Problem9210--ABC288 —— E - Wish List

9210: ABC288 —— E - Wish List

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

### 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

### 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

### Output

Print the answer.

Constraints

### 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 1 Input

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

Sample 1 Output

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 2 Input

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 2 Output

533

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