COCI '18 Contest 6 #3 Sličice

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Points: 10 (partial)
Time limit: 1.0s
Memory limit: 64M

Problem type

Nikola is a passionate collector of albums with images of football players. He and his friends compete with each other in a game they invented based on the albums whose images are currently being collected. The images in that album are divided into N teams, each of which has exactly M football players. The main rule of the game is that the total number of points a person wins for i^{th} team is B_x, where x is the total number of unique pictures of football players of that team collected by the person. They have also agreed that the array B is growing, i.e. having more unique images of football players of a team means having more or equal points.

Nikola would like to win as many points as possible in the game. For each team x the amount of unique images Nikola currently owns of that team, P_x, is known.

Ivan is a friend of Nikola who has already collected the entire album twice and when he heard about the game Nikola plays with his friends, he decided to give him any K images that Nikola wants. After finding out about this joyful news, Nikola wondered what is the maximal number of points he could have after Ivan gives him K images. Too excited for this news, he is not able to count and begs you to answer his question.

Input

In the first line there are integer numbers N, M and K (1 \le N, M \le 500, 1 \le K \le \min(N·M, 500)), numbers from the task's text.

In the second line there is an array P consisting of N non-negative integer numbers (0 \le P_i \le M).

In the third line there is an array B consisting of M+1 non-negative integer numbers (0 \le B_i \le 100\,000), amount of points Nikola gets for i (0 \le i \le M) unique images of a team.

For every t between 0 and M-1 it holds B_t \le B_{t+1}.

It is also holds that K \le N·M - (P_1 + P_2 + \dots + P_N).

Output

In the only line print the answer to Nikola's question.

Scoring

In test samples totally worth 20% of the points it will hold K = 2.

Sample Input 1

4 4 3
4 2 3 1
0 1 3 6 10

Sample Output 1

31

Explanation for Sample Output 1

Nikola is most likely to ask Ivan to give him an image of the third team and two from the second, so that his score is 31 (10 + 10 + 10 + 1).

Sample Input 2

4 3 5
1 1 2 3
0 1 2 3

Sample Output 2

12

Sample Input 3

3 6 2
2 4 1
31 38 48 60 75 91 120

Sample Output 3

206

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