文理学院程序设计在线练习


Farm

Time Limit: 1 Second(s)    Memory Limit: 32 MB

Total Submission(s): 53   Accepted Submission(s): 8
Problem Description

Different heroes have different potential,and usually late heros need a period of development to strengthen. Now we need you to explore the potential for each hero.
We assume that a hero attribute value is a positive integer X and a skill also is expressed as a positive integer Y,if X can be divided by Y,we say hero X have the skill Y.What’s more,the damage of Y equal the sum of Y’s divisor.So we say a hero’s potential equal to the sum of skill’s damage which the skill he have.
For example,Saber’s attribute value is 8,so she have skills of 1,2,4 and 8.There were 1,3,7,15 damage.So Saber’s potential is 26.
The result is very large, so need to mod 1000000007 (1e9 + 7).

Input

The first line is the number of test cases T(T<=100).
Each test case has one line containing one integer X.
X(0<=X<=1000000000)

Output

For each test case, output one line that contains an integer equals to the hero’s potential.

Sample Input
2
8
3
Sample Output
26
5
Source

2014市赛