A16373 | 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.