You are given a rectangular cake of dimensions h $ imes$ w and two integer arrays horizontalCuts and verticalCuts where:

• horizontalCuts[i] is the distance from the top of the rectangular cake to the $i^{ ext{th}}$ horizontal cut.

• verticalCuts[j] is the distance from the left of the rectangular cake to the $j^{ ext{th}}$ vertical cut.

Return the maximum area of a piece of cake after you make all the horizontal and vertical cuts.

Note: Since the answer can be large, return it modulo $10^9 + 7$.

Constraints:

• $2 \leq$ h, w $\leq 10^9$

• $1 \leq$ horizontalCuts.length $\leq \min($ h $- 1, 10^5)$

• $1 \leq$ verticalCuts.length $\leq \min($ w $- 1, 10^5)$

• $1 \leq$ horizontalCuts[i] $<$ h

• $1 \leq$ verticalCuts[i] $<$ w

• All the elements in horizontalCuts are distinct.

• All the elements in verticalCuts are distinct.

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.