Problem B

Statement
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Description:
You are given an array $$$a_1, a_2, \dots, a_n$$$, where all elements are different.

You have to perform exactly $$$k$$$ operations with it. During each operation, you do exactly one of the following two actions (you choose which to do yourself):

- find two minimum elements in the array, and delete them;
- find the maximum element in the array, and delete it.

You have to calculate the maximum possible sum of elements in the resulting array.

Input Format:
The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case consists of two lines:

- the first line contains two integers $$$n$$$ and $$$k$$$ ($$$3 \le n \le 2 \cdot 10^5$$$; $$$1 \le k \le 99999$$$; $$$2k < n$$$) — the number of elements and operations, respectively.
- the second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$; all $$$a_i$$$ are different) — the elements of the array.

Additional constraint on the input: the sum of $$$n$$$ does not exceed $$$2 \cdot 10^5$$$.

Output Format:
For each test case, print one integer — the maximum possible sum of elements in the resulting array.

Note:
In the first testcase, applying the first operation produces the following outcome:

- two minimums are $$$1$$$ and $$$2$$$; removing them leaves the array as $$$[5, 10, 6]$$$, with sum $$$21$$$;
- a maximum is $$$10$$$; removing it leaves the array as $$$[2, 5, 1, 6]$$$, with sum $$$14$$$.

$$$21$$$ is the best answer.

In the second testcase, it's optimal to first erase two minimums, then a maximum.