Problem: There is a tree with N vertices, numbered 1, 2, \ldots, N. For each i (1 \leq i \leq N - 1), the i-th edge connects Vertex x_i and y_i.

Taro has decided to paint each vertex in white or black, so that any black vertex can be reached from any other black vertex by passing through only black vertices.

You are given a positive integer M. For each v (1 \leq v \leq N), answer the following question:

* Assuming that Vertex v has to be black, find the number of ways in which the vertices can be painted, modulo M.

Constraints

* All values in input are integers.
* 1 \leq N \leq 10^5
* 2 \leq M \leq 10^9
* 1 \leq x_i, y_i \leq N
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N M
x_1 y_1
x_2 y_2
:
x_{N - 1} y_{N - 1}


Output

Print N lines. The v-th (1 \leq v \leq N) line should contain the answer to the following question:

* Assuming that Vertex v has to be black, find the number of ways in which the vertices can be painted, modulo M.

Examples

Input

3 100
1 2
2 3


Output

3
4
3


Input

4 100
1 2
1 3
1 4


Output

8
5
5
5


Input

1 100


Output

1


Input

10 2
8 5
10 8
6 5
1 5
4 8
2 10
3 6
9 2
1 7


Output

0
0
1
1
1
0
1
0
1
1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author lewin
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        VSubtree solver = new VSubtree();
        solver.solve(1, in, out);
        out.close();
    }

    static class VSubtree {
        public static int M;
        public int n;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.nextInt();
            M = in.nextInt();
            VSubtree.Vertex[] vs = new VSubtree.Vertex[n];
            for (int i = 0; i < n; i++) vs[i] = new VSubtree.Vertex(i);
            for (int i = 0; i < n - 1; i++) {
                int a = in.nextInt() - 1, b = in.nextInt() - 1;
                vs[a].addEdge(vs[b]);
                vs[b].addEdge(vs[a]);
            }
            vs[0].dfs(null);
            for (int i = 0; i < n; i++) {
                out.println((vs[i].prod_down * vs[i].get_prod_up()) % M);
            }
        }

        static class Vertex {
            public ArrayList<VSubtree.Vertex> adj;
            public int id;
            public long prod_before;
            public long prod_after;
            public long prod_down;
            public long prod_up;
            public VSubtree.Vertex prevChild;
            public VSubtree.Vertex nextChild;
            public VSubtree.Vertex par;

            public Vertex(int id) {
                this.id = id;
                adj = new ArrayList<>();
                prod_before = -1;
                prod_after = -1;
                prod_down = -1;
                prod_up = -1;
            }

            public void addEdge(VSubtree.Vertex other) {
                adj.add(other);
            }

            public void dfs(VSubtree.Vertex parent) {
                VSubtree.Vertex pv = null;
                par = parent;
                prod_down = 1;
                for (VSubtree.Vertex next : adj) {
                    if (parent != null && next.id == parent.id) continue;
                    next.dfs(this);
                    prod_down = prod_down * (1 + next.prod_down) % M;
                    if (pv != null) {
                        pv.nextChild = next;
                        next.prevChild = pv;
                    }
                    pv = next;
                }
            }

            public long get_prod_up() {
                if (prod_up != -1) return prod_up;

                prod_up = par == null ? 0 : par.get_prod_up();
                prod_up = prod_up * get_prod_before() % M;
                prod_up = prod_up * get_prod_after() % M;
                prod_up += 1;
                return prod_up;
            }

            public long get_prod_before() {
                if (prod_before != -1) return prod_before;
                return prod_before = prevChild == null ? 1 : (1 + prevChild.prod_down) * prevChild.get_prod_before() % M;
            }

            public long get_prod_after() {
                if (prod_after != -1) return prod_after;
                return prod_after = nextChild == null ? 1 : (1 + nextChild.prod_down) * nextChild.get_prod_after() % M;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (this.numChars == -1) {
                throw new InputMismatchException();
            } else {
                if (this.curChar >= this.numChars) {
                    this.curChar = 0;

                    try {
                        this.numChars = this.stream.read(this.buf);
                    } catch (IOException var2) {
                        throw new InputMismatchException();
                    }

                    if (this.numChars <= 0) {
                        return -1;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int c;
            for (c = this.read(); isSpaceChar(c); c = this.read()) {
                ;
            }

            byte sgn = 1;
            if (c == 45) {
                sgn = -1;
                c = this.read();
            }

            int res = 0;

            while (c >= 48 && c <= 57) {
                res *= 10;
                res += c - 48;
                c = this.read();
                if (isSpaceChar(c)) {
                    return res * sgn;
                }
            }

            throw new InputMismatchException();
        }

        public static boolean isSpaceChar(int c) {
            return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
}