## GOPI_SW - Gopi and Sandwich

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Gopi is fond of sandwiches. Once his friend asks him to give part of his sandwich. But, Gopi wants to give him as little sandwich as possible. So, he devices a method.

He divides the sandwich into n parts, where each part is a unit fraction( fractions of the form 1/p where p is integer) of the original sandwich. Among all these parts he chooses the smallest part and gives it to his friend. Help Gopi to find the smallest part possible.

### Input

First line contains t(1<=t<=105) the number of test cases. The next t lines contain one integer per line denoting n(2<=n<=106) the number of parts the sandwich can be divided.

### Output

Output one line per test case containing the denominator of the smallest part. Since, the answer can be very large, print Answer modulo 109 + 7

### Example

```Input:
1```
```3

Output:
6```
`Explaination:`
`The possible ways of dividing the sandwich into 3 parts are:`
` 1/3, 1/3, 1/31/3,1/3,1/3`
`1/6,1/2,1/3`
`1/4,1/4,1/2`
```Among these, the second way has the smallest part. Hence the output is 6
1/6, 1/2, 1/3```