T=100;
N=100;
M=1000;
P=[|478,615,949,663,949,741,678,934,6541,6549,5863,142,540,5100,8854,636,620,424,35,976,572,110,52,417,288,517,855,321,3676,553,660,829,309,81,408,702,760,657,851,26,281,3824,578,100,725,115,2991,95,952,696,676,519,712,796,188,689,400,686,538,614,743,922,703,508,438,751,544,557,269,81,198,318,935,615,797,521,8353,174,445,355,223,325,4668,159,679,127,810,41,579,956,443,620,428,903,425,69,474,561,31,653,
|484,619,961,671,959,748,690,937,6547,6622,5958,142,546,5211,8947,648,630,426,35,977,572,110,52,421,290,526,857,322,3231,556,662,838,315,81,414,716,769,664,851,26,283,3847,581,101,726,116,2996,95,964,711,682,527,727,804,191,701,402,697,544,621,750,923,710,511,439,758,551,568,272,81,198,321,941,627,804,525,8488,176,451,361,224,325,4700,160,680,127,813,41,585,967,451,626,433,920,427,69,483,564,31,660,
|490,622,980,674,962,762,702,949,6693,6637,6015,143,555,5309,9021,653,641,430,35,977,575,110,52,422,290,530,865,327,3245,556,666,849,315,81,414,723,775,678,867,26,287,3855,581,101,741,116,3057,96,979,716,685,530,731,814,192,701,408,709,554,629,764,934,719,514,439,770,559,580,273,81,200,322,949,633,805,534,8494,176,459,367,228,331,4805,160,684,128,815,41,595,978,454,629,439,933,434,69,491,571,31,669,
|493,630,996,675,974,764,710,964,6811,6681,6025,144,566,5419,9169,653,644,438,35,981,579,110,52,428,292,540,883,330,3299,564,676,857,318,81,417,735,776,686,884,26,290,3919,588,101,756,116,3126,97,997,718,697,536,746,830,194,704,410,717,558,631,780,938,719,523,447,771,570,590,276,81,202,325,968,638,815,543,8569,177,462,368,230,332,4870,161,691,128,828,41,605,991,458,638,447,935,440,69,491,582,31,676,
|497,631,1010,681,986,771,715,973,6896,6699,6038,146,568,5460,9346,667,646,445,35,984,580,111,52,431,295,545,895,332,3338,572,677,874,320,81,417,737,783,695,887,26,294,3980,600,101,768,117,3135,97,1010,728,703,537,747,842,197,705,412,724,563,641,780,946,720,526,454,773,574,595,280,81,202,331,984,645,818,549,8632,178,466,369,231,338,4894,162,692,128,830,41,615,1009,467,649,456,950,445,69,493,589,31,683,
|497,644,1014,694,1001,784,727,974,7034,6133,6061,147,569,5539,9484,676,648,445,35,1003,583,111,52,433,299,549,898,337,3363,581,686,876,324,81,422,741,790,703,887,26,298,3989,612,101,781,118,3173,97,1013,735,709,540,760,847,199,714,417,735,570,646,789,965,725,528,463,788,586,606,284,81,205,334,997,647,831,549,8749,179,473,375,232,338,4995,163,706,128,844,41,622,1027,470,654,461,960,454,69,499,592,31,688,
|502,649,1031,706,1019,789,730,992,7130,6265,6141,149,579,5629,9496,679,650,451,35,1025,589,112,52,436,301,558,913,337,3384,593,694,880,329,81,423,752,795,705,906,26,298,4040,617,102,784,118,3195,97,1031,740,716,546,764,864,200,728,424,741,580,655,806,981,735,533,463,800,591,612,284,81,206,334,1011,650,834,550,8754,180,476,375,236,338,5001,165,707,129,862,41,630,1035,475,667,467,969,458,69,500,595,31,689,
|510,659,1038,712,1020,793,734,1004,5371,6343,6198,149,584,5641,9526,684,658,456,35,1035,598,112,52,442,306,561,926,343,3406,593,695,884,334,81,423,753,810,708,918,26,298,4064,624,103,793,118,3243,97,1040,746,731,551,774,875,201,735,425,757,591,657,806,996,736,544,464,811,599,619,288,81,208,335,1031,655,841,554,8923,183,479,376,237,341,5053,167,712,130,870,41,638,1042,475,667,467,974,460,69,502,605,31,689,
|510,662,1046,717,1032,804,746,1006,5468,6477,6263,149,594,5721,9526,693,661,457,35,1049,603,112,52,450,306,569,931,344,3464,596,709,893,339,81,423,760,822,721,926,26,300,4141,633,103,435,118,3253,98,1046,749,738,558,785,889,201,749,427,761,602,664,819,998,736,551,464,822,609,625,290,81,208,339,1043,665,851,557,9125,184,484,377,240,347,5148,167,717,130,876,41,641,1063,483,673,473,978,468,69,503,605,31,699,
|511,673,1056,722,1048,820,754,1027,5541,6484,6349,149,600,5827,9665,707,674,466,35,1060,606,113,52,457,306,571,947,347,3495,601,719,909,343,81,430,765,832,734,944,26,302,4174,638,103,438,119,3259,99,1055,750,752,560,788,908,201,759,428,764,605,674,821,1019,738,558,471,836,620,633,290,81,210,340,1048,669,867,558,9306,186,484,377,240,351,5225,167,718,131,888,41,652,1079,484,678,478,997,476,69,510,608,31,705,
|511,675,1057,727,1070,830,765,1028,5626,6513,6413,150,608,5830,9807,707,687,466,35,1071,612,113,52,458,307,571,965,350,3523,605,725,926,345,81,430,774,841,738,952,26,304,4232,651,103,447,120,3286,99,1059,762,759,569,797,913,202,771,430,764,610,676,834,1031,740,559,474,850,631,642,290,81,210,343,1058,678,873,567,9391,188,494,377,240,352,5231,169,730,132,900,41,664,1091,484,680,478,1006,477,69,515,612,31,718,
|513,683,1080,735,1071,846,772,1050,5725,6567,6536,150,612,5895,9979,719,692,473,35,1084,616,113,52,459,312,579,975,355,3595,605,738,936,348,81,431,777,858,744,964,26,308,4277,654,103,454,120,3295,100,1067,776,775,579,811,926,205,784,430,771,610,677,840,1052,749,560,474,867,643,649,294,81,211,349,1079,689,885,568,9445,190,495,377,243,355,5299,170,744,134,902,41,676,1115,491,690,486,1006,484,69,522,621,31,732,
|518,694,1091,740,1089,853,774,1060,5765,6597,6595,152,622,5939,10000,726,695,474,35,1091,623,113,52,460,313,591,983,360,3674,608,745,956,349,81,433,787,867,745,966,26,312,4359,655,104,454,121,3303,100,1072,786,784,585,827,940,206,793,438,773,618,680,848,1074,752,560,481,867,644,655,299,81,212,353,1095,690,897,580,9563,192,496,379,247,357,5344,170,747,135,916,41,683,1123,501,691,491,1021,494,69,533,623,31,747,
|520,698,1105,751,1103,869,775,1071,5778,6688,6626,153,627,5985,10000,736,708,475,35,1113,624,114,52,462,315,599,988,364,3743,620,746,965,353,81,434,791,869,753,978,26,315,4442,663,105,458,121,3362,100,1094,791,799,592,837,948,209,795,444,777,621,684,852,1074,765,566,482,882,648,657,300,81,215,355,1115,697,905,587,9621,194,496,384,250,364,5443,170,756,136,917,41,691,1137,508,695,496,1038,494,69,536,627,31,747,
|530,711,1105,764,1109,877,789,1089,5855,6747,6694,155,640,6021,10000,750,721,479,35,1130,626,114,52,462,316,601,1003,370,3755,621,750,970,354,81,437,803,873,757,988,26,321,4523,663,106,463,122,3389,101,1111,794,810,598,842,967,211,802,446,787,627,687,867,1092,769,569,482,887,654,670,302,81,215,355,1116,697,922,594,9761,194,498,388,252,364,5551,171,759,136,937,41,704,1139,511,703,506,1054,497,69,543,634,31,759,
|532,717,1111,770,1124,883,796,1106,5875,6841,6738,155,652,6143,10000,751,736,19,35,1131,633,115,52,468,320,607,1006,370,3759,625,760,986,358,81,442,803,876,761,1009,26,325,4578,668,107,466,123,3413,101,1113,795,819,604,849,976,214,803,453,791,635,687,872,1097,769,577,486,887,655,678,302,81,217,360,1118,704,937,604,9854,194,502,394,256,368,5599,173,763,138,947,41,717,1161,519,711,506,1058,504,69,550,645,31,761,
|532,732,1126,778,1141,890,812,1111,5930,6992,6886,155,653,6262,10000,764,738,19,35,1153,637,115,52,470,320,617,1018,370,3829,629,766,994,361,81,447,815,888,769,1024,26,331,4644,671,108,475,123,3469,102,1127,810,831,614,851,979,214,815,456,801,647,696,887,1111,773,581,493,899,660,688,307,81,219,363,1120,718,944,605,9881,196,510,400,257,368,5701,173,764,138,964,41,732,1171,527,723,515,1067,512,69,555,652,31,765,
|541,732,1144,789,1147,904,816,1126,6021,7090,6901,155,661,6307,10000,772,742,19,35,1171,643,115,52,470,322,624,1031,370,3916,635,780,1005,364,81,453,830,901,769,1036,26,332,4742,676,108,477,123,3526,103,1135,812,832,621,868,997,216,824,457,803,653,701,903,1131,788,585,497,906,669,692,311,81,219,365,1134,724,956,610,9907,196,511,403,261,373,5764,174,768,140,968,41,745,1183,538,734,515,1080,518,69,565,662,31,773,
|547,739,1168,794,1159,919,828,1127,6021,7113,6903,157,668,6435,10000,780,750,19,35,1188,655,116,52,478,328,631,1045,377,3939,641,790,1015,367,81,461,837,913,779,1049,26,334,4849,686,108,477,124,3589,103,1151,825,833,623,876,1009,219,834,464,810,654,714,913,1141,796,596,507,923,671,705,313,81,223,369,1143,729,956,614,9948,197,519,404,264,373,5866,176,782,142,969,41,758,1197,543,745,518,1103,518,69,574,668,31,783,
|556,742,1171,795,1175,922,845,1138,6126,7252,6942,158,673,6554,10000,786,766,19,35,1198,662,116,52,487,329,632,1055,377,3981,649,797,1034,374,81,467,839,928,786,1050,26,338,4936,693,109,485,125,3650,103,1170,836,844,625,883,1009,220,846,473,818,668,717,913,1155,806,608,516,934,680,717,319,81,227,369,1160,732,966,626,10000,200,521,406,265,374,5925,177,794,142,982,41,770,1206,551,751,518,1109,528,69,579,681,31,796,
|559,744,1179,797,1185,936,854,1159,6168,7415,7067,158,687,6643,10000,802,782,19,35,1218,675,117,52,491,334,640,1066,379,4047,662,811,1049,381,81,474,845,944,792,1052,26,342,4944,701,109,489,126,3724,104,1187,844,849,634,891,1026,224,849,481,821,670,724,932,1174,814,612,520,952,682,721,323,81,230,369,1164,745,975,631,10000,202,529,414,269,378,6002,179,809,143,995,41,782,1227,555,767,523,1130,530,69,589,683,31,812,
|566,747,1184,802,1189,950,864,1160,6184,7524,7150,159,701,6645,10000,813,789,19,35,1243,680,118,52,498,338,641,1083,385,4066,669,819,1052,387,81,482,846,958,797,1057,26,348,5030,705,110,493,127,3750,105,1210,854,856,639,903,1048,224,858,488,830,676,734,951,1194,822,619,524,960,696,721,323,81,230,371,1186,755,995,632,10000,205,539,418,272,381,6062,180,823,145,1013,41,795,1245,556,768,534,1137,538,69,599,687,31,819,
|566,756,1209,812,1205,965,871,1166,6257,7680,7155,159,702,6693,10000,815,800,19,35,1250,682,118,52,500,340,651,1097,389,4154,678,822,1053,390,81,492,856,966,799,1064,26,355,5053,712,110,499,128,3774,106,1223,870,868,645,904,1071,228,871,498,835,676,738,957,1213,824,620,531,966,705,734,323,81,232,373,1205,767,1012,641,10000,207,545,420,275,383,6104,181,825,146,1033,41,811,1262,562,774,545,1160,539,69,605,697,31,823,
|573,761,1214,820,1228,983,876,1179,6287,7768,7185,159,712,6800,10000,825,813,19,35,1261,684,118,52,502,346,663,1116,395,4230,679,834,1056,393,81,496,864,981,809,1073,26,362,5123,713,111,504,128,3807,107,1236,875,870,658,912,1091,230,874,503,846,676,753,969,1217,835,621,534,983,720,749,328,81,234,379,1219,781,1013,654,10000,208,554,421,277,385,6198,184,831,146,1047,41,822,1266,573,790,547,1166,543,69,616,709,31,840,
|582,765,1240,824,1255,983,889,1197,6321,7792,7232,159,722,6807,10000,825,826,19,35,1285,696,119,52,510,349,675,1136,396,4296,692,850,1076,396,81,503,879,988,818,1091,26,368,5140,717,111,513,129,3892,107,1260,875,873,663,912,1114,230,888,505,847,688,769,989,1239,842,631,544,1003,721,759,331,81,234,380,1232,786,1031,662,10000,211,562,421,278,392,6201,187,840,147,1055,41,830,1286,585,801,555,1183,545,69,625,716,31,843,
|593,778,1244,828,1261,983,893,1201,6411,7819,7362,161,731,6921,10000,825,828,19,35,1286,704,120,52,515,349,678,1139,396,4345,695,868,1077,398,81,507,890,999,826,1110,26,368,5157,723,112,516,130,3922,108,1272,887,889,668,928,1126,230,900,507,855,691,774,997,1256,843,641,544,1024,735,763,336,81,234,381,1256,802,1048,664,10000,212,564,423,283,398,6269,190,844,149,1062,41,835,1300,586,811,560,1209,554,69,636,722,31,845,
|595,783,1257,839,1266,1002,893,1220,6539,7832,7493,161,732,7028,10000,840,835,19,35,1304,717,120,52,521,352,689,1147,400,4434,699,884,1099,400,81,515,890,1004,832,1117,26,373,5166,738,113,517,131,3934,109,1296,888,897,672,934,1145,230,916,512,857,695,790,1010,1274,861,642,552,1030,743,772,341,81,234,382,1262,819,1049,673,10000,212,568,430,285,398,6300,192,855,150,1074,41,848,1325,591,811,565,1221,564,69,645,728,31,845,
|600,796,1259,839,1273,1007,903,1243,6582,7875,7591,163,736,7126,10000,841,845,19,35,1314,725,121,52,526,353,695,1171,400,4508,705,903,1106,405,81,516,904,1011,847,1136,26,373,5230,753,114,525,132,3999,110,1323,889,915,674,942,1157,232,918,517,867,700,807,1025,1300,876,646,562,1032,758,778,343,81,238,389,1290,828,1067,678,10000,212,574,438,286,398,6320,195,861,152,1081,41,862,1345,602,813,568,1239,564,69,650,736,31,851,
|609,796,1275,854,1299,1021,907,1247,6591,8019,7693,165,739,7237,10000,849,862,19,35,1329,731,121,52,526,356,705,1172,408,4585,713,919,1122,405,81,525,913,1019,854,1159,26,373,5320,764,114,535,132,4060,110,1324,900,924,686,958,1164,234,924,520,875,713,808,1031,1304,890,648,567,1034,760,782,348,81,241,396,1306,828,1067,691,10000,215,584,446,286,403,6438,198,864,153,1087,41,868,1368,611,822,571,1261,571,69,652,736,31,864,
|611,812,1278,862,1315,1030,914,1270,6712,8125,7706,166,747,7324,10000,867,880,19,35,1350,737,121,52,531,359,709,1179,416,4656,727,930,1146,409,81,536,925,1039,861,1181,26,375,5352,767,115,539,133,4147,111,1341,905,940,694,959,1168,235,931,523,876,723,811,1039,1304,890,652,577,1044,769,789,349,81,243,402,1307,829,1074,695,10000,216,588,451,287,406,6444,201,866,155,1089,41,877,1381,613,834,574,1283,574,69,657,742,31,867,
|620,815,1294,877,1340,1048,921,1291,6848,8303,7719,167,761,7394,10000,882,898,19,35,1351,749,122,52,532,361,712,1189,423,4664,727,938,1168,409,81,539,936,1060,862,1207,26,380,5373,774,116,550,133,4148,112,1364,911,943,707,976,1184,235,946,533,878,724,823,1052,1307,905,656,586,1064,783,802,354,81,244,405,1327,829,1085,707,10000,217,598,459,292,410,6566,204,868,155,1099,41,881,1406,619,850,577,1296,577,69,664,748,31,871,
|629,830,1322,877,1367,1050,939,1307,6955,8464,7834,169,777,7470,10000,899,904,19,35,1369,751,122,52,542,364,717,1213,428,4755,737,952,1183,410,81,540,955,1070,879,1218,26,384,5465,774,116,550,135,4210,112,1394,920,959,710,994,1198,235,966,542,893,738,830,1061,1320,919,662,593,1086,786,805,360,81,246,413,1346,830,1100,719,10000,219,609,467,294,417,6614,204,879,155,1103,41,887,1435,621,863,580,1309,588,69,675,749,31,888,
|634,841,1339,877,1375,1052,949,1314,7102,8638,7917,170,781,7504,10000,899,918,19,35,1399,760,122,52,542,370,723,1225,430,4803,750,957,1204,412,81,541,974,1071,882,1234,26,384,5533,790,116,556,135,4254,113,1401,938,961,712,1008,563,237,969,550,909,742,830,1061,1335,938,668,602,1097,800,821,367,81,248,418,1349,833,1121,734,10000,220,615,471,295,420,6713,207,888,155,1127,41,887,1463,633,863,585,1332,597,69,676,749,31,889,
|647,856,1355,889,1378,1070,967,1341,7146,8826,8080,171,784,7603,10000,899,929,19,35,1403,768,123,52,547,376,731,1234,434,4832,763,969,1207,412,81,544,989,1074,889,1238,26,387,5613,801,117,557,136,4342,114,1431,948,976,717,1016,567,240,985,554,928,748,834,1071,1361,952,681,603,1120,815,826,368,81,251,419,1358,850,1132,749,10000,222,621,477,295,426,6734,210,901,156,1144,41,900,1476,636,867,593,1342,599,69,689,749,31,906,
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