1046 A^B Mod C

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1046 A^B Mod C

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给出3个正整数A B C，求A^B Mod C。

例如，3 5 8，3^5 Mod 8 = 3。

Input

3个正整数A B C，中间用空格分隔。(1 <= A,B,C <= 10^9)

Output

输出计算结果

Input示例

3 5 8

Output示例

A ^ B MOD C = A ^ (B % Phi(C) + Phi(C)) Mod C (B >= Phi(C))

Phi(C)为欧拉函数，指小于等于C的且与C互质的数的个数

#include <iostream>#include <cstring>#include <cstdlib>#include <cstdio>#include <string>#include <cmath>#include <set>#include <queue>#include <algorithm>#include <vector>using namespace std;#define esp  1e-8const double PI = acos(-1.0);const int inf = 1000000005;const long long mod = 1000000007;//freopen("in.txt","r",stdin); //输入重定向,输入数据将从in.txt文件中读取//freopen("out.txt","w",stdout); //输出重定向,输出数据将保存在out.txt文件中long long A, B, C;long long eular(long long x){long long res = x;long long ans = x;for (int i = 2; i * i <= x; ++ i){if (res % i == 0)ans = ans / i * (i - 1);while (res % i == 0)res /= i;}if (res > 1)ans = ans / res * (res - 1);return ans;}long long power(long long a, long long b){long long res = 1;while (b){if (b & 1)res = res * a % C;b >>= 1;a = a * a % C;}return res % C;}int main(){while (cin >> A >> B >> C){long long x = (B % eular(C) + eular(C));//cout << eular(C) << endl;if (B >= eular(C))cout << power(A, x) << endl;elsecout << power(A, B) << endl;}}

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