快速幂，就当个模板了

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include<cassert>
#include<set>
using namespace std ;
#ifdef DeBUG
#define bug assert
#else
#define bug //
#endif
int pow3(int a, int b)
{
    int r = 1, base = a;
    while(b != 0)
    {
        if(b & 1)
            r =(r* base)%100;
        base =(base* base)%100;
        b >>= 1;
    }
    return r;
}

int main()
{
    #ifdef DeBUG
        freopen("C:\Users\Sky\Desktop\1.in","r",stdin);
    #endif
    
    int n;
    int i,j,k;
    int t;
    int m;
    int sum;
    scanf("%d",&t);
    while(t--)
    {
        sum=0;
        int now=0;
        scanf("%d%d",&n,&m);
        for(i=1;i<=n;i++)
        {
            sum=(sum+pow3(i,m))%100;
        }
        if(sum<10)
        printf("0%d
",sum);
        else
        printf("%d
",sum);
    }
    return 0;
}

位操作版

int pow3(int a, int b)
{
 int r = 1, base = a;
 while(b != 0)
 {
  if(b & 1)
   r *= base;
  base *= base;
  b >>= 1;
 }
 return r;
}

int pow2(int a, int b)
{
 int r = 1, base = a;
 while(b != 0)
 {
  if(b % 2)
   r *= base;
  base *= base;
  b /= 2;
 }
 return r;
}