Mathematical knowledge -- understanding and examples of fast power

Fast power ： Find out quickly a^k mod p Result .

1<=a,k,p<=1e9.

The fast power is actually Preprocessing come out ：

  therefore a^k It can be expressed as （ Binary representation ）：

  Explain ： come out a^(2^0)=a outside , The rest of the pretreatment has been in square .

  Example ：875. Fast power - AcWing Question bank

Topic ：

 

Code ：

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod=1e9+7;
int qmi(int a,int k,int p)
{
    int res=1;
    while(k)
    {
        if(k&1) res=(ll)res*a%p;
        k>>=1;
        a=(ll) a*a%p;
    }
    return res;
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int n;
    cin>>n;
    while(n--)
    {
        int a,k,p;
        cin>>a>>k>>p;
        cout<<qmi(a,k,p)<<endl;
    }
    return 0;
}