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.*;

public class E{
	static int _to[],_min[];
	static long _sum[];
	static int to[],min[];
	static long sum[];
	static int N;
	static void f(long k){
		if(k == 1){
			to = new int[N];
			min = new int[N];
			sum = new long[N];
			for(int i = 0; i < N; i++){
				to[i] = _to[i];
				min[i] = _min[i];
				sum[i] = _sum[i];
			}
		}else{
			f(k/2);
			int nextto[] = new int[N];
			int nextmin[] = new int[N];
			long nextsum[] = new long[N];
			for(int i = 0; i < N; i++){
				nextto[i] = to[to[i]];
				nextmin[i] = Math.min(min[i],min[to[i]]);
				nextsum[i] = sum[i] + sum[to[i]];
			}

			if(k%2 == 1){
				for(int i = 0; i < N; i++){
					nextmin[i] = Math.min(nextmin[i],_min[nextto[i]]);
					nextsum[i] = nextsum[i] + _sum[nextto[i]];
					nextto[i] = _to[nextto[i]];
				}
			}

			to = nextto;
			min = nextmin;
			sum = nextsum;
		}
	}

	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		N = sc.nextInt();
		_to = new int[N];
		_min = new int[N];
		_sum = new long[N];

		long k = sc.nextLong();
		for(int i = 0; i < N; i++)
			_to[i] = sc.nextInt();
		for(int i = 0; i < N; i++)
			_sum[i] = _min[i]  = sc.nextInt();

		f(k);

		for(int i = 0; i < N; i++)
			System.out.println(sum[i] + " " + min[i]);
	}	
}