zoj3785 What day is that day?

It's Saturday today, what day is it after 1¹ + 2² + 3³ + ... + N^N days?

Input

There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:

There is only one line containing one integer N (1 <= N <= 1000000000).

Output

For each test case, output one string indicating the day of week.

Sample Input

2
1
2

Sample Output

Sunday
Thursday

Hint

A week consists of Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday.

题目大意：今天是星期六，输入n，问1¹ + 2² + 3³ + ... + N^N 天后是星期几？

思路：因为n是10亿，解法必定是数学方法或者找规律。注意到7是素数，所以可以使用费马小定理进行简化。即当p是素数是，a^(p-1) mod p=1，简化后发现每42个数就会出现一个循环，得数mod7=6。所以求解过程就是先求出n由几个42组成，对于42取余的剩下的部分就可以直接模拟做了。

 /*
  * Author:  Joshua
  * Created Time:  2014/5/17 13:18:55
  * File Name: j.cpp
  */
 #include<cstdio>
 #include<iostream>
 #include<cstring>
 #include<cstdlib>
 #include<cmath>
 #include<algorithm>
 #include<string>
 #include<map>
 #include<set>
 #include<vector>
 #include<queue>
 #include<stack>
 #include<ctime>
 #include<utility>
 #define M0(x) memset(x, 0, sizeof(x))
 #define MP make_pair
 #define Fi first
 #define Se second
 #define rep(i, a, b) for (int i = (a); i <= (b); ++i)
 #define red(i, a, b) for (int i = (a); i >= (b); --i)
 #define PB push_back
 #define Inf 0x3fffffff
 #define eps 1e-8
 typedef long long LL;
 using namespace std;

 string ans[]={"Saturday","Sunday","Monday","Tuesday","Wednesday","Thursday","Friday"};

 void solve()
 {
     int n,m,t=,temp;
     scanf("%d",&n);
     m=n/;
     t=(t+m*)%;
     for (int i=;i<=n%;i++)
     {
       temp=;
       for (int j=;j<=i;j++)
         temp=(temp*i)%;
         t=(t+temp)%;
     }
     cout<<ans[t]<<endl;
 }
 int main()
 {
     int tt;
     scanf("%d",&tt);
     while (tt)
     {
         tt--;
         solve();
     }
     return ;
 }

许久没写了，代码太丑，大家凑合着看。。。