CF1921D.Very Different Array

Petya has an array $a_i$ of $n$ integers. His brother Vasya became envious and decided to make his own array of $n$ integers.

To do this, he found $m$ integers $b_i$ ($m\ge n$), and now he wants to choose some $n$ integers of them and arrange them in a certain order to obtain an array $c_i$ of length $n$.

To avoid being similar to his brother, Vasya wants to make his array as different as possible from Petya's array. Specifically, he wants the total difference $D = \sum_{i=1}^{n} |a_i - c_i|$ to be as large as possible.

Help Vasya find the maximum difference $D$ he can obtain.

彼得亚有一个包含 $n$ 个整数的数组 $a_i$。他的弟弟瓦夏心生嫉妒，决定也构造一个长度为 $n$ 的整数数组。

为此，他找来了 $m$ 个整数 $b_i$（其中 $m \ge n$），现在他想从中选出 $n$ 个数，并以某种顺序排列，构成一个长度为 $n$ 的数组 $c_i$。

为了避免与哥哥的数组过于相似，瓦夏希望自己的数组与彼得亚的数组尽可能不同。具体而言，他希望总差异值 $D = \sum_{i=1}^{n} |a_i - c_i|$ 尽可能大。

请帮助瓦夏求出他所能得到的最大差异值 $D$。

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. This is followed by a description of the test cases.

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

The second line of each test case contains $n$ integers $a_i$ ($1\le a_i\le 10^9$). The third line of each test case contains $m$ integers $b_i$ ($1\le b_i\le 10^9$).

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

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \le t \le 100$），表示测试用例的数量。随后是各测试用例的描述。

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

每个测试用例的第二行包含 $n$ 个整数 $a_i$（$1\le a_i\le 10^9$）。每个测试用例的第三行包含 $m$ 个整数 $b_i$（$1\le b_i\le 10^9$）。

保证在一个测试中，所有测试用例的 $m$ 值之和不超过 $2 \cdot 10^5$。

For each test case, output a single integer — the maximum total difference $D$ that can be obtained.

对于每个测试用例，输出一个整数——所能获得的最大总差值 $D$。

In the first example, Vasya can, for example, create the array $(1, 5, 7, 2)$. Then the total difference will be $D = |6-1|+|1-5|+|2-7|+|4-2| = 5+4+5+2 = 16$.

In the second example, all the integers available to Vasya are equal to 1, so he can only create the array $(1, 1, 1)$, for which the difference $D = 0$.

In the third example, Vasya can, for example, create the array $(5, 4, 3, 2, 1)$. Then the total difference will be $D = |1-5|+|2-4|+|3-3|+|4-2|+|5-1| = 4+2+0+2+4 = 12$.

在第一个例子中，瓦西娅可以例如构造数组 $(1, 5, 7, 2)$。此时总差值为 $D = |6-1|+|1-5|+|2-7|+|4-2| = 5+4+5+2 = 16$。

在第二个例子中，瓦西娅可使用的所有整数均为 $1$，因此他只能构造数组 $(1, 1, 1)$，此时差值 $D = 0$。

在第三个例子中，瓦西娅可以例如构造数组 $(5, 4, 3, 2, 1)$。此时总差值为 $D = |1-5|+|2-4|+|3-3|+|4-2|+|5-1| = 4+2+0+2+4 = 12$。