You are given a multiplication table of size m$\times$n, where each element at position mat[i][j] is calculated as $i \times j$ (with 1-based indexing).

Your task is to find the $k^{th}$ smallest element in this table, given the m, n, and k values.

Constraints:

• $1 \leq$ m, n $\leq 3 \times 10^4$

• $1 \leq$ k $\leq$ m $\times$n

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 on how to solve this problem.

Implement your solution in the following coding playground.