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.InputStreamReader;
import java.io.PrintWriter;
import java.util.BitSet;
import java.util.StringTokenizer;

public class E {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st;
	static PrintWriter out = new PrintWriter(System.out);

	static void solve() throws Exception {
		int n = nextInt();
		long k = nextLong();
		int fs[] = new int[n];
		for (int i = 0; i < fs.length; i++) {
			fs[i] = nextInt();
		}
		long[] ws = new long[n];
		for (int i = 0; i < ws.length; i++) {
			ws[i] = nextInt();
		}
		long pot = 1;
		int exp = 0;
		while (pot <= k) {
			pot *= 2;
			exp++;
		}
		int[][] parentIdx = new int[n][exp];
		long[][] sum = new long[n][exp];
		long[][] min = new long[n][exp];
		for (int i = 0; i < n; i++) {
			parentIdx[i][0] = fs[i];
			sum[i][0] = ws[i];
			min[i][0] = ws[i];
		}
		for (int e = 1; e < exp; e++) {
			for (int i = 0; i < n; i++) {
				parentIdx[i][e] = parentIdx[parentIdx[i][e - 1]][e - 1];
				sum[i][e] = sum[i][e - 1] + sum[parentIdx[i][e - 1]][e - 1];
				min[i][e] = Math.min(min[i][e - 1], min[parentIdx[i][e - 1]][e - 1]);
			}
		}
		BitSet kBitSet = BitSet.valueOf(new long[] { k });
		for (int i = 0; i < n; i++) {
			long si = 0, mi = Long.MAX_VALUE;
			int curNode = i;
			for (int bit = 0; bit < exp; bit++) {
				if (kBitSet.get(bit)) {
					si += sum[curNode][bit];
					mi = Math.min(mi, min[curNode][bit]);
					curNode = parentIdx[curNode][bit];
				}
			}
			out.println(si + " " + mi);
		}
	}

	public static void main(String[] args) throws Exception {
		solve();
		out.close();
	}

	static String next() throws Exception {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(br.readLine());
		}
		return st.nextToken();
	}

	static int nextInt() throws Exception {
		return Integer.parseInt(next());
	}

	static long nextLong() throws Exception {
		return Long.parseLong(next());
	}

}