【数学 扩展欧拉定理】luogu_5091 欧拉定理

题意

求$a^{b}modm$

思路

因为$b$很大所以不能直接算，这要用到扩展欧拉定理：
当$a,m\in \mathbb{Z}$时有：
$a^b\equiv \{\begin{array}{c}{a}^b,b<\phi (m)\\ a^{bmod\phi (m)+\phi (m)},b\ge \phi (m)\end{array}$

代码

#include<cstdio>

long long a, m, b, phi, f, p;

int power(int a, int b) {
	long long res = 1;
	for (; b; b >>= 1) {
		if (b & 1) res = res * a % p;
		a = (long long)a * a % p;
	}
	return res;
}

int main() {
	scanf("%d %d", &a, &m);
	phi = p = m;
	for (int i = 2; i * i <= m; i++) {
		if (m % i) continue;
		phi = phi / i * (i - 1);
		while (m % i == 0) m /= i;
	}
	if (m > 1) phi = phi / m * (m - 1);
	char c = getchar();
	while (c < '0' || c > '9') c = getchar();
	while (c >= '0' && c <= '9') {
		b = b * 10 + c - 48;
		if (b >= phi) b %= phi, f = 1;
		c = getchar();
	}
	if (f) b += phi;
	printf("%d", power(a, b));
}