k1 = 361602627459517/100000000000000
k2 = 152264278250403/100000000000000
k3 = 54620785996429/100000000000000
k4 = 176731907237/125000000000
k5 = 1156996315233/20000000000000
k6 = 11858328594357/5000000000000
k7 = 61147678228061/25000000000000
k8 = 972544685826559/10000000000000000
k9 = 150650172583633/1000000000000000
k10 = 64470276664977/50000000000000
k11 = 40097870751449/20000000000000
k12 = 57322624756517/2000000000000
k13 = 31794795429367/25000000000000
k14 = 458901437554149/5000000000000
k15 = 160033122150611/10000000000000000
k16 = 522749670547203/100000000000
k17 = 48804037501331/2500000000000000
k18 = 7265796009049/40000000000000
k19 = 349720846528477/10000000000000
k20 = 40681289836487/2000000000000
k21 = 655543523218919/100000000000000
k22 = 8370041054987/312500000000000
k23 = 291552070998833/50000000000000
k24 = 83191369333877/500000000000000
k25 = 198306450999093/1000000000000000
k26 = 274357223013613/50000000000000
k27 = 162943604164789/1000000000000000
k28 = 435621076587497/100000000000000000
k29 = 168308889432487/1000000000000000
k30 = 1/10
k31 = 1