Description

There are $n$ students. Each student took the final exams of all $m$ courses and is anxiously waiting for the results to be announced.

Student $i$ hopes to know the results of all courses on or before day $t_i$. If on day $t_i$ at least one course has not been announced, the student will wait until the last course is announced; each day of waiting incurs $C$ unhappiness.

For course $i$, according to the original plan, its result will be announced on day $b_i$.

You can adjust announcement days using the following two operations:

1. Move some teachers from course $X$ to course $Y$. After the adjustment, the announcement day of course $X$ is delayed by one day, and that of course $Y$ is moved one day earlier. Each such operation incurs $A$ unhappiness.
2. Add some teachers to course $Z$, which moves the announcement day of course $Z$ one day earlier. Each such operation incurs $B$ unhappiness.

In both operations, the parameters $X$, $Y$, and $Z$ can be chosen arbitrarily. Each operation can be performed multiple times, and the parameters can be re-chosen each time.

Please minimize the total unhappiness by applying operations reasonably, and output the minimum possible total unhappiness.

Input Format

• The first line contains three non-negative integers $A, B, C$, which are the unhappiness costs, as described in the Description.
• The second line contains two positive integers $n, m$, the numbers of students and courses, respectively.
• The third line contains $n$ positive integers $t_i$, the desired announcement days for each student.
• The fourth line contains $m$ positive integers $b_i$, the originally planned announcement days for each course.

Output Format

Output a single integer on one line, the minimum total unhappiness.

100 100 2
4 5
5 1 2 3
1 1 2 3 3

6

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

33

Hint

Sample Explanation 1

Because the unhappiness caused by adjustments is too large, the best plan here is to make no adjustments. Among all $5$ courses, the slowest is announced on day $3$.
Student $1$ hopes for results by day $5$, so no unhappiness is incurred.
Student $2$ hopes for results by day $1$, so the incurred unhappiness is $(3 - 1) \times 2 = 4$.
Student $3$ hopes for results by day $2$, so the incurred unhappiness is $(3 - 2) \times 2 = 2$.
Student $4$ hopes for results by day $3$, so no unhappiness is incurred.
The total unhappiness is $4 + 2 = 6$.

Constraints

Translated by ChatGPT 5