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.NoSuchElementException;
import java.util.Scanner;

public class EAnalysisOfPathesInFunctionalGraph {

	static int n;
	static long k;
	static int[][] parent;
	static long[][] weights;
	static long[][] sum;
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		n = in.nextInt(); k = in.nextLong();
		int K = Long.numberOfTrailingZeros(Long.highestOneBit(k)) + 1;
		parent = new int[n][K];
		for (int i = 0; i < n; i++) {
			parent[i][0] = in.nextInt();
		}
		weights = new long[n][K];
		for (int i = 0; i < n; i++) {
			weights[i][0] = in.nextLong();
		}
		sum = new long[n][K];
		for (int i = 0; i < n; i++) {
			sum[i][0] = weights[i][0];
		}
		int[] poss = new int[n];
		for (int i = 0; i < n; i++) {
			poss[i] = i;
		}
		for (int j = 1; j < K; j++) {
			for (int i = 0; i < n; i++) {
				parent[i][j] = parent[parent[i][j-1]][j-1];
				weights[i][j] = Math.min(weights[i][j-1], weights[parent[i][j-1]][j-1]);
				sum[i][j] = sum[i][j-1] + sum[parent[i][j-1]][j-1];
			}
		}
		long[] s = new long[n];
		long[] m = new long[n];
		for (int i = 0; i < n; i++) {
			m[i] = Long.MAX_VALUE;
		}
		for (int j = 0; j < K; j++) {
			if (((1L << j) & k) != 0) {
				for (int i = 0; i < n; i++) {
					s[i] += sum[poss[i]][j];
					m[i] = Math.min(m[i], weights[poss[i]][j]);
					poss[i] = parent[poss[i]][j];
				}
			}
		}
		for (int i = 0; i < n; i++) {
			System.out.println(s[i] + " " + m[i]);
		}
	}

}