CF1585C.Minimize Distance

A total of $n$ depots are located on a number line. Depot $i$ lies at the point $x_i$ for $1 \le i \le n$.

You are a salesman with $n$ bags of goods, attempting to deliver one bag to each of the $n$ depots. You and the $n$ bags are initially at the origin $0$. You can carry up to $k$ bags at a time. You must collect the required number of goods from the origin, deliver them to the respective depots, and then return to the origin to collect your next batch of goods.

Calculate the minimum distance you need to cover to deliver all the bags of goods to the depots. You do not have to return to the origin after you have delivered all the bags.

共有 $n$ 个仓库位于一条数轴上。对于 $1 \le i \le n$，第 $i$ 个仓库位于坐标 $x_i$ 处。

你是一名推销员，携带 $n$ 袋货物，需将其中一袋货物送达每个仓库。你与这 $n$ 袋货物初始时均位于原点 $0$。你每次最多可携带 $k$ 袋货物。你必须从原点取走所需数量的货物，将其运送到对应仓库，然后返回原点取下一批货物。

请计算将全部 $n$ 袋货物送达各仓库所需经过的最短总路程。在完成全部货物的配送后，你无需再返回原点。

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 $2 \cdot 10^5$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10\,500$）。随后是测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $k$（$1 \le k \le n \le 2 \cdot 10^5$）。

每个测试用例的第二行包含 $n$ 个整数 $x_1, x_2, \ldots, x_n$（$-10^9 \le x_i \le 10^9$）。某些仓库的位置可能相同。

保证所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^5$。

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.

对于每个测试用例，输出一个整数，表示将所有货物袋运送至仓库所需经过的最小距离。

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.

在第一个测试用例中，你每次只能携带一个包裹。因此，以下是一个能实现最小旅行距离的解序列：$0 \to 2 \to 0 \to 4 \to 0 \to 3 \to 0 \to 1 \to 0 \to 5$，其中每个 $0$ 表示你返回原点并取走一个包裹，每个正整数表示你将该包裹送达位于该坐标的仓库，总距离为 $25$ 单位。需注意，存在其他同样能达到该距离的序列。

在第二个测试用例中，你可在多种可行序列中选择如下序列以实现最小旅行距离：$0 \to 6 \to 8 \to 7 \to 0 \to 5 \to 4 \to 3 \to 0 \to (-5) \to (-10) \to (-15)$，总距离为 $41$。可以证明，$41$ 是该测试用例的最优距离。