## TOUGH - Bits. Exponents and Gcd

Rastas's has been given a number n. Being weak at mathematics, she has to consider all the numbers from 1 to 2n - 1 so as to become perfect in calculations. (You can assume each number is consider as a soldier).

We define the strength of number i as the number of set bits (bits equal to 1) in binary representation of number i.

If the greatest common divisor of numbers a and b is gcd(a, b),

Rastas would like to calculate the function S which is equal to: As the friend of Rastas, it's your duty to calculate S modulo 109 + 7.

### Input

The first line of the input contains the number of test cases, T. Each of the next T lines contains an integer n, as mentioned in the question

### Output

For each value of n given, find the value of the function S.

### Constraints

Sum of n over all test cases doesn't exceed 2500.

### Example

```Input:
3 ```
`1 `
`2 `
`5`
`Output: `
`0 `
`3`
```680
``` adi100: 2019-05-23 16:40:50 Nice Problem, enjoyed solving it. azam_9: 2016-02-06 07:34:14 getting tle..any suggestions?? REPLY-> Your solution is brute force. Try something else. Last edit: 2016-02-06 08:54:35 (Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†): 2016-02-06 00:10:28 Nice math problem ;-)