Miller-Rabin Template

// Randomized Primality Test (Miller-Rabin):
//   Error rate: 2^(-TRIAL)
//   Almost constant time. srand is needed

#include<chrono>
mt19937 rng((int)chrono::steady_clock::now().time_since_epoch().count());

ll ModularMultiplication(ll a, ll b, ll m){
	ll ret = 0, c = a;
	while(b){
		if(b & 1) ret = (ret + c) % m;
		b >>= 1; c = (c + c) % m;
	}
	return ret;
}

ll ModularExponentiation(ll a, ll n, ll m){
	ll ret = 1, c = a;
	while(n){
		if(n & 1) ret = ModularMultiplication(ret, c, m);
		n >>= 1; c = ModularMultiplication(c, c, m);
	}
	return ret;
}

bool Witness(ll a, ll n){
	ll u = n - 1;
	int t = 0;
	while(!(u & 1)){ u >>= 1; t++; }
	ll x0 = ModularExponentiation(a, u, n), x1;
	rep(i, 1, t){
		x1 = ModularMultiplication(x0, x0, n);
		if(x1 == 1 && x0 != 1 && x0 != n - 1) return true;
		x0 = x1;
	}
	if(x0 != 1) return true;
	return false;
}

ll Random(ll n){
	ll ret = rng(); ret *= 32768;
	ret += rng(); ret *= 32768;
	ret += rng();
	return ret % n;
}

bool IsPrimeFast(ll n, int TRIAL){
	while(TRIAL--){
		ll a = Random(n - 2) + 1;
		if(Witness(a, n)) return false;
	}
	return true;
}

int main()
{
	return 0;
}