You are given a positive integer `p`. Consider an array `nums` (1-indexed) that consists of the integers in the inclusive range `[1, 2p - 1]` 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 `2nd` 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 `109 + 7`.

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.
        - The resulting array is [001, 110, 011, 100, 001, 110, 111].
    - In the second operation we can swap the middle bit of the third and fourth elements.
        - The resulting array is [001, 110, 001, 110, 001, 110, 111].
    The array product is 1 * 6 * 1 * 6 * 1 * 6 * 7 = 1512, which is the minimum possible product.

Constraints:

- `1 <= p <= 60`