Leetcode 3539. Find Sum of Array Product of Magical Sequences

Count the sum of products of all length-m sequences of indices (0..n-1) whose sum of 2^{index} has exactly k set bits; the challenge is to count weighted sequences by index multiplicities while correctly handling binary carries in the sum of powers of two. With m ≤ 30 and n ≤ 50 this is typically solved by dynamic programming over bit positions and carries (or equivalent combinatorics) to accumulate the product contributions modulo 1e9+7.