Yet another expected value problem

You are given a matrix $A$ having $N$ rows and $M$ columns. You are also given an integer $K$. Initially all rows and columns are unprocessed. You initialize a variable `ans` to be $0$. You do the following experiment until all rows and columns have been processed: - From the list of unprocessed rows and columns, choose one uniformly at random. Let the sum of this selected row/column be $S$. Add