You are given a $0$ indexed integer array nums and a positive integer k.

In one operation, you can choose two distinct indices i and j such that $0 \leq$ i, j $<$ nums.length, and simultaneously replace nums[i] with (nums[i] AND nums[j]) and nums[j] with (nums[i] OR nums[j]), where AND denotes the bitwise AND operation and OR denotes the bitwise OR operation.

You may apply this operation any number of times.

Return the maximum possible sum of squares of any k elements chosen from the final array. Since the result can be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ k $\leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.