Leetcode 3426. Manhattan Distances of All Arrangements of Pieces

Compute the total sum of pairwise Manhattan distances over all ways to place k identical pieces on an m×n grid (one per cell), modulo 1e9+7. The core challenge is combinatorial counting: for each pair of cells count how many arrangements include that pair (choose the other k−2 cells) and exploit that Manhattan distance separates into independent row and column contributions to aggregate efficiently.