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.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		long k = in.nextLong();
		int[][] next = new int[n][35];
		long[][] sums = new long[n][35];
		int[][] mins = new int[n][35];
		for(int i=0;i<n;i++){
			next[i][0] = in.nextInt();
		}
		for(int i=0;i<n;i++){
			int temp = in.nextInt();
			mins[i][0] = temp;
			sums[i][0] = temp;
		}
		for(int j=1;j<=34;j++){
			for(int i=0;i<n;i++){
				next[i][j] = next[next[i][j-1]][j-1];
				sums[i][j] = sums[i][j-1] + sums[next[i][j-1]][j-1];
				mins[i][j] = Math.min(mins[i][j-1], mins[next[i][j-1]][j-1]);
//				System.out.println(i + " " + j + " " + next[i][j] + " " + sums[i][j] + " " + mins[i][j]);
			}
		}
		for(int i=0;i<n;i++){
			long sum = 0;
			int min = Integer.MAX_VALUE;
			int curr = i;
			for(int j=34;j>=0;j--){
//				System.out.println(j + " " + ((long)1 << j) + " " + (k & ((long)1 << j)));
				if((k & ((long)1 << j)) != 0){
					sum += sums[curr][j];
					min = Math.min(min, mins[curr][j]);
					curr = next[curr][j];
//					System.out.println(curr);
				}
			}
			System.out.println(sum + " " + min);
		}
	}

}