func S(p int64) int64 {
// p1 = (p-1)! = p-1 (mod p)
// p2 = (p-2)! = 1 (mod p)
// p3 = (p-3)! = inv(p-2) (mod p)
// p4 = (p-4)! = inv(p-3) * inv(p-2) = inv(p-3) * p3 (mod p)
// p5 = (p-5)! = inv(p-4) * inv(p-3) * inv(p-2) = inv(p-4) * p4 (mod p)
var p3 int64 = mathutil.ModularInverse(p-2, p)
var p4 int64 = (mathutil.ModularInverse(p-3, p) * p3) % p
var p5 int64 = (mathutil.ModularInverse(p-4, p) * p4) % p
return (p3 + p4 + p5) % p
}
func BuildFactorialTables() {
factorialMod = make([]int64, maxPrime+1)
inverseFactorialMod = make([]int64, maxPrime+1)
var prod int64 = 1
var invProd int64 = 1
for i := int64(1); i <= maxPrime; i++ {
prod = (prod * i) % modPrime
invProd = (invProd * mathutil.ModularInverse(i, modPrime)) % modPrime
factorialMod[i] = prod
inverseFactorialMod[i] = invProd
}
}