Minimum Non-Zero Product of the Array Elements
You are given a positive integer p.
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:
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 10^9 + 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, 10^1, 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
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