# 1802. Maximum Value at a Given Index in a Bounded Array

<https://leetcode.com/problems/maximum-value-at-a-given-index-in-a-bounded-array>

## Description

You are given three positive integers: `n`, `index`, and `maxSum`. You want to construct an array `nums` (**0-indexed**)that satisfies the following conditions:

* `nums.length == n`
* `nums[i]` is a **positive** integer where `0 <= i < n`.
* `abs(nums[i] - nums[i+1]) <= 1` where `0 <= i < n-1`.
* The sum of all the elements of `nums` does not exceed `maxSum`.
* `nums[index]` is **maximized**.

Return `nums[index]` *of the constructed array*.

Note that `abs(x)` equals `x` if `x >= 0`, and `-x` otherwise.

**Example 1:**

```
**Input:** n = 4, index = 2,  maxSum = 6
**Output:** 2
**Explanation:** nums = [1,2,**2**,1] is one array that satisfies all the conditions.
There are no arrays that satisfy all the conditions and have nums[2] == 3, so 2 is the maximum nums[2].
```

**Example 2:**

```
**Input:** n = 6, index = 1,  maxSum = 10
**Output:** 3
```

**Constraints:**

* `1 <= n <= maxSum <= 109`
* `0 <= index < n`

## ac

```java
```


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