Happy 2004

发布时间: 2016年12月3日 16:34   最后更新: 2016年12月3日 16:34   时间限制: 1000ms   内存限制: 65536M

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.

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.

For each test case, in a separate line, please output the result of S modulo 29.

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1
10000
0
6
10

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