【模板】数学相关（费马小定理求逆元、求最大公约数、埃氏筛法、区间筛法、快速幂）

C++版本：

费马小定理求逆元

a^(p-2)是a在模p意义下的乘法逆元（p为质数）。

求最大公约数

int gcd(int a, int b) {
	if (b == 0)return a;
	return gcd(b, a%b);
}

埃氏筛法

int sieve(int n) {
	int p = 0;
	for (int i = 0; i <= n; i++)is_prime[i] = true;
	is_prime[0] = is_prime[1] = false;
	for (int i = 2; i <= n; i++) {
		if (is_prime[i]) {
			prime[p++] = i;
			for (int j = 2 * i; j <= n; j += i)is_prime[j] = false;
		}
	}
	return p;
}

区间筛法

void segment_sieve(ll a, ll b) {
	for (int i = 0; (ll)i*i <= b; i++)is_prime_small[i] = true;
	for (int i = 0; i < b - a; i++)is_prime[i] = true;
	for (int i = 2; (ll)i*i < b; i++) {
		if (is_prime_small[i]) {
			for (int j = 2 * i; (ll)j*j < b; j += i)is_prime_small[j] = false;
			for (ll j = max(2LL, (a + i - 1) / i)*i; j < b; j += i)is_prime[j - a] = false;
		}
	}
}

快速幂

ll mod_pow(ll x, ll n, ll mod) {  //快速幂
	ll res = 1;
	while (n > 0) {
		if (n & 1)res = res * x%mod;
		x = x * x%mod;
		n >>= 1;
	}
	return res;
}