T=100;
N=100;
M=1000;
P=[|473,520,1823,216,865,736,717,3277,272,595,990,615,873,335,783,142,815,669,5853,222,5116,4530,827,847,723,146,8,299,302,8665,437,595,488,889,43,34,636,167,52,64,4957,549,789,792,532,569,899,42,573,893,1490,8826,90,6989,783,216,486,973,520,686,43,536,262,341,942,609,1162,72,6237,326,357,191,312,104,23,173,573,965,33,1642,721,182,970,915,22,721,678,709,688,543,7226,741,344,775,354,699,601,970,699,26,
|477,527,1857,217,881,746,718,3316,275,600,1008,617,888,337,796,142,825,672,5931,226,5141,4619,837,858,724,147,8,304,302,8813,444,607,496,897,43,34,647,168,52,64,5025,560,796,803,532,576,907,42,578,896,1523,8859,90,7089,788,216,491,984,521,696,43,539,267,342,948,613,1168,72,6250,330,364,192,314,104,23,175,573,981,33,1670,730,185,980,933,22,729,690,713,698,544,7314,743,344,777,356,709,601,970,708,26,
|477,527,1880,220,899,751,732,3345,277,608,1014,628,902,342,808,142,836,681,5996,226,5189,4645,840,863,728,149,8,305,305,8919,449,612,497,913,43,34,660,170,52,64,5043,568,808,804,538,585,915,42,582,908,1523,9057,91,7176,792,218,495,1001,523,701,43,544,267,344,954,617,1176,72,6339,330,367,192,320,104,23,176,585,983,33,1689,736,185,993,936,22,736,692,715,706,547,7417,757,346,782,361,724,603,972,713,26,
|477,531,1897,221,913,763,747,3376,277,611,1029,632,905,342,811,142,844,685,6106,228,5221,4694,847,878,737,151,8,311,310,9074,458,615,507,918,43,34,673,172,52,64,5074,576,823,816,545,587,916,42,582,909,1554,9175,91,7336,792,218,504,1016,530,715,43,545,269,350,973,620,1195,72,6474,331,372,195,321,105,23,179,595,993,33,1715,741,188,1013,939,22,747,705,729,709,548,7420,768,350,794,367,726,610,978,713,26,
|486,540,1933,221,916,779,753,3450,277,622,1044,632,905,344,821,142,851,685,6197,230,5326,4791,860,895,746,153,8,313,311,9184,461,628,516,927,43,34,685,173,52,64,5158,587,827,832,546,587,935,42,592,927,1560,9350,92,7421,805,221,504,1017,530,729,43,545,271,350,992,632,1221,72,6550,331,375,198,327,105,23,179,600,1014,33,1728,741,190,1016,959,22,757,709,743,712,551,7471,774,352,809,370,726,617,996,725,26,
|493,544,1956,221,930,781,768,3491,278,629,1066,632,906,344,838,142,867,689,6204,232,5371,4842,864,910,755,155,8,316,315,9226,462,628,524,934,43,34,685,174,52,64,5183,597,830,849,554,596,947,42,600,935,1563,9484,92,7447,805,224,508,1022,530,732,43,549,271,354,994,641,1227,72,6697,337,378,199,331,106,23,179,612,1034,33,1764,754,190,1026,960,22,769,721,747,718,554,7480,778,359,812,370,734,620,998,725,26,
|499,544,1981,223,932,788,782,3525,279,634,1069,636,923,345,841,144,872,693,6283,236,5477,4902,879,910,762,156,8,322,320,9310,465,633,531,935,43,34,687,174,52,64,5183,598,846,862,561,603,951,42,603,949,1583,9663,93,7595,814,228,514,1042,537,745,43,553,275,356,1011,645,1243,72,6723,341,380,199,331,106,23,182,619,1048,33,1786,767,193,1029,965,22,784,735,760,732,554,7553,783,359,821,376,735,630,1015,735,26,
|499,555,1992,226,940,797,782,3543,281,643,1071,636,942,347,853,145,872,702,6396,238,5527,4956,897,918,767,156,8,324,324,9433,470,635,537,948,43,34,687,175,52,64,5201,599,864,869,565,615,967,42,610,953,1597,9874,93,7679,815,228,522,1060,548,752,43,562,278,360,1018,651,1250,72,6815,346,385,201,334,107,23,185,623,1063,33,1810,775,196,1047,969,22,790,749,770,747,563,7658,785,364,832,382,736,637,1037,742,26,
|509,564,2031,229,953,807,788,3577,285,650,1078,647,958,349,859,145,876,710,6419,241,5588,4968,898,934,770,158,8,325,326,9643,478,645,541,967,43,34,689,176,52,64,5299,608,869,871,576,618,976,42,613,959,1597,9959,93,7798,827,229,533,1070,557,761,43,569,283,366,1023,657,1277,72,6967,348,389,204,334,108,23,185,635,1074,33,1832,790,198,1047,973,22,804,765,777,750,566,7682,796,369,847,385,743,642,1054,751,26,
|516,572,2037,231,960,811,800,3585,289,654,1088,659,964,354,869,146,886,712,6440,245,5613,5040,898,944,778,158,8,329,326,9715,486,645,547,971,43,34,700,179,52,64,5354,613,883,882,580,624,979,42,620,969,1606,9984,93,7933,845,231,542,1070,561,775,43,571,283,367,1045,657,1304,72,6996,353,391,204,336,108,23,187,641,1094,33,1873,803,200,1054,979,22,808,768,779,758,569,7756,808,370,849,391,744,647,1068,756,26,
|524,578,2045,235,974,820,817,3625,293,659,1104,667,979,354,881,146,886,722,6485,248,5724,5136,901,952,790,160,8,333,327,9765,496,645,550,980,43,34,712,180,52,64,5471,613,893,896,582,637,984,42,629,971,1632,10000,94,8079,845,231,543,1074,561,779,43,576,283,368,1068,657,1313,72,7139,353,398,205,338,109,23,189,646,1102,33,1880,814,202,1077,987,22,811,777,793,770,577,7837,810,377,855,398,758,651,1082,769,26,
|524,579,2051,239,988,827,820,3627,293,673,1111,678,980,355,898,146,901,732,6556,249,5836,5140,917,960,798,160,8,333,329,9917,504,656,557,995,43,34,712,182,52,64,5542,618,910,904,590,641,988,42,638,974,1645,10000,95,8239,851,233,547,1083,562,791,43,586,288,374,1073,657,1336,72,7192,360,406,205,338,109,23,191,649,1124,33,1901,824,203,1100,1005,22,827,782,793,778,580,7842,825,377,857,401,763,652,1088,774,26,
|528,582,2063,241,999,836,829,3675,297,677,1130,688,981,356,910,147,914,733,6652,249,5961,5191,936,977,809,161,8,333,331,9975,512,669,563,1013,43,34,717,182,52,64,5547,628,927,907,599,652,1003,42,646,977,1645,10000,95,8337,862,236,556,1097,567,808,43,590,290,381,1090,669,1350,72,7250,365,413,205,339,109,23,191,660,1139,33,1921,840,204,1107,1019,22,833,789,797,786,589,7882,833,378,863,407,765,655,1096,782,26,
|531,589,2079,245,1006,839,838,3700,300,678,1137,692,992,356,927,147,929,736,6772,251,6030,5288,943,984,813,163,8,336,331,10000,516,677,574,1031,43,34,720,185,52,64,5594,632,937,909,602,656,1023,42,653,985,1670,10000,96,8485,864,239,557,1114,570,825,43,593,293,383,1099,674,1373,72,7291,365,413,208,345,110,23,193,673,1140,33,1944,854,205,1129,1020,22,837,789,809,802,598,8036,837,384,876,410,777,661,1118,783,26,
|540,595,2090,248,1027,846,852,3735,305,682,1139,698,1007,363,937,149,941,741,6831,254,6106,5394,948,984,818,164,8,340,335,10000,521,680,576,1045,43,34,728,185,52,64,5653,643,953,909,604,667,1032,42,653,1005,1698,10000,96,8509,872,243,567,1129,574,831,43,601,298,388,1104,681,1392,72,7294,367,420,209,345,111,23,194,679,1155,33,1946,866,205,1135,1039,22,841,795,825,819,605,8040,837,386,895,417,790,661,1138,788,26,
|548,603,2105,251,1029,855,856,3738,307,688,1158,698,1013,369,952,149,955,755,6880,256,6244,5490,968,997,834,166,8,342,340,10000,525,686,576,1052,43,34,735,187,52,64,5664,653,958,924,606,670,1046,42,658,1018,1712,10000,96,8523,873,244,576,1131,581,848,43,608,298,389,1121,681,1402,72,7406,370,427,211,347,111,23,196,683,1171,33,1950,873,205,1158,1053,22,855,809,842,825,613,8069,838,387,899,420,806,670,1152,799,26,
|551,615,2105,253,1031,869,858,3759,307,698,1175,703,1022,376,965,150,968,762,7010,256,6279,5510,981,1018,849,168,8,347,342,10000,535,693,579,1072,43,34,739,188,52,64,5729,660,975,930,611,684,1049,42,667,1034,1720,10000,96,8621,881,248,582,1140,586,858,43,609,303,390,1124,692,1430,72,7462,374,435,211,353,112,23,196,695,1173,33,1959,877,205,1162,1056,22,869,820,854,838,619,8151,838,393,910,426,808,677,1172,804,26,
|561,627,2135,255,1046,886,858,3763,309,704,1200,705,1024,377,980,151,982,764,7152,257,6388,5568,997,1030,851,169,8,349,348,10000,540,695,591,1092,43,34,748,190,52,64,5841,665,993,941,623,698,1053,42,670,1048,1752,10000,96,8733,894,249,588,1147,597,871,43,621,304,397,1146,703,1436,72,7546,380,440,214,354,112,23,197,709,1174,33,2001,889,207,1172,1072,22,875,829,861,846,625,8235,856,398,918,427,819,691,1189,807,26,
|564,633,2139,259,1050,893,866,3848,313,715,1223,713,1025,383,1000,151,995,772,7158,257,6511,5648,1007,1036,855,171,8,352,353,10000,542,709,596,1104,43,34,752,190,52,64,5903,678,999,950,633,713,1069,42,684,1068,1789,10000,97,8906,901,252,594,1155,603,890,43,630,305,397,1163,710,1457,72,7610,381,448,217,354,112,23,198,714,1198,33,2030,903,208,1191,1079,22,878,841,867,858,630,8350,870,401,921,431,826,697,1196,815,26,
|573,645,2147,261,1058,904,875,3923,315,725,1223,725,1036,389,1003,151,995,780,7210,260,6562,5761,1024,1041,863,171,8,359,356,10000,550,720,608,1107,43,34,759,192,52,64,5953,689,1000,967,636,720,1081,42,693,1074,1812,10000,97,8931,907,256,597,1173,611,903,43,638,305,401,1185,724,1461,72,7726,386,456,218,356,112,23,198,717,1212,33,2058,916,208,1203,1084,22,883,852,885,874,638,8360,885,409,941,436,837,711,1198,826,26,
|579,648,2176,265,1063,920,893,3972,320,735,1240,732,1052,391,1004,153,1010,787,7353,260,6570,5881,1033,1047,876,173,8,366,360,10000,560,734,615,1131,43,34,767,194,52,64,6052,696,1020,982,638,721,1081,42,702,1075,1812,10000,98,9095,916,260,602,1184,624,903,43,649,306,409,1197,729,1490,72,7824,391,460,219,357,112,23,198,730,1218,33,2088,920,209,1203,1095,22,892,864,892,877,650,8460,902,415,959,441,845,726,1208,827,26,
|580,654,2220,270,1075,933,895,3996,322,741,1247,736,1075,393,1009,153,1014,797,7501,260,6710,5926,1051,1057,889,175,8,368,363,10000,569,746,623,1154,43,34,768,194,52,64,6074,701,1031,989,641,731,1095,42,703,1075,1812,10000,98,9121,916,261,603,1198,626,905,43,650,312,416,1208,743,1499,72,7890,398,461,222,359,113,23,199,734,1229,33,2106,929,212,1218,1107,22,902,877,902,890,658,8632,921,422,963,450,857,732,1214,827,26,
|587,660,2231,270,1093,943,898,4026,327,754,1265,741,1078,394,1010,153,1014,806,7552,260,6723,5988,1068,1061,907,176,8,374,368,10000,572,752,632,1155,43,34,779,195,52,64,6092,707,1034,1007,646,738,1118,42,710,1092,1824,10000,99,9145,936,262,610,1201,631,921,43,662,317,419,1218,743,1528,72,7960,402,464,223,366,113,23,199,748,1240,33,2144,938,213,1243,1131,22,908,894,909,893,658,8700,923,430,964,457,873,745,1236,829,26,
|589,663,2278,274,1112,950,914,4037,332,770,1273,749,1095,395,1015,155,1027,821,7641,263,6767,6098,1071,1068,908,179,8,375,372,10000,581,762,637,1173,43,34,795,195,52,64,6202,708,1052,1009,659,751,1123,42,713,1103,1842,10000,99,9164,938,265,619,1201,633,939,43,672,322,420,1241,748,1534,72,8022,407,469,227,372,113,23,200,748,1266,33,2165,952,214,1262,1148,22,924,911,928,905,659,8852,925,430,984,460,891,752,1240,846,26,
|590,669,2312,274,1120,956,914,4063,335,772,1281,758,1102,397,1037,157,1047,836,7692,263,6811,6197,1074,1075,908,182,8,379,378,10000,591,772,642,1177,43,34,806,196,52,64,6316,720,1058,1009,670,764,1126,42,719,1109,1879,10000,99,9206,942,266,619,1212,639,958,43,673,328,421,1258,756,1539,72,8188,411,470,231,372,114,23,200,757,1276,33,2210,963,215,1269,1154,22,935,919,942,916,673,8908,940,431,984,460,892,763,1247,862,26,
|602,681,2333,276,1130,966,925,4115,336,779,1297,761,1124,400,1043,157,1064,841,7853,263,6843,6247,1095,1089,913,182,8,382,381,10000,602,782,647,1189,43,34,810,197,52,64,6454,722,1063,1016,671,774,1149,42,725,1119,1906,10000,100,9243,944,271,625,1234,651,972,43,685,330,428,1284,756,1542,72,8364,411,473,232,375,115,23,200,768,1289,33,2250,968,217,1271,1161,22,938,928,942,926,681,8963,942,439,987,467,900,779,1259,879,26,
|611,683,2354,279,1145,986,933,4147,342,795,1310,761,1138,403,1053,158,1064,858,7927,264,6864,6283,1113,1109,929,182,8,388,383,10000,610,795,650,1190,43,34,817,200,52,64,6588,724,1075,1026,680,782,1173,42,739,1133,1942,10000,100,9450,944,276,628,1251,656,990,43,690,334,431,1300,764,1548,72,8518,413,477,236,376,116,23,203,770,1295,33,2300,988,217,1277,1175,22,949,930,948,945,688,9087,954,445,1001,472,902,788,1264,888,26,
|615,692,2371,282,1154,992,950,4220,344,800,1322,771,1160,408,1057,159,1087,873,8067,264,6992,6350,1123,1125,941,184,8,390,388,10000,623,802,663,1209,43,34,817,202,52,64,6711,739,1086,1027,689,792,1184,42,748,1140,1960,10000,101,9464,945,281,637,1257,668,1004,43,703,334,438,1317,780,1564,72,8542,418,485,237,382,117,23,206,783,1298,33,2314,1005,220,134,1186,22,968,941,958,950,689,9217,958,447,1014,481,916,794,1284,892,26,
|626,703,2374,284,1162,1009,962,4278,349,808,1322,776,1182,410,1077,160,1088,889,8223,266,7070,6353,1145,1145,947,184,8,391,388,10000,630,819,667,1221,43,34,827,202,52,64,6771,753,1092,1027,697,796,1206,42,762,1146,1988,10000,101,9556,965,286,650,1278,672,1022,43,710,337,447,1330,781,1591,72,8598,419,486,239,388,118,23,207,791,1309,33,2329,1026,223,134,1195,22,981,953,958,965,689,9236,975,449,1016,485,919,807,1285,899,26,
|637,713,2386,287,1174,1020,967,4286,355,822,1341,790,1200,414,1084,160,1097,899,8361,267,7177,6379,1151,1165,949,186,8,396,394,10000,630,835,670,1225,43,34,827,203,52,64,6810,766,1110,1035,712,809,1210,42,774,1157,2009,10000,101,9731,985,288,659,1301,672,1043,43,724,339,450,1335,781,1619,72,8755,422,490,240,393,119,23,207,798,1309,33,2376,1026,225,135,1221,22,995,953,960,971,689,9427,992,451,1028,485,921,819,1296,914,26,
|648,724,2389,287,1179,1023,983,4309,357,822,1349,803,1204,419,1097,160,1104,917,8395,178,7293,6467,1155,1183,964,187,8,399,398,10000,631,851,672,1238,43,34,841,205,52,64,6838,781,1116,1040,714,821,1218,42,774,1163,2045,10000,102,9802,996,292,662,1308,672,1051,43,728,339,453,1336,795,1626,72,8898,422,494,241,396,120,23,209,799,1321,33,2410,1035,229,137,1236,22,1002,972,980,987,703,9585,995,451,1035,487,930,831,1299,916,26,
|648,735,2396,291,1182,1039,1003,4334,359,831,1377,804,1216,423,1106,162,1121,928,8515,180,7325,6593,1156,1192,966,188,8,405,404,10000,637,862,680,1264,43,34,842,207,52,64,6937,795,1133,1045,723,830,1219,42,777,1170,2048,10000,103,9926,1007,295,671,1321,684,1073,43,742,342,459,1336,804,1640,72,9006,427,500,243,402,121,23,209,815,1327,33,2410,1040,232,138,1262,22,1013,987,990,988,703,9659,1011,451,1046,489,950,832,1313,921,26,
|648,743,2430,292,1201,1055,1014,4351,360,831,1388,805,1236,423,1114,163,1145,947,8626,182,7418,6743,1161,1195,970,188,8,406,406,10000,643,880,690,1270,43,34,859,208,52,64,6963,803,1144,1060,724,845,1233,42,791,1178,2078,10000,103,10000,1024,295,680,1333,687,1074,43,751,344,462,1346,809,1670,72,9096,435,506,247,407,121,23,210,816,1348,33,2428,1062,232,138,1263,22,1020,987,1002,993,715,9738,1013,454,1055,492,959,833,1338,921,26,
|651,743,2478,292,1206,1067,1014,4426,364,833,1391,812,1236,429,1126,163,1170,965,8790,183,7583,6795,1183,1215,986,189,8,411,411,10000,653,885,699,1274,43,34,860,208,52,64,6989,819,1162,1061,738,861,1238,42,806,1204,2110,10000,103,10000,1043,298,684,1341,694,1084,43,762,347,464,1347,823,1674,72,9256,443,512,247,412,122,23,213,822,1376,33,2453,1078,236,140,1284,22,1022,1005,1018,1005,726,9749,1025,461,1074,498,964,838,1367,929,26,
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