Cards and Joy
Description
There 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.
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 $t \in [2..k]$.
Print one integer — the maximum possible total joy levels of the players among all possible card distributions.
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.
Samples
4 3
1 3 2 8 5 5 8 2 2 8 5 2
1 2 2 5
2 6 7
21
3 3
9 9 9 9 9 9 9 9 9
1 2 3
1 2 3
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 $0$.