You are given three integers n, m, and k, representing the lengths of two logs and the maximum log length that a truck can transport.

Each truck can carry at most one log of length at most k. If a log has a length strictly greater than k, it must be cut into smaller pieces such that every resulting piece has a length of at most k.

Dividing a log of length $L$ into two logs of lengths $a$ and $b$ (where $a + b = L$) incurs a cost of $a imes b$.

Return the minimum total cost to cut the logs so that all pieces can be transported.

Constraints:

• $2 \leq$ k $\leq 10^5$

• $1 \leq$ n, m $\leq 2 imes$ k

• The input is generated such that it is always possible to transport the logs.

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.