Description

There are $m$ schools, each with an expected cutoff score $a_i$. There are $n$ students, with estimated scores $b_i$.

Based on the estimated scores of the $n$ students, recommend one school to each student such that the difference between the school’s expected cutoff score and the student’s estimated score is minimized (either higher or lower—after all, it’s just an estimate). This minimum difference is called dissatisfaction. Find the minimum possible sum of dissatisfaction over all students.

Input Format

The first line contains two integers $m, n$.

The second line contains $m$ numbers, representing the expected cutoff scores of the $m$ schools.

The third line contains $n$ numbers, representing the estimated scores of the $n$ students.

Output Format

Output one line, the minimum sum of dissatisfaction.

4 3
513 598 567 689
500 600 550

32

Hint

Constraints:

For $30\%$ of the testdata, $1 \le n, m \le 10^3$, and the estimated scores and cutoffs are $\le 10^4$.

For $100\%$ of the testdata, $1 \le n, m \le 10^5$, the estimated scores and cutoffs are $\le 10^6$, and all are non-negative integers.

Translated by ChatGPT 5