CP-Algorithms Library

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:heavy_check_mark: cp-algo/number_theory/primality_bases.hpp

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Code

#ifndef CP_ALGO_NUMBER_THEORY_PRIMALITY_BASES_HPP
#define CP_ALGO_NUMBER_THEORY_PRIMALITY_BASES_HPP
#include <cstdint>

constexpr uint16_t base_table1[] = 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constexpr uint16_t base_table2[] = {15,135,13,60,15,117,65,29};
#endif
#line 1 "cp-algo/number_theory/primality_bases.hpp"


#include <cstdint>

constexpr uint16_t base_table1[] = 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5645,40577,7163,9925,279,2009,407,2693,9102,5273,10107,1422,115,12049,119,11801,341,9129,8514,1614,1043,2349,366,903,3702,3609,2705,2328,1414,2293,2727,2113,3127,19308,2329,1023,10175,925,8544,4115,2194,1359,9252,138,817,7897,918,323,8530,2829,1751,5581,25658,1517,445,2397,163,241,14777,171,2782,3930,39974,1277,318,12735,12044,4934,2323,6697,698,6036,4694,5269,587,8445,2218,4630,1954,3981,8067,8187,4522,1041,10402,37117,1182,1543,11430,9242,834,3537,11522,33957,4995,491,2279,4122,637,8722,3317,6163,1349,455,843,995,681,42,1783,959,3095,1469,28598,9902,5909,1163,8572,1722,566,9001,2725,3226,7830,2051,1354,1151,8228,1735,19522,6446,178,1223,5197,51,1074,893,381,5286,8925,27691,681,1239,9390,1159,7178,598,10187,10721,12067,891,9191,783,2377,2889,137,5050,2581,394,5383,1110,6173,9401,9059,1275,10477,2108,2211,510,8195,4039,13323,4398,4829,1828,5146,5553,9105,209,9466,201,941,8550,3713,2761,12454,3582,3270,15090,3446,8658,7411,2694,419,9631,8598,5405,911,2447,2630,5381,2755,4395,3385,8224,3201,10432,2437,4091,8499,2335,777,20517,643,2641,5426,2302,1266,386,1115,2494,165,2802,4617,695,1625,922,701,1757,8954,510,2072,4207,1966,7815,914,26081,2099,917,4625,6695,7186,6210,117,5026,1271,5254,1715,4462,5370,8965,1593,1116,2115,673,1307,62,3722,4870,1913,253,8632,550,876,205,943,20717,1486,1779,3334,3878,1266,499,7989,15711,7187,4325,8247,658,5398,2698,3269,1706,5141,30431,1649,1094,13996,3847,4390,3694,15908,17573,20205,2870,14429,2837,383,2124,2607,5042,5186,1502,2006,8628,2963,2653,442,1579,1353,3183,893,3977,8346,11853,714,417,466,762,967,495,275,10096,3197,3982,1911,2821,21737,2510,9330,1671,6513,8563,6061,2022,2153,4302,8330,1195,5967,10342,543,766,519,2371,511,417,1446,14731,389,2687,431,319,117,561,638,2563,4293,1303,1289,5850,467,2709,1828,154,24097,419,178,2094,587,653,9920,6697,3799,3747,323,1437,2619,1630,1379,924,3523,8811,1134,1299,991,1659,11179,3105,34590,8896,362,2595,1254,1393,379,6677,571,155,379,4726,501,1186,1025,447,10505,975,754,1386,2117,20220,5143,7843,2795,3011,713,389,1101,767,1116,447,1307,2059,4058,3598,610,2921,2353,166,4433,199,1477,4025,9850,301,5006,14630,693,10889,12815,151,2526,4595,1159,4087,1795,7707,30981,10557,10197,5281,6233,7310,1823,2131,4621,2283,3510,1310,1449,4606,2231,326,2062,9019,10527,3577,6812,4229,323,669,2413,3601,4041,2151,8904,10171,5683,1349,2763,7486,1189,771,1139,3803,12249,431,13170,1091,37694,3891,9607,2221,5779,7870,11678,998,969,2133,8933,14255,11624,2465,15753,2838,4187,3367,1286,5679,2186,715,2143,998,342,751,12177,6259,1302,571,8110,7923,12334,8286,1113,1222,8769,371,876,7991,2706,4717,2705,541,394,1883,7507,643,835,357,929,8694,8122,1973,2503,357,130,937,8681,975,91,123,13290,4583,2078,3270,2682,8936,8249,1775,8519,1439,6295,4151,10817,8942,3263,18933,1293,183,4601,9155,5481,481,39192,358,16721,419,2142,4135,16945,10998,6490,1175,8490,846,6409,12493,23326,2899,415,36491,13051,866,161,22,2150,849,4670,3849,489,833,549,5675,14716,8764,1685,161,4785,30101,1067,635,126,1387,5495,985,1942,166,453,2101,8602,1389,6802,193,4307,1302,6233,3138,1199,3111,10278,2852,8693,13152,10313,10246,66,554,1941,8070,5726,9988,1997,693,2405,549,350,11750,5111,6237,5873,4531,1289,1709,2238,831,202,2893,1726,47,23812,1553,1053,2927,635,5906,4088,1084,7304,7714,1363,3417,2427,3119,7934,4549,2271,1330,1483,650,223,649,7917,3966,7318,411,8992,2455,1135,4953,919,2130,610,1844,137,403,3757,9114,1366,646,8467,7277,7171,2442,93,857,895,2134,38617,11100,12622,67,3883,5807,743,5005,731,10084,69,46255,865,6671,1071,3798,1855,1426,3361,571,2697,161,286,497,2207,2038,2015,12745,10440,313,1443,8753,11702,267,7226,27666,398,1309,170,10128,1398,1839,8276,3414,55,3107,3154,2405,1814,8903,4845,1417,1667,2427,549,818,475,1499,1169,767,537,1697,2386,2075,3673,1871,9379,1938,3229,1237,222,209,5473,5589,4397,9112,5233,12487,1835,149,7860,5289,10055,4185,53,1394,2265,2610,6079,8316,13263,3475,9011,22,159,6061,82,2361,349,25061,10631,2375,10013,9529,10695,17510,231,9334,1798,1263,4233,1565,23669,930,1958,4258,1674,6817,33844,2653,5899,749,1627,639,4551,2575,11826,2063,8731,1695,514,339,233,3975,1795,7759,1851,1463,3431,1310,4105,4382,3243,9196,4133,14732,1146,4154,3782,1494,1370,2986,5165,12898,2091,143,11820,22253,874,3347,14570,13432,29171,581,12929,770,9338,3913,2067,466,1442,1065,10328,3273,197,4811,8897,5417,1769,206,119,3406,6754,309,3909,646,3677,3514,8797,1435,301,9215,3730,7282,165,3381,303,6369,2627,115,761,3695,1233,1297,1803,1130,122,511,58,6426,1389,1433,9102,943,2795,13162,9905,899,9740,8719,517,5115,4977,1486,8259,7163,13549,7561,305,119,973,7698,5619,5326,5772,32611,8846,1709,4641,782,2503,3905,4051,4923,165,16132,16827,1913,6590,322,741,522,7666,1655,5087,468,8541,1169,4455,22993,2801,6623,446,1979,10923,3503,32053,523,5721,9608,955,11766,49919,1982,66,3347,9508,439,145,5697,1026,1569,};
constexpr uint16_t base_table2[] = {15,135,13,60,15,117,65,29};


#ifndef CP_ALGO_NUMBER_THEORY_PRIMALITY_BASES_HPP
#define CP_ALGO_NUMBER_THEORY_PRIMALITY_BASES_HPP
#include <cstdint>
constexpr uint16_t base_table1[]={1814,1307,1714,6838,1801,179,219,1317,6834,3281,8345,4034,1899,5746,4977,117,12578,18141,4434,4236,543,9046,4005,385,4231,3425,859,1450,2199,4262,7025,1562,717,5611,5298,871,1959,258,4543,8969,1075,15030,21041,7917,913,15929,3450,9218,518,11775,7993,175,107,407,4738,14388,86,6360,3535,3818,8083,11,4337,19601,32654,2566,974,1549,5047,1542,1941,3887,933,295,106,823,1529,7999,8424,2958,17995,1430,8541,5213,341,13034,4437,4058,21281,715,1898,434,1298,8930,33,3466,397,14181,2685,2179,15160,271,175,5403,1303,2091,4133,466,2143,3908,2819,159,358,302,7778,2001,1029,182,7405,13580,26511,11758,743,4841,12448,3585,3123,1959,3999,1906,597,8293,2508,8231,8676,485,4925,12605,22286,1099,1385,382,10310,746,293,415,2947,61,295,4797,11775,2902,4254,12326,1335,1541,17775,8067,13739,4254,685,3963,2258,3827,1151,2962,1981,1043,2910,8555,2478,3181,1399,12907,5843,2056,7,598,17287,609,1823,9968,12866,9614,1177,1799,8135,8861,6242,3655,8700,11136,3693,229,6637,8587,4915,820,6594,8899,3012,833,5439,402,387,9998,10074,401,9281,2246,12470,7919,1533,2725,947,6314,6681,2733,10132,1535,7066,17066,1529,507,29293,5893,6323,551,506,1686,394,2355,2394,199,8744,3451,1759,12630,8251,21127,603,1349,16013,1916,657,3143,10920,344,1522,3123,10732,635,4927,2641,2786,554,77,8759,2047,8638,233,19015,237,29990,4033,110,3949,351,293,12792,2370,3878,9235,1477,14719,4439,4571,3606,6895,1256,8271,2189,73,1006,28711,1970,8162,1034,1258,3018,5062,2381,1326,19172,17936,17446,4714,7939,975,11261,17179,1138,9907,7654,8844,213,3378,7937,118,3421,1217,7742,52,18125,381,1131,545,9748,8528,1219,2206,415,6235,50334,74,397,1773,1150,16385,1419,8899,811,3813,2511,10359,17270,22652,9646,34497,3474,141,1554,1287,4642,1571,934,2834,101,749,258,302,26159,1291,5105,1783,7310,415,1558,2393,13393,263,1362,7985,9569,8240,2279,5018,8430,1961,6005,17635,3622,4213,36293,9985,11,1254,2251,27396,239,17364,3863,4615,7899,3674,5531,199,8996,1293,6098,514,8538,17311,2015,6226,4459,5731,887,5449,8085,1851,206,2925,8337,2363,9490,1085,590,9094,78,7190,2843,86,497,1658,113,24990,5302,3141,18856,16074,5754,9497,1757,1353,4013,3739,6930,6179,813,6894,2527,2218,14648,397,2979,3074,2314,6521,18390,2157,10642,1177,5007,391,1982,4373,26,1917,1567,3091,22352,9374,935,3263,8242,3239,3558,18600,9839,2440,5325,6414,1303,2995,109,5731,9966,1478,8867,9094,284,433,1750,277,9773,22660,181,127,279,641,851,199,539,1190,446,10526,2566,677,127,2404,9715,8319,15005,3086,2779,3951,7,6929,461,27337,8909,9543,5150,6703,3327,769,901,851,2227,819,1879,3130,4927,2302,802,7599,1163,71,33,925,5550,2971,8201,23865,114,5886,1145,19851,6219,1877,613,827,11302,5726,1237,769,590,9156,9048,6049,7379,5462,12522,5706,823,8431,3349,1623,2245,5198,1329,14794,6193,2266,9722,3716,10294,2009,1193,233,3979,1077,418,941,4613,8635,26786,1507,8508,258,1419,5225,7485,1051,13020,31711,22593,3331,3338,12526,161,5338,7302,78,23889,571,26734,8013,8305,9053,1566,2482,191,12703,1703,3385,654,26390,3647,2639,8498,3813,1161,7777,117,2265,813,8069,2053,2091,5033,6637,8588,15954,325,1713,9719,1983,619,107,419,9104,9019,8688,577,1773,237,3379,2946,1151,13815,1119,1393,11565,2177,530,265,1663,4058,11031,12256,2443,173,1405,1258,8592,4364,4883,1201,2470,119,2775,37084,6690,1067,10479,337,4147,19565,853,4005,1790,855,2329,481,585,2616,1741,10908,17057,9267,4403,10597,4963,7154,3079,8245,3271,10807,1513,691,2821,5285,681,9822,690,566,46,639,141,6706,9308,1009,7433,24590,29,25809,710,4839,2857,17910,383,4630,2993,1059,39,13218,10597,6607,3466,3029,8639,1646,8895,231,4885,3305,5734,10310,5954,7773,3329,587,14302,9806,2130,189,1267,7397,12364,953,299,5297,3354,1921,2486,6827,2202,2369,15279,871,713,8273,1227,9691,3475,469,865,2230,353,6249,9310,1546,38417,2199,1789,9051,6555,3766,1701,10210,1270,3279,8620,3039,929,2029,618,6641,7122,4215,34,89,5251,1293,6401,409,537,935,26421,2882,4129,55,7427,369,12218,9918,1870,4888,1449,1430,4430,5291,1699,2074,67,12096,6687,8414,573,2803,887,2435,1138,2413,4129,205,2190,1654,3697,3170,3538,1574,555,1338,2822,1077,610,8391,1539,11,6637,1053,179,698,1495,1217,1436,9935,778,310,801,718,1066,3066,261,839,651,3293,20997,8527,8721,2146,37272,3607,9206,698,9983,28805,221,3686,11549,348,181,1293,3846,2717,6926,5133,137,1785,9727,2325,2723,8678,607,3010,8749,8855,10668,2675,301,7899,8191,9141,6622,9435,1579,1539,3261,5773,218,1654,4466,739,3366,2047,557,3189,7558,2867,2810,3842,1663,4635,34027,269,9256,3533,4074,1022,3365,1633,15096,8323,9249,1767,1326,39,9211,165,8797,9519,1006,5738,18521,323,1746,10996,1517,8204,6547,4359,1834,2966,716,715,2470,1443,8518,2938,1962,2387,10961,851,5533,553,5150,934,554,157,4429,15949,2194,1657,1449,7391,377,2065,3307,6695,2731,1141,813,3238,8318,2255,9003,618,3697,24981,4401,1523,219,721,6284,6220,7747,333,12835,5619,949,4346,1206,846,8063,6167,1383,6843,10299,3085,9018,277,221,12774,1173,1926,21591,4182,2194,8223,3983,550,2254,8371,606,1202,29,1273,6557,8808,7918,3797,2941,1566,15003,1955,2796,2583,233,10105,1418,2889,24939,9590,3573,613,70,247,934,1822,895,4197,30570,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58,1666,11487,5645,40577,7163,9925,279,2009,407,2693,9102,5273,10107,1422,115,12049,119,11801,341,9129,8514,1614,1043,2349,366,903,3702,3609,2705,2328,1414,2293,2727,2113,3127,19308,2329,1023,10175,925,8544,4115,2194,1359,9252,138,817,7897,918,323,8530,2829,1751,5581,25658,1517,445,2397,163,241,14777,171,2782,3930,39974,1277,318,12735,12044,4934,2323,6697,698,6036,4694,5269,587,8445,2218,4630,1954,3981,8067,8187,4522,1041,10402,37117,1182,1543,11430,9242,834,3537,11522,33957,4995,491,2279,4122,637,8722,3317,6163,1349,455,843,995,681,42,1783,959,3095,1469,28598,9902,5909,1163,8572,1722,566,9001,2725,3226,7830,2051,1354,1151,8228,1735,19522,6446,178,1223,5197,51,1074,893,381,5286,8925,27691,681,1239,9390,1159,7178,598,10187,10721,12067,891,9191,783,2377,2889,137,5050,2581,394,5383,1110,6173,9401,9059,1275,10477,2108,2211,510,8195,4039,13323,4398,4829,1828,5146,5553,9105,209,9466,201,941,8550,3713,2761,12454,3582,3270,15090,3446,8658,7411,2694,419,9631,8598,5405,911,2447,2630,5381,2755,4395,3385,8224,3201,10432,2437,4091,8499,2335,777,20517,643,2641,5426,2302,1266,386,1115,2494,165,2802,4617,695,1625,922,701,1757,8954,510,2072,4207,1966,7815,914,26081,2099,917,4625,6695,7186,6210,117,5026,1271,5254,1715,4462,5370,8965,1593,1116,2115,673,1307,62,3722,4870,1913,253,8632,550,876,205,943,20717,1486,1779,3334,3878,1266,499,7989,15711,7187,4325,8247,658,5398,2698,3269,1706,5141,30431,1649,1094,13996,3847,4390,3694,15908,17573,20205,2870,14429,2837,383,2124,2607,5042,5186,1502,2006,8628,2963,2653,442,1579,1353,3183,893,3977,8346,11853,714,417,466,762,967,495,275,10096,3197,3982,1911,2821,21737,2510,9330,1671,6513,8563,6061,2022,2153,4302,8330,1195,5967,10342,543,766,519,2371,511,417,1446,14731,389,2687,431,319,117,561,638,2563,4293,1303,1289,5850,467,2709,1828,154,24097,419,178,2094,587,653,9920,6697,3799,3747,323,1437,2619,1630,1379,924,3523,8811,1134,1299,991,1659,11179,3105,34590,8896,362,2595,1254,1393,379,6677,571,155,379,4726,501,1186,1025,447,10505,975,754,1386,2117,20220,5143,7843,2795,3011,713,389,1101,767,1116,447,1307,2059,4058,3598,610,2921,2353,166,4433,199,1477,4025,9850,301,5006,14630,693,10889,12815,151,2526,4595,1159,4087,1795,7707,30981,10557,10197,5281,6233,7310,1823,2131,4621,2283,3510,1310,1449,4606,2231,326,2062,9019,10527,3577,6812,4229,323,669,2413,3601,4041,2151,8904,10171,5683,1349,2763,7486,1189,771,1139,3803,12249,431,13170,1091,37694,3891,9607,2221,5779,7870,11678,998,969,2133,8933,14255,11624,2465,15753,2838,4187,3367,1286,5679,2186,715,2143,998,342,751,12177,6259,1302,571,8110,7923,12334,8286,1113,1222,8769,371,876,7991,2706,4717,2705,541,394,1883,7507,643,835,357,929,8694,8122,1973,2503,357,130,937,8681,975,91,123,13290,4583,2078,3270,2682,8936,8249,1775,8519,1439,6295,4151,10817,8942,3263,18933,1293,183,4601,9155,5481,481,39192,358,16721,419,2142,4135,16945,10998,6490,1175,8490,846,6409,12493,23326,2899,415,36491,13051,866,161,22,2150,849,4670,3849,489,833,549,5675,14716,8764,1685,161,4785,30101,1067,635,126,1387,5495,985,1942,166,453,2101,8602,1389,6802,193,4307,1302,6233,3138,1199,3111,10278,2852,8693,13152,10313,10246,66,554,1941,8070,5726,9988,1997,693,2405,549,350,11750,5111,6237,5873,4531,1289,1709,2238,831,202,2893,1726,47,23812,1553,1053,2927,635,5906,4088,1084,7304,7714,1363,3417,2427,3119,7934,4549,2271,1330,1483,650,223,649,7917,3966,7318,411,8992,2455,1135,4953,919,2130,610,1844,137,403,3757,9114,1366,646,8467,7277,7171,2442,93,857,895,2134,38617,11100,12622,67,3883,5807,743,5005,731,10084,69,46255,865,6671,1071,3798,1855,1426,3361,571,2697,161,286,497,2207,2038,2015,12745,10440,313,1443,8753,11702,267,7226,27666,398,1309,170,10128,1398,1839,8276,3414,55,3107,3154,2405,1814,8903,4845,1417,1667,2427,549,818,475,1499,1169,767,537,1697,2386,2075,3673,1871,9379,1938,3229,1237,222,209,5473,5589,4397,9112,5233,12487,1835,149,7860,5289,10055,4185,53,1394,2265,2610,6079,8316,13263,3475,9011,22,159,6061,82,2361,349,25061,10631,2375,10013,9529,10695,17510,231,9334,1798,1263,4233,1565,23669,930,1958,4258,1674,6817,33844,2653,5899,749,1627,639,4551,2575,11826,2063,8731,1695,514,339,233,3975,1795,7759,1851,1463,3431,1310,4105,4382,3243,9196,4133,14732,1146,4154,3782,1494,1370,2986,5165,12898,2091,143,11820,22253,874,3347,14570,13432,29171,581,12929,770,9338,3913,2067,466,1442,1065,10328,3273,197,4811,8897,5417,1769,206,119,3406,6754,309,3909,646,3677,3514,8797,1435,301,9215,3730,7282,165,3381,303,6369,2627,115,761,3695,1233,1297,1803,1130,122,511,58,6426,1389,1433,9102,943,2795,13162,9905,899,9740,8719,517,5115,4977,1486,8259,7163,13549,7561,305,119,973,7698,5619,5326,5772,32611,8846,1709,4641,782,2503,3905,4051,4923,165,16132,16827,1913,6590,322,741,522,7666,1655,5087,468,8541,1169,4455,22993,2801,6623,446,1979,10923,3503,32053,523,5721,9608,955,11766,49919,1982,66,3347,9508,439,145,5697,1026,1569,};constexpr uint16_t base_table2[]={15,135,13,60,15,117,65,29};
#endif

#line 1 "cp-algo/number_theory/primality_bases.hpp"
#include <cstdint>
constexpr uint16_t base_table1[]={1814,1307,1714,6838,1801,179,219,1317,6834,3281,8345,4034,1899,5746,4977,117,12578,18141,4434,4236,543,9046,4005,385,4231,3425,859,1450,2199,4262,7025,1562,717,5611,5298,871,1959,258,4543,8969,1075,15030,21041,7917,913,15929,3450,9218,518,11775,7993,175,107,407,4738,14388,86,6360,3535,3818,8083,11,4337,19601,32654,2566,974,1549,5047,1542,1941,3887,933,295,106,823,1529,7999,8424,2958,17995,1430,8541,5213,341,13034,4437,4058,21281,715,1898,434,1298,8930,33,3466,397,14181,2685,2179,15160,271,175,5403,1303,2091,4133,466,2143,3908,2819,159,358,302,7778,2001,1029,182,7405,13580,26511,11758,743,4841,12448,3585,3123,1959,3999,1906,597,8293,2508,8231,8676,485,4925,12605,22286,1099,1385,382,10310,746,293,415,2947,61,295,4797,11775,2902,4254,12326,1335,1541,17775,8067,13739,4254,685,3963,2258,3827,1151,2962,1981,1043,2910,8555,2478,3181,1399,12907,5843,2056,7,598,17287,609,1823,9968,12866,9614,1177,1799,8135,8861,6242,3655,8700,11136,3693,229,6637,8587,4915,820,6594,8899,3012,833,5439,402,387,9998,10074,401,9281,2246,12470,7919,1533,2725,947,6314,6681,2733,10132,1535,7066,17066,1529,507,29293,5893,6323,551,506,1686,394,2355,2394,199,8744,3451,1759,12630,8251,21127,603,1349,16013,1916,657,3143,10920,344,1522,3123,10732,635,4927,2641,2786,554,77,8759,2047,8638,233,19015,237,29990,4033,110,3949,351,293,12792,2370,3878,9235,1477,14719,4439,4571,3606,6895,1256,8271,2189,73,1006,28711,1970,8162,1034,1258,3018,5062,2381,1326,19172,17936,17446,4714,7939,975,11261,17179,1138,9907,7654,8844,213,3378,7937,118,3421,1217,7742,52,18125,381,1131,545,9748,8528,1219,2206,415,6235,50334,74,397,1773,1150,16385,1419,8899,811,3813,2511,10359,17270,22652,9646,34497,3474,141,1554,1287,4642,1571,934,2834,101,749,258,302,26159,1291,5105,1783,7310,415,1558,2393,13393,263,1362,7985,9569,8240,2279,5018,8430,1961,6005,17635,3622,4213,36293,9985,11,1254,2251,27396,239,17364,3863,4615,7899,3674,5531,199,8996,1293,6098,514,8538,17311,2015,6226,4459,5731,887,5449,8085,1851,206,2925,8337,2363,9490,1085,590,9094,78,7190,2843,86,497,1658,113,24990,5302,3141,18856,16074,5754,9497,1757,1353,4013,3739,6930,6179,813,6894,2527,2218,14648,397,2979,3074,2314,6521,18390,2157,10642,1177,5007,391,1982,4373,26,1917,1567,3091,22352,9374,935,3263,8242,3239,3558,18600,9839,2440,5325,6414,1303,2995,109,5731,9966,1478,8867,9094,284,433,1750,277,9773,22660,181,127,279,641,851,199,539,1190,446,10526,2566,677,127,2404,9715,8319,15005,3086,2779,3951,7,6929,461,27337,8909,9543,5150,6703,3327,769,901,851,2227,819,1879,3130,4927,2302,802,7599,1163,71,33,925,5550,2971,8201,23865,114,5886,1145,19851,6219,1877,613,827,11302,5726,1237,769,590,9156,9048,6049,7379,5462,12522,5706,823,8431,3349,1623,2245,5198,1329,14794,6193,2266,9722,3716,10294,2009,1193,233,3979,1077,418,941,4613,8635,26786,1507,8508,258,1419,5225,7485,1051,13020,31711,22593,3331,3338,12526,161,5338,7302,78,23889,571,26734,8013,8305,9053,1566,2482,191,12703,1703,3385,654,26390,3647,2639,8498,3813,1161,7777,117,2265,813,8069,2053,2091,5033,6637,8588,15954,325,1713,9719,1983,619,107,419,9104,9019,8688,577,1773,237,3379,2946,1151,13815,1119,1393,11565,2177,530,265,1663,4058,11031,12256,2443,173,1405,1258,8592,4364,4883,1201,2470,119,2775,37084,6690,1067,10479,337,4147,19565,853,4005,1790,855,2329,481,585,2616,1741,10908,17057,9267,4403,10597,4963,7154,3079,8245,3271,10807,1513,691,2821,5285,681,9822,690,566,46,639,141,6706,9308,1009,7433,24590,29,25809,710,4839,2857,17910,383,4630,2993,1059,39,13218,10597,6607,3466,3029,8639,1646,8895,231,4885,3305,5734,10310,5954,7773,3329,587,14302,9806,2130,189,1267,7397,12364,953,299,5297,3354,1921,2486,6827,2202,2369,15279,871,713,8273,1227,9691,3475,469,865,2230,353,6249,9310,1546,38417,2199,1789,9051,6555,3766,1701,10210,1270,3279,8620,3039,929,2029,618,6641,7122,4215,34,89,5251,1293,6401,409,537,935,26421,2882,4129,55,7427,369,12218,9918,1870,4888,1449,1430,4430,5291,1699,2074,67,12096,6687,8414,573,2803,887,2435,1138,2413,4129,205,2190,1654,3697,3170,3538,1574,555,1338,2822,1077,610,8391,1539,11,6637,1053,179,698,1495,1217,1436,9935,778,310,801,718,1066,3066,261,839,651,3293,20997,8527,8721,2146,37272,3607,9206,698,9983,28805,221,3686,11549,348,181,1293,3846,2717,6926,5133,137,1785,9727,2325,2723,8678,607,3010,8749,8855,10668,2675,301,7899,8191,9141,6622,9435,1579,1539,3261,5773,218,1654,4466,739,3366,2047,557,3189,7558,2867,2810,3842,1663,4635,34027,269,9256,3533,4074,1022,3365,1633,15096,8323,9249,1767,1326,39,9211,165,8797,9519,1006,5738,18521,323,1746,10996,1517,8204,6547,4359,1834,2966,716,715,2470,1443,8518,2938,1962,2387,10961,851,5533,553,5150,934,554,157,4429,15949,2194,1657,1449,7391,377,2065,3307,6695,2731,1141,813,3238,8318,2255,9003,618,3697,24981,4401,1523,219,721,6284,6220,7747,333,12835,5619,949,4346,1206,846,8063,6167,1383,6843,10299,3085,9018,277,221,12774,1173,1926,21591,4182,2194,8223,3983,550,2254,8371,606,1202,29,1273,6557,8808,7918,3797,2941,1566,15003,1955,2796,2583,233,10105,1418,2889,24939,9590,3573,613,70,247,934,1822,895,4197,30570,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58,1666,11487,5645,40577,7163,9925,279,2009,407,2693,9102,5273,10107,1422,115,12049,119,11801,341,9129,8514,1614,1043,2349,366,903,3702,3609,2705,2328,1414,2293,2727,2113,3127,19308,2329,1023,10175,925,8544,4115,2194,1359,9252,138,817,7897,918,323,8530,2829,1751,5581,25658,1517,445,2397,163,241,14777,171,2782,3930,39974,1277,318,12735,12044,4934,2323,6697,698,6036,4694,5269,587,8445,2218,4630,1954,3981,8067,8187,4522,1041,10402,37117,1182,1543,11430,9242,834,3537,11522,33957,4995,491,2279,4122,637,8722,3317,6163,1349,455,843,995,681,42,1783,959,3095,1469,28598,9902,5909,1163,8572,1722,566,9001,2725,3226,7830,2051,1354,1151,8228,1735,19522,6446,178,1223,5197,51,1074,893,381,5286,8925,27691,681,1239,9390,1159,7178,598,10187,10721,12067,891,9191,783,2377,2889,137,5050,2581,394,5383,1110,6173,9401,9059,1275,10477,2108,2211,510,8195,4039,13323,4398,4829,1828,5146,5553,9105,209,9466,201,941,8550,3713,2761,12454,3582,3270,15090,3446,8658,7411,2694,419,9631,8598,5405,911,2447,2630,5381,2755,4395,3385,8224,3201,10432,2437,4091,8499,2335,777,20517,643,2641,5426,2302,1266,386,1115,2494,165,2802,4617,695,1625,922,701,1757,8954,510,2072,4207,1966,7815,914,26081,2099,917,4625,6695,7186,6210,117,5026,1271,5254,1715,4462,5370,8965,1593,1116,2115,673,1307,62,3722,4870,1913,253,8632,550,876,205,943,20717,1486,1779,3334,3878,1266,499,7989,15711,7187,4325,8247,658,5398,2698,3269,1706,5141,30431,1649,1094,13996,3847,4390,3694,15908,17573,20205,2870,14429,2837,383,2124,2607,5042,5186,1502,2006,8628,2963,2653,442,1579,1353,3183,893,3977,8346,11853,714,417,466,762,967,495,275,10096,3197,3982,1911,2821,21737,2510,9330,1671,6513,8563,6061,2022,2153,4302,8330,1195,5967,10342,543,766,519,2371,511,417,1446,14731,389,2687,431,319,117,561,638,2563,4293,1303,1289,5850,467,2709,1828,154,24097,419,178,2094,587,653,9920,6697,3799,3747,323,1437,2619,1630,1379,924,3523,8811,1134,1299,991,1659,11179,3105,34590,8896,362,2595,1254,1393,379,6677,571,155,379,4726,501,1186,1025,447,10505,975,754,1386,2117,20220,5143,7843,2795,3011,713,389,1101,767,1116,447,1307,2059,4058,3598,610,2921,2353,166,4433,199,1477,4025,9850,301,5006,14630,693,10889,12815,151,2526,4595,1159,4087,1795,7707,30981,10557,10197,5281,6233,7310,1823,2131,4621,2283,3510,1310,1449,4606,2231,326,2062,9019,10527,3577,6812,4229,323,669,2413,3601,4041,2151,8904,10171,5683,1349,2763,7486,1189,771,1139,3803,12249,431,13170,1091,37694,3891,9607,2221,5779,7870,11678,998,969,2133,8933,14255,11624,2465,15753,2838,4187,3367,1286,5679,2186,715,2143,998,342,751,12177,6259,1302,571,8110,7923,12334,8286,1113,1222,8769,371,876,7991,2706,4717,2705,541,394,1883,7507,643,835,357,929,8694,8122,1973,2503,357,130,937,8681,975,91,123,13290,4583,2078,3270,2682,8936,8249,1775,8519,1439,6295,4151,10817,8942,3263,18933,1293,183,4601,9155,5481,481,39192,358,16721,419,2142,4135,16945,10998,6490,1175,8490,846,6409,12493,23326,2899,415,36491,13051,866,161,22,2150,849,4670,3849,489,833,549,5675,14716,8764,1685,161,4785,30101,1067,635,126,1387,5495,985,1942,166,453,2101,8602,1389,6802,193,4307,1302,6233,3138,1199,3111,10278,2852,8693,13152,10313,10246,66,554,1941,8070,5726,9988,1997,693,2405,549,350,11750,5111,6237,5873,4531,1289,1709,2238,831,202,2893,1726,47,23812,1553,1053,2927,635,5906,4088,1084,7304,7714,1363,3417,2427,3119,7934,4549,2271,1330,1483,650,223,649,7917,3966,7318,411,8992,2455,1135,4953,919,2130,610,1844,137,403,3757,9114,1366,646,8467,7277,7171,2442,93,857,895,2134,38617,11100,12622,67,3883,5807,743,5005,731,10084,69,46255,865,6671,1071,3798,1855,1426,3361,571,2697,161,286,497,2207,2038,2015,12745,10440,313,1443,8753,11702,267,7226,27666,398,1309,170,10128,1398,1839,8276,3414,55,3107,3154,2405,1814,8903,4845,1417,1667,2427,549,818,475,1499,1169,767,537,1697,2386,2075,3673,1871,9379,1938,3229,1237,222,209,5473,5589,4397,9112,5233,12487,1835,149,7860,5289,10055,4185,53,1394,2265,2610,6079,8316,13263,3475,9011,22,159,6061,82,2361,349,25061,10631,2375,10013,9529,10695,17510,231,9334,1798,1263,4233,1565,23669,930,1958,4258,1674,6817,33844,2653,5899,749,1627,639,4551,2575,11826,2063,8731,1695,514,339,233,3975,1795,7759,1851,1463,3431,1310,4105,4382,3243,9196,4133,14732,1146,4154,3782,1494,1370,2986,5165,12898,2091,143,11820,22253,874,3347,14570,13432,29171,581,12929,770,9338,3913,2067,466,1442,1065,10328,3273,197,4811,8897,5417,1769,206,119,3406,6754,309,3909,646,3677,3514,8797,1435,301,9215,3730,7282,165,3381,303,6369,2627,115,761,3695,1233,1297,1803,1130,122,511,58,6426,1389,1433,9102,943,2795,13162,9905,899,9740,8719,517,5115,4977,1486,8259,7163,13549,7561,305,119,973,7698,5619,5326,5772,32611,8846,1709,4641,782,2503,3905,4051,4923,165,16132,16827,1913,6590,322,741,522,7666,1655,5087,468,8541,1169,4455,22993,2801,6623,446,1979,10923,3503,32053,523,5721,9608,955,11766,49919,1982,66,3347,9508,439,145,5697,1026,1569,};constexpr uint16_t base_table2[]={15,135,13,60,15,117,65,29};
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