Given three integers a, b, and n, find an integer x satisfying $0 \leq$ x $< 2^n$ such that the product (a XOR x) * (b XOR x) is maximized.

Return the maximum possible product modulo $10^9 + 7$.

Constraints:

• $0 \leq$ a, b $< 2^{50}$

• $0 \leq$ n $\leq 50$

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.