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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class E {

	private static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
	private static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	
	private static class Pair {
		public int min;
		public long sum;
		public Pair(int min, long sum) {
			this.min = min;
			this.sum = sum;
		}
	}
	
	private static int n;
	private static long k;
	private static int[] next;
	private static long[] ws;
	
	private static Pair combine(Pair a, Pair b) {
		return new Pair(Math.min(a.min, b.min), a.sum + b.sum);
	}
	
	public static void main(String[] args) throws IOException {
		// read input
		String[] s = in.readLine().split(" ");
		n = Integer.parseInt(s[0]);
		k = Long.parseLong(s[1]);
		s = in.readLine().split(" ");
		next = new int[n];
		for (int i = 0; i < n; ++i)
			next[i] = Integer.parseInt(s[i]);
		s = in.readLine().split(" ");
		ws = new long[n];
		for (int i = 0; i < n; ++i)
			ws[i] = Long.parseLong(s[i]);
		// next power
		int[][] nextPow = new int[n][34];
		for (int i = 0; i < n; ++i)
			nextPow[i][0] = next[i];
		for (int j = 1; j < nextPow[0].length; ++j)
			for (int i = 0; i < n; ++i)
				nextPow[i][j] = nextPow[nextPow[i][j - 1]][j - 1];
		// preprocess
		Pair[][] pp = new Pair[n][34];
		for (int x = 0; x < n; ++x)
			pp[x][0] = new Pair((int) ws[x], ws[x]);
		for (int i = 1; i < pp[0].length; ++i)
			for (int x = 0; x < n; ++x)
				pp[x][i] = combine(pp[x][i - 1], pp[nextPow[x][i - 1]][i - 1]);
		// solve
		for (int x = 0; x < n; ++x) {
			Pair ans = new Pair(Integer.MAX_VALUE, 0);
			int y = x;
			long kk = k;
			for (int i = 0; kk > 0; ++i) {
				if ((kk&1) == 1) {
					ans = combine(ans, pp[y][i]);
					y = nextPow[y][i];
				}
				kk = (kk >> 1);
			}
			out.println(ans.sum + " " + ans.min);
		}
		out.flush();
	}

}