You are given an integer array points of length $n$ and an integer m.

You start at index $-1$ with an array gameScore of size $n$, where each element is initialized to $0$.

In each move, you must change your current index by $1$:

• If your current index is $-1$, you must move to index $0$.

• If your current index is at least $0$, you can either move to index $i + 1$ (provided $i + 1 < n$) or move to index $i - 1$ (provided $i - 1 \geq 0$).

Each time you visit an index $i$, the value gameScore[i] increases by points[i].

You are allowed to make at most m moves.

Return the maximum possible minimum value of gameScore across all its elements after at most m moves.

Constraints:

• $2 \leq n ==$ points.length $\leq 5 imes 10^4$

• $1 \leq$ points[i] $\leq 10^6$

• $1 \leq$ 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.