@param m `1 <= m` @return x mod m

@param n `1 <= n` @return same with std::bit::countr_zero

@param a `0 <= a < m` @param b `0 <= b < m` @return `a * b % m`

@param b `1 <= b` @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g

(rem, mod)