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
hide comments
adi100:
20190523 16:40:50
Nice Problem, enjoyed solving it. 

azam_9:
20160206 07:34:14
getting tle..any suggestions??


(Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†):
20160206 00:10:28
Nice math problem ;) 
Added by:  likecs 
Date:  20160205 
Time limit:  1s 
Source limit:  10000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 GOSU JSMONKEY 
Resource:  Own problem 