Aniket Verma aka Math Bond flaunts his mathematics skill whenever he gets the opportunity. But this time he gets into trouble when he meets Sakshi, another mathematician. Sakshi gave him a problem and asked him to solve. Help Aniket to solve the problem.

Given a number N, find the sum of all products x*y such that N/x = y (Integer Division).

Input
The first line of input file contains an integer T, the number of test cases. Each of the next T lines contain an integer N.

Output
Output T lines containing answer to corresponding test case.
Since the sum can be very large, you have to output this modulo 1000000007.

Constraints
1 ≤ T ≤ 500

1 ≤ N ≤ 10^9

Example
Input:
3
2
3
5

Output:
4
8
21

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