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.*;
import java.util.*;

public class CF702E {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		long k = Long.parseLong(st.nextToken());
		int l = 0;
		while (1L << l <= k)
			l++;
		int[][] ff = new int[l][n];
		long[][] ss = new long[l][n];
		int[][] mm = new int[l][n];
		st = new StringTokenizer(br.readLine());
		for (int i = 0; i < n; i++)
			ff[0][i] = Integer.parseInt(st.nextToken());
		st = new StringTokenizer(br.readLine());
		for (int i = 0; i < n; i++)
			ss[0][i] = mm[0][i] = Integer.parseInt(st.nextToken());
		for (int d = 1; d < l; d++)
			for (int i = 0; i < n; i++) {
				int j = ff[d - 1][i];
				ff[d][i] = ff[d - 1][j];
				ss[d][i] = ss[d - 1][i] + ss[d - 1][j];
				mm[d][i] = Math.min(mm[d - 1][i], mm[d - 1][j]);
			}
		PrintWriter pw = new PrintWriter(System.out);
		for (int i = 0; i < n; i++) {
			long s = 0;
			int m = (int) 1e8;
			int j = i;
			for (int d = 0; 1L << d <= k; d++)
				if ((k & 1L << d) > 0) {
					s += ss[d][j];
					m = Math.min(m, mm[d][j]);
					j = ff[d][j];
				}
			pw.println(s + " " + m);
		}
		pw.close();
	}
}