Consider a positive integer X,and let S be the sum of all positive integer divisors of 2004^X. Your job is to determine S modulo 29 (the rest of the division of S by 29).
Take X = 1 for an example. The positive integer divisors of 2004^1 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002 and 2004. Therefore S = 4704 and S modulo 29 is equal to 6.
Input
The input consists of several test cases. Each test case contains a line with the integer X (1 <= X <= 10000000).
A test case of X = 0 indicates the end of input, and should not be processed.
Output
For each test case, in a separate line, please output the result of S modulo 29.
Sample Input
1100000
Sample Output
610
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#include<stdio.h>
#include<string.h>
//int exgcd(int a,int b,int &x,int &y)
//{
// if(b==0)
// {
// x=1;y=0;return a;
// }
// int r=exgcd(b,a%b,x,y);
// int tmp=x;x=y;y=tmp-a/b*y;
// return r;
// }
long long kuai(long long a,long long b)
{
long long x=1;a=a%29;
while(b>0)
{
if(b%2==1)
x=(x*a)%29;
b=b/2;a=a*a%29;
}
return x;
}
int main()
{
// int x,y;
// int k=exgcd(332,29,x,y);
long long t;
while(scanf("%lld",&t),t!=0)
{
long long ans=(kuai(2,2*t+1)-1)*(kuai(3,t+1)-1)*(kuai(167,t+1)-1)*9%29;
printf("%lld\n",ans);
}
return 0;
}