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.*;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            String filename = "";
            if (filename.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(filename + ".in"));
                out = new PrintWriter(filename + ".out");
            }
        }
    }

    String readString() {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), " :");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long readLong() {
        return Long.parseLong(readString());
    }

    double readDouble() {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    class Graph {
        int[][] graph;
        List<Integer>[] temp;
        int n;

        Graph(int n) {
            this.n = n;
            graph = new int[n][];
            temp = createGraphList(n);
        }

        void add(int x, int y) {
            temp[x].add(y);
            temp[y].add(x);
        }

        void addDir(int x, int y) {
            temp[x].add(y);
        }

        void build() {
            for (int i = 0; i < n; i++) {
                graph[i] = new int[temp[i].size()];
                for (int j = 0; j < temp[i].size(); j++) graph[i][j] = temp[i].get(j);
            }
        }

        void buildWithUniq() {
            for (int i = 0; i < n; i++) {
                HashSet<Integer> uniqSet = new HashSet<>();
                uniqSet.addAll(temp[i]);
                graph[i] = new int[uniqSet.size()];
                int index = 0;
                for (int x : uniqSet) {
                    graph[i][index++] = x;
                }
            }
        }
    }

    public static void main(String[] args) {
        new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    class Edge {
        int to;
        long sum;
        long min;

        public Edge(int to, long sum, long min) {
            this.to = to;
            this.sum = sum;
            this.min = min;
        }
    }

    class EdgeContainer {

        Edge[] edges;

        EdgeContainer(Edge[] edges) {
            this.edges = edges;
        }

        EdgeContainer multiply(EdgeContainer b) {
            int n = edges.length;
            Edge[] edges = new Edge[n];
            for (int i = 0; i < n; i++) {
                Edge cur = this.edges[i];
                Edge sec = b.edges[cur.to];
                edges[i] = new Edge(sec.to, cur.sum + sec.sum, Math.min(cur.min, sec.min));
            }
            return new EdgeContainer(edges);
        }
    }

    EdgeContainer binpow(EdgeContainer a, long k) {
        if (k == 1) {
            return a;
        }

        if (k % 2 == 1) {
            return binpow(a, k - 1).multiply(a);
        } else {
            EdgeContainer half = binpow(a, k / 2);
            return half.multiply(half);
        }
    }

    private void solve() {
        int n = readInt();
        long k = readLong();
        Edge[] edges = new Edge[n];
        int[] f = new int[n];
        long[] w = new long[n];
        for (int i = 0; i < n; i++) f[i] = readInt();
        for (int i = 0; i < n; i++) w[i] = readInt();

        for (int i = 0; i < n; i++) {
            edges[i] = new Edge(f[i], w[i], w[i]);
        }
        EdgeContainer container = new EdgeContainer(edges);
        EdgeContainer res = binpow(container, k);
        for (int i = 0; i < n; i++) {
            out.println(res.edges[i].sum + " " + res.edges[i].min);
        }
    }


}