School Recommendation

Problem Description

There are $m$ schools, the $i$-th of which has an expected admission cutoff $a_i$; and there are $n$ students, the $i$-th of whom has an estimated score $b_i$.

Now we must recommend one school for each student. For a given student, among all schools the one whose cutoff differs least from the student's estimated score is recommended; this minimal difference (in absolute value) is called that student's dissatisfaction. Compute the sum of all students' dissatisfaction.

Input Format

The first line contains two positive integers $m, n$, the number of schools and the number of students respectively.

The second line contains $m$ non-negative integers $a_1, a_2, \dots, a_m$, the expected cutoffs of the schools.

The third line contains $n$ non-negative integers $b_1, b_2, \dots, b_n$, the estimated scores of the students.

Output Format

Output one line containing a single non-negative integer: the sum of all students' dissatisfaction.

Sample Input

4 3
513 598 567 689
500 600 550

Sample Output

32

Sample Explanation

The $m=4$ schools have cutoffs $513, 598, 567, 689$; the $n=3$ students have estimated scores $500, 600, 550$.

• The first student's score is $500$; its difference from cutoff $513$ is $|500-513|=13$, so the dissatisfaction is $13$.
• The second student's score is $600$; its difference from cutoff $598$ is $|600-598|=2$, so the dissatisfaction is $2$.
• The third student's score is $550$; its difference from cutoff $567$ is $|550-567|=17$, so the dissatisfaction is $17$.

The total dissatisfaction is $13+2+17=32$.

Constraints

• For $30\%$ of the data: $1\le n,m\le 10^3$, $0\le a_i,b_i\le 10^4$;
• For $100\%$ of the data: $1\le n,m\le 10^5$, $0\le a_i,b_i\le 10^6$.