Task

Given a number k, find the smallest integer n such that if any k elements are removed from the set {1, 2, ..., n}, one can still find k distinct numbers among the remaining elements with sum of n.

[input] integer k
The number of elements to be removed.

[set] 2 ≤ k ≤ 10000

[output] an integer
The smallest value of n.

Example

For k = 2, the output should be 7.

The initial set is {1, 2, 3, 4, 5, 6, 7}.

No matter what 2 elements you remove, (1, 6), (2, 5), or (3, 4) will sum up to 7.

Why isn't the result 6? Because: In set {1, 2, 3, 4, 5, 6}, if we remove 2 elements (1,2), or (4,5) the remaining elements do not contain 2 elements that sum up to 6.

Tests

removeK(2)

removeK(3)

removeK(10)

removeK(25)

Good luck!

This challenge comes from myjinxin2015 on CodeWars. Thank you to CodeWars, who has licensed redistribution of this challenge under the 2-Clause BSD License!

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