Count Set Bits Problem Statement

Given a positive integer N, compute the total number of '1's in the binary representation of all numbers from 1 to N. Return this count modulo 1e9+7 because the result can be very large.

Input:

The first line contains an integer T representing the number of test cases.
Each of the next T lines contains a single integer N, the value for each test case.

Output:

For each test case, return an integer denoting the count of set bits from 1 to N modulo 1e9+7.
Output each result on a new line.

Example:

Input:

2
3
5

Output:

4
7

Explanation:

For N = 3, the numbers are 1 (0b1), 2 (0b10), and 3 (0b11). Total set bits = 4.
For N = 5, the numbers are 1 (0b1), 2 (0b10), 3 (0b11), 4 (0b100), 5 (0b101). Total set bits = 7.

Constraints:

• 1 ≤ T ≤ 100
• 1 ≤ N ≤ 10^9
• Time limit: 1 second

Note:

Implement the function and return the results, as the output mechanism has been handled.