Maximum Value at a Given Index in a Bounded Array

Statement

Given three positive integers, n, index, and maxSum, output the nums[index] by constructing an array of nums with the length of n, which satisfies the following conditions:

• The length of the array nums is equal to n.

• Each element nums[i] is a positive integer, where $1$$\leq$ i $\lt$ n.

• The absolute difference between two consecutive elements, nums[i] and nums[i+1], is at most $1$.

• The sum of all elements in nums does not exceed maxSum.

• The element at nums[index] contains the maximum value.

Constraints:

• $1$$\leq$n $\leq$maxSum $\leq$$10^9$

• $0$$\leq$index $\lt$n

Examples