# Daily Challenge #284 - Remove K

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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