1969. Minimum Non-Zero Product of the Array Elements

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

class Solution {
    int modPow(unsigned long long n,unsigned  long long p, int m = 1e9 + 7) {
        if(!p) return 1;
        unsigned long long res = modPow(n, p>>1, m);
        return p & 1 ? (res * res % m) * (n % m) % m : res * res % m; 
    }
public:
    int minNonZeroProduct(int p) {
        unsigned long long n = (1ll << p) - 1, m = 1e9 + 7;
        return n % m * modPow(n - 1, n >> 1, m) % m;
    }
};