Minimum Non-Zero Product of the Array Elements

Given p, you may swap corresponding bits between any pair of numbers in the set {1,...,2^p-1}; compute the minimum possible non-zero product of the array modulo 1e9+7. Core insight: bit rearrangement lets you form one value 2^p-2 and (2^{p-1}-1) pairs whose products equal 2^p-1, so the minimum product is (2^p-2) * (2^p-1)^(2^{p-1}-1), computed with modular exponentiation (p ≤ 60).