You are given an $m imes n$ cake and two integer arrays horizontalCut of size $m - 1$ and verticalCut of size $n - 1$, where:

• horizontalCut[i] represents the cost to make a cut along horizontal line $i$.

• verticalCut[j] represents the cost to make a cut along vertical line $j$.

In one operation, you can slice an existing piece of cake along a horizontal or vertical line into two pieces. The cost of the operation is the cost associated with that cut line.

Return the minimum total cost required to cut the entire cake into $1 imes 1$ pieces.

Constraints:

• $1 \leq m, n \leq 10^5$

• horizontalCut.length $= m - 1$

• verticalCut.length $= n - 1$

• $1 \leq$ horizontalCut[i], verticalCut[i] $\leq 10^3$

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.