775, 64083703, 643099431, 85309264, 164513058, 220820842, 710334986, 316527486, 991001351, 114521959, 590348303, 573345149, 942822839, 414338509, 444481003, 809246208, 545755686, 712879479, 247676165, 618666968, 758030440, 87668591, 788814047, 175741681, 139795991, 757171597, 462131022, 314375418, 836969380, 557824521, 250734354, 557942363, 818376406, 255203821, 934037679, 388038762, 421207400, 86182044, 923107372, 546222869, 920472837, 873435735, 558551270, 722797332, 603731413, 194484157, 283054229, 83986534, 155071727, 844742134, 184629317, 772785507, 11575542, 512268741, 610783475, 355565651, 196090394, 830859238, 763859922, 656880765, 291723975, 298569005, 259564945, 398861552, 600134528, 760357589, 633801515, 554286304, 980254733, 633934445, 315884391, 505615566, 747588075, 238161273, 633840050, 761370877, 590841244, 753120652, 900503825, 179028760, 295377742, 732959321, 440596463, 687762097, 741233722, 837472151, 828014712, 531090522, 616172036, 394742230, 125001685, 886821249, 644355814, 594439564, 508932081, 201854982, 503513263, 818533629, 883229010, 552859686, 322538807, 690530499, 913144387, 931348835, 311690717, 64746366, 26318557, 984623605, 173804126, 934862984, 235244840, 807469953, 262648981, 267371033, 926676288, 484241193, 85223764, 284258465, 992958818, 136908029, 833912487, 699008379, 732290527, 812215008, 770570499, 88061078, 506584189, 591328548, 727300512, 595389715, 64933953, 779385780, 267264924, 409421416, 69026071, 10975144, 339841549, 289315815, 466034781, 559978100, 804639860, 242908550, 400056977, 681339886, 695981043, 767246853, 753568182, 73414977, 591820980, 733306411, 529923273, 552430980, 654751398, 264792320, 573704660, 874332167, 515030874, 446396718, 313232778, 905596666, 984481577, 759490974, 992161975, 892014614, 725101009, 384159136, 818292488, 917319268, 811971651, 670413415, 96341710, 13161988, 572323985, 474055570, 901815957, 436912680, 179534514, 296933136, 120991225, 805482280, 66056247, 105329176, 216416812, 488077322, 497190694, 605836176, 614616161, 928687595, 230867214, 872009380, 824881159, 481679282, 850615907, 341753572, 473165486, 403480023, 600960989, 824157566, 45951091, 452365888, 715156466, 365134184, 121310268, 531814575, 808785003, 628850412, 74786273, 521227142, 59899592, 784919606, 712866979, 390289458, 33269442, 29135873, 272388523, 951554207, 361823134, 103356225, 19815021, 157077822, 772863471, 583770574, 525585746, 814883096, 462336962, 206245717, 310324205, 28657954, 552395578, 935789242, 847478480, 690940993, 484520324, 50324538, 15287181, 21106089, 627249796, 959622344, 805214967, 641322585, 258909488, 31590334, 563628810, 233747698, 431060505, 890586710, 387772039, 185794093, 474982944, 231633959, 994912916, 270902327, 646986961, 716379575, 982626260, 370107946, 82416903, 38526350, 544456992, 837456490, 860869092, 866561623, 150738364, 940708274, 430394496, 337372246, 621828109, 207764430, 812824360, 439597658, 307398104, 60511553, 850922516, 854529603, 596415240, 285349744, 982965529, 491500644, 945192749, 294561184, 958133315, 289668518, 381138045, 496333932, 656273644, 948570900, 699450483, 19898817, 229660702, 100247209, 222234781, 322234638, 941019814, 384961373, 526120683, 648221054, 103211641, 809477786, 77594942, 40135564, 474451581, 695842759, 468656442, 825794603, 728802553, 157726896, 126834502, 414713291, 924928115, 54760371, 135225877, 493930723, 325109369, 928507428, 424316868, 538121585, 336617447, 224201438, 7391732, 625530049, 327223214, 821281461, 415552844, 303147374, 397279776, 198989518, 713720005, 723505372, 338255970, 398144668, 93052323, 235226361, 787618508, 116341442, 217084532, 553269420, 808066464, 378082841, 228955756, 379576977, 671386232, 336017700, 882386003, 931832821, 407312844, 409461069, 792554337, 349250907, 134262596, 949127204, 16182162, 384103513, 549789344, 445945814, 713411004, 886498520, 764544683, 419671780, 443998252, 521182016, 455398877, 103763841, 124566497, 350964832, 570317990, 354950632, 858916107, 996047649, 980905398, 176664250, 931353114, 827051978, 181973129, 565236680, 280347944, 961487961, 185858413, 252755720, 712164462, 423827938, 177657520, 606973128, 623622703, 382170402, 110382177, 150387976, 904938299, 626151943, 792122840, 409050165, 188860827, 561242683, 84804703, 492885926, 994486598, 891285622, 31843927, 705217515, 763978263, 980989287, 947540694, 865445289, 810178998, 942840831, 910624458, 5063672, 172152884, 918540338, 680702085, 440495588, 43772898, 62046088, 561512784, 106247731, 557616975, 395369403, 331605131, 706662804, 425356758, 173666802, 375945738, 492104379, 967229481, 186787006, 551398106, 574097733, 219253983, 713012970, 629754038, 295937044, 210748830, 985249812, 874370938, 96692622, 180527712, 640666512, 413831290, 290114390, 649967989, 974555578, 864898440, 977152452, 403598370, 635500480, 825533480, 58945601, 84149305, 979269977, 247249928, 755720381, 566557412, 640282652, 758033860, 853904563, 717903046, 781483671, 680529758, 65304955, 474360482, 595778427, 865525789, 992406722, 614779949, 171523235, 153141964, 609385354, 765044970, 706530640, 233544618, 664693275, 854164940, 863857047, 799362758, 795889362, 805033650, 100049547, 593706108, 686015262, 78837213, 855809530, 813170571, 14623921, 66764954, 829193125, 798070882, 68402368, 592046188, 141764090, 119383594, 915086306, 758612522, 272671828, 87130117, 956124586, 32738522, 214767398, 817815972, 59900206, 518839642, 922760864, 447311209, 358579325, 12282356, 873381404, 306696792, 894840786, 419544985, 882931649, 21837650, 632729049, 921634199, 261344286, 787548004, 5214907, 122236995, 231536678, 595439128, 73921802, 881400619, 386848972, 833660450, 292445347, 581047068, 77761756, 477078128, 258661077, 710505568, 664972335, 272962444, 917083423, 440502966, 288084005, 901826540, 163264175, 404421186, 387311050, 752318450, 881002427, 816731377, 149448013, 232802574, 475648027, 888984084, 159156351, 317654488, 419193857, 578467704, 881034011, 992214937, 230073200, 563450145, 946077815, 791037000, 305072848, 954289492, 809239668, 754128233, 66165545, 665558475, 61043645, 892787666, 643168791, 124648862, 315662977, 195769508, 905305870, 456393569, 40535620, 258817271, 753840568, 567609400, 961346577, 779762750, 461219678, 449915173, 371899181, 169533827, 854665615, 736209016, 606407254, 116053533, 708402972, 235884108, 790397575, 465270209, 994293668, 115684202, 502968018, 945514595, 41540729, 404580128, 598995856, 988919554, 173319771, 291709544, 17168485, 160331188, 334913124, 479454503, 37412625, 191515617, 749321812, 898688507, 105492725, 975966220, 432340186, 503211675, 656103397, 462120779, 354308183, 856150379, 204033492, 558239951, 715098641, 698429715, 473680459, 336076034, 865298126, 535541869, 232853611, 671805227, 821111138, 525685918, 880654769, 891765378, 339717278, 9538500, 916695324, 133796259, 34281928, 522824473, 150349959, 448776947, 642807902, 41545010, 342828273, 195038239, 703424333, 106825429, 612733556, 835021978, 280374469, 943073357, 104756847, 928800976, 819339745, 910524599, 624446102, 482801653, 271051978, 703522352, 723543622, 395220108, 889839568, 302989577, 147018503, 369906801, 588284438, 500936489, 136885855, 494903438, 373306315, 217449828, 232128156, 445548903, 648381747, 761174677, 915270592, 494602219, 65523067, 691615337, 792212013, 828982318, 413989109, 232732162, 229798869, 445723944, 348062667, 156190225, 378754946, 928189698, 336854069, 584248839, 272664571, 957193825, 115615715, 613058239, 205055516, 160335126, 269811780, 4286646, 707414461, 939620350, 703197539, 640370543, 998364538, 676107902, 77792905, 931544164, 106292208, 27558237, 127958458, 140863112, 386268514, 150133055, 307396248, 818819508, 550125942, 890644888, 478670581, 208091207, 665856068, 555064631, 704687817, 103680848, 59090626, 765489627, 982515733, 445331984, 29300289, 408892699, 418970987, 299817934, 214248223, 572570339, 422372248, 418856322, 142265638, 757834554, 496553361, 850243152, 853137692, 488036858, 495935478, 746213252, 226346147, 5036078, 995910568, 352655509, 520407548, 931657206, 576892226, 114675649, 356387701, 674864747, 871152973, 38260503, 638109902, 204979585, 615322532, 945919128, 820521669, 660878873, 356536215, 341601345, 147531361, 507157538, 980475848, 549902559, 460915057, 835839450, 271658136, 958431949, 675708273, 683584293, 440698074, 110537118, 794692513, 133382095, 441144801, 543787475, 121089931, 367771333, 417033243, 129131222, 648512620, 617122042, 224698555, 613171454, 593791520, 405429066, 981650957, 176123233, 888108020, 11747154, 831994101, 38726945, 274792494, 126595067, 96444451, 941155352, 735956007, 925645773, 143243650, 414328386, 351102817, 417159960, 559168579, 174439282, 440278615, 624954583, 914595062, 621761948, 703665155, 692307167, 18638226, 967981897, 816622373, 484898992, 330873096, 821166354, 547088451, 827334586, 776170320, 100995054, 372747417, 737019226, 566514824, 961012849, 49243795, 187893206, 441272304, 302632425, 575293937, 984896209, 924259612, 59400173, 6625532, 757396913, 376695457, 329301189, 427695297, 713577868, 955919778, 249108104, 726134903, 151054645, 162018717, 323968210, 977877280, 991687298, 14062447, 348930103, 549421992, 396415836, 195304052, 887864397, 570342011, 741121874, 103763928, 547199889, 628009460, 524730982, 775110257, 230716993, 624863801, 551654646, 104855343, 394969457, 517231547, 108219231, 467293715, 663417844, 728278227, 965149211, 446691504, 62625069, 413045314, 156243575, 559205074, 36904222, 673203449, 291915668, 41516615, 84174786, 506572028, 486850534, 84003455, 970909801, 966414170, 858185989, 552886469, 67316469, 673587229, 363460920, 220469465, 888067471, 194356662, 362045859, 67991955, 92459565, 694412782, 758269225, 201046872, 82984418, 844607778, 893090476, 890903152, 78004247, 908161318, 175400364, 760247912, 300255729, 577470537, 719978888, 255901036, 463821578, 579022732, 749785765, 863217675, 135330789, 20689235, 779598909, 462521453, 679548327, 319291364, 124201198, 807931446, 86371721, 610121886, 882284781, 684711286, 158257746, 116339318, 304599914, 188181854, 674909414, 589998840, 467696202, 63724913, 73071048, 698357385, 127940322, 334183030, 702822660, 625147150, 203388232, 711150891, 27326532, 746019299, 653406445, 971636658, 833306100, 384247287, 925624076, 872684210, 872786222, 548427049, 745005188, 390576078, 402987758, 785660382, 492640067, 568549322, 825212518, 395274658, 673220246, 895196932, 267292645, 50507419, 347108680, 514162807, 848058347, 726559936, 611874806, 747787056, 631216685, 564516638, 585405763, 940014756, 266179855, 71137557, 437881641, 363598559, 661412742, 938051587, 213621331, 32044183, 842201181, 798277727, 246396143, 216981440, 680648784, 358022604, 651995542, 628251523, 3786279, 846765506, 662001015, 867384213, 236084608, 426586408, 257229878, 828224122, 152212885, 590123055, 98293378, 983748505, 77185945, 575794173, 462410276, 529394666, 363687696, 498263111, 728827739, 395739068, 530772725, 568215136, 15883103, 80023350, 590760388, 388451282, 220194300, 392194157, 249173897, 124439132, 742541024, 258908836, 708669682, 658981138, 905813241, 125125499, 742372726, 774876878, 41532126, 365981807, 926932584, 331774586, 310706969, 112125430, 237777119, 442496950, 601984421, 129217228, 579974968, 197864920, 710014808, 201093326, 874917543, 709099708, 611642716, 414006346, 804188396, 795897201, 469041221, 935144765, 600830504, 210302244, 484608264, 235351964, 373411163, 286926462, 915208047, 762102981, 115420492, 836346669, 320601019, 854989659, 535038138, 53722431, 197766607, 546206617, 351369417, 852676862, 134070724, 729411412, 499773292, 317335480, 972503725, 501580557, 644936609, 891709308, 444618246, 955657881, 549814995, 606107396, 72322419, 309858793, 877904839, 598545659, 410975015, 361030226, 513600740, 973297325, 219911985, 134935500, 893716178, 873059817, 225997111, 898720047, 838927469, 928493203, 797266581, 828179423, 690561868, 809593990, 353335453, 514015143, 906095541, 550081278, 994670424, 973706018, 182680780, 360641631, 65651320, 51643948, 761082286, 710099339, 724635501, 358777838, 772775631, 666035464, 251517449, 746688173, 459031061, 959447549, 172028075, 528881483, 551812806, 253011615, 710341743, 309511415, 264437877, 588774009, 731593910, 872813596, 654868163, 2484944, 11643993, 456616471, 173676569, 445004432, 361374933, 984626499, 619215940, 483828010, 507244892, 268581382, 985159256, 758591432, 467886424, 59882000, 329669009, 79309453, 650897252, 991419397, 447876216, 433659145, 699750246, 669666264, 625044446, 73696315, 543167346, 327310799, 962707349, 946153893, 279264188, 528902732, 80542430, 1757013, 754192230, 571639738, 834970072, 406490704, 225007156, 554830359, 866853140, 899745702, 580327059, 428189888, 528961797, 596963828, 663774124, 218555148, 406891558, 312910051, 298923970, 792288435, 998622743, 220893524, 876466906, 5511199, 771899156, 662340008, 384177154, 378430125, 511986136, 892990281, 294142032, 906669208, 890048737, 294010798, 495669466, 731896862, 650536648, 917285021, 91750519, 809670147, 74407879, 614114411, 315126714, 435502464, 52287083, 146630573, 513957067, 613829910, 415777227, 954254375, 375488563, 166988398, 302051345, 618586901, 447799816, 815343482, 506622670, 748942773, 648858825, 468562302, 339728687, 790287726, 935251696, 353538765, 399875091, 46248566, 666462582, 711262695, 943540952, 730649602, 781835481, 421733962, 876809786, 577187363, 924942364, 337339589, 386166823, 898290094, 142240963, 264693520, 506166681, 895462100, 755969713, 415650899, 254733420, 299354324, 764780562, 558530957, 836142377, 623568220, 803757323, 461560484, 119034797, 85781558, 51842794, 587231514, 420838520, 152485345, 171094014, 679676068, 459247921, 363421359, 924120407, 392565591, 249274564, 838817055, 724872632, 201531450, 404203182, 887550489, 678887529, 9880978, 751567224, 510151911, 386177701, 245025095, 467447609, 925710838, 184129262, 175224623, 952176056, 175665130, 633276200, 300620548, 809374446, 721506057, 193257737, 860277344, 3101656, 176980797, 111111314, 469050897, 579473451, 286447778, 101344961, 260538540, 438735913, 117283945, 814009515, 897954011, 327596840, 163201932, 548304311, 949545805, 989395929, 493661571, 327663129, 143219073, 58372017, 245422824, 285256489, 47598457, 316393457, 787776944, 435014344, 387875551, 522790587, 92801696, 650011436, 783956570, 933114355, 806722073, 868459332, 773011941, 202658545, 129491977, 834199093, 44391863, 721587155, 112060713, 880070695, 962807037, 827034077, 5758136, 193251324, 187874226, 556862594, 662844128, 127103838, 103510455, 623094818, 106762943, 427161429, 121018575, 433611166, 867916563, 429842765, 255449550, 103080059, 887669348, 297222530, 564861225, 442965739, 107413023, 795119435, 744257458, 450852008, 443713794, 164245428, 214941470, 367780254, 361366840, 833274358, 842089250, 477023400, 91960927, 509849941, 409322788, 563731149, 605638165, 626529201, 208395069, 569301200, 64841180, 907068952, 494489354, 218892988, 754460900, 962903396, 928311911, 630140064, 437448801, 870847537, 506281524, 674387339, 332540507, 317587921, 249846132, 83210083, 543745835, 60870673, 72286752, 469563091, 764353733, 659042036, 43851399, 785618254, 635570937, 880149337, 568208600, 328424069, 337921385, 443122372, 752632425, 194351960, 815327117, 496299014, 615901655, 475725662, 744948215, 18551741, 813950829, 309022822, 330038945, 1428555, 865806228, 335499092, 412828235, 307904052, 473656098, 496986963, 652605502, 293856491, 578193333, 720194746, 766263861, 404649834, 735976730, 963997282, 298944212, 204926673, 176695693, 524948691, 965716068, 62993944, 408407445, 624701975, 269549080, 743010659, 287198784, 548138570, 441783728, 88710767, 272493208, 695487391, 841407540, 258823755, 442562425, 379262591, 429575468, 529477315, 445537877, 922039663, 967113450, 527903462, 934971219, 864280868, 695773933, 220974118, 46263403, 209565156, 40704989, 706512939, 565126114, 357428181, 655588109, 81805122, 515261475, 6873397, 238185839, 826204905, 524856180, 32072578, 929438850, 825050245, 769005442, 396219519, 31366595, 264703906, 424045563, 336256090, 23109466, 966881796, 907488210, 594431202, 734623135, 284191685, 584394305, 605122730, 230812255, 488082935, 790458813, 539105593, 210875963, 743912621, 993892457, 9721178, 789125497, 566441073, 202461884, 644642509, 362301289, 62901466, 690583656, 580548957, 4949605, 916226794, 368917574, 134387906, 140819130, 618690435, 800029650, 259009290, 509108534, 483979089, 859459688, 497353834, 595822345, 97001627, 474642531, 333264238, 234453628, 781326782, 610727532, 540848899, 952446146, 596740916, 65661003, 636149265, 985644373, 147239024, 957995102, 952940346, 894861903, 202411017, 163376843, 442203989, 14663936, 914184516, 895995725, 866844878, 839461577, 613683576, 17222795, 259119444, 307748030, 53483142, 19481477, 783575583, 200649392, 175851599, 364637563, 806076208, 868018637, 580106, 692941590, 461925025, 883831478, 764774195, 182871589, 129489810, 152142195, 901705056, 633905579, 847925821, 829822209, 577023860, 454007537, 335011486, 941775091, 898774583, 805094867, 251849764, 284376827, 812875764, 72836270, 778112093, 785911898, 168277662, 48759802, 232304962, 15924706, 900561976, 610846866, 352340221, 868264417, 394570596, 226391919, 549970300, 794556315, 641890486, 519476224, 191911135, 20660975, 828593222, 190249476, 751452402, 903229694, 26766918, 175992545, 552367642, 848721108, 547930086, 731783943, 456223794, 177678593, 626145402, 328204328, 738853598, 944054594, 732621946, 515125977, 893718684, 308340925, 499693369, 251743806, 562160055, 489629623, 329992081, 231490358, 172667214, 339168668, 998406466, 745201532, 357819479, 939282578, 725195537, 588057131, 719151715, 904729216, 634274903, 119775195, 58862299, 845958825, 136600927, 640928629, 966828601, 814854855, 881662042, 600344884, 133671083, 83757160, 528889714, 343526875, 710604939, 852214518, 851128843, 42931589, 101149806, 638069242, 570715540, 237523980, 169531142, 283865329, 533901879, 13367782, 897021352, 787470158, 970216478, 244093245, 258477014, 93456989, 291713185, 695480296, 621072124, 22252099, 614321081, 578361858, 655643666, 101377578, 70683917, 231637278, 679212722, 98691928, 101501870, 86462229, 132182254, 58251049, 662361463, 65954446, 244614707, 977608085, 568339033, 578418015, 599970843, 175403853, 217438666, 557102968, 999393381, 353035988, 13352398, 694139236, 97853896, 594820885, 254592026, 602570186, 818730157, 428149931, 377332670, 877687352, 941705822, 16819036, 584496935, 897416511, 584241346, 80397696 ], 7738 ], "output": 4524118270907 } ], "haskell_template": "makeSubKSumEqual :: [Int] -> Int -> Int\nmakeSubKSumEqual arr k ", "ocaml_template": "let makeSubKSumEqual (arr: int list) (k: int) : int = ", "scala_template": "def makeSubKSumEqual(arr: List[Int],k: Int): Int = { \n \n}", "java_template": "public static int makeSubKSumEqual(List arr, int k) {\n\n}", "python_template": "class Solution(object):\n def makeSubKSumEqual(self, arr, k):\n \"\"\"\n :type arr: List[int]\n :type k: int\n :rtype: int\n \"\"\"\n " }