T=80;
N=100;
M=500;
P=[|6369,397,420,1560,1673,267,246,86,9396,162,139,105,265,74,364,499,239,189,371,103,7198,3491,9004,6742,1428,73,3681,399,274,205,5991,336,437,341,27,4255,54,304,482,77,330,323,209,102,6,378,134,439,76,85,77,250,6016,342,8859,1326,964,377,51,373,373,308,264,6012,307,115,293,138,133,170,437,233,199,127,227,380,486,175,11,411,3716,57,139,47,385,47,98,391,139,159,305,140,267,7551,317,197,157,194,90,75,
|6442,399,423,1564,1710,271,248,86,9481,164,139,105,270,74,371,501,240,189,371,103,7320,3520,9186,6895,1459,73,3757,405,274,206,6072,340,440,341,27,4310,54,307,483,77,334,327,211,103,6,378,134,441,76,85,77,250,6126,348,8918,1334,980,383,51,379,375,314,268,6138,310,115,293,139,134,170,446,236,201,128,231,384,490,176,11,418,3752,57,139,47,388,47,98,393,139,161,307,141,269,7641,322,198,157,195,90,75,
|6514,406,427,1592,1745,274,248,86,9556,164,141,105,271,74,377,504,243,190,373,103,7450,3570,9378,7041,1469,73,3792,413,275,207,6075,343,442,345,27,4331,54,307,488,77,339,329,214,103,6,385,136,445,76,85,77,252,6178,349,8951,1349,999,390,51,385,381,319,271,6224,310,115,298,140,136,171,447,240,202,129,232,386,495,176,11,426,3763,57,141,47,390,47,99,398,139,163,313,142,273,7815,327,200,157,197,90,75,
|6602,409,432,1606,1777,276,252,86,9761,164,143,105,272,74,382,514,245,190,378,103,7457,3583,9584,7106,1476,73,3824,416,276,210,6147,343,449,351,27,4383,54,310,493,77,339,335,216,104,2,390,137,448,76,85,77,254,85,355,9076,1371,1011,393,51,389,382,321,274,6268,312,116,301,140,136,173,447,242,203,130,234,393,495,178,11,427,3833,57,141,47,390,47,100,398,139,163,315,142,251,7985,328,200,159,200,90,75,
|6623,414,438,1624,1804,278,254,86,9801,164,143,105,274,74,389,522,248,190,378,104,7598,3586,9604,7161,1494,73,3878,424,278,212,6171,349,449,354,27,4399,54,315,502,77,344,335,218,104,2,393,138,453,76,85,77,254,85,357,9138,1395,1019,394,51,390,389,322,278,6296,318,116,305,142,136,174,448,243,204,130,236,400,504,180,11,427,3858,57,142,47,396,47,100,406,141,163,320,144,251,7999,333,201,161,203,90,75,
|6654,416,446,1637,1816,282,256,86,9912,166,143,106,275,74,394,527,252,193,379,105,7696,3640,9764,7204,1508,73,3894,431,280,213,6210,355,453,359,27,4411,54,319,510,77,346,336,221,104,2,399,139,462,76,85,77,32,85,359,9289,1415,1021,399,51,393,394,324,280,6385,323,116,306,143,137,176,449,247,206,130,239,408,505,180,11,433,3937,57,144,47,400,47,101,413,142,165,322,144,254,8149,339,202,163,204,91,75,
|6780,417,450,1638,1841,282,258,86,10000,168,144,106,279,51,394,533,256,194,385,106,7722,3670,9891,7279,1515,73,3954,436,281,216,6296,361,459,365,27,4473,54,4,510,77,351,340,224,104,2,401,139,467,76,85,77,32,85,361,9501,1428,1022,406,51,397,396,327,283,6439,328,117,307,144,137,178,452,250,208,131,239,415,512,183,11,440,3974,57,146,47,406,47,101,416,142,167,324,146,257,8241,339,205,164,204,91,75,
|6810,419,451,1667,1857,282,262,86,10000,168,146,106,281,51,394,539,257,195,389,107,7863,3704,10000,7409,1537,73,4020,437,283,219,6331,367,463,367,27,4486,54,4,518,77,352,346,228,105,2,405,140,472,76,85,77,32,85,362,9591,1450,1024,409,51,401,399,327,287,6458,333,117,311,144,137,179,456,250,209,132,243,423,512,185,11,446,4049,54,147,47,411,47,102,418,142,168,328,148,258,8400,341,206,166,204,91,75,
|6822,424,453,1701,1872,286,265,86,10000,169,148,107,286,51,401,550,257,197,393,108,7931,3758,10000,7451,1548,73,4093,438,283,219,6373,370,466,367,27,4493,54,4,527,77,356,350,228,106,2,408,140,472,76,85,77,32,85,364,9668,1481,1040,412,51,409,399,329,288,6465,335,118,317,146,137,179,457,252,212,134,247,430,519,188,11,446,4098,54,147,47,413,47,103,425,142,168,331,148,260,8522,343,209,168,207,91,75,
|6875,428,454,1729,1902,291,266,86,10000,170,148,108,289,51,406,552,258,200,400,109,7932,3773,10000,7477,690,73,4127,439,287,222,6491,377,469,369,27,4563,54,4,534,77,356,354,228,106,2,408,141,472,76,85,77,32,85,369,9840,1510,1043,415,51,417,400,331,289,6546,337,119,319,146,139,182,459,254,215,135,247,436,521,191,11,451,4169,54,149,47,417,47,104,429,142,169,336,148,261,8715,348,210,168,208,91,75,
|6979,428,462,1748,1906,295,268,86,10000,170,148,108,291,51,413,555,261,203,400,109,7957,3839,10000,7497,700,73,4171,442,287,224,6518,382,478,376,27,898,54,4,539,77,358,359,232,106,2,414,142,475,76,85,77,32,85,373,9972,1525,1049,418,51,425,403,332,290,6694,337,120,324,147,139,182,462,254,218,136,249,441,528,194,11,452,4176,54,150,47,417,47,105,432,142,169,341,149,261,8846,348,210,168,208,92,75,
|7072,429,466,1753,1923,298,271,86,10000,170,150,108,292,51,416,563,266,205,402,109,7989,3845,10000,7543,705,73,4205,450,292,228,6542,382,479,380,27,912,54,4,549,77,364,361,234,106,2,416,143,483,76,85,77,32,85,379,10000,1536,1068,424,51,428,411,332,293,6846,343,120,326,147,140,183,468,257,222,138,250,445,533,194,11,457,4219,54,152,47,423,47,106,438,143,170,346,149,266,8913,348,212,168,209,93,75,
|7166,432,471,1767,1964,303,273,86,10000,170,150,109,295,51,416,569,268,207,406,109,8004,3868,10000,7554,716,73,4260,451,297,230,6639,386,486,387,27,923,54,4,551,77,365,361,234,107,2,417,144,488,76,85,77,32,85,386,10000,1559,1089,432,51,433,415,336,294,6999,349,121,329,149,141,184,477,257,226,140,250,447,541,194,11,461,4299,54,152,47,430,47,107,441,143,63,348,150,269,9084,351,215,168,210,94,75,
|7287,438,479,1785,1987,306,277,86,10000,171,150,109,296,51,422,570,272,210,408,109,8126,3897,10000,7638,722,73,4341,455,301,232,6674,389,488,390,27,924,54,4,561,77,371,365,236,108,2,417,144,492,76,85,77,32,85,392,10000,1591,1096,436,51,441,423,338,295,7092,353,122,334,151,141,1,486,257,229,141,251,453,550,197,11,468,4303,54,153,47,433,47,107,450,145,63,349,151,273,9241,352,215,169,211,95,75,
|7348,445,273,1797,2004,310,279,86,10000,172,151,110,296,51,424,575,274,210,415,110,8239,3981,10000,7735,727,73,4431,456,305,232,6708,390,490,397,27,942,54,4,562,77,374,370,239,108,2,422,145,497,76,85,77,32,85,393,10000,1614,1102,438,51,446,431,339,296,7235,358,122,334,151,143,1,495,257,229,141,251,454,560,200,11,477,4339,54,154,47,439,47,107,456,145,63,355,152,274,9393,359,215,170,214,96,75,
|7360,449,278,1817,2015,314,284,86,10000,174,151,111,299,51,424,578,277,210,417,111,8241,4022,10000,7743,736,73,4500,461,307,235,6797,390,490,399,27,943,54,4,566,77,375,375,242,109,2,424,147,497,76,85,77,32,85,395,10000,1640,1116,443,51,449,436,340,298,7337,364,122,340,152,145,1,501,260,230,142,254,454,561,201,11,480,4400,54,156,47,439,47,108,456,145,63,360,153,279,9538,363,217,171,216,96,75,
|7475,454,279,1857,2026,319,288,86,10000,174,151,112,302,51,425,590,281,211,422,112,8252,4037,10000,7915,744,73,4591,467,309,239,6930,395,494,403,27,951,54,4,569,68,382,379,244,109,2,430,149,499,76,85,77,32,85,400,10000,1647,1121,452,51,455,444,341,301,7401,370,123,345,153,146,1,507,260,233,143,257,459,568,203,11,487,4437,54,156,47,440,47,109,462,145,63,366,155,280,9569,368,217,173,218,96,75,
|7478,455,281,1862,2028,325,291,86,10000,177,151,113,302,51,430,590,283,211,427,113,8371,4100,10000,7953,752,73,4627,474,309,240,6995,399,496,410,27,960,54,4,573,68,389,384,246,110,2,430,150,508,76,85,77,32,85,406,10000,1663,1145,456,51,456,447,342,304,7545,377,112,350,155,147,1,513,262,234,143,261,461,570,205,11,494,4528,54,156,47,446,47,110,469,147,63,372,155,283,9647,369,220,173,219,97,75,
|7577,458,282,1881,2073,325,295,86,10000,179,153,114,304,51,435,597,286,214,434,114,8418,4192,10000,8049,755,73,4660,475,309,243,7070,404,503,416,27,978,54,4,575,68,396,391,246,110,2,436,151,512,76,85,77,32,85,413,10000,1671,1158,458,51,465,455,345,306,7548,384,113,351,156,148,1,514,262,238,143,265,466,571,205,11,496,4614,54,158,47,450,47,111,474,148,63,377,156,288,9786,374,222,173,223,97,75,
|7669,459,286,1920,2077,329,298,86,10000,179,155,114,306,51,441,609,289,215,435,114,8562,4244,10000,8216,758,73,4193,478,310,247,7142,410,506,420,27,989,54,4,586,68,400,396,248,111,2,440,152,516,76,85,77,32,85,414,10000,1691,1182,459,51,474,457,346,307,7586,391,113,355,158,149,1,515,265,240,144,268,466,580,205,11,260,4659,54,160,47,454,47,111,483,149,63,383,158,289,9988,375,226,174,226,98,75,
|7764,468,291,1950,2122,330,299,86,10000,179,156,114,311,51,441,610,290,217,443,115,8580,4272,10000,8263,772,73,4238,483,313,251,7142,416,514,423,27,1002,54,4,598,68,406,402,252,112,2,446,152,520,76,85,77,32,85,414,10000,1726,1206,461,51,479,458,347,309,7757,398,113,355,159,151,1,515,267,244,145,268,469,590,208,11,55,4715,54,160,47,454,47,112,490,150,63,386,159,291,10000,376,229,174,228,98,75,
|7790,475,296,1959,2138,331,302,86,10000,181,158,115,313,51,449,620,293,218,447,116,8614,4323,10000,8263,781,73,4295,485,316,252,7262,419,516,426,27,1020,54,4,598,68,410,403,256,113,2,447,152,529,76,85,77,32,85,416,10000,1741,1217,467,51,482,464,351,314,7815,401,114,355,159,152,1,518,268,247,147,270,474,600,211,11,55,4743,54,161,47,460,47,112,493,152,63,392,161,295,10000,381,229,177,229,99,75,
|7809,484,300,1980,2147,334,302,86,10000,181,160,116,318,51,455,631,294,221,452,117,8643,4388,10000,8397,791,73,4353,491,316,253,7273,420,523,430,27,1023,54,4,603,68,418,407,256,114,2,452,152,536,76,85,77,32,85,420,10000,1771,1219,473,51,489,464,351,314,7872,408,115,87,160,152,1,526,272,248,148,275,475,611,212,11,55,4778,54,163,47,461,47,113,499,153,63,396,163,297,10000,382,231,180,230,99,75,
|7863,485,301,1990,2190,340,304,86,10000,183,161,117,320,51,460,631,297,225,455,118,8707,4454,10000,8506,792,73,4401,499,317,256,7312,426,524,432,27,1041,54,4,609,68,418,411,256,114,2,456,153,539,76,85,77,32,85,421,10000,1781,1242,475,51,497,464,354,320,7980,415,115,88,162,154,1,533,273,249,150,279,482,623,213,11,55,4839,54,163,47,464,47,113,501,155,63,400,164,300,10000,388,235,182,233,99,75,
|7905,488,305,2000,2217,341,309,86,10000,186,162,117,324,51,465,638,300,228,464,118,8739,4475,10000,8507,807,73,4493,501,320,260,7382,430,533,434,27,1045,54,4,620,68,426,413,258,115,2,457,154,545,76,85,77,32,85,428,10000,1818,1263,475,51,499,469,359,321,8042,420,115,88,164,155,1,533,276,253,151,281,486,624,215,11,55,4844,54,163,47,465,47,114,509,157,63,406,165,301,10000,388,239,183,233,100,75,
|7920,494,306,2001,2227,345,310,86,10000,188,164,118,327,51,474,650,303,232,473,118,8873,4531,10000,8615,815,73,4528,503,322,260,7407,432,538,439,27,1052,54,4,623,68,433,420,261,115,2,457,155,552,76,85,77,32,85,434,10000,1839,1284,479,51,503,475,359,323,8117,427,116,89,164,155,1,540,281,257,153,283,494,625,217,11,55,2033,54,163,47,469,47,115,512,159,63,413,165,306,10000,394,243,186,237,101,75,
|7997,502,309,2001,2276,350,315,86,10000,189,166,118,327,51,481,652,308,232,476,119,8910,4625,10000,8785,821,73,4528,509,328,262,7461,438,546,448,27,1056,54,4,626,68,435,421,264,115,2,459,155,553,76,85,77,32,85,435,10000,1879,1297,486,51,513,476,364,325,8118,430,117,89,164,157,1,547,285,259,155,287,497,637,219,11,55,2076,54,165,47,475,47,116,513,159,63,421,167,309,10000,397,247,187,240,101,75,
|8082,510,315,2012,2313,352,321,86,10000,190,168,118,331,51,487,655,311,236,481,119,9021,4648,10000,8915,831,73,4550,519,328,265,7477,440,547,457,27,1074,54,4,634,68,442,427,264,116,2,465,157,558,76,85,77,32,85,443,10000,1889,1310,494,51,520,483,367,329,8229,432,118,89,164,159,1,553,289,262,155,208,497,642,222,11,55,2098,54,167,47,479,47,116,516,160,63,427,168,310,10000,401,250,190,240,101,75,
|8137,513,316,2056,2348,354,326,86,10000,190,169,118,332,51,490,658,317,238,486,119,9067,4725,10000,9084,843,45,4644,519,334,268,7591,444,547,462,27,1090,54,4,642,68,451,428,265,116,2,472,158,564,76,85,77,32,85,451,10000,1928,1310,494,51,527,1,374,332,289,438,118,89,166,159,1,561,292,267,156,211,497,654,226,11,55,2124,54,169,47,489,47,116,519,162,63,429,168,314,10000,402,250,191,242,102,75,
|8240,516,320,2086,2394,354,329,86,10000,192,171,119,332,51,494,669,323,240,494,120,9143,4832,10000,9087,860,45,4712,523,340,270,7687,449,556,466,27,1097,54,4,645,68,460,436,268,116,2,478,158,568,76,85,77,32,85,457,10000,1969,1325,495,51,531,1,381,333,293,445,119,89,167,161,1,564,297,270,158,213,506,660,227,11,55,2164,54,169,47,494,47,117,520,162,63,433,168,316,10000,406,253,194,245,103,75,
|8252,524,322,2129,2441,361,335,86,10000,193,172,119,338,51,504,578,326,240,496,120,9259,4842,5335,9089,872,45,4744,529,346,273,7724,451,565,471,27,1100,54,4,655,68,466,441,271,116,2,482,159,575,76,85,77,32,85,458,10000,1971,1337,496,51,541,1,386,335,296,445,120,89,168,162,1,570,300,270,158,214,508,667,231,11,55,2206,54,171,47,495,47,118,527,162,63,436,169,320,10000,409,254,197,247,104,75,
|8339,527,326,2154,2478,368,335,86,10000,193,174,29,344,51,504,590,332,241,501,120,9311,4942,5434,9199,876,45,4782,539,346,274,7872,455,567,477,27,1112,54,4,661,68,469,443,275,117,2,490,160,582,76,85,77,32,85,466,10000,1981,1358,503,51,548,1,388,340,298,451,120,89,170,164,1,571,302,274,159,217,517,667,233,11,55,2236,54,173,47,504,47,118,528,162,63,444,171,321,10000,409,258,199,250,104,75,
|8373,531,328,2161,2524,370,335,86,10000,193,177,29,345,51,512,599,335,242,503,120,9464,4997,5547,9232,886,45,4848,542,346,277,8023,460,568,484,27,1121,54,4,672,68,477,446,279,118,2,496,161,585,76,85,77,32,85,470,10000,1989,1364,510,51,554,1,389,344,300,454,120,89,172,164,1,571,305,276,159,218,519,672,233,11,55,2271,54,174,47,506,47,118,539,163,63,451,171,326,10000,412,260,201,254,104,75,
|8448,538,333,2186,2524,370,339,86,10000,195,180,29,347,51,516,603,340,243,506,120,9467,5079,5609,9402,905,45,4858,546,349,280,8060,468,577,488,27,1125,54,3,679,68,481,451,282,119,2,506,162,597,76,85,77,32,85,471,10000,2002,1377,513,51,563,1,389,345,302,457,121,90,174,166,1,576,309,277,160,220,521,672,234,11,55,2319,54,176,47,507,47,118,547,165,63,456,173,327,10000,414,262,203,255,104,75,
|8564,546,337,2210,2570,374,344,86,10000,197,181,29,353,51,526,612,345,246,508,121,9603,5161,5666,9492,915,45,4940,555,352,284,8137,477,577,498,27,1145,54,3,685,68,483,457,284,120,2,514,162,600,76,85,77,32,85,472,10000,2033,1399,523,51,564,1,391,345,306,460,121,90,174,167,1,578,310,277,160,222,524,676,234,11,55,2329,54,176,47,509,47,119,552,165,63,463,174,327,10000,414,262,203,257,105,49,
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