You are given a positive integer p. Consider an array nums containing all integers in the inclusive range $[1, 2^p - 1]$ represented in binary form.

In one operation, you may choose two elements from nums and swap their bits at any corresponding bit position.

Return the minimum non zero product of all elements in nums after applying any number of operations. Since the result can be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ p $\leq 60$

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.