Minimize Distance

Description:

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10\,500$$$). Description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 2 \cdot 10^5$$$).

The second line of each test case contains $$$n$$$ integers $$$x_1, x_2, \ldots, x_n$$$ ($$$-10^9 \le x_i \le 10^9$$$). It is possible that some depots share the same position.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, output a single integer denoting the minimum distance you need to cover to deliver all the bags of goods to the depots.

Sample Input:

4
5 1
1 2 3 4 5
9 3
-5 -10 -15 6 5 8 3 7 4
5 3
2 2 3 3 3
4 2
1000000000 1000000000 1000000000 1000000000

Sample Output:

25
41
7
3000000000

Note:

In the first test case, you can carry only one bag at a time. Thus, the following is a solution sequence that gives a minimum travel distance: $$$0 \to 2 \to 0 \to 4 \to 0 \to 3 \to 0 \to 1 \to 0 \to 5$$$, where each $$$0$$$ means you go the origin and grab one bag, and each positive integer means you deliver the bag to a depot at this coordinate, giving a total distance of $$$25$$$ units. It must be noted that there are other sequences that give the same distance.

In the second test case, you can follow the following sequence, among multiple such sequences, to travel minimum distance: $$$0 \to 6 \to 8 \to 7 \to 0 \to 5 \to 4 \to 3 \to 0 \to (-5) \to (-10) \to (-15)$$$, with distance $$$41$$$. It can be shown that $$$41$$$ is the optimal distance for this test case.