311015: 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.

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 $2 \cdot 10^5$.

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

9
4 6
6 1 2 4
3 5 1 7 2 3
3 4
1 1 1
1 1 1 1
5 5
1 2 3 4 5
1 2 3 4 5
2 6
5 8
8 7 5 8 2 10
2 2
4 1
9 6
4 6
8 10 6 4
3 10 6 1 8 9
3 5
6 5 2
1 7 9 7 2
5 5
9 10 6 3 7
5 9 2 3 9
1 6
3
2 7 10 1 1 5

16
0
12
11
10
23
15
25
7

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 $D = |1-5|+|2-4|+|3-3|+|4-2|+|5-1| = 4+2+0+2+4 = 12$.