1969 - Minimum Non-Zero Product of the Array Elements.

Medium

You are given a positive integer p. Consider an array nums ( 1-indexed ) that consists of the integers in the inclusive range <code>1, 2^p - 1</code> in their binary representations. You are allowed to do the following operation any number of times:

• Choose two elements x and y from nums.

• Choose a bit in x and swap it with its corresponding bit in y. Corresponding bit refers to the bit that is in the same position in the other integer.

For example, if x = 1101 and y = 0011, after swapping the <code>2^nd</code> bit from the right, we have x = 1111 and y = 0001.

Find the minimum non-zero product of nums after performing the above operation any number of times. Return this product modulo <code>10⁹ + 7</code>.

Note: The answer should be the minimum product before the modulo operation is done.

Example 1:

Input: p = 1

Output: 1

Explanation: nums = 1. There is only one element, so the product equals that element.

Example 2:

Input: p = 2

Output: 6

Explanation: nums = 01, 10, 11.

Any swap would either make the product 0 or stay the same.

Thus, the array product of 1 \* 2 \* 3 = 6 is already minimized.

Example 3:

Input: p = 3

Output: 1512

Explanation: nums = 001, 010, 011, 100, 101, 110, 111

• In the first operation we can swap the leftmost bit of the second and fifth elements.

• In the second operation we can swap the middle bit of the third and fourth elements.

The array product is 1 \* 6 \* 1 \* 6 \* 1 \* 6 \* 7 = 1512, which is the minimum possible product.

Constraints:

• 1 <= p <= 60