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^\text{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 \cdot 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 \cdot 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