Problem: You are given a functional graph. It is a directed graph, in which from each vertex goes exactly one arc. The vertices are numerated from 0 to n - 1.

Graph is given as the array f0, f1, ..., fn - 1, where fi — the number of vertex to which goes the only arc from the vertex i. Besides you are given array with weights of the arcs w0, w1, ..., wn - 1, where wi — the arc weight from i to fi.

<image> The graph from the first sample test.

Also you are given the integer k (the length of the path) and you need to find for each vertex two numbers si and mi, where:

  * si — the sum of the weights of all arcs of the path with length equals to k which starts from the vertex i; 
  * mi — the minimal weight from all arcs on the path with length k which starts from the vertex i. 



The length of the path is the number of arcs on this path.

Input

The first line contains two integers n, k (1 ≤ n ≤ 105, 1 ≤ k ≤ 1010). The second line contains the sequence f0, f1, ..., fn - 1 (0 ≤ fi < n) and the third — the sequence w0, w1, ..., wn - 1 (0 ≤ wi ≤ 108).

Output

Print n lines, the pair of integers si, mi in each line.

Examples

Input

7 3
1 2 3 4 3 2 6
6 3 1 4 2 2 3


Output

10 1
8 1
7 1
10 2
8 2
7 1
9 3


Input

4 4
0 1 2 3
0 1 2 3


Output

0 0
4 1
8 2
12 3


Input

5 3
1 2 3 4 0
4 1 2 14 3


Output

7 1
17 1
19 2
21 3
8 1

Solution (in JAVA):

Solution:
import java.io.PrintWriter;
import java.util.Scanner;

public class TaskE{
  public static void main(String[] args) {
    TaskE tE = new TaskE();
    PrintWriter pw = new PrintWriter(System.out);
    tE.solve(new Scanner(System.in), pw);
    pw.close();
  }

  public void solve(Scanner input, PrintWriter output) {
  	int n = input.nextInt();
  	long k = input.nextLong();
  	int[][] parent = new int[n][35];
    for (int i = 0; i < n; i++) {
      parent[i][0] = input.nextInt();
    }

    long[][] sum = new long[n][35];
  	long[][] min = new long[n][35];
  	for (int i = 0; i < n; i++) {
      sum[i][0] = input.nextLong();
      min[i][0] = sum[i][0];
  	}

    for (int i = 1; i < 35; i++) {
      for (int node = 0; node < n; node++) {
        parent[node][i] = parent[parent[node][i - 1]][i - 1];
        sum[node][i] = sum[node][i - 1] + sum[parent[node][i - 1]][i - 1];
        min[node][i] = Math.min(min[node][i - 1], min[parent[node][i - 1]][i - 1]);
      }
    }

    for (int i = 0; i < n; i++) {
      long minResult = Long.MAX_VALUE;
      long totalDist = 0;
      int p = i;
      for (int j = 0; j < 35; j++) {
        if ((k & (1L << j)) != 0) {
          minResult = Math.min(minResult, min[p][j]);
          totalDist += sum[p][j];
          p = parent[p][j];
        }
      }
      output.println(totalDist + " " + minResult);
    }
  }
}