k[1] = 588783148144923/1000000000000000
k[2] = 114598191621279/1000000000000000
k[3] = 355183987378767/1000000000000000
k[4] = 58872345769809/500000000000000
k[5] = 100000000000003/100000000000000000000
k[6] = 20001799972057/20000000000000000000
k[7] = 162471039450073/1000000000000
k[8] = 191297262771509/1000000000000
k[9] = 131984219165251/100000000000
k[10] = 645999307230137/1000000000000
k[11] = 85438890403697/12500000000000
k[12] = 28219407624011/250000000000000
k[13] = 197034304659041/5000000000000
k[14] = 407307409980937/1000000000000
k[15] = 426091167840583/5000000000000000
k[16] = 133594212383381/2000000000000000
k[17] = 920526565951487/10000000000000000
k[18] = 596841598127919/10000000000000000
k[19] = 57735769471617/6250000000
k[20] = 162862384561137/500000000000000
k[21] = 118873655169353/1000000000000000
k[22] = 91092957615177/20000000000000
k[23] = 386414745483539/500000000000
k[24] = 20192645073029/6250000000000
k[25] = 502329152478409/100000000000000000
k[26] = 359214586722219/5000000000000000
k[27] = 1
k[28] = 1
k[29] = 50004498363847/5000000000000000000
k[30] = 701139988718817/10000000000000000
k[31] = 100000000000011/100000000000000000000
k[32] = 154821166783837/1000000000000000
k[33] = 66810061799101/5000000000000000
k[34] = 58915457309741/1000000000000000000
k[35] = 11232996494689/50000000000000
k[36] = 30651903722779/25000000000000000
k[37] = 135347628753573/5000000000000000
k[38] = 494101368038079/50000000000
k[39] = 586017882122243/100000000000000000
k[40] = 109458423149719/100000000000
k[41] = 29840734372287/31250000000000
k[42] = 1
k[43] = 1
k[44] = 1
k[45] = 1
k[46] = 1
k[47] = 1
k[48] = 1
k[49] = 1
k[50] = 1
k[51] = 1
k[52] = 1
k[53] = 1
k[54] = 1
k[55] = 1
k[56] = 1
k[57] = 20
k[58] = 20
k[59] = 20
k[60] = 35
k[61] = 26