Problem:


Score : 600 points

Problem Statement

Let us define the oddness of a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n} as \sum_{i = 1}^n |i - p_i|.

Find the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Constraints

All values in input are integers.

1 \leq n \leq 50

0 \leq k \leq n^2

Input

Input is given from Standard Input in the following format:

n k

Output

Print the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Sample Input 1

3 2

Sample Output 1

2

There are six permutations of {1,\ 2,\ 3}. Among them, two have oddness of 2:  {2,\ 1,\ 3} and {1,\ 3,\ 2}.

Sample Input 2

39 14

Sample Output 2

74764168



Sample input:
3 2


Sample output:
2

Submission status: Accepted

Solution code:
a = [[], [1], [1, 1], [1, 2, 3], [1, 3, 7, 9, 4], [1, 4, 12, 24, 35, 24, 20], [1, 5, 18, 46, 93, 137, 148, 136, 100, 36], [1, 6, 25, 76, 187, 366, 591, 744, 884, 832, 716, 360, 252], [1, 7, 33, 115, 327, 765, 1523, 2553, 3696, 4852, 5708, 5892, 5452, 4212, 2844, 1764, 576], [1, 8, 42, 164, 524, 1400, 3226, 6436, 11323, 17640, 25472, 33280, 40520, 44240, 45512, 40608, 35496, 25632, 18108, 8064, 5184], [1, 9, 52, 224, 790, 2350, 6072, 13768, 27821, 50461, 83420, 127840, 182256, 242272, 301648, 350864, 382576, 389232, 373536, 332640, 273060, 208548, 136512, 81792, 46656, 14400], [1, 10, 63, 296, 1138, 3708, 10538, 26480, 59673, 121626, 226787, 390144, 628744, 949472, 1355952, 1826464, 2341600, 2833632, 3282464, 3584160, 3765600, 3719664, 3531924, 3093336, 2642364, 2010240, 1508544, 963072, 621504, 259200, 158400], [1, 11, 75, 381, 1582, 5582, 17222, 47194, 116457, 261163, 537459, 1022981, 1817652, 3040352, 4810720, 7230928, 10360160, 14178912, 18577792, 23327872, 28132048, 32571504, 36310464, 38903904, 40028724, 39552156, 37457388, 33941412, 29314944, 24179904, 18835776, 13777344, 9452736, 5716800, 3211200, 1742400, 518400], [1, 12, 88, 480, 2137, 8096, 26860, 79376, 211811, 515308, 1153268, 2391936, 4633331, 8438664, 14557048, 23874176, 37407760, 56117824, 80906752, 112162240, 150052400, 193572736, 241706624, 291576384, 341323776, 386160048, 424359540, 450394992, 464545584, 461528208, 446428476, 413557632, 373573440, 321120000, 268449408, 210332160, 162330624, 112550400, 77788800, 46540800, 28497600, 11404800, 6739200], [1, 13, 102, 594, 2819, 11391, 40344, 127508, 364587, 952559, 2293742, 5126898, 10710633, 21042989, 39117852, 69175664, 116857024, 189256368, 294745440, 442503456, 641759376, 900689616, 225195321, 617201401, 74227554, 586823330, 140227131, 711888699, 274217080, 795069832, 242715461, 585116357, 796764497, 861974465, 769155485, 525176285, 146566301, 650715556, 73773796, 455145195, 828946802, 226153586, 685663993, 216281593, 828705600, 536385600, 309484800, 166924800, 87609600, 25401600], [1, 14, 117, 724, 3645, 15626, 58741, 197280, 600215, 1671266, 4295107, 10259436, 22922995, 48184950, 95816051, 181136304, 327071752, 566117888, 942525072, 513281017, 349163810, 532145419, 154557773, 309226767, 88509354, 563257605, 789064441, 766807654, 474675580, 795689314, 599134613, 627066840, 658988947, 307608398, 337632800, 295701193, 44870369, 150212311, 705302359, 336038622, 452522163, 797367958, 62674553, 57993322, 777736994, 845298906, 452367755, 90655804, 810196653, 976943895, 564798323, 582118351, 994783972, 869862386, 697759993, 660441600, 381024000], [1, 15, 133, 871, 4633, 20979, 83313, 295803, 952299, 2809009, 7656027, 19414457, 46086247, 102967901, 217634463, 437195525, 838372452, 540635289, 722168530, 638311860, 640827391, 196046908, 898688562, 478199884, 793020369, 808862771, 562236075, 94791602, 385333320, 237794527, 197694759, 398043392, 504456766, 579736664, 78137089, 793367253, 961295251, 280517488, 179779783, 947563092, 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771071664, 636940611], [1, 17, 168, 1220, 7172, 35852, 157132, 616084, 2192506, 7159090, 21631676, 60902460, 160707468, 399489140, 939796228, 101060910, 481320121, 151453550, 952463061, 931694473, 957528293, 554162053, 990142499, 644946993, 651797781, 791594351, 556120466, 271969917, 107619398, 710253075, 280526462, 615698879, 99748930, 775178221, 257586036, 645364809, 806795120, 340635512, 801741075, 790520661, 68328385, 331513794, 351728404, 931812262, 91105169, 176869824, 445724501, 370449983, 359815736, 918724628, 869062973, 659791249, 657727222, 395793733, 32692523, 78858425, 151369211, 628504487, 842750087, 152091477, 889718876, 908002421, 944598446, 656459208, 712920845, 47550280, 92244967, 110652620, 951703750, 217822851, 901098263, 655149074, 861896271, 859184013, 992613245, 768042116, 807916959, 335381553, 909568095, 153171069, 827990317, 681893483], [1, 18, 187, 1424, 8764, 45832, 210072, 861400, 3206786, 10957868, 34666130, 102239488, 282743580, 736889224, 817936097, 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450172023, 562637973, 109112418, 545193132, 195217263, 976304283], [1, 21, 250, 2166, 15097, 89189, 461164, 2132144, 8950214, 34503182, 123236828, 410729140, 284813823, 790835929, 594736274, 153822108, 374418504, 157537842, 147846917, 133568389, 483576696, 508616649, 656867821, 84463125, 640047601, 955370715, 182167616, 49108700, 229345632, 795610484, 502493987, 857101031, 142485158, 996679960, 742503997, 723858587, 317526153, 365342533, 250775491, 442738912, 408346120, 881242865, 135363327, 231979623, 347291745, 824934645, 995772018, 164592917, 354883487, 450805745, 963969802, 171006181, 92161176, 169883419, 961669090, 26844445, 393784092, 571606470, 464707158, 34144520, 652396373, 745405475, 202923498, 135935314, 703695236, 776259115, 48310283, 874186699, 219390686, 510394758, 751965065, 418424556, 8781061, 736058807, 674014147, 674780706, 590530540, 4352977, 803825827, 167292329, 541083402, 260679638, 665083995, 939990721, 816665296, 886017767, 669822229, 694816125, 643235536, 937314556, 115942268, 261159535, 687177905, 12245758, 694615643, 977706180, 217949106, 118952653, 898868241, 856650616, 42954342, 330321980, 535121720, 982503521, 719423135, 714354007, 18745970, 333448882, 302037622, 935654015, 778423936, 317991952, 284756555, 504736970, 155871365, 118263505, 797065125, 640838446, 258037348, 34344762, 502389803, 911086550], [1, 22, 273, 2460, 17807, 109158, 585339, 2805752, 12209406, 48792492, 180680070, 624410736, 25734764, 199973794, 977710523, 571365953, 412869707, 328237414, 214863466, 633048751, 257394955, 317735309, 673309005, 193600985, 704135816, 514918834, 650479735, 33606857, 490034801, 698396427, 67986999, 220797055, 218864611, 931163713, 940790978, 675674698, 85542051, 543018292, 61247584, 910803604, 831296179, 923943160, 89478028, 104500393, 161998091, 254912705, 539249258, 547749719, 357852173, 690014841, 206926249, 893887199, 747112232, 382059625, 148865046, 301618706, 260333115, 442306036, 247371284, 782005651, 233300621, 920894203, 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n, k = map(int, input().split())
if k % 2 == 1:
  print(0)
else:
  print(a[n][k // 2] if k // 2 < len(a[n]) else 0)