You are given an integer array nums, where nums[i] is the number of balls in the $i$th bag. You may perform at most maxOperations operations.

In one operation, choose a bag containing $x$ balls and split it into two non empty bags containing $a$ and $b$ balls such that $a + b = x$.

Define the penalty as the maximum number of balls in any bag after performing at most maxOperations operations. Return the minimum possible penalty.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ maxOperations, nums[i] $\leq 10^9$

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.