FZU 1759 题解 欧拉降幂

本题考点：欧拉降幂

Super A^B mod C

Given A,B,C, You should quickly calculate the result of A^B mod C. (1<=A,C<=1000000000,1<=B<=10^1000000).

Input

There are multiply testcases. Each testcase, there is one line contains three integers A, B and C, separated by a single space.

Output

For each testcase, output an integer, denotes the result of A^B mod C.

Sample Input

3 2 4

2 10 1000

Sample Output

1

23

分析：欧拉降幂的模板题

直接套公式即可：

AC代码:

#include<iostream>

#include<cstdio>

#include<cstring>

using namespace std;

typedef long long ll;

ll a,p;

char b[];

ll phi(ll x)

{

    ll res=x;

    ll a=x;

    for(int i=;i*i<=x;i++)

    {

        if(a%i==)

        {

            res=res/i*(i-);

            while(a%i==)    a/=i;

        }

    }

    if(a>)    res=res/a*(a-);

    return res;

}

ll qp(ll a,ll b,ll p)

{

    ll ans=;

    while(b)

    {

        if(b&)

        {

            ans=(ans*a)%p;

        }

        a=(a*a)%p;

        b>>=;

    }

    return ans;

}

int main()

{

    //freopen("input.txt","r",stdin);

    while(scanf("%lld %s %lld",&a,&b,&p)!=EOF)

    {

        ll len=strlen(b);

        ll res=;

        ll pp=phi(p);

        for(int i=;i<len;i++)

        {

            res=(res*+b[i]-'')%pp;

        }

        printf("%lld\n",qp(a,res,p));

    }

    return ;

}