Peter is a Star Wars nerd, and has ~N~ plastic lightsabers with various amounts of strength that he bought to play with his friends. Unfortunately, Peter has no real life friends, and now needs to find something to do with his lightsabers.

Peter decides that he will put his lightsabers on display for all to see. However, Peter is very picky about how this design must look. Specifically, there must be between ~A~ and ~B~ lightsabers put on display, and any two adjacent lightsabers must have different colors. Since Peter is lazy, he wants to be as efficient as possible with this process, and as such, the lightsabers must be left in the relative order they are originally in.

Peter wants to flex on his friends (wait...), so he wants you find him the maximum sum of strength values for his lightsabers on display.

Input Specification

The first line will contain ~3~ integers, ~N~ ~(1 \leq N \leq 10^5),~ ~A,B~ ~(1 \leq A \leq B \leq N)~.

The next line will contain ~N~ integers ~s_i~ ~(-10^9 \leq s_i \leq 10^9)~, the strength of the ~i^{th}~ lightsaber.

The final line will contain ~N~ integers ~c_i~ ~(1 \leq c_i \leq N)~, the colour of the ~i^{th}~ lightsaber.

Output Specification

One line, the maximum sum of strength values for Peter's display.

Subtasks

Subtask 1 [10%]

~1 \leq N \leq 20~

Subtask 2 [20%]

~1 \leq N \leq 200~

Subtask 3 [30%]

~1 \leq N \leq 5000~

Subtask 4 [40%]

~1 \leq N \leq 100000~

~A = 1, B = N~

Sample Input 1

4 2 3
-1 3 4 -5
1 2 2 3

Sample Output 1

3