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.*;
import java.math.*;




public class analysisofpathinfunctionalgraph {
	static ArrayList<Integer> g[],w[];
	public static void main(String[] args) throws Exception
	{
		InputReader in=new InputReader(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int n=in.nextInt();
		long k=in.nextLong();
		int[][] next=new int[35][n];
		long[][] sum=new long[35][n];
		long[][] min=new long[35][n];
		for(int i=0;i<n;i++)
		{
			next[0][i]=in.nextInt();
		}
		for(int i=0;i<n;i++)
		{
			sum[0][i]=in.nextLong();
			min[0][i]=sum[0][i];
		}
		
		for(int i=1;i<35;i++)
		{
			for(int j=0;j<n;j++)
			{
				next[i][j]=next[i-1][next[i-1][j]];
				sum[i][j]=sum[i-1][j]+sum[i-1][next[i-1][j]];
				min[i][j]=Math.min(min[i-1][j], min[i-1][next[i-1][j]]);
			}
		}
		//System.out.println(Arrays.deepToString(sum));
		for(int i=0;i<n;i++)
		{
			long mm=(long)(1e18);
			long ss=0;
			int cur=i;
			long len=k;
			for(int j=34;j>=0;j--)
			{
				if(((1l)<<j)<=len)
				{
					ss+=sum[j][cur];
					mm=Math.min(mm,min[j][cur]);
					cur=next[j][cur];
					len-=(1l<<j);
				}
			}
			pw.println(ss+" "+mm);
			
		}
		pw.close();
	}
	static class InputReader {

		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar;
		private int snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			int res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			long res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}