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Explore Offerings by SCALER # Different Bits Sum Pairwise

Problem Description

We define `f(X, Y)` as the number of different corresponding bits in the binary representation of X and Y.
For example, `f(2, 7)` = 2, since the binary representation of 2 and 7 are `010` and `111`, respectively. The first and the third bit differ, so f(2, 7) = 2.

You are given an array of N positive integers, A1, A2,..., AN. Find sum of `f(Ai, Aj)` for all pairs (i, j) such that 1 ≤ i, j ≤ N. Return the answer modulo 109+7.

Problem Constraints

1 <= N <= 105

1 <= A[i] <= 231 - 1

Input Format

The first and only argument of input contains a single integer array A.

Output Format

Return a single integer denoting the sum.

Example Input

Input 1:

` A = [1, 3, 5]`

Input 2:

` A = [2, 3]`

Example Output

Ouptut 1:

` 8`

Output 2:

` 2`

Example Explanation

Explanation 1:

``` f(1, 1) + f(1, 3) + f(1, 5) + f(3, 1) + f(3, 3) + f(3, 5) + f(5, 1) + f(5, 3) + f(5, 5)
= 0 + 1 + 1 + 1 + 0 + 2 + 1 + 2 + 0 = 8```

Explanation 2:

` f(2, 2) + f(2, 3) + f(3, 2) + f(3, 3) = 0 + 1 + 1 + 0 = 2`

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details. Hints
• Hint 1
• Solution Approach
• Complete Solution

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