Find Sorted Submatrices With Maximum Element at Most K

Given an integer matrix and a value K, count the submatrices whose entries are sorted non-decreasingly (by rows and columns) and whose maximum element is ≤ K. The difficulty lies in combining the structural monotonicity constraint with an upper-bound on values to count all qualifying submatrices efficiently (using histogram/stack or sliding-window style techniques rather than brute force).