Find the Kth Smallest Sum of a Matrix With Sorted Rows

Given an m×n matrix whose rows are sorted, pick exactly one element from each row and return the k-th smallest possible total sum; the challenge is to avoid enumerating the exponential (n^m) combinations by exploiting row order and the small k (≤200) via techniques like iteratively merging rows keeping only k smallest sums or binary-search-with-pruned counting.