Cards and Joy

Description:

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.

Sample Input:

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

Sample Output:

21

Sample Input:

3 3
9 9 9 9 9 9 9 9 9
1 2 3
1 2 3

Sample 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 $$$0$$$.