2017 Multi-University Training Contest - Team 3：1008&hdu6063、RXD and math

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本文介绍了一个数学问题的解决方案，该问题涉及计算μ函数与根号下特定形式的表达式的组合，并提供了使用快速幂算法进行高效计算的方法。

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题目：

RXD and math

Problem Description

RXD is a good mathematician.
One day he wants to calculate:

\sum i = 1 n k μ 2 (i) \times ⌊ n k i - - - \sqrt ⌋

output the answer module

109+7.

1≤n,k≤1018

μ (n) = 1 (n = 1)

μ (n) = (- 1) k (n = p 1 p 2 \dots p k)

μ (n) = 0 (o t h e r w i s e)

p1,p2,p3…pk are different prime numbers

Input

There are several test cases, please keep reading until EOF.
There are exact 10000 cases.
For each test case, there are 2 numbers

n,k.

Output

For each test case, output "Case #x: y", which means the test case number and the answer.

Sample Input

10 10

Sample Output

Case #1: 999999937

思路：

通过求出几组(n,k)，易得出答案为n^k%(1e9+7)

code:

#include<bits/stdc++.h>
using namespace std;
#define mod 1000000007
__int64 speedmi(__int64 a,__int64 b)
{
        __int64 ans=1;
        while(b>0){
                if(b%2==1) ans=(ans*a)%mod;
                b=b/2;
                a=(a*a)%mod;
        }
        return ans;
}
int main()
{
        __int64 n,k,sum;
        int op=1;
        while(~scanf("%I64d%I64d",&n,&k)){
                printf("Case #%d: %I64d\n",op++,speedmi(n%mod,k));
        }
        return 0;
}