https://thesobersobber.github.io/CP-Snippets/fac
int fac[maxn]; int inv[maxn]; fac[1] = inv[1] = 1; for (int i=2; i<maxn; i++){ fac[i] = (fac[i-1] * i)%mod; inv[i] = power(fac[i], mod - 2); }