Maximum Value at a Given Index in a Bounded Array

Try to solve the Maximum Value at a Given Index in a Bounded Array problem.

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 11≤\leq i <\lt n.

  • The absolute difference between two consecutive elements, nums[i] and nums[i+1], is at most 11.

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

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

Constraints:

  • 11≤\leqn ≤\leqmaxSum ≤\leq10910^9

  • 00≤\leqindex <\ltn

Examples

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