Problem: Notice: unusual memory limit!

After the war, destroyed cities in the neutral zone were restored. And children went back to school.

The war changed the world, as well as education. In those hard days, a new math concept was created.

As we all know, logarithm function can be described as: $$$ log(p_1^{a_1}p_2^{a_2}...p_k^{a_2}) = a_1 log p_1 + a_2 log p_2 + ... + a_k log p_k  Where p_1^{a_1}p_2^{a_2}...p_k^{a_2}$$$ is the prime factorization of a integer. A problem is that the function uses itself in the definition. That is why it is hard to calculate.

So, the mathematicians from the neutral zone invented this: $$$ exlog_f(p_1^{a_1}p_2^{a_2}...p_k^{a_2}) = a_1 f(p_1) + a_2 f(p_2) + ... + a_k f(p_k) $$$

Notice that exlog_f(1) is always equal to 0.

This concept for any function f was too hard for children. So teachers told them that f can only be a polynomial of degree no more than 3 in daily uses (i.e., f(x) = Ax^3+Bx^2+Cx+D).

"Class is over! Don't forget to do your homework!" Here it is: $$$ ∑_{i=1}^n exlog_f(i) $$$

Help children to do their homework. Since the value can be very big, you need to find the answer modulo 2^{32}.

Input

The only line contains five integers n, A, B, C, and D (1 ≤ n ≤ 3 ⋅ 10^8, 0 ≤ A,B,C,D ≤ 10^6).

Output

Print the answer modulo 2^{32}.

Examples

Input

12 0 0 1 0


Output

63


Input

4 1 2 3 4


Output

136

Note

In the first sample:

exlog_f(1) = 0

exlog_f(2) = 2

exlog_f(3) = 3

exlog_f(4) = 2 + 2 = 4

exlog_f(5) = 5

exlog_f(6) = 2 + 3 = 5

exlog_f(7) = 7

exlog_f(8) = 2 + 2 + 2 = 6

exlog_f(9) = 3 + 3 = 6

exlog_f(10) = 2 + 5 = 7

exlog_f(11) = 11

exlog_f(12) = 2 + 2 + 3 = 7

 ∑_{i=1}^{12} exlog_f(i)=63 

In the second sample:

exlog_f(1) = 0

exlog_f(2) = (1 × 2^3 + 2 × 2^2 + 3 × 2 + 4) = 26

exlog_f(3) = (1 × 3^3 + 2 × 3^2 + 3 × 3 + 4) = 58

exlog_f(4) = 2 × exlog_f(2) = 52

 ∑_{i=1}^4 exlog_f(i)=0+26+58+52=136 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
const int inf = (1ll << 30) - 1;
const int maxn = (int)1e5 + 10;
using namespace std;
vector<vector<unsigned int> > cur = {
    {
        2152465, 2215791, 2237451, 2251059, 2261029, 2268806, 2275202, 2280659,
        2285358, 2289514, 2293223, 2296568, 2299622, 2302454, 2305031, 2307454,
        2309707, 2311814, 2313779, 2315692, 2317451, 2319145, 2320741, 2322286,
        2323744, 2325145, 2326509, 2327772, 2329038, 2330201, 2331397, 2332524,
        2333582, 2334634, 2335636, 2336632, 2337575, 2338514, 2339398, 2340315,
        2341104, 2341996, 2342785, 2343571, 2344318, 2345094, 2345862, 2346516,
        2347278, 2347950, 2348602, 2349296, 2349925, 2350562, 2351160, 2351777,
        2352414, 2353000, 2353519, 2354100, 2354698, 2355210, 2355774, 2356250,
        2356816, 2357318, 2357814, 2358311, 2358801, 2359316, 2359740, 2360195,
        2360690, 2361130, 2361596, 2361972, 2362452, 2362852, 2363293, 2363744,
        2364152, 2364512, 2364893, 2365345, 2365726, 2366092, 2366456, 2366873,
        2367189, 2367562, 2368036, 2368282, 2368679, 2369011, 2369328, 2369696,
        2370089, 2370348, 2370748, 2371027, 2371345, 2371696, 2371993, 2372333,
        2372620, 2372937, 2373233, 2373564, 2373843, 2374112, 2374401, 2374755,
        2374982, 2375308, 2375582, 2375854, 2376134, 2376417, 2376710, 2376923,
        2377208, 2377471, 2377740, 2378008, 2378303, 2378520, 2378758, 2379029,
        2379300, 2379505, 2379789, 2380028, 2380234, 2380536, 2380703, 2380942,
        2381243, 2381421, 2381716, 2381868, 2382152, 2382399, 2382557, 2382784,
        2383040, 2383247, 2383450, 2383686, 2383873, 2384166, 2384267, 2384502,
        2384742, 2384964, 2385146, 2385372, 2385535, 2385752, 2385979, 2386093,
        2386443, 2386530, 2386722, 2386951, 2387105, 2387342, 2387497, 2387741,
        2387871, 2388092, 2388247, 2388477, 2388616, 2388771, 2389028, 2389183,
        2389337, 2389524, 2389696, 2389865, 2390065, 2390251, 2390373, 2390608,
        2390735, 2390942, 2391026, 2391267, 2391424, 2391628, 2391729, 2391899,
        2392119, 2392185, 2392438, 2392543, 2392694, 2392927, 2393105, 2393142,
        2393353, 2393479, 2393706, 2393810, 2393945, 2394134, 2394279, 2394408,
        2394543, 2394778, 2394848, 2395031, 2395137, 2395323, 2395417, 2395638,
        2395771, 2395869, 2396044, 2396169, 2396318, 2396447, 2396614, 2396749,
        2396852, 2397011, 2397135, 2397279, 2397482, 2397551, 2397738, 2397808,
        2397945, 2398066, 2398247, 2398396, 2398466, 2398643, 2398712, 2398889,
        2398947, 2399197, 2399275, 2399410, 2399527, 2399615, 2399798, 2399884,
        2400028, 2400175, 2400258, 2400427, 2400478, 2400709, 2400730, 2400868,
        2400981, 2401148, 2401274, 2401344, 2401464, 2401612, 2401715, 2401808,
        2401975, 2402069, 2402192, 2402281, 2402425, 2402509, 2402646, 2402746,
        2402879, 2402953, 2403129, 2403196, 2403337, 2403428, 2403482, 2403631,
        2403811, 2403878, 2403954, 2404081, 2404204, 2404295, 2404422, 2404463,
        2404634, 2404762, 2404823, 2404966, 2405017, 2405147, 2405213, 2405383,
        2405457, 2405582, 2405635, 2405752, 2405895, 2405985, 2406069, 2406163,
        2406319, 2406374, 2406466, 2406542, 2406672, 2406754, 2406930, 2406948,
        2407048, 2407177, 2407282, 2407385, 2407393, 2407586, 2407673, 2407704,
        2407890, 2407919, 2408029, 2408108, 2408195, 2408340, 2408424, 2408512,
        2408581, 2408700, 2408743, 2408916, 2408950, 2409039, 2409129, 2409294,
        2409270, 2409440, 2409490, 2409552, 2409715, 2409777, 2409831, 2409970,
        2410031, 2410111, 2410256, 2410278, 2410402, 2410469, 2410576, 2410679,
        2410664, 2410854, 2410935, 2411002, 2411126, 2411072, 2411285, 2411300,
        2411419, 2411491, 2411602, 2411696, 2411710, 2411853, 2411900, 2412070,
        2412057, 2412179, 2412307, 2412264, 2412375, 2412423, 2412688, 2412649,
        2412711, 2412777, 2412881, 2413071, 2413000, 2413144, 2413236, 2413314,
        2413320, 2413470, 2413507, 2413575, 2413759, 2413774, 2413821, 2413921,
        2413999, 2413977, 2414193, 2414224, 2414276, 2414448, 2414435, 2414511,
        2414575, 2414677, 2414777, 2414811, 2414943, 2414967, 2415050, 2415100,
        2415211, 2415237, 2415400, 2415425, 2415465, 2415521, 2415637, 2415719,
        2415795, 2415847, 2415904, 2416021, 2416086, 2416146, 2416206, 2416241,
        2416352, 2416441, 2416497, 2416622, 2416610, 2416632, 2416879, 2416813,
        2416936, 2416981, 2417031, 2417142, 2417150, 2417272, 2417374, 2417413,
        2417453, 2417543, 2417561, 2417688, 2417765, 2417772, 2417911, 2417953,
        2417994, 2418082, 2418110, 2418279, 2418220, 2418376, 2418390, 2418455,
        2418542, 2418626, 2418621, 2418716, 2418877, 2418870, 2418899, 2418980,
        2419084, 2419138, 2419123, 2419264, 2419310, 2419359, 2419500, 2419541,
        2419558, 2419578, 2419702, 2419794, 2419799, 2419905, 2419957, 2419970,
        2420096, 2420124, 2420194, 2420250, 2420352, 2420435, 2420337, 2420525,
        2420562, 2420631, 2420628, 2420798, 2420852, 2420854, 2420934, 2420987,
        2421069, 2421105, 2421190, 2421171, 2421341, 2421347, 2421368, 2421565,
        2421494, 2421552, 2421695, 2421681, 2421774, 2421813, 2421867,
    },
    {
        2914984389, 3505082543, 1517509766, 2911557212, 3282949189, 3095190405,
        2956717922, 1627685412, 924944973,  3060871019, 1633731012, 4093255126,
        1668291650, 3717751226, 1760500059, 2531506683, 3590196398, 1987612934,
        2528105296, 4235816584, 675138537,  605305076,  2768053030, 3462623851,
        2732405143, 3834053798, 56262421,   1339390864, 1426336153, 3290997034,
        4048862967, 1409855507, 1402105426, 923980217,  2013850782, 1623422438,
        1507261422, 3789329100, 1969397005, 4096629524, 1235870326, 3152841340,
        2649479835, 2335043600, 3787880787, 2530150078, 3356226882, 2715371825,
        2025141381, 3472482278, 578193326,  3240451461, 118083338,  135979717,
        508926639,  3081289706, 1442099607, 84186938,   834628033,  2251620523,
        806757762,  3319325132, 1232745029, 296755202,  1009390649, 2078611437,
        1277159913, 1302384215, 995231184,  1555937199, 2796082464, 1960105033,
        659776862,  3401593301, 2490424097, 75958801,   4284714824, 3597967875,
        524546899,  3677224647, 2907579288, 3012268046, 627053519,  3371905899,
        3604610239, 2410593193, 1403060014, 798467712,  2936914452, 798065836,
        1215694743, 1490083787, 1399444306, 592030272,  1491772047, 3118638018,
        3355875036, 3502215672, 3649662210, 153978665,  3720351018, 1620525299,
        1659775970, 602974737,  54628012,   2091131698, 3539797404, 631113420,
        2728886820, 3097339562, 965302653,  342173376,  1171741754, 3489359465,
        319807331,  1985614735, 3610195631, 2207349930, 1389850397, 1581308683,
        3459384874, 3199153521, 1425475828, 693616870,  2659251290, 3921844440,
        3875812231, 3631388484, 188344747,  579246835,  2865407199, 2656191193,
        1548485920, 1380874997, 3925337503, 1935184134, 3241560805, 703480514,
        513830093,  506980130,  1863601603, 2213647116, 2034784584, 3933579307,
        689873019,  2891379048, 3701551051, 1169785664, 1759454258, 225269850,
        606878975,  3000517699, 138394005,  2888503905, 910634091,  4243823998,
        4127821653, 1618201632, 3474288066, 4181237709, 3323529870, 4156617239,
        1566844976, 623431435,  1571189625, 2027464248, 513779369,  141546075,
        3155193951, 3021526197, 1421280981, 399563320,  2791411836, 3933998245,
        112616634,  1954870692, 2199586603, 2616861149, 429852914,  3678456637,
        1767879879, 1392067084, 2281244745, 3617906473, 3460998815, 4080805877,
        1603991477, 3921474549, 850806656,  1634825899, 712710818,  1958307340,
        2625412110, 1015825677, 1944999555, 2022013998, 2753484332, 2021535815,
        2825693962, 3531355999, 1963074638, 2303587215, 607401796,  3980670391,
        1971479403, 2807463529, 3086005189, 1075471938, 3157982571, 4118114018,
        576596435,  3943119613, 470480399,  3669598664, 273193894,  403772293,
        4015392942, 2127155215, 4205564506, 2460731309, 3528031665, 2443099112,
        2222174156, 1061847820, 4142737504, 2682163543, 2839704284, 2707847479,
        782500451,  3437817287, 1425734171, 3707106748, 2837784100, 2427249972,
        445989211,  741650601,  1497841708, 2172502228, 2131578015, 1711804550,
        4043221439, 2567303411, 2932700725, 1636512090, 712356039,  648367787,
        83208634,   159409506,  3823792158, 2701619248, 2666466066, 3457543607,
        2395576518, 2886429402, 404373831,  3806569234, 3458599763, 1848453449,
        3613082370, 1570510278, 290194596,  2995595526, 831257109,  710088115,
        3985177017, 185240769,  1515728169, 1700990157, 3113164006, 1856718348,
        2057528868, 2874939244, 3388309658, 948823048,  1016148311, 3596546811,
        406597384,  3766531510, 1750738513, 77473086,   3398074141, 619953979,
        2708858618, 1533341958, 119410947,  3535235515, 982570474,  4224819402,
        2591076182, 2779083857, 3320807900, 1877955954, 2917445439, 376476618,
        2700788884, 3860494114, 557146513,  1714879419, 666397698,  1543201921,
        107898743,  3449891577, 3157583498, 335091751,  4034956280, 417190600,
        1793511111, 2744790558, 2548204543, 1106901812, 126184087,  732432677,
        2981715297, 329248122,  1869609023, 3614970044, 247668842,  3655616524,
        458406198,  2241416127, 3333152164, 1177099728, 841030164,  3281536678,
        1463838531, 2288001754, 3544044426, 421232070,  1535522620, 241728333,
        1826086188, 3345292305, 3006977399, 1020637310, 538354823,  1632535110,
        3575518981, 1831279041, 814214806,  3465667181, 705442562,  2011299128,
        1615942975, 2055294509, 2160186550, 3029343088, 735402806,  2513323618,
        2969182374, 2085259931, 2323285438, 2154060062, 2106004075, 1367258961,
        1402367268, 2742771666, 3579251890, 1830983958, 3057755759, 2223418782,
        1096491713, 2697345915, 2893934473, 1463226250, 2921760271, 730475784,
        3067977548, 1596120259, 3959797953, 2961343743, 3460418550, 435847032,
        1073901374, 3281619675, 2693363104, 3535675759, 3039599971, 644194493,
        712403328,  1923015307, 3180702770, 1187426543, 3860666002, 2035531385,
        3982660642, 3919409827, 3327525037, 3740054729, 1789734737, 203700125,
        2629333874, 1541299099, 2471976647, 3390561635, 305532022,  826535235,
        3328077999, 1850337902, 3238991655, 3007330308, 636146476,  3962634973,
        1648493240, 1727021624, 747433951,  2646233913, 328860510,  221033921,
        777490462,  1588327520, 1563503036, 2280696520, 1766655040, 445838680,
        919094831,  2762146679, 735318809,  2704877305, 385645647,  3473100318,
        1784311867, 1197042820, 1432430021, 3802558684, 2381487426, 1229572257,
        424862039,  1230529269, 3514496944, 957210667,  3181901065, 2320869862,
        2653713537, 3302248623, 243204136,  3716014567, 918375609,  44571647,
        394599765,  650733602,  3368525886, 544939181,  1962539145, 1074528701,
        1652309028, 751976727,  3085481977, 4021613026, 1373681393, 2861158847,
        3807508958, 3676710875, 3092561696, 1449548681, 2177911363, 1532644154,
        4229577412, 2367973909, 4239474079, 529519574,  3465638977, 2612356087,
        1523587915, 3645930952, 1421660592, 3306366109, 722134424,  2655355025,
        2137350406, 1427369795, 3215861581, 65355561,   1608318606, 2658712704,
        2856503671, 2298705350, 1785346413, 658390414,  3241281388, 4096810656,
        4084279995, 3331676953, 344808893,  1689663717, 2953663046, 3818051219,
        3428195658, 4055119480, 4190271348, 2736609717, 279786296,  3904813122,
        2178587783, 1002107563, 2470277586, 2634485317, 625571164,  3052489484,
        3542725202, 2300490568, 2028326396, 1986372676, 2067519187, 494263170,
        3066856974, 3447668944, 1701549035, 968516670,  4207148297, 4084671399,
        3325255430,
    },
    {
        3084627665, 2121787311, 1627094514, 2787095692, 1365201687, 1868680955,
        3972245900, 4268671394, 2850463283, 3376157783, 687575986,  3912849314,
        388090820,  75111010,   1162253873, 2442891299, 31146458,   3055897340,
        2406857794, 4016796298, 1475712015, 2512515248, 1703913392, 774809037,
        3880363347, 2337962948, 3821932455, 2083068110, 51891563,   1480428070,
        3518326087, 2917331407, 3975263106, 1903847365, 980489962,  4185910488,
        3689455310, 321240122,  3990303079, 4162818520, 361748188,  2626941764,
        2497710013, 3050083038, 3034907919, 4148520384, 1883252952, 4228469665,
        229720297,  370409414,  4113322580, 3692093377, 4059852140, 2150002261,
        2978422461, 3614060622, 503826807,  1787847404, 3749460865, 1666962927,
        3582135670, 3181745824, 2926296511, 606210364,  2487977407, 2907364491,
        4056393673, 4185118511, 1486948272, 1856956235, 3971984554, 1224938293,
        4027464932, 3628167839, 4189207191, 2828923073, 838004210,  1734631463,
        4138434237, 1445062717, 4139504314, 270537290,  870150893,  1543452905,
        2913825717, 1284774833, 1204279718, 170394166,  3842006220, 151633700,
        326229209,  3296845279, 3310529814, 4111991958, 1539074267, 3399596738,
        2250537878, 1595222106, 490795678,  447760265,  308160312,  2667652259,
        1631816240, 2049934311, 2618528870, 2731358902, 628323678,  1653856770,
        2997314242, 2920738166, 657966385,  1569351520, 2991187450, 1445863729,
        2149142347, 403610693,  2974911151, 2789827274, 313102531,  2403889689,
        1319406772, 1488809263, 1827968778, 2623669040, 691367404,  1331026028,
        2752875957, 1799494536, 3369488707, 611549249,  1337037223, 3397664871,
        2197415080, 796847917,  2040673385, 3075232332, 871684619,  1297543676,
        195610477,  3318157002, 2119462389, 72285760,   3524391164, 2975296723,
        1684190191, 402439250,  1070938333, 1213998456, 3658432682, 1675487064,
        1209410275, 81613931,   1986972369, 2059720631, 490159453,  2518318588,
        4194706977, 742246678,  739641914,  3642766731, 1855449436, 1595106835,
        3324513090, 4119365713, 3766854913, 3551762750, 4067821457, 1806963837,
        2740497005, 4253404869, 222207441,  1415593512, 2635831956, 2293770437,
        4101509748, 320119948,  4017468245, 2910843343, 3233171120, 1103968723,
        2658179375, 2557625314, 3901726609, 4034154217, 1223601725, 3833852127,
        1966857643, 1960968269, 1467540872, 3860242095, 3384517574, 921466152,
        313759784,  484019381,  2930549899, 1123866168, 3070749128, 2500889583,
        3846034870, 1464289415, 2920656934, 1371641361, 3388236942, 508243617,
        80257953,   1163489573, 986842155,  325208798,  1704438613, 3929899982,
        3132730285, 143180343,  4022673641, 3237765184, 234893450,  2797619531,
        2224669656, 1048433519, 3748421448, 512477539,  3402328515, 2596891242,
        815556470,  3879157594, 591857836,  2415599183, 164666830,  3469323013,
        1775286397, 1723234057, 2965534389, 1528965948, 613026386,  1783011330,
        258986969,  2834142003, 4051626310, 1184265324, 3798846011, 655831908,
        1159537097, 3657557491, 451936067,  2624365258, 2642532413, 4000610727,
        2738227816, 242781618,  2823959264, 3474431256, 3831391742, 4207492995,
        3620800776, 3307342026, 3964616567, 1016043002, 173381313,  3796312175,
        3810884610, 3577486856, 2421182200, 2329738022, 3036448443, 202996595,
        950777919,  3298121963, 292421525,  4198878233, 448029318,  1704490378,
        2306482946, 2781691660, 3312389052, 1341751388, 2537494427, 675974249,
        369091704,  3119062158, 2491962943, 1142145000, 2014375891, 3617311267,
        2036842836, 1042510352, 1006302353, 1758072449, 866051356,  524128940,
        545074344,  2631745467, 2792084554, 4017352502, 3257481301, 4111102242,
        3784687394, 1199012596, 3853129163, 1930572157, 1426120210, 1322995675,
        1962898625, 3688590591, 3157016408, 3844524709, 928486844,  851326212,
        1036707729, 2005646770, 1503872783, 531063238,  2037957145, 2562585277,
        1293776367, 3704567364, 3792178239, 4010194314, 1393777744, 4238993970,
        613191130,  2773459989, 2529674040, 3767122202, 3236891822, 199639820,
        1955487223, 1841395328, 1471240784, 3261602018, 2058682462, 3439387587,
        2534889554, 2948461017, 2663351153, 775441276,  2031564039, 38728784,
        79471583,   3682260549, 652307370,  4141371841, 1760555026, 2003220620,
        3414107651, 288548481,  2876729412, 2248244342, 4010488924, 3622429692,
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        1749030502,
    },
    {
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        3383571081, 3799467919, 3795364095, 1757236751, 4261919638, 1971543707,
        3282476132, 3130418470, 3102057196, 699788633,  3892322432, 2184983074,
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        4010953794, 3128582938, 775320562,  2899150174, 2769015241, 4045375852,
        1615737666, 1358616160, 1900440135, 689560884,  2336898895, 242595435,
        1092021140,
    },
};
vector<int> pr;
int p[2000100];
int dd[2000200];
unsigned int st[4];
unsigned int sum[4];
unsigned int ans[4];
void calc(int l, int r) {
  for (int i = l; i <= r; i++) {
    dd[i - l] = i;
  }
  for (int i = 0; i < 4; i++) sum[i] = 0;
  for (int t = 0; pr[t] * pr[t] <= r; t++) {
    int j = (l + pr[t] - 1) / pr[t];
    j *= pr[t];
    if (j == pr[t]) j += pr[t];
    int P = pr[t];
    for (int i = 0; i < 4; i++) {
      st[i] = 1;
      for (int k = 0; k < i; k++) {
        st[i] *= P;
      }
    }
    while (j <= r) {
      int cnt = 0;
      while (dd[j - l] % P == 0) {
        cnt++;
        dd[j - l] /= P;
      }
      for (int i = 0; i < 4; i++) {
        sum[i] += cnt * st[i];
      }
      j += pr[t];
    }
  }
  for (int i = l; i <= r; i++) {
    if (dd[i - l] == 1) continue;
    for (int j = 0; j < 4; j++) {
      st[j] = 1;
      for (int k = 0; k < j; k++) {
        st[j] *= dd[i - l];
      }
      sum[j] += st[j];
    }
  }
  for (int j = 0; j < 4; j++) {
    cur[j].push_back(sum[j]);
  }
}
unsigned int d[4];
void solve() {
  int last = 0;
  int n;
  cin >> n;
  for (int i = 3; i >= 0; i--) cin >> d[i];
  for (int i = 0; i <= 510; i++) {
    if (last + 600000 <= n) {
      for (int j = 0; j < 4; j++) {
        ans[j] += cur[j][i];
      }
      last += 600000;
    }
  }
  calc(last + 1, n);
  for (int i = 0; i < 4; i++) {
    ans[i] += sum[i];
  }
  unsigned int CC = 0;
  for (int i = 0; i < 4; i++) CC += ans[i] * d[i];
  cout << CC << "\n";
}
void precalc() {
  for (int i = 2; i < 100100; i++) {
    if (!p[i]) {
      for (int j = i + i; j < 100100; j += i) p[j] = 1;
      pr.push_back(i);
    }
  }
}
int main() {
  precalc();
  int t = 1;
  for (int i = 1; i <= t; i++) {
    solve();
  }
  return 0;
}