扩展欧拉定理(模板:P5091)

发布时间 2023-07-12 09:57:43作者: 陌上&初安

题意:

1

思路:

1
1

模板代码:

// -----------------
//#pragma GCC optimize(2)
#include <iostream>
#include <cstring>
#include <algorithm>
#define IOS ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie(0);
#define endl '\n'
#define int long long 
using namespace std;

int a,m;
string s;

int qmi(int a, int k, int p) 
{
    int res = 1 % p;
    while (k)
    {
        if (k & 1) res = res * a % p;
        a = a * a % p;
        k >>= 1;
    }
    return res;
}

int phi(int x)  // 暴力筛欧拉数
{
    int res = x;
    for (int i = 2; i <= x / i; i ++ )
        if (x % i == 0)
        {
            res = res / i * (i - 1);
            while (x % i == 0) x /= i;
        }
    if (x > 1) res = res / x * (x - 1);
    return res;
}

void solve()
{
    cin >> a >> m;
    cin >> s;
    int mod = phi(m);
    int ans = 0,ff = 0;
    for(int i = 0; i < s.size(); i ++)
    {
        ans = ans * 10 + (s[i] - '0');
        if(ans >= mod )  ff = 1,ans %= mod;
    }
    if(ff) ans += mod;  // ans 大于过 mod
    cout << qmi(a, ans, m) << endl;
}

signed main()
{
    IOS  
    int T = 1;
    //cin >> T;
    while(T --) { solve(); }
    return 0;
}