You are given a $0$ indexed integer array nums containing n non negative integers.

In one operation, you may:

• Select an integer i such that $1 \leq$ i $< n$ and nums[i] $> 0$.

• Decrease nums[i] by $1$.

• Increase nums[i - 1] by $1$.

Return the minimum possible value of the maximum integer in nums after applying any number of operations.

Constraints:

• n $==$ nums.length

• $2 \leq$ n $\leq 10^5$

• $0 \leq$ nums[i] $\leq 10^9$

Input: nums = [4,4,4]-List[int]
Output: 4-int
Explanation: The array already has a maximum value of 4, and no operation can reduce the first element, so the minimum possible maximum is 4.

Input: nums = [0,5]-List[int]
Output: 3-int
Explanation: Move 2 units from the second element to the first, producing [2,3]. No arrangement can make the maximum value less than 3.

Input: nums = [8,0,0]-List[int]
Output: 8-int
Explanation: The first element cannot transfer units to the right, so it remains 8 and determines the minimum possible maximum.

Input: nums = [1,0,10,0]-List[int]
Output: 4-int
Explanation: Transfer units leftward from the third element to produce an arrangement such as [4,3,4,0], whose maximum is 4. A smaller maximum is not possible.

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.