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.*;
import java.io.*;

public class R702E {
    FastScanner in;
    PrintWriter out;
    node[] f;

    void solve() {
        int n=in.nextInt();
        long k=in.nextLong();
        f=new node[n];
        for(int i=0; i<n; i++) {
            f[i]=new node(in.nextInt());
        }
        for(int i=0; i<n; i++) {
            long w=in.nextLong();
            f[i].s=w;
            f[i].m=w;
        }
        f=binpow(f, k);
        for(int i=0; i<n; i++)
            System.out.println(f[i].s+" "+f[i].m);
    }

    node[] umn(node[] f1, node[] f2) {
        node[]res=new node[f1.length];
        for(int i=0; i<f1.length; i++) {
            res[i]=new node(f2[f1[i].to].to, f1[i].s+f2[f1[i].to].s, Math.min(f1[i].m, f2[f1[i].to].m));
        }
        return res;
    }
    node[] umn (node[] f1){
        return umn(f1, f1);
    }

    node[] binpow(node[] a, long s){
        node[] res=new node[a.length];
        for(int i=0; i<a.length; i++)
            res[i]=new node(i, 0, Long.MAX_VALUE);
        while(s>0) {
            if (s%2==1) {
                res = umn(res, a);
                s--;
            }
            else {
                a=umn(a);
                s/=2;
            }
        }
        return res;
    }

    class node {
        int to;
        long s;
        long m;
        public node(int to) {
            this.to=to;
        }
        public node(int to, long s, long m) {
            this.to=to;
            this.s=s;
            this.m=m;
        }
    }

    void run() {
        try {
            in = new FastScanner(new File("CF.in"));
            out = new PrintWriter(new File("CF.out"));

            solve();

            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {

        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    public static void main(String[] args) {
        new R702E().runIO();
    }

}