indices.h

#include<iostream>
using namespace std;
int indices[] ={3,7,24,29,37,44,50,55,56,70,72,82,85,90,92,94,104,106,112,118,130,135,146,148,158,169,172,183,184,208,210,221,224,228,230,233,237,238,247,248,249,250,252,268,276,288,290,307,315,316,322,332,334,340,350,355,359,363,385,400,406,411,413,422,423,434,444,458,459,461,463,465,468,470,476,487,493,499,502,516,539,559,563,585,592,600,625,627,629,638,658,668,672,674,676,683,685,690,691,694,701,704,709,717,725,729,733,735,742,748,752,765,768,775,777,782,783,784,791,793,804,808,814,817,822,833,834,836,838,847,865,866,874,878,879,893,898,902,903,906,907,908,909,922,926,928,929,933,938,940,941,948,954,968,976,980,981,990,991,1000,1012,1020,1024,1028,1037,1043,1045,1047,1052,1054,1056,1062,1067,1072,1074,1075,1095,1107,1110,1119,1135,1137,1146,1171,1202,1203,1208,1211,1232,1239,1246,1247,1251,1252,1259,1261,1268,1274,1279,1285,1290,1293,1295,1305,1308,1321,1323,1326,1328,1334,1338,1346,1352,1355,1357,1358,1362,1366,1371,1392,1393,1401,1405,1408,1411,1412,1415,1420,1422,1431,1434,1439,1444,1453,1457,1460,1475,1482,1492,1494,1497,1502,1503,1509,1513,1527,1544,1549,1550,1564,1570,1579,1587,1602,1603,1607,1611,1613,1618,1622,1634,1642,1644,1651,1669,1679,1682,1688,1693,1703,1704,1713,1718,1723,1728,1739,1743,1744,1746,1748,1752,1759,1766,1769,1775,1798,1800,1810,1819,1823,1828,1829,1841,1849,1850,1858,1861,1867,1881,1906,1911,1913,1918,1923,1930,1931,1932,1934,1935,1949,1952,1969,1974,1982,1983,1993,1995,2030,2036,2039,2042,2049,2055,2056,2059,2067,2068,2089,2090,2092,2093,2096,2101,2102,2104,2108,2113,2114,2116,2117,2122,2136,2142,2148,2150,2161,2182,2187,2192,2195,2196,2212,2215,2221,2228,2229,2234,2249,2255,2263,2270,2273,2281,2286,2303,2309,2312,2313,2326,2329,2335,2340,2348,2350,2371,2380,2385,2387,2388,2390,2398,2402,2407,2410,2414,2424,2425,2435,2440,2462,2470,2480,2481,2485,2506,2515,2520,2526,2528,2529,2531,2542,2557,2578,2582,2584,2585,2601,2607,2608,2613,2622,2627,2636,2640,2641,2648,2672,2673,2693,2699,2716,2719,2734,2736,2762,2768,2769,2776,2778,2789,2791,2796,2802,2804,2805,2812,2829,2832,2844,2848,2850,2863,2867,2868,2870,2872,2883,2912,2916,2924,2935,2939,2948,2951,2954,2959,2968,2969,2973,2977,2980,2981,2985,2987,2993,2995,2996,2998,3003,3007,3012,3014,3017,3028,3030,3055,3059,3070,3072,3079,3082,3083,3087,3100,3103,3105,3115,3123,3124,3127,3128,3144,3146,3154,3156,3157,3158,3163,3184,3194,3202,3212,3216,3222,3231,3247,3262,3272,3275,3300,3311,3319,3322,3345,3354,3359,3372,3375,3397,3405,3415,3422,3423,3427,3428,3430,3433,3436,3439,3454,3458,3473,3482,3483,3498,3504,3505,3513,3551,3557,3565,3572,3585,3587,3592,3593,3599,3602,3606,3611,3612,3613,3621,3627,3633,3636,3638,3654,3657,3678,3679,3683,3686,3692,3698,3701,3703,3707,3714,3718,3720,3729,3732,3748,3753,3755,3803,3806,3816,3827,3854,3860,3862,3863,3876,3881,3882,3885,3886,3887,3893,3916,3921,3922,3925,3926,3927,3930,3935,3952,3954,3957,3958,3959,3967,3974,3976,3989,3993,3997,4002,4003,4010,4031,4039,4040,4048,4051,4053,4054,4067,4073,4080,4092,4097,4107,4111,4125,4126,4132,4140,4146,4148,4158,4167,4177,4179,4182,4184,4201,4209,4221,4226,4229,4246,4248,4261,4267,4272,4274,4278,4286,4294,4306,4335,4341,4343,4344,4357,4364,4366,4369,4382,4384,4386,4388,4389,4406,4409,4413,4427,4434,4435,4439,4446,4454,4456,4458,4464,4466,4470,4475,4480,4498,4507,4514,4523,4531,4536,4540,4543,4556,4571,4574,4579,4591,4594,4612,4620,4632,4647,4662,4663,4668,4671,4684,4690,4693,4707,4733,4734,4769,4777,4789,4795,4803,4808,4811,4815,4817,4820,4835,4882,4885,4887,4889,4891,4892,4900,4909,4917,4920,4932,4937,4946,4963,4964,4969,4982,4985,4995,5014,5017,5022,5036,5045,5048,5050,5054,5074,5077,5088,5090,5099,5110,5116,5124,5128,5133,5134,5138,5141,5147,5150,5154,5156,5157,5158,5163,5170,5172,5178,5186,5205,5208,5216,5217,5218,5220,5225,5231,5243,5244,5247,5249,5250,5257,5269,5270,5279,5281,5282,5292,5295,5305,5307,5308,5322,5323,5327,5330,5338,5351,5359,5365,5367,5368,5370,5372,5373,5378,5381,5383,5388,5390,5392,5397,5417,5421,5422,5424,5425,5431,5451,5454,5455,5462,5464,5465,5466,5467,5470,5472,5476,5481,5483,5486,5490,5496,5501,5529,5536,5540,5546,5548,5558,5565,5574,5583,5586,5595,5602,5603,5613,5619,5622,5624,5625,5629,5646,5685,5691,5700,5701,5722,5727,5730,5742,5743,5750,5757,5758,5781,5807,5815,5838,5840,5843,5844,5850,5862,5865,5867,5875,5880,5882,5898,5900,5908,5926,5931,5937,5953,5958,5964,5967,5971,5974,5975,5976,5977,5979,6005,6007,6009,6026,6028,6030,6061,6078,6080,6093,6097,6101,6104,6105,6106,6111,6118,6121,6124,6130,6131,6143,6148,6154,6155,6157,6162,6164,6168,6169,6174,6175,6179,6189,6200,6202,6209,6213,6216,6220,6221,6225,6248,6255,6262,6270,6280,6281,6283,6287,6290,6296,6299,6300,6310,6311,6319,6329,6333,6336,6343,6344,6353,6357,6358,6363,6371,6373,6376,6388,6389,6395,6398,6401,6405,6408,6411,6414,6415,6424,6435,6437,6450,6455,6460,6461,6481,6483,6487,6489,6495,6501,6512,6518,6523,6530,6531,6546,6547,6558,6574,6581,6591,6594,6595,6596,6605,6623,6626,6635,6636,6638,6644,6646,6648,6651,6654,6661,6666,6681,6695,6697,6698,6702,6705,6712,6715,6716,6720,6723,6727,6731,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179,20181,20201,20202,20216,20256,20264,20283,20291,20297,20301,20310,20311,20312,20323,20324,20326,20327,20331,20337,20338,20340,20345,20357,20358,20360,20363,20368,20370,20377,20378,20384,20385,20394,20403,20407,20419,20424,20425,20434,20437,20443,20447,20453,20454,20474,20481,20486,20504,20515,20518,20520,20521,20533,20540,20543,20546,20550,20551,20574,20579,20580,20583,20587,20591,20594,20603,20611,20613,20614,20620,20631,20645,20650,20654,20658,20673,20676,20682,20692,20696,20702,20703,20704,20706,20711,20718,20725,20730,20738,20741,20745,20751,20752,20757,20761,20765,20767,20770,20781,20799,20809,20811,20817,20819,20820,20823,20831,20844,20846,20862,20868,20869,20885,20889,20895,20921,20924,20926,20927,20928,20929,20938,20939,20950,20962,20966,20967,20972,20973,20980,20994,20999,21002,21006,21020,21026,21031,21035,21037,21048,21049,21053,21062,21066,21080,21081,21084,21088,21101,21103,21108,21109,21111,21113,21120,21133,21140,21151,21155,21158,21171,21178,21194,21202,21215,21233,21257,21270,21275,21279,21284,21286,21292,21296,21310,21316,21317,21327,21328,21330,21334,21340,21367,21371,21376,21377,21379,21380,21381,21399,21404,21407,21411,21419,21421,21424,21444,21448,21453,21460,21478,21485,21490,21495,21499,21504,21520,21526,21528,21531,21536,21553,21560,21565,21566,21567,21571,21572,21573,21578,21585,21586,21592,21606,21608,21621,21626,21635,21636,21641,21651,21653,21655,21661,21664,21668,21670,21674,21684,21696,21702,21706,21714,21716,21717,21720,21721,21725,21733,21745,21758,21763,21775,21785,21791,21802,21808,21809,21811,21828,21830,21838,21840,21841,21847,21848,21873,21878,21882,21886,21892,21895,21899,21921,21935,21941,21947,21950,21952,21961,21970,21983,21986,21989,22000,22005,22011,22012,22015,22026,22036,22048,22051,22054,22061,22067,22068,22078,22086,22093,22095,22103,22113,22114,22116,22118,22120,22121,22124,22130,22134,22148,22166,22168,22170,22181,22191,22194,22207,22213,22238,22241,22257,22260,22270,22283,22294,22305,22314,22315};
int id[6710] = {129,14,41,62,63,143,103,152,120,71,83,108,29,72,163,85,50,108,59,42,20,98,53,84,72,111,111,96,76,68,92,115,38,54,81,76,69,144,51,79,67,113,62,46,151,150,129,92,69,69,20,58,38,22,31,163,13,61,16,53,40,107,75,151,82,47,90,17,150,164,65,18,84,64,131,45,116,38,84,137,102,92,104,98,49,150,72,43,78,151,65,78,92,71,129,108,86,66,29,74,58,25,117,26,86,13,75,58,102,140,79,71,135,20,72,174,70,43,58,44,98,71,141,56,15,158,69,66,74,108,116,51,36,75,155,147,75,78,21,72,83,53,28,44,33,77,27,29,76,25,48,154,30,57,115,65,162,36,59,164,24,105,150,73,157,119,66,46,72,15,56,57,20,72,32,117,16,87,70,70,29,85,86,164,140,82,127,69,72,27,14,25,71,27,14,102,75,54,128,84,90,69,21,33,74,125,69,78,69,116,121,97,48,55,14,162,37,58,79,34,92,110,40,88,90,61,85,63,72,36,107,56,174,113,19,96,163,55,56,58,78,64,116,84,17,148,118,25,15,63,103,62,23,149,93,89,53,134,59,19,16,76,117,71,137,103,82,64,121,22,30,74,47,58,102,55,148,76,83,48,43,37,52,23,18,127,66,46,141,38,20,62,82,80,49,73,45,116,150,27,16,82,85,46,83,99,124,93,25,76,27,68,71,99,108,33,39,85,72,34,82,82,107,117,77,150,71,114,118,59,14,124,54,41,62,70,69,96,80,22,77,81,107,78,77,37,122,80,74,103,73,23,30,107,58,74,90,77,75,87,80,21,23,40,73,79,173,26,15,113,56,75,134,45,21,17,63,46,22,29,70,69,117,67,60,46,115,89,22,57,71,28,53,67,89,117,87,95,83,78,126,15,18,74,112,52,31,18,138,108,39,36,28,29,66,77,23,36,32,34,32,45,72,46,13,75,52,37,103,19,77,75,133,90,76,73,97,21,27,131,180,167,27,83,15,148,72,65,101,150,74,90,159,53,109,49,71,140,60,79,61,44,24,64,77,61,76,99,15,72,84,69,14,79,166,86,45,109,100,59,48,84,54,73,118,47,36,86,57,15,119,114,58,70,113,83,81,169,105,71,45,14,98,56,114,23,91,54,64,61,11,87,120,110,79,85,30,82,102,117,92,91,133,28,72,13,96,106,12,97,37,68,108,42,123,65,86,98,122,73,12,109,91,81,122,64,38,63,46,16,29,57,71,86,122,46,99,24,90,69,45,110,68,62,71,48,68,75,51,85,113,62,110,89,22,45,39,50,32,84,89,104,44,111,55,110,39,45,57,70,62,69,35,173,75,62,48,58,65,99,131,107,96,35,73,66,109,86,73,54,38,71,89,167,161,50,78,25,22,32,91,87,35,24,31,96,151,153,97,48,17,62,56,108,61,19,55,81,68,71,85,53,90,97,89,64,57,12,54,30,18,38,71,17,15,68,73,50,71,44,23,33,44,69,105,163,74,18,106,110,55,41,110,115,93,19,72,123,112,138,67,160,118,61,40,34,56,69,43,171,20,64,67,62,51,21,89,66,84,29,70,99,26,119,19,45,82,57,40,74,82,118,109,27,121,125,16,112,72,67,114,48,131,110,71,85,51,86,72,64,117,115,120,63,27,89,70,49,77,153,102,52,66,33,16,80,49,122,78,15,50,13,14,151,47,48,128,137,16,106,99,159,12,56,142,142,68,80,36,23,76,71,33,61,44,133,70,90,63,161,76,94,63,136,114,106,88,14,68,128,77,24,75,58,95,115,37,55,74,70,88,23,68,92,70,123,57,81,22,101,51,128,108,104,69,56,25,13,88,99,20,38,82,85,144,74,65,75,27,101,61,45,154,90,155,76,150,63,18,67,59,74,150,128,58,77,76,71,91,166,57,70,79,94,137,104,68,93,73,145,34,92,116,38,16,173,12,153,69,121,109,19,51,130,144,122,59,97,20,63,138,25,44,140,72,36,15,82,85,106,159,88,127,95,22,77,71,91,129,46,86,57,37,71,30,55,52,118,44,88,128,131,78,78,91,45,83,78,39,18,136,169,145,58,51,129,109,118,22,77,93,52,157,31,16,118,55,19,127,81,48,74,57,113,22,54,131,40,81,21,116,84,145,138,67,85,53,38,67,50,169,29,137,81,86,82,144,117,161,61,52,96,115,113,94,78,73,116,43,120,89,17,23,35,13,27,64,90,119,85,28,121,58,174,88,85,36,82,20,80,90,62,37,152,38,68,71,29,77,98,173,140,159,22,27,87,70,87,85,120,41,136,151,77,24,122,38,132,16,50,67,56,81,169,126,22,168,53,43,16,94,32,70,19,15,104,69,27,58,62,33,18,66,65,79,23,93,120,95,73,53,148,128,69,15,67,79,93,47,40,57,58,151,78,20,54,98,69,65,137,49,93,131,79,42,145,53,97,148,94,81,72,105,17,37,19,97,89,31,147,89,62,30,39,82,60,93,34,67,35,41,55,82,147,13,146,102,74,90,60,64,139,45,128,140,39,31,71,155,104,55,95,99,49,18,83,156,26,91,17,12,71,76,78,25,64,88,75,37,63,59,22,66,97,55,65,81,14,63,85,120,30,64,54,84,22,28,106,91,80,105,46,74,73,164,67,98,61,94,82,138,119,24,152,66,74,33,71,43,96,21,52,79,50,39,85,26,19,70,90,47,51,14,38,29,87,43,80,25,74,117,15,49,75,78,86,61,83,14,101,82,72,39,55,73,159,115,14,112,32,37,60,78,65,60,69,113,41,78,69,69,19,54,29,95,55,105,96,101,68,86,119,63,74,80,101,145,112,89,74,120,94,18,126,96,137,139,67,125,78,36,52,102,78,84,23,75,100,38,71,67,15,66,23,48,94,147,26,62,72,167,41,17,59,51,107,82,105,83,37,106,47,173,59,111,12,58,56,89,177,153,157,101,19,43,107,160,23,121,59,23,73,35,77,40,80,32,108,88,145,18,19,165,32,26,85,159,72,124,99,102,74,70,112,163,45,86,67,167,16,12,30,94,73,59,75,179,38,26,52,67,81,50,81,53,76,39,129,45,136,89,147,59,72,88,28,58,20,17,108,77,17,74,88,30,24,27,66,38,180,21,105,60,64,116,83,121,46,108,93,42,103,96,56,34,22,70,70,109,31,87,35,86,86,92,28,79,85,59,56,54,35,91,110,53,92,54,68,53,55,31,59,14,78,92,31,65,56,78,146,75,96,62,66,101,59,111,21,113,83,23,108,48,114,54,14,55,35,131,131,74,64,16,71,94,90,82,85,32,81,121,108,24,72,165,104,17,103,69,66,105,11,113,29,22,43,120,38,54,71,78,23,100,159,79,91,82,109,89,83,80,173,36,64,31,58,132,129,96,120,58,72,77,71,21,78,68,88,82,116,172,29,126,19,31,55,89,49,93,24,172,76,65,42,36,25,59,73,22,156,57,80,1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