You are given two integer arrays value and decay of equal length, along with an integer m.

You can make at most m selections across the available indices. When you choose an index i:

• The first time index i is selected, you gain value[i].

• Each subsequent time index i is selected, the gained value decreases by decay[i]. If index i has previously been selected $k$ times, choosing it again provides $\max(0,$ value[i] $- k \times$ decay[i]$)$.

Return the maximum total value you can achieve after at most m selections.

Constraints:

• $1 \leq$ value.length $=$ decay.length $\leq 10^5$

• $1 \leq$ value[i], decay[i] $\leq 10^9$

• $1 \leq$ m $\leq 10^9$

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.