Problem Statement

There are N items in a shop, numbered as Item $1, Item 2, \ldots, Item N$.
For each $i = 1, 2, \ldots, N$, the regular price of Item i is A_i yen. For each item, there is only one in stock.
Takahashi wants M items: Item $X_1, Item X_2, \ldots, Item X_M$.
He repeats the following until he gets all items he wants.

Let r be the number of unsold items now.
Choose an integer j such that $1 \leq j \leq r$, and buy the item with the j-th smallest item number among the unsold items, for its regular price plus C_j yen.

Print the smallest total amount of money needed to get all items Takahashi wants.
Takahashi may also buy items other than the ones he wants.

Input

The input is given from Standard Input in the following format:
N M
$A_1 A_2 \ldots A_N$
$C_1 C_2 \ldots C_N$
$X_1 X_2 \ldots X_M$

Output

Print the answer.

Constraints

• $1 \leq M \leq N \leq 5000$
• $1 \leq A_i \leq 10^9$
• $1 \leq C_i \leq 10^9$
• $1 \leq X_1 \lt X_2 \lt \cdots \lt X_M \leq N$
• All values in the input are integers.

Sample Input 1

5 2
3 1 4 1 5
9 2 6 5 3
3 5

Sample Output 1

17

Here is a way for Takahashi to get all items he wants with the smallest total amount of money.

• Initially, five items, Items 1, 2, 3, 4, 5, are remaining.
  Choose j = 5 to buy the item with the fifth smallest item number among the remaining, Item 5, for A_5 + C_5 = 5 + 3 = 8 yen.
• Then, four items, Items 1, 2, 3, 4, are remaining.
  Choose j = 2 to buy the item with the second smallest item number among the remaining, Item 2, for A_2 + C_2 = 1 + 2 = 3 yen.
• Then, three items, Items 1, 3, 4, are remaining.
  Choose j = 2 to buy the item with the second smallest item number among the remaining, Item 3, for A_3 + C_2 = 4 + 2 = 6 yen.

Now, Takahashi has all items he wants, Items 3 and 5, (along with Item 2, which is not wanted) for a total cost of 8 + 3 + 6 = 17 yen, the minimum possible.

Sample Input 2

20 8
29 27 79 27 30 4 93 89 44 88 70 75 96 3 78 39 97 12 53 62
32 38 84 49 93 53 26 13 25 2 76 32 42 34 18 77 14 67 88 12
1 3 4 5 8 14 16 20

Sample Output 2

533

见题面 Input 部分

见题面 Output 部分