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Determine the Minimum Sum of a k-avoiding Array

You are given two integers, n and k.

You are given two integers, n and k.

An array of distinct positive integers is called a k-avoiding array if there does not exist any pair of distinct elements that sum to k.

Return the minimum possible sum of a k-avoiding array of length n.

Example 1

Input: n = 5, k = 4

Output: 18

Explanation: Consider the k-avoiding array [1,2,4,5,6], which has a sum of 18. It can be proven that there is no k-avoiding array with a sum less than 18.

Example 2

Input: n = 2, k = 6

Output: 3

Explanation: We can construct the array [1,2], which has a sum of 3. It can be proven that there is no k-avoiding array with a sum less than 3.

Constraints

  • 1 <= n, k <= 50

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