CoderForces999F-Cards and Joy

F. Cards and Joy

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

There are nn players sitting at the card table. Each player has a favorite number. The favorite number of the jj-th player is fjfj.

There are k⋅nk⋅n cards on the table. Each card contains a single integer: the ii-th card contains number cici. Also, you are given a sequence h1,h2,…,hkh1,h2,…,hk. 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 kk 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 htht if the player holds tt cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0t=0), his joy level is 00.

Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h1,…,hkh1,…,hk is the same for all the players.

Input

The first line of input contains two integers nn and kk (1≤n≤500,1≤k≤101≤n≤500,1≤k≤10) — the number of players and the number of cards each player will get.

The second line contains k⋅nk⋅n integers c1,c2,…,ck⋅nc1,c2,…,ck⋅n (1≤ci≤1051≤ci≤105) — the numbers written on the cards.

The third line contains nn integers f1,f2,…,fnf1,f2,…,fn (1≤fj≤1051≤fj≤105) — the favorite numbers of the players.

The fourth line contains kk integers h1,h2,…,hkh1,h2,…,hk (1≤ht≤1051≤ht≤105), where htht is the joy level of a player if he gets exactly tt cards with his favorite number written on them. It is guaranteed that the condition ht−1<htht−1<ht holds for each t∈[2..k]t∈[2..k].

Output

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

Examples

input

Copy

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

output

Copy

21

input

Copy

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

output

Copy

0

Note

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

• Player 11 gets cards with numbers [1,3,8][1,3,8];
• Player 22 gets cards with numbers [2,2,8][2,2,8];
• Player 33 gets cards with numbers [2,2,8][2,2,8];
• Player 44 gets cards with numbers [5,5,5][5,5,5].

Thus, the answer is 2+6+6+7=212+6+6+7=21.

In the second example, no player can get a card with his favorite number. Thus, the answer is 00.

题意：n∗kn∗k张卡片分给n个人，每人k张。第二行输入n∗kn∗k张卡片上面写的数字，第三行输入nn个人喜欢的数字，第四行输入k个数字，h[i]h[i]表示拿到ii张自己喜欢的卡片可以获得的快乐值。问所有人快乐值之和最大为多少？

题解：DP,dp[i][j],表示i个相同的数字给j个人(这j个人都喜欢这相同的数字)；cnt[i]表示数字i的数量，num[j]表示喜欢j 的人数；

状态转换方程为：dp[i][j]=max(dp[i][j],dp[i-u][j-1]+w[u]);(1=<u<=k)

AC代码为：

#include<bits/stdc++.h>
using namespace std;

const int maxn=1e5+10;
int n,k,a[maxn],f[5005],w[15];
int cnt[maxn],num[maxn],dp[5005][521];

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    memset(cnt,0,sizeof cnt);
    memset(num,0,sizeof num);
    cin>>n>>k;
    for(int i=1;i<=n*k;i++) cin>>a[i],cnt[a[i]]++;
    for(int i=1;i<=n;i++) cin>>f[i],num[f[i]]++;
    for(int i=1;i<=k;i++) cin>>w[i];
    
    for(int i=1;i<=n*k;i++)
    {
        dp[i][1]=w[min(i,k)];
        for(int j=2;j<=n;j++)
        {
            for(int u=1;u<=min(i,k);u++) 
                dp[i][j]=max(dp[i][j],dp[i-u][j-1]+w[u]);
        }
    }
    long long ans=0;
    for(int i=1;i<maxn;i++) if(num[i]) ans+=dp[cnt[i]][num[i]];
    cout<<ans<<endl;
    
    return 0;
}