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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

/*
 public class _702E {

 }

 */

public class _702E
{
	public void solve() throws FileNotFoundException
	{
		InputStream inputStream = System.in;

		InputHelper inputHelper = new InputHelper(inputStream);

		PrintStream out = System.out;

		// actual solution
		int n;
		long k;

		n = inputHelper.readInteger();
		k = inputHelper.readLong();

		int[] f = new int[n];
		int[] w = new int[n];

		for (int i = 0; i < n; i++)
		{
			f[i] = inputHelper.readInteger();
		}

		for (int i = 0; i < n; i++)
		{
			w[i] = inputHelper.readInteger();
		}

		int logk = 0;

		long ck = k;
		while (ck > 0)
		{
			ck /= 2;
			logk++;
		}

		if ((k & (k - 1)) == 0)
		{
			logk--;
		}

		int[][] d = new int[n][logk + 1];
		long[][] s = new long[n][logk + 1];
		int[][] m = new int[n][logk + 1];

		for (int i = 0; i < n; i++)
		{
			d[i][0] = f[i];
			s[i][0] = w[i];
			m[i][0] = w[i];
		}

		for (int i = 1; i <= logk; i++)
		{
			for (int j = 0; j < n; j++)
			{
				d[j][i] = d[d[j][i - 1]][i - 1];
				s[j][i] = s[j][i - 1] + s[d[j][i - 1]][i - 1];
				m[j][i] = Math.min(m[j][i - 1], m[d[j][i - 1]][i - 1]);
			}
		}

		ArrayList<Integer> ah1 = new ArrayList<Integer>();
		ArrayList<Integer> ah2 = new ArrayList<Integer>();

		int ri = 0;
		ck = k;
		int cl = logk;

		while (true)
		{
			if ((1L << cl) == ck)
			{
				ah1.add(ri);
				ah2.add(cl);
				break;
			}
			else if ((1L << cl) < ck && (1L << (cl + 1)) > ck)
			{
				ah1.add(ri);
				ah2.add(cl);
				ri = d[ri][cl];
				ck -= (1L << cl);
			}
			cl--;
		}

		for (int i = 0; i < n; i++)
		{
			long sum = 0;
			int min = Integer.MAX_VALUE;
			ri = i;
			for (int j = 0; j < ah1.size(); j++)
			{
				sum += s[ri][ah2.get(j)];
				min = Math.min(m[ri][ah2.get(j)], min);
				ri = d[ri][ah2.get(j)];
			}

			System.out.println(sum + " " + min);
		}
		// end here
	}

	public static void main(String[] args) throws FileNotFoundException
	{
		(new _702E()).solve();
	}

	class InputHelper
	{
		StringTokenizer tokenizer = null;
		private BufferedReader bufferedReader;

		public InputHelper(InputStream inputStream)
		{
			InputStreamReader inputStreamReader = new InputStreamReader(
					inputStream);
			bufferedReader = new BufferedReader(inputStreamReader, 16384);
		}

		public String read()
		{
			while (tokenizer == null || !tokenizer.hasMoreTokens())
			{
				try
				{
					String line = bufferedReader.readLine();
					if (line == null)
					{
						return null;
					}
					tokenizer = new StringTokenizer(line);
				}
				catch (IOException e)
				{
					e.printStackTrace();
				}
			}

			return tokenizer.nextToken();
		}

		public Integer readInteger()
		{
			return Integer.parseInt(read());
		}

		public Long readLong()
		{
			return Long.parseLong(read());
		}
	}
}