T=100;
N=100;
M=1000;
P=[|4860,5022,188,75,180,397,767,204,8507,785,2828,530,915,94,879,281,386,8570,695,5556,6962,394,401,294,5825,515,869,5449,19,514,758,691,339,324,950,68,93,287,401,2601,952,4063,301,68,748,417,128,2393,368,2020,762,858,278,419,8727,76,9997,805,8358,769,654,405,221,3324,584,9442,554,376,612,951,3347,409,538,468,119,368,682,9964,6811,692,27,261,759,340,888,700,2614,790,78,902,673,955,239,703,3988,904,666,1271,655,207,
|4907,5090,190,75,180,402,780,204,8549,794,2833,539,921,95,898,285,392,8754,704,5657,7085,399,405,298,5854,521,877,5482,19,522,774,698,341,324,950,68,94,287,407,2624,956,4155,306,68,750,422,128,2438,370,2030,772,869,282,423,8896,76,10000,814,8500,777,658,411,224,3359,596,9461,555,379,623,967,3407,417,541,475,119,375,689,10000,6837,695,27,263,762,341,895,711,2638,805,78,911,685,974,241,703,4010,916,673,1292,667,207,
|4985,5153,193,75,183,408,792,207,8610,800,2878,549,936,96,900,287,393,8864,711,5706,7089,405,408,300,5952,522,892,5528,19,522,790,707,342,327,956,68,95,291,409,2638,956,4190,311,68,750,424,129,2460,377,2072,776,874,282,426,8903,76,10000,830,8546,790,660,411,228,3401,603,9625,560,380,632,977,3436,419,546,481,119,377,698,10000,6973,701,27,268,776,347,913,724,2672,821,78,918,686,986,241,711,4028,923,677,1295,680,208,
|5003,5186,193,75,185,415,807,209,8791,806,2931,553,938,97,914,290,401,9045,721,5771,7172,413,414,305,5984,533,903,5532,19,525,804,719,346,328,959,68,96,294,417,2668,976,4234,313,68,758,425,130,2504,380,2081,788,882,287,431,8967,76,10000,846,8694,802,674,411,229,3451,610,9655,571,387,640,980,3491,423,552,489,120,383,706,10000,7014,712,27,272,781,352,917,731,2701,822,78,924,692,989,245,711,4048,941,682,1310,684,210,
|5041,5270,195,75,185,421,813,209,8804,819,2959,563,944,98,924,293,403,9161,726,5833,7175,414,418,306,5984,534,903,5535,19,533,811,719,350,332,960,68,97,297,424,2713,986,4264,319,68,771,428,131,2512,383,2122,802,899,288,433,9032,76,10000,846,8760,818,684,416,231,3452,623,9845,578,392,644,989,3518,426,552,496,120,389,709,10000,7061,722,27,275,790,356,924,745,2723,836,78,929,696,1008,246,714,4103,951,691,1325,691,211,
|5064,5324,197,75,186,423,830,212,8822,834,3008,568,959,98,942,294,411,9270,726,5864,7212,416,420,308,6083,537,907,5593,19,539,812,719,355,334,961,68,98,297,429,2754,986,4283,319,68,783,430,133,2542,385,2133,809,901,291,439,9199,76,10000,854,8883,823,695,421,235,3496,624,9902,587,398,646,1002,3589,428,558,506,120,389,723,10000,7159,724,27,276,801,358,940,746,2733,854,78,931,696,1029,249,715,4169,951,703,1341,695,212,
|5119,5336,199,75,189,423,833,213,8866,838,3023,570,969,98,945,299,419,9442,727,5984,7342,424,427,308,6189,546,911,5595,19,548,828,729,360,336,970,68,99,301,433,2795,990,4351,320,68,786,433,134,2548,386,2152,809,901,295,443,9379,76,10000,856,8950,839,697,422,238,3566,628,9942,589,401,659,1004,3665,436,562,508,121,395,729,10000,7197,726,27,277,803,364,954,755,2733,864,78,933,703,1045,251,730,4217,968,704,1346,704,212,
|5175,5415,200,75,191,424,849,216,8982,846,3079,575,975,99,952,299,422,9501,735,6075,7428,429,431,310,6305,554,916,5603,19,551,840,729,367,342,991,68,100,301,438,2839,999,4384,322,68,799,441,136,2594,388,2198,822,918,299,448,9530,76,10000,867,8980,853,699,430,238,3576,628,10000,591,403,673,1005,3690,443,568,510,121,403,737,10000,7246,736,27,281,808,371,962,756,2762,871,78,937,708,1052,254,734,4257,984,707,1369,714,212,
|5212,5452,201,75,192,426,849,217,9093,854,3107,580,990,100,963,300,422,9589,739,6104,7589,429,436,313,6336,554,936,5625,19,553,847,736,369,347,1000,68,100,303,442,2881,1008,4423,327,68,802,443,137,2600,392,2235,827,924,300,457,9542,76,10000,882,9080,871,710,434,238,3645,630,10000,596,408,673,1022,3767,451,580,516,122,409,746,10000,7409,738,27,283,824,378,972,763,2785,885,78,947,710,1070,258,748,4316,985,722,1385,716,214,
|5286,5570,201,75,195,434,856,217,9169,863,3161,586,1005,101,966,305,428,9767,750,6208,7731,430,442,315,6349,563,941,5733,19,564,854,746,370,350,1009,68,101,307,446,2936,1029,4475,328,68,814,449,139,2621,393,2263,833,944,302,465,9575,76,10000,897,9259,887,712,442,242,3683,631,10000,602,415,686,1037,3828,452,587,526,123,413,752,10000,7536,741,27,287,828,380,972,764,2825,886,78,966,723,1082,260,760,4318,987,724,1387,725,216,
|5310,5666,204,75,195,439,862,220,9230,875,3230,595,1025,102,966,309,431,9906,753,6224,7758,430,447,321,6466,573,953,5796,19,574,865,757,372,357,1016,68,102,312,448,2945,1030,4523,334,68,823,452,140,2651,393,2296,845,947,305,474,9761,76,10000,913,9310,905,712,450,246,3703,638,10000,604,417,699,1053,3864,461,597,530,123,420,765,10000,7602,742,27,290,832,385,993,775,2845,888,78,986,729,1088,263,762,4344,997,734,1401,731,217,
|5335,5697,206,75,196,448,872,220,9357,892,3291,595,1030,102,987,315,433,10000,755,6272,7758,435,447,324,6497,581,954,5850,19,577,880,763,374,358,1029,68,102,318,453,2956,1039,4523,337,68,833,454,142,2708,400,2300,857,965,310,481,9779,76,10000,929,9505,911,718,451,248,3780,649,10000,615,419,711,1059,3899,463,597,538,124,424,780,10000,7672,754,27,295,845,390,999,782,2882,898,78,1005,732,1089,264,765,4423,1018,743,1412,737,218,
|5424,5817,206,75,199,454,884,222,9544,894,3291,597,1037,103,990,315,440,10000,764,6415,7872,440,454,326,6505,587,969,5931,19,581,894,769,381,361,1031,68,102,318,457,2969,1058,4543,338,68,850,462,143,2724,401,2342,866,983,313,491,9966,76,10000,949,9692,925,723,459,252,3860,658,10000,627,424,725,1059,3909,464,602,539,124,432,788,10000,7699,766,27,298,856,393,1010,786,2921,907,78,1027,744,1098,265,779,4463,1019,747,1441,749,222,
|5471,5907,206,75,199,454,894,226,9581,899,3300,601,1051,103,996,318,441,10000,771,6478,7921,447,459,327,6506,594,976,5971,19,582,907,779,386,361,1049,68,102,322,458,2998,1067,4577,339,68,864,467,144,2740,405,2369,880,988,313,501,10000,76,10000,955,9889,927,729,461,256,3933,662,10000,632,432,730,1064,3979,465,604,545,125,437,788,10000,7808,777,27,299,865,395,1015,787,2969,923,78,1033,758,1098,268,782,4512,1033,755,1462,762,222,
|5476,6005,206,75,200,456,900,229,9740,903,3316,607,1057,104,996,323,449,10000,781,6499,7958,454,460,330,6628,599,988,5983,19,589,914,795,388,361,1060,68,102,327,462,3043,1088,4629,343,68,882,474,145,2745,410,2405,895,990,315,502,10000,76,10000,963,9992,929,732,464,256,3935,670,10000,638,435,735,1079,4010,468,604,551,126,442,793,10000,7856,783,27,301,876,399,1020,801,3022,936,78,1047,767,1100,268,783,4524,1036,765,1484,768,226,
|5579,6091,207,75,202,464,906,229,9820,911,3390,607,1068,104,1001,329,454,10000,83,6531,8023,456,468,334,6701,604,997,6031,19,600,923,796,390,362,1081,68,103,331,471,3066,1092,4674,343,68,901,477,147,2786,416,2436,895,990,317,511,10000,76,10000,975,10000,949,744,465,259,4002,676,10000,650,441,739,1094,4063,470,608,552,127,443,795,10000,7927,798,27,305,878,401,1028,804,3043,952,78,1062,782,1120,273,787,4614,1047,774,1490,769,226,
|5624,6219,208,75,203,466,908,231,9977,929,3397,612,1082,105,1021,334,457,10000,83,6623,8138,456,474,334,6771,606,1012,6165,19,609,934,801,393,363,1095,68,104,335,474,3128,1092,4682,347,68,914,484,149,2837,424,2482,912,1007,323,511,10000,76,10000,985,10000,969,747,469,263,4025,679,10000,662,443,754,1118,4087,476,613,554,128,450,809,10000,8007,814,27,309,886,408,1030,815,3053,970,78,1071,798,1123,273,794,4690,1053,775,1497,773,228,
|5735,6228,208,75,203,468,919,235,10000,941,3471,621,1094,106,1037,334,458,10000,83,6653,8323,464,474,334,6912,606,1026,6296,19,620,954,816,400,369,1115,68,27,340,482,3157,1116,4778,347,68,930,490,150,2858,431,2534,923,1028,327,514,10000,76,10000,1005,10000,989,752,476,268,4032,689,10000,664,448,759,1136,4132,477,615,554,129,457,824,10000,8107,822,27,313,894,411,1049,820,3116,990,78,1074,803,1129,273,794,4755,1060,785,1526,775,231,
|5822,6304,208,75,205,468,925,237,10000,947,3498,630,1103,107,1056,339,459,10000,83,6729,8325,471,474,339,6972,618,1040,6406,19,629,974,832,405,375,1129,68,27,342,483,3168,1136,4790,348,68,930,494,150,2879,432,2557,943,1050,329,518,10000,76,10000,1007,10000,989,759,484,272,4072,698,10000,670,450,769,1140,4144,485,620,562,129,458,827,10000,8143,826,27,319,906,416,1062,824,3162,998,78,1079,818,1135,277,796,4850,1081,787,1556,786,234,
|5869,6440,210,75,207,475,932,239,10000,951,3556,631,1127,107,1078,345,466,10000,83,6867,8373,476,474,341,7092,630,1056,6426,19,635,987,840,413,382,1129,68,27,347,493,3192,1160,4854,350,68,937,504,152,2884,439,2582,948,1053,332,519,10000,76,10000,1026,10000,996,768,487,273,4078,700,10000,680,456,772,1161,4148,486,629,562,129,464,831,10000,8273,831,27,324,921,423,1079,830,3190,1017,78,1097,818,1149,282,806,4947,1083,788,1561,797,237,
|5987,6505,212,75,207,483,945,241,10000,964,3586,638,1128,107,1092,350,466,10000,83,7022,8515,479,475,347,7150,641,1066,6564,19,646,989,841,416,383,1132,68,27,353,499,3203,1162,4859,352,68,937,511,154,2949,447,2614,959,1062,334,525,10000,76,10000,1029,10000,1014,768,495,273,4109,706,10000,688,460,782,1166,4151,488,629,570,129,467,848,10000,8399,846,27,330,936,429,1099,842,3237,1037,78,1119,823,1167,284,806,5054,1088,804,1594,805,239,
|6060,6647,214,75,209,489,948,245,10000,964,3626,650,1147,108,1116,356,473,10000,83,7079,8616,482,482,348,7159,652,1077,6630,19,648,995,841,418,390,1133,68,27,356,503,3274,1164,4869,356,68,940,511,156,3009,454,2673,969,1074,339,531,10000,76,10000,1048,10000,1019,783,502,277,4200,719,10000,700,469,797,1177,4217,488,639,574,129,469,854,10000,8451,850,27,331,956,437,1117,847,3266,1042,78,1126,837,1184,285,807,5123,1100,819,1604,812,242,
|6162,6714,214,75,212,495,948,247,10000,971,3680,654,1168,109,1124,360,475,10000,83,7088,8717,482,485,352,7169,653,1098,6761,19,656,999,849,425,391,1135,68,27,357,508,3305,1168,4959,363,68,942,514,158,3019,461,2685,975,1097,345,542,10000,76,10000,1068,10000,1038,800,507,277,4253,725,10000,714,477,811,1189,4279,490,644,579,130,476,865,10000,8627,862,27,337,973,443,1123,861,3323,1052,78,1132,850,1210,286,823,5207,1112,824,1613,815,244,
|6165,6777,217,75,212,502,959,248,10000,989,3724,668,1173,109,1136,364,476,10000,83,7128,8864,483,494,353,7295,666,1100,6812,19,660,1020,851,429,396,1155,68,27,362,514,3323,1191,5023,366,68,958,517,160,3086,461,2734,976,1112,346,552,10000,76,10000,1082,10000,1045,801,512,280,4328,728,10000,724,486,819,1193,4294,494,656,588,131,482,874,10000,8708,878,27,339,993,448,1139,873,3347,1065,78,1146,867,1224,288,837,5278,1127,830,1635,821,244,
|6252,6820,219,75,214,509,968,251,10000,1009,3768,677,1197,109,1140,368,481,10000,83,7284,8967,487,496,360,7401,680,1122,6962,19,666,1037,863,437,396,1165,68,27,365,517,3375,1194,5062,373,68,974,523,162,3125,468,2779,977,1118,347,563,10000,76,10000,1093,10000,1054,803,516,282,4388,740,10000,724,490,833,1202,4390,498,662,595,132,490,878,10000,8760,887,27,345,1008,454,1162,888,3357,1072,78,1160,869,1244,292,840,5315,1147,847,1647,824,246,
|6308,6887,223,75,216,509,976,255,10000,1028,3797,691,1197,109,1153,372,486,10000,83,7293,9062,490,498,361,7467,682,1133,6993,19,679,1043,863,443,400,1177,68,27,368,518,3408,1208,5085,373,68,993,528,163,3162,471,2838,978,1140,349,574,10000,76,10000,1093,10000,1060,819,516,282,4417,751,10000,728,495,846,1212,4448,501,670,597,133,490,894,10000,8884,899,27,348,1015,462,1184,894,3422,1094,78,1179,887,1248,295,847,5330,1166,848,1665,837,248,
|6371,6977,224,75,217,514,982,259,10000,1037,3801,697,1217,110,1172,377,490,10000,83,7315,9172,492,502,366,7525,695,1141,7107,19,685,1057,864,450,405,1180,68,27,369,526,3457,1209,5132,374,68,993,530,164,3220,472,2868,990,1154,352,575,10000,76,10000,1100,10000,1081,826,521,287,4427,758,10000,728,501,857,1216,4495,508,684,608,135,491,911,10000,8993,910,27,349,1015,468,1187,906,3474,1099,78,1180,889,1275,296,861,5448,1187,863,1702,848,250,
|6417,6997,225,75,217,517,1003,263,10000,1051,3839,704,1226,110,1197,384,497,10000,83,7427,9248,492,511,371,7614,701,1152,7140,19,685,1059,881,456,405,1198,68,27,375,528,3490,1212,5219,379,68,1014,533,164,3289,481,2917,1007,1171,356,585,10000,76,10000,1123,10000,1085,828,526,288,4453,761,10000,728,506,870,1227,4516,515,698,610,135,495,919,10000,9132,913,27,349,1030,476,1199,912,3552,1120,78,1189,904,1286,298,877,5502,1209,872,1729,859,250,
|6424,7135,226,75,218,519,1013,264,10000,1061,3863,705,1240,111,1214,385,499,10000,83,7521,9253,493,519,378,7637,710,1165,7281,19,696,1063,889,462,411,1222,68,27,380,529,3562,1217,5261,386,68,1017,534,165,3308,483,2958,1012,1190,361,594,10000,76,10000,1145,10000,1106,843,529,293,4465,762,10000,735,507,887,1236,4587,518,699,616,137,496,935,10000,9234,929,27,356,1043,481,1199,924,3608,1143,78,1198,906,1310,299,893,5620,1210,882,1729,863,250,
|6435,7146,230,75,222,522,1017,265,10000,1075,3931,711,1240,111,1222,390,505,10000,83,7627,9395,498,527,384,7739,722,1165,7406,19,704,1068,903,471,418,1226,68,27,387,530,3610,1238,5288,388,68,1024,538,166,3373,490,3010,1025,1215,366,602,10000,76,10000,1162,10000,1108,844,534,295,4561,774,10000,743,508,888,1249,4684,523,712,623,138,500,937,10000,9245,940,27,356,1051,486,1202,927,3682,1149,78,1205,912,1335,303,899,5625,1219,885,1759,872,252,
|6527,7220,230,75,226,533,1024,268,10000,1088,4014,711,1254,111,1229,391,509,10000,83,7655,9460,499,538,391,7762,728,1182,7450,19,718,1071,919,479,426,1252,68,27,387,536,3625,1255,5289,389,68,1046,541,167,3420,491,3010,1028,1235,373,602,10000,76,10000,1184,10000,1114,853,543,299,4628,789,10000,756,509,896,1262,4762,526,719,631,140,501,941,10000,9290,941,27,361,1060,490,1212,936,3749,1161,78,1210,930,1362,303,910,5687,1226,904,1770,874,253,
|6598,7309,230,75,228,536,1033,269,10000,1106,4076,724,1267,112,1243,398,512,10000,83,7715,9652,508,547,395,7841,740,1199,7481,19,731,1094,939,485,427,1264,68,27,387,541,3665,1274,5305,390,68,1065,546,169,3448,495,3044,1042,1241,376,606,10000,76,10000,1195,10000,1130,871,549,303,4683,802,10000,762,518,909,1269,4765,531,730,638,140,502,953,10000,9376,945,27,362,1079,490,1225,937,3778,1166,78,1227,945,1370,304,924,5767,1243,910,1802,882,254,
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