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F. Cards and Joy

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are $$$n$$$ players sitting at the card table. Each player has a favorite number. The favorite number of the $$$j$$$-th player is $$$f_j$$$.

There are $$$k \cdot n$$$ cards on the table. Each card contains a single integer: the $$$i$$$-th card contains number $$$c_i$$$. Also, you are given a sequence $$$h_1, h_2, \dots, h_k$$$. Its meaning will be explained below.

The players have to distribute all the cards in such a way that each of them will hold exactly $$$k$$$ cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals $$$h_t$$$ if the player holds $$$t$$$ cards containing his favorite number. If a player gets no cards with his favorite number (i.e., $$$t=0$$$), his joy level is $$$0$$$.

Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence $$$h_1, \dots, h_k$$$ is the same for all the players.

Input

The first line of input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 500, 1 \le k \le 10$$$) — the number of players and the number of cards each player will get.

The second line contains $$$k \cdot n$$$ integers $$$c_1, c_2, \dots, c_{k \cdot n}$$$ ($$$1 \le c_i \le 10^5$$$) — the numbers written on the cards.

The third line contains $$$n$$$ integers $$$f_1, f_2, \dots, f_n$$$ ($$$1 \le f_j \le 10^5$$$) — the favorite numbers of the players.

The fourth line contains $$$k$$$ integers $$$h_1, h_2, \dots, h_k$$$ ($$$1 \le h_t \le 10^5$$$), where $$$h_t$$$ is the joy level of a player if he gets exactly $$$t$$$ cards with his favorite number written on them. It is guaranteed that the condition $$$h_{t - 1} < h_t$$$ holds for each $$$t \in [2..k]$$$.

Output

Print one integer — the maximum possible total joy levels of the players among all possible card distributions.

Examples

Input

4 3

1 3 2 8 5 5 8 2 2 8 5 2

1 2 2 5

2 6 7

Output

21

Input

3 3

9 9 9 9 9 9 9 9 9

1 2 3

1 2 3

Output

0

Note

In the first example, one possible optimal card distribution is the following:

- Player $$$1$$$ gets cards with numbers $$$[1, 3, 8]$$$;
- Player $$$2$$$ gets cards with numbers $$$[2, 2, 8]$$$;
- Player $$$3$$$ gets cards with numbers $$$[2, 2, 8]$$$;
- Player $$$4$$$ gets cards with numbers $$$[5, 5, 5]$$$.

Thus, the answer is $$$2 + 6 + 6 + 7 = 21$$$.

In the second example, no player can get a card with his favorite number. Thus, the answer is $$$0$$$.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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