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 M{
    final long mod = 163577857, IINF = (long)1e19;
    final int MAX = (int)1e6+1, MX = (int)1e7+1, INF = (int)1e9;
    FastReader in;
    PrintWriter out;
    boolean multipleTC = false;
 
    public static void main(String[] args) throws Exception{
        new M().run();
    }
    
    void run() throws Exception{
        in = new FastReader();
        out = new PrintWriter(System.out);
        for(int i = 1, t = (multipleTC)?ni():1; i<=t; i++)solve(i);
        out.flush();    
        out.close();
    }
    int B = 37;
    void solve(int TC) throws Exception{
        int n = ni();
        long k = nl();
        int[][] f = new int[n][B];
        long[][] w  = new long[n][B], min = new long[n][B];
        for(int i = 0; i< n; i++)f[i][0] = ni();
        for(int i = 0; i< n; i++)w[i][0] = min[i][0] = nl();
        for(int b = 1; b< B; b++){
            for(int i = 0; i< n; i++){
                f[i][b] = f[f[i][b-1]][b-1];
                w[i][b] = w[i][b-1]+w[f[i][b-1]][b-1];
                min[i][b] = Math.min(min[i][b-1], min[f[i][b-1]][b-1]);
            }
        }
        for(int i = 0; i< n; i++){
            long sum = 0, mi = IINF;
            int cur = i;
            for(int b = B-1; b>=0; b--){
                if(((k>>b)&1)==1){
                    sum += w[cur][b];
                    mi = Math.min(mi,min[cur][b]);
                    cur = f[cur][b];
                }
            }
            pn(sum+" " + mi);
        }
    }
    
    int[] reverse(int[] a){
        int[] o = new int[a.length];
        for(int i = 0; i< a.length; i++)o[i] = a[a.length-i-1];
        return o;   
    }
 
    int[] sort(int[] a){
        if(a.length==1)return a;
        int mid = a.length/2;
        int[] b = sort(Arrays.copyOfRange(a,0,mid)), c = sort(Arrays.copyOfRange(a,mid,a.length));
        for(int i = 0, j = 0, k = 0; i< a.length; i++){
            if(j<b.length && k<c.length){
                if(b[j]<c[k])a[i] = b[j++];
                else a[i] = c[k++];
            }else if(j<b.length)a[i] = b[j++];
            else a[i] = c[k++];
        }
        return a;
    }
 
    long[] sort(long[] a){
        if(a.length==1)return a;
        int mid = a.length/2;
        long[] b = sort(Arrays.copyOfRange(a,0,mid)), c = sort(Arrays.copyOfRange(a,mid,a.length));
        for(int i = 0, j = 0, k = 0; i< a.length; i++){
            if(j<b.length && k<c.length){
                if(b[j]<c[k])a[i] = b[j++];
                else a[i] = c[k++];
            }else if(j<b.length)a[i] = b[j++];
            else a[i] = c[k++];
        }
        return a;
    }
 
    int[] ia(int ind,int n){
        int[] out = new int[ind+n];
        for(int i = 0; i< n; i++)out[ind+i] = ni();
        return out;
    }
 
    long[] la(int ind, int n){
        long[] out = new long[ind+n];
        for(int i = 0; i< n; i++)out[ind+i] = nl();
        return out;
    }
 
    double[] da(int ind, int n){
        double[] out = new double[ind+n];
        for(int i = 0; i< n; i++)out[ind+i] = nd();
        return out;
    }
 
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bitcount(long n){return (n==0)?0:(1+bitcount(n&(n-1)));}
    void p(Object o){out.print(o);}
    void pn(Object o){out.println(o);}
    void pni(Object o){out.println(o);out.flush();}
    String n(){return in.next();}
    String nln(){return in.nextLine();}
    int ni(){return Integer.parseInt(in.next());}
    long nl(){return Long.parseLong(in.next());}
    double nd(){return Double.parseDouble(in.next());}
 
    class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }
 
        String next(){
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException  e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            }catch (IOException e){
                e.printStackTrace();
            }   
            return str;
        }
    }
}