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

We need to find the $k^{th}$ smallest number in a multiplication table of size $m \times n$, where the element at the position $(i, j)$ is the product $i \times j$. A direct approach to constructing the multiplication table and sorting the numbers would be inefficient. Instead of building the table explicitly, we can use the sorted properties of the multiplication table and binary search to find the ...