T=100;
N=100;
M=1000;
P=[|183,266,232,163,107,1552,680,558,580,743,861,356,865,9009,514,768,100,416,90,390,2142,724,912,626,3488,499,351,418,9939,396,482,856,178,6468,221,641,922,874,562,120,705,378,518,403,1212,789,777,125,415,806,233,755,249,423,904,15,789,9803,489,848,658,1265,271,632,699,359,238,732,41,109,248,447,652,206,362,984,142,450,644,592,272,134,156,8269,106,979,571,2481,632,635,271,203,416,47,775,685,957,452,35,452,
|184,270,236,163,107,1564,80,563,587,745,865,362,865,9063,523,774,101,424,91,397,2176,728,922,636,3524,503,353,420,10000,403,488,857,180,6534,222,654,936,886,568,120,712,378,526,408,1233,806,793,126,417,821,236,759,250,431,910,15,791,9837,496,861,668,1283,271,642,713,363,242,744,41,110,249,449,663,207,369,996,144,455,645,597,275,135,157,8288,107,990,573,2505,641,645,274,206,421,47,780,694,978,453,35,456,
|187,272,236,164,107,1564,80,564,594,752,873,369,868,9188,528,775,102,424,91,400,2190,731,929,649,3555,507,356,425,10000,410,490,859,183,6588,222,666,947,897,571,120,716,379,527,123,1241,821,810,126,417,832,238,764,251,438,927,15,797,9926,504,870,670,1298,276,652,715,368,242,759,41,110,250,455,670,207,376,998,145,459,645,606,276,136,158,8389,107,995,577,2526,654,652,275,206,428,47,794,702,999,246,35,457,
|190,276,236,164,108,1575,80,571,594,752,875,370,884,9265,531,782,102,425,91,408,2213,746,933,656,3635,514,360,433,10000,413,490,864,186,6738,224,672,955,912,574,121,730,383,535,123,543,835,818,126,423,837,239,773,255,438,941,15,812,10000,506,886,675,1315,277,661,721,370,243,769,41,110,251,455,671,210,381,1016,145,463,650,606,279,137,160,8476,108,1010,585,2567,667,653,276,206,435,47,802,714,1000,249,35,462,
|192,279,238,165,108,1579,80,579,600,766,886,372,895,9297,532,795,102,428,92,412,2243,758,934,663,3692,519,361,441,10000,413,495,877,189,6833,228,677,967,925,578,121,733,384,543,124,548,843,835,126,426,854,240,785,259,446,958,15,828,10000,511,904,683,1343,282,666,736,370,247,780,41,110,252,460,673,210,386,1038,147,471,654,614,280,137,162,8518,108,1028,585,2625,680,661,278,209,440,47,802,728,1021,250,35,462,
|195,281,242,167,109,1580,80,584,602,766,893,378,902,9373,537,805,102,435,93,415,2252,765,936,673,3764,527,367,441,10000,419,500,881,191,6901,232,686,978,925,582,122,734,390,552,124,558,843,847,126,433,866,243,789,262,449,958,15,829,10000,518,920,691,1358,283,666,741,370,250,788,41,110,255,464,674,213,388,1058,149,476,662,621,281,139,164,8600,109,1032,34,2633,681,667,279,211,448,47,805,730,1023,251,35,463,
|198,281,242,169,110,1605,80,585,613,779,901,382,919,9533,542,815,102,441,94,420,2261,775,951,681,3801,533,368,446,10000,421,503,889,193,7043,236,691,986,943,587,122,747,392,555,125,568,853,863,126,436,866,245,796,263,455,974,15,834,10000,519,939,693,1382,287,673,750,377,250,801,41,111,258,472,676,214,390,1070,151,476,662,630,281,141,164,8726,110,1048,34,2643,693,671,280,214,456,47,808,740,1034,252,35,463,
|200,284,243,171,110,1627,80,597,624,779,905,15,920,9721,550,816,98,447,94,424,2294,776,965,687,3856,536,372,447,10000,421,507,895,194,7099,238,697,1006,961,591,122,758,394,565,126,577,861,875,127,441,870,249,808,266,459,983,15,837,10000,519,944,706,1390,292,678,760,383,254,818,41,111,259,481,689,214,390,1085,151,478,668,631,284,143,165,8734,110,1051,34,2674,704,680,285,217,461,47,812,745,1046,256,35,470,
|200,289,244,173,111,1647,80,604,627,780,907,15,925,9888,561,824,98,453,95,430,2298,786,978,689,3870,540,376,455,10000,424,510,908,194,7260,240,703,1015,962,597,123,769,396,573,127,580,867,875,127,445,872,252,823,270,461,1003,15,854,10000,519,964,706,1414,292,684,775,386,258,834,41,112,261,484,690,215,391,1086,151,479,679,637,284,144,167,8912,111,1072,34,2701,704,682,287,218,466,47,818,756,1060,258,35,472,
|201,292,248,175,111,1667,80,615,635,782,918,15,944,9894,562,830,99,454,96,438,2341,799,978,693,3953,542,381,458,10000,425,516,925,197,7370,241,715,1021,977,606,123,771,399,573,127,581,867,882,127,450,887,252,830,275,466,1007,15,872,10000,519,976,706,1432,297,693,787,392,262,835,41,113,264,488,699,215,398,1089,153,488,689,644,284,144,167,9082,112,1072,34,2755,712,694,291,219,466,47,833,766,1077,260,35,478,
|203,295,251,175,112,143,80,621,641,790,922,15,947,9907,569,837,100,457,96,439,2345,802,991,703,4015,545,384,463,10000,426,524,931,200,7378,244,729,1022,996,611,123,781,404,578,127,584,880,894,128,455,894,255,842,280,469,1019,15,887,10000,526,977,706,1440,298,693,795,393,267,835,41,114,268,498,703,215,404,1108,155,493,703,646,288,145,169,9160,112,1086,34,2812,725,703,291,219,469,47,848,780,1084,262,35,482,
|205,299,254,177,113,143,80,629,648,791,934,15,966,10000,579,845,100,465,96,441,2393,819,1011,715,4067,556,386,464,10000,428,534,937,203,7524,244,735,1024,1001,617,124,786,406,587,128,586,880,903,129,462,913,259,857,280,470,1041,15,892,10000,536,990,719,1457,303,697,795,400,271,846,41,114,273,502,709,215,412,1131,155,499,708,659,289,147,171,9348,112,1096,34,2849,730,715,293,222,475,47,863,782,1084,262,35,492,
|206,304,254,178,113,145,80,642,661,800,935,15,972,10000,590,847,101,472,96,448,2406,833,1016,721,4103,564,393,464,10000,433,544,957,203,7621,248,739,1036,1002,630,124,795,411,590,128,587,884,907,130,469,914,260,873,281,479,1043,15,911,10000,539,999,724,1460,304,707,811,402,271,858,41,114,275,504,722,218,412,1134,157,500,709,665,291,147,173,9464,113,1111,34,2910,744,725,297,226,484,47,867,787,1107,262,35,493,
|207,306,256,178,114,147,80,648,666,812,938,15,987,10000,590,861,101,472,97,454,2408,848,1017,725,4155,567,397,470,10000,434,549,959,204,7792,249,749,1047,1012,643,125,812,414,597,129,598,893,914,130,473,930,262,885,285,485,1044,15,911,10000,544,1005,739,1468,306,711,818,408,276,874,41,114,280,513,729,219,419,1157,157,500,722,678,293,148,175,9660,114,1122,34,2918,755,728,298,230,485,47,878,798,1114,265,35,494,
|207,309,257,179,114,149,80,657,667,820,958,15,990,10000,596,870,101,479,97,463,2415,866,1019,726,4200,567,403,479,10000,438,551,973,207,7827,253,749,1059,1023,655,126,826,420,605,130,606,901,934,131,482,930,264,886,289,490,1047,15,924,10000,547,1020,740,1478,307,721,833,414,281,891,41,115,280,516,738,223,420,1164,157,500,735,681,297,150,178,9701,115,1144,34,2968,761,742,299,234,492,47,894,806,1116,269,35,501,
|210,311,259,179,115,149,80,670,679,825,959,15,1010,2851,601,887,101,482,97,471,2466,873,1037,739,4274,576,410,479,10000,439,562,992,210,7831,257,749,1068,1039,666,127,841,423,609,130,612,914,948,132,482,941,268,892,293,495,1053,15,943,10000,558,1041,754,1508,308,724,843,415,281,891,41,115,283,521,750,226,424,1186,158,510,742,689,297,150,179,9796,116,1147,34,3029,763,754,302,238,500,47,906,807,1126,271,35,507,
|212,312,259,179,115,151,80,674,686,828,971,15,1013,2906,609,893,101,483,97,480,2520,880,1046,750,4287,579,412,481,10000,445,568,1001,213,7853,261,751,1084,1045,679,127,842,428,615,131,618,932,963,134,484,952,272,910,294,500,1074,15,945,10000,568,1051,764,1528,311,736,856,423,281,893,41,116,284,525,757,229,432,1186,159,511,750,691,298,151,182,10000,116,1163,34,3088,778,765,304,241,504,47,910,813,1135,273,35,515,
|213,316,261,179,115,153,80,678,686,842,971,15,1016,2937,610,893,102,490,98,480,2548,891,1063,764,4340,588,419,484,10000,447,575,1003,213,7900,167,752,1105,1048,693,128,844,432,623,133,629,948,974,134,494,957,275,913,295,501,1082,15,961,10000,579,1074,764,1554,313,739,861,431,283,907,41,117,284,529,765,229,434,1207,160,512,756,695,301,152,183,10000,117,1186,34,3148,778,780,304,245,507,47,929,828,1139,276,35,524,
|213,320,261,179,115,153,80,682,700,851,981,15,1023,3000,620,906,103,493,99,490,2599,892,1083,777,4379,598,427,484,10000,452,579,1025,216,8067,168,768,1121,1064,697,36,845,438,636,133,632,967,974,134,495,977,280,926,299,503,1089,15,981,10000,582,1096,776,1562,316,749,868,432,287,502,41,118,285,537,775,233,437,1231,155,512,761,699,306,154,185,10000,118,1196,34,3168,787,788,308,246,510,47,931,840,1140,277,35,531,
|213,324,266,181,116,154,80,682,702,857,1000,15,1027,3058,629,918,103,497,100,498,2623,905,1092,787,4379,610,429,493,10000,457,583,1036,219,8116,170,781,1143,1068,710,36,855,439,643,134,643,970,987,135,500,994,282,937,302,508,1110,15,1001,10000,589,1114,783,1591,320,750,885,433,290,504,41,118,288,538,789,236,439,1253,155,512,771,704,306,154,185,10000,118,1217,30,3199,801,805,309,250,511,47,944,618,1152,279,35,542,
|213,324,271,182,117,154,80,688,707,867,1019,15,1040,3116,637,931,103,505,101,507,2639,922,1100,801,4477,618,431,497,10000,460,432,1051,221,8264,172,791,1166,1085,715,36,862,446,649,134,644,986,1007,137,509,1015,282,944,302,517,1125,15,1023,10000,601,1117,793,1625,323,764,896,433,290,506,41,118,288,543,796,238,448,1260,155,513,781,718,310,154,186,10000,119,1233,30,3243,803,820,315,254,519,47,949,621,1152,279,35,549,
|215,325,275,184,117,156,80,700,718,867,216,15,1043,3117,645,932,103,510,101,512,2650,937,1113,803,4558,626,434,503,10000,466,432,1056,222,8412,174,799,1179,1103,718,36,878,451,655,135,646,988,1009,139,513,1034,285,964,306,524,1137,15,1043,10000,603,1139,797,1626,327,773,905,439,292,512,41,118,290,543,812,242,455,1266,155,519,797,721,310,156,186,10000,120,1241,19,3252,804,820,319,256,528,47,958,625,1169,282,35,556,
|218,329,280,186,117,158,80,714,726,884,217,15,1062,3158,648,952,103,512,102,520,2707,939,1117,818,4585,638,434,511,10000,467,440,1057,224,8524,177,801,1191,1116,720,36,893,452,665,136,300,1009,1014,141,513,1046,289,965,310,530,1150,15,1058,10000,607,1156,811,1650,209,773,918,444,297,516,41,118,293,552,821,246,463,1273,157,526,802,726,311,156,188,10000,120,302,19,3282,812,833,321,258,534,47,976,633,1184,283,35,566,
|222,335,282,186,117,158,80,728,730,887,219,15,1080,3164,649,958,103,520,103,521,2716,954,1119,834,4668,645,437,511,10000,470,440,1057,224,8647,177,812,1192,1116,721,36,910,459,673,138,305,1031,1023,143,523,1067,289,980,316,536,1170,15,1066,10000,619,1160,817,1662,209,782,925,450,298,517,41,119,295,559,832,246,466,1297,159,530,811,739,315,156,189,10000,121,304,19,3344,820,841,326,262,545,47,979,634,1188,287,35,578,
|226,340,286,187,118,159,80,728,741,890,222,15,1081,3193,652,966,103,530,103,523,2776,972,1141,837,4765,647,437,513,10000,479,441,1072,227,8683,180,817,1192,1121,721,36,918,462,676,138,307,1038,1043,145,529,1090,294,992,317,538,1172,15,1074,10000,629,1171,820,1670,209,783,934,451,300,521,41,120,299,568,850,249,472,1313,159,536,822,744,319,158,189,10000,121,308,19,3395,833,846,330,264,552,47,995,638,1210,291,35,583,
|227,344,289,190,118,160,80,739,742,900,224,15,1084,3223,665,974,104,540,104,523,2819,987,1151,852,4802,660,446,519,10000,480,450,1083,228,8799,183,820,1199,1123,728,36,932,468,676,138,307,1039,1050,145,530,1094,299,996,319,539,1183,15,1074,10000,637,1180,821,1676,211,785,947,456,302,526,41,121,300,570,854,251,480,1325,159,542,838,747,319,160,189,10000,121,311,19,3423,834,856,330,264,562,47,1001,638,1230,292,35,584,
|228,347,290,191,119,161,80,750,75,901,228,15,1095,3285,670,991,104,542,105,523,2848,996,1154,858,4836,665,447,520,10000,484,453,1084,232,8872,184,820,1218,833,728,36,940,471,680,140,312,1046,1050,147,537,1096,299,1013,320,547,1198,15,1095,10000,640,1194,834,1704,211,794,959,464,304,530,41,122,304,576,868,252,484,1342,161,545,844,755,324,160,170,10000,121,315,19,3453,845,873,331,267,562,47,1004,641,1257,139,35,592,
|230,350,293,194,120,162,80,766,75,902,229,15,1109,3326,681,1008,105,549,105,534,2851,1002,1179,867,4918,667,449,530,10000,494,457,1107,236,8920,187,837,1220,846,736,36,942,474,688,142,313,1053,1070,147,460,1108,299,1030,323,553,1208,15,1100,10000,643,1219,836,1742,212,806,962,472,309,531,41,122,305,586,880,256,494,789,163,550,853,757,328,161,171,10000,121,317,19,3510,851,877,332,271,571,47,1020,652,1264,140,35,592,
|231,354,293,197,120,164,80,779,75,913,232,15,1113,3342,695,1019,106,560,106,544,2891,1014,1191,885,4992,676,453,541,10000,494,459,1124,236,8935,188,842,1241,864,738,36,944,477,697,143,317,1071,1090,147,460,1119,302,1040,325,556,1210,15,1103,10000,652,1231,848,1751,214,823,976,479,310,538,41,123,307,588,886,260,501,793,164,555,870,771,328,161,171,10000,122,318,19,3518,862,883,335,271,575,47,1026,152,1283,140,35,597,
|233,355,293,198,121,164,80,789,75,914,236,15,1130,3401,708,1031,107,566,107,547,2954,1020,1203,887,5051,677,460,551,10000,504,467,1145,238,9004,190,855,1265,881,741,36,963,477,712,143,323,1090,1093,149,469,1122,305,1056,325,566,1233,15,1119,10000,656,1244,853,1770,216,831,996,489,313,547,41,124,307,596,898,261,506,801,164,555,872,781,330,161,173,10000,123,320,19,3587,875,897,338,272,580,47,1030,153,1287,141,35,606,
|234,360,294,201,122,166,80,804,75,927,236,15,1149,3458,716,1040,107,569,107,556,3018,1035,1210,902,5074,682,466,557,10000,508,475,1148,240,9165,193,868,1280,894,749,36,966,484,714,145,326,1091,1097,149,469,1131,307,1058,119,578,1256,15,1124,10000,668,1244,867,1774,218,841,1005,499,313,556,41,124,309,601,906,262,513,811,165,560,883,788,333,162,174,10000,124,325,19,3633,884,910,341,274,581,47,1033,154,1292,141,35,610,
|235,363,294,203,123,168,80,804,75,936,238,15,1153,3469,716,1045,107,572,108,563,3038,1040,1217,902,5151,682,467,568,10000,513,479,1169,240,9207,194,873,1303,903,756,36,969,484,726,147,330,1105,1098,151,473,1152,312,1080,120,583,1257,15,1128,10000,671,1265,870,1801,222,842,1025,505,319,559,41,124,311,613,924,266,521,825,165,566,898,795,339,162,177,10000,124,331,19,3675,896,926,341,279,584,47,1042,154,1299,142,35,622,
|236,363,295,206,124,169,80,806,75,941,240,15,1153,3527,729,1064,107,581,108,564,3100,1053,1232,911,5209,684,471,573,10000,515,479,1172,243,9289,96,875,1307,913,768,36,969,486,729,148,334,1118,1122,19,480,1158,316,1103,120,589,1258,15,1132,10000,676,1292,885,1827,222,848,1036,512,320,561,41,124,312,463,924,269,524,829,167,577,911,796,340,162,177,10000,125,331,19,3725,913,938,344,284,593,47,1046,156,1322,144,35,628,
|239,367,295,209,125,169,80,808,75,947,244,15,1163,3578,740,1082,108,588,109,570,3170,1060,1241,912,5299,685,479,582,10000,520,487,1190,243,9438,96,881,1315,931,777,36,984,492,731,149,340,1135,1146,19,481,1174,318,1111,120,599,1264,15,1157,10000,690,1316,886,1837,222,852,1045,519,325,567,41,125,315,472,944,269,524,833,168,581,929,807,342,164,180,10000,125,334,19,3768,922,946,350,287,599,47,1054,156,1332,145,35,633,
|241,371,295,209,125,170,80,814,75,956,246,15,1166,3604,752,1084,109,593,109,575,3187,1063,1262,922,5351,691,489,586,10000,529,496,1196,247,9488,97,881,1343,932,777,36,990,502,738,150,345,1152,1159,19,491,1178,319,1121,120,607,1267,15,1170,10000,692,1328,901,1872,222,864,1057,522,326,574,41,125,318,473,959,273,530,844,170,587,944,808,344,166,183,10000,125,336,19,3850,935,958,355,289,608,47,1057,158,1361,145,35,636,
|245,374,297,210,126,172,80,824,75,957,247,15,1167,3675,759,1095,109,603,109,583,3124,1079,1289,936,5458,703,490,589,10000,529,500,1219,251,9691,97,892,1343,937,783,36,1006,508,741,151,351,1161,1171,19,500,1183,319,800,120,610,1286,15,1191,10000,695,1340,905,1877,224,870,1073,523,331,579,41,126,322,482,963,275,531,857,172,595,945,814,345,168,185,10000,126,336,19,3915,945,964,359,292,614,47,1080,158,1370,147,35,640,
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|120,424,339,1,131,189,80,957,75,562,275,15,1348,4211,879,1264,117,704,118,649,3634,1209,1512,1089,5737,151,383,678,10000,593,573,1424,270,10000,32,1040,1539,1032,901,36,1115,558,840,171,399,1342,592,19,405,1320,247,944,125,670,1470,15,1397,10000,491,1548,1018,2188,244,998,1220,593,379,651,41,34,347,490,1121,307,622,968,191,680,1114,65,394,186,205,10000,128,389,19,4626,1066,959,413,325,698,47,1199,177,1533,159,35,759,
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|121,432,346,1,134,192,80,983,75,570,281,15,1372,4298,887,1290,117,722,119,656,3680,884,1535,1115,5765,155,396,695,10000,603,591,1436,278,10000,32,1079,1559,1066,930,36,1120,580,868,174,413,1367,611,19,408,1351,253,962,127,674,1510,15,1410,10000,505,1569,1031,2211,252,1023,1239,602,386,671,41,34,348,501,1142,308,633,971,194,697,1117,65,398,189,206,10000,128,392,19,4720,1095,977,422,328,717,47,1208,181,1584,160,35,769,
|122,437,352,1,134,192,80,999,75,576,284,15,1392,4360,903,1295,117,732,120,669,3720,884,1558,1117,5878,157,404,705,10000,612,591,1468,283,10000,32,1084,1582,1072,940,36,1138,588,872,176,413,1395,624,19,410,1370,253,977,128,684,1517,15,1422,533,508,1589,1048,2245,252,1045,1251,608,388,676,41,34,351,506,1151,310,641,992,194,700,1135,65,401,192,206,6025,129,400,19,4763,1097,981,428,333,724,47,1221,182,1606,161,35,780,
|123,442,358,1,135,194,80,1008,75,584,288,15,1400,4445,915,1309,117,738,120,672,3754,900,1571,1137,5954,157,411,719,10000,620,593,1498,283,10000,32,1094,1616,1087,942,36,1146,590,875,176,420,1395,628,19,410,1385,255,980,129,684,1519,15,1451,542,508,1618,1060,2285,255,1055,1253,610,393,680,41,34,358,508,1173,311,644,994,195,709,1138,65,406,192,209,6089,130,408,19,4802,1115,988,436,339,728,47,1241,183,1616,161,35,795,
|123,445,362,1,136,194,80,1021,75,26,291,15,1421,4539,918,1335,118,739,121,677,3817,902,1572,1154,6013,159,412,723,10000,626,593,1509,286,10000,32,1110,1642,1106,955,36,1159,598,889,176,426,1417,636,19,416,1388,259,985,130,687,1544,15,1471,547,518,1635,1070,2313,256,1058,1276,615,396,683,41,34,364,515,1194,315,653,1006,196,718,1156,65,412,193,212,6098,130,411,19,4846,1133,1004,257,345,743,47,1247,183,1617,163,35,810,
|123,445,369,1,136,197,80,1028,75,26,295,15,1431,4620,923,1354,119,746,122,689,3864,902,1591,1179,6132,160,417,726,10000,639,594,1526,290,10000,32,1120,1673,1108,963,36,1182,609,898,177,433,1447,647,19,417,1395,260,996,130,691,1551,15,1492,553,518,1654,1075,2338,259,1071,1288,616,399,696,41,34,368,521,1205,317,657,137,198,730,1174,65,413,193,214,6163,130,413,19,4856,1147,1009,261,347,743,47,1251,186,1638,164,35,810,
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|123,460,372,1,138,200,80,1047,75,26,299,15,1475,4728,936,1399,120,752,123,701,3972,925,1612,1212,6216,164,427,749,10000,646,602,1578,299,10000,32,1151,1706,1144,986,36,1227,628,908,181,442,1466,654,19,423,1426,265,1022,131,707,1608,15,1551,567,532,1679,1096,2367,266,1078,1328,623,407,703,41,34,380,529,1249,319,670,139,200,738,1210,58,428,195,220,6261,130,420,19,5039,1165,1033,267,353,771,47,1260,191,1679,167,35,830,
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