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 RoadToPostOffice {
	static Node[][] f;
	static String kVal;
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		long k = in.nextLong();
		int[] a = new int[n];
		int[] w = new int[n];
		f = new Node[34][n];
		for (int i = 0; i < n; i++)
			a[i] = in.nextInt();
		for (int i = 0; i < n; i++)
			w[i] = in.nextInt();

		for (int i = 0; i < n; i++) {
			f[0][i] = new Node(a[i], w[i], w[i]);
		}

		for (int i = 1; i < 34; i++) {
			for (int j = 0; j < n; j++) {
				int to = f[i - 1][f[i - 1][j].to].to;
				long sum = f[i - 1][j].sum + f[i - 1][f[i - 1][j].to].sum;
				int min = Math.min(f[i - 1][j].min, f[i - 1][f[i - 1][j].to].min);
				f[i][j] = new Node(to, sum, min);
			}
		}
		kVal = Long.toBinaryString(k);
		for (int i = 0; i < n; i++) {
			Node result = get(i);
			System.out.println(result.sum + " " + result.min);
		}
	}

	public static Node get(int start) {
		Node result = new Node(start, 0, Integer.MAX_VALUE);
		for (int i = 0; i < kVal.length(); i++) {
			if (kVal.charAt(i) == '1') {
				int usefulSum = kVal.length() - i - 1;
				result = new Node(f[usefulSum][result.to].to, result.sum + f[usefulSum][result.to].sum,
						Math.min(result.min, f[usefulSum][result.to].min));
			}
		}
		return result;
	}
}

class Node {
	int to;
	long sum;
	int min;

	public Node(int x, long y, int z) {
		this.to = x;
		this.sum = y;
		this.min = z;
	}
}