Takahashi will play a game using a piece on an array of squares numbered 1, 2, \cdots, N. Square i has an integer C_i written on it. Also, he is given a permutation of 1, 2, \cdots, N: P_1, P_2, \cdots, P_N.

Now, he will choose one square and place the piece on that square. Then, he will make the following move some number of times between 1 and K (inclusive):

* In one move, if the piece is now on Square i (1 \leq i \leq N), move it to Square P_i. Here, his score increases by C_{P_i}.



Help him by finding the maximum possible score at the end of the game. (The score is 0 at the beginning of the game.)

Constraints

* 2 \leq N \leq 5000
* 1 \leq K \leq 10^9
* 1 \leq P_i \leq N
* P_i \neq i
* P_1, P_2, \cdots, P_N are all different.
* -10^9 \leq C_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
P_1 P_2 \cdots P_N
C_1 C_2 \cdots C_N


Output

Print the maximum possible score at the end of the game.

Examples

Input

5 2
2 4 5 1 3
3 4 -10 -8 8


Output

8


Input

2 3
2 1
10 -7


Output

13


Input

3 3
3 1 2
-1000 -2000 -3000


Output

-1000


Input

10 58
9 1 6 7 8 4 3 2 10 5
695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719


Output

29507023469
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

  public static void main(String[] args) throws Exception{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    String[] head = br.readLine().split(" ");
    String[] p_line = br.readLine().split(" ");
    String[] c_line = br.readLine().split(" ");
    br.close();
    int n = Integer.parseInt(head[0]);
    int k = Integer.parseInt(head[1]);

    int[] p = new int[n];
    long[] c = new long[n];
    for (int i = 0; i < n; i++) {
      p[i] = Integer.parseInt(p_line[i]) - 1;
    }
    for (int i = 0; i < n; i++) {
      c[i] = Long.parseLong(c_line[i]);
    }
    long answer = Long.MIN_VALUE;
    long[] c_total = new long[n];
    boolean[] isVisit = new boolean[n];
    Arrays.fill(isVisit, false);
    for (int i = 0; i < n; i++) {
      int idx = i;
      int size = 0;
      if (isVisit[idx] == true) {
        continue;
      } else {
        size = 0;
        while (true) {
          if (isVisit[idx] == true) {
            break;
          }
          c_total[size] = c[p[idx]];
          if (size != 0) {
            c_total[size] += c_total[size - 1];
          }
          isVisit[idx] = true;
          idx = p[idx];
          size++;
        }

        if(c_total[size - 1] > 0) {
          answer = Math.max(answer, c_total[size - 1] * (k / size));
        }
        
        for (int start = 0; start < size; start++) {
          for (int count = 1; count < size; count++) {
            long val;
            if (count > k) {
              continue;
            }
            int to = (start + count - 1) % size;
            if (start <= to) {
              val = c_total[to];
              if (start != 0) {
                val -= c_total[start - 1];
              }
            } else {
              val = c_total[size - 1] - c_total[start - 1] + c_total[to];
            }
            if (c_total[size - 1] > 0) {
              val += (c_total[size - 1] * ((k - count) / size));
            }
            answer = Long.max(answer, val);
          }
        }
      }
    }
    System.out.println(answer);
  }
}