You are given an $m imes n$ matrix mat where each row is sorted in nondecreasing order, and an integer k.

You can select exactly one element from each row to form a combination. The sum of a combination is the total of its chosen elements.

Return the $k^{ ext{th}}$ smallest combination sum among all possible choices.

Constraints:

• m == mat.length

• n == mat[i].length

• $1 \leq$ m, n $\leq 40$

• $1 \leq$ mat[i][j] $\leq 5000$

• $1 \leq$ k $\leq \min(200, n^m)$

• mat[i] is sorted in nondecreasing order.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.