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We define `f(X, Y)`

as number of different corresponding bits in binary representation of X and Y. For example, `f(2, 7)`

= 2, since 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, A_{1}, A_{2} ,…, A_{N}. Find sum of f(A_{i}, A_{j}) for all pairs (i, j) such that 1 ≤ i, j ≤ N. Return the answer modulo 10^{9}+7.

For example,

```
A=[1, 3, 5]
We return
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
```

- Hint 1
- Solution Approach
- Complete Solution

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