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.*;
import java.io.IOException;
import java.lang.Thread.State;
import java.util.*;
//import javafx.util.Pair; 
//import java.util.concurrent.LinkedBlockingDeque;




    
  public class Main {
        
        public static long mod = (long)Math.pow(10, 9)+7 ;
        public static double epsilon=0.00000000008854;//value of epsilon
        public static InputReader sc = new InputReader(System.in);
        public static PrintWriter pw = new PrintWriter(System.out);
        
        public static ArrayList<ArrayList <Integer>> GetGraph(int n,int m){
            ArrayList<ArrayList <Integer>> g=new ArrayList<>();
            for(int i=0;i<n;i++){
                g.add(new ArrayList<>());
            }
            for(int i=0;i<m;i++){
                //int t=sc.nextInt();
                int u=sc.nextInt()-1;
                int v=sc.nextInt()-1;
                g.get(u).add(v);
                //if(t==0)
                g.get(v).add(u);
            }
            return g;
        }
        
        public static int find(int a,int p[]){
            if(a!=p[a]){
               p[a]=find(p[a], p);
            }
             return p[a];
        }
        public static void Union(int a,int b,int p[]){
            p[find(b, p)]=find(a, p);
        }
        public static long gcd(long a,long b){
            while(b>0){
                long t=b;
                b=a%b;
                a=t;
            }
            return a;
        }
        public static void dfs(ArrayList<ArrayList <Integer>> g,long val[],int u,int vis[],long m,int p[]){
            vis[u]=1;
            //boolean f=false;
            val[u]=1;
            for(int i=0;i<g.get(u).size();i++){
                int v=g.get(u).get(i);
                if(vis[v]==0){
                    p[v]=u;
                    dfs(g, val, v, vis,m,p);
                    val[u]*=(val[v]+1);
                    val[u]%=m;
                }
                
            }
            vis[u]=2;
        }
        public static void dfs1(ArrayList<ArrayList <Integer>> g,long val[],int u,int p[],long m,long ans[],long up[]){
           // vis[u]=1;
            //boolean f=false;
            ans[u]=(val[u]*(up[u]+1))%m;
            int n=g.get(u).size();
            long pre[]=new long [n];
            long suf[]=new long [n];
            long k=1;
            for(int i=0;i<n;i++){
                int v=g.get(u).get(i);
                if(v!=p[u]){
                    k*=(val[v]+1);
                    k%=m;
                }
                pre[i]=k;
            }
            k=1;
            for(int i=n-1;i>=0;i--){
                int v=g.get(u).get(i);
                if(v!=p[u]){
                    k*=(val[v]+1);
                    k%=m;
                }
                suf[i]=k;
            }
            
            for(int i=0;i<g.get(u).size();i++){
                int v=g.get(u).get(i);
                 k=1;
                if(i>0){
                    k*=pre[i-1];
                    k%=m;
                }
                if(i<n-1){
                    k*=suf[i+1];
                    k%=m;
                }
                if(v!=p[u]){
                    k*=(up[u]+1);
                    k%=m;
                    up[v]=k;
                    dfs1(g, val, v, p, m, ans, up);
                }
                
            }
        }
        
    public static long modu(long p,long mod){
        if(p>=mod){
             p=-mod;
        }
        return p;
    }
    public static long pow(long x,long y,long mod){
		long ans=1;
		while(y>0){
			if((y&1)==1){
				ans=(ans*x)%mod;
			}
			y=y>>1;
			x=(x*x)%mod;
		}
		return ans;
    } 
	 public static void rec(int mask,int i,ArrayList<Integer> not,int groupmask,long val[],long dp[]){
        if(i==not.size()){
            dp[(mask|groupmask)]=Math.max(dp[(mask|groupmask)], dp[mask]+val[groupmask]);
            return;
        }
        rec(mask, i+1, not, groupmask, val, dp);
        rec(mask, i+1, not, groupmask|(1<<not.get(i)), val, dp);
     }
        public static void main(String[] args) {
            // code starts..
           int n=sc.nextInt();
           int m=sc.nextInt();
           ArrayList<ArrayList<Integer>> g=GetGraph(n, n-1);
           long val[]=new long[n];
           int p[]=new int[n];
           p[0]=-1;
           long ans[]=new long [n];
           long up[]=new long[n];
           dfs(g, val, 0, new int[n], m, p);
           dfs1(g, val, 0, p, m, ans, up);
           for(int i=0;i<n;i++){
               pw.println(ans[i]);
           }
                         
            // Code ends...
            pw.flush();
            pw.close();
        }
       
        public static Comparator<Integer[]> column(int i){
            return 
            new Comparator<Integer[]>() {
                @Override
                public int compare(Integer[] o1, Integer[] o2) {
                    return o1[i].compareTo(o2[i]);//for ascending
                    //return o2[i].compareTo(o1[i]);//for descending
                }
            };
        }
        public static Comparator<Pair> C(){
            return 
            new Comparator<Pair>() {
                @Override
                public int compare(Pair o1, Pair o2) {
                    return o2.le-o1.le;//for des
                }
            };
        }
        
        public static Comparator<Integer[]> pair(){
            return 
            new Comparator<Integer[]>() {
                @Override
                public int compare(Integer[] o1, Integer[] o2) {
                    int result=o1[0].compareTo(o2[0]);
                    if(result==0)
                    result=o1[1].compareTo(o2[1]);
                    return result;
                }
            };
        }
        
        public static String reverseString(String s){
            StringBuilder input1 = new StringBuilder(); 
            input1.append(s);  
            input1 = input1.reverse();
            return input1.toString();
        }
        public static int[] scanArray(int n){
            int a[]=new int [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextInt();
    
            return a;
        }
        public static long[] scanLongArray(int n){
            long a[]=new long [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextLong();
    
            return a;
        }
        public static String [] scanStrings(int n){
            String a[]=new String [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextLine();
    
            return a;
        }
        
    }
    
    class InputReader {
    
            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int curChar, snumChars;
            private SpaceCharFilter filter;
    
            public InputReader(InputStream stream) {
                this.stream = stream;
            }
    
            public int snext() {
                if (snumChars == -1)
                    throw new InputMismatchException();
                if (curChar >= snumChars) {
                    curChar = 0;
                    try {
                        snumChars = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (snumChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }
    
            public int nextInt() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
    
            public long nextLong() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
    
            public int[] nextIntArray(int n) {
                int a[] = new int[n];
                for (int i = 0; i < n; i++) {
                    a[i] = nextInt();
                }
                return a;
            }
    
            public String readString() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
            }
    
            public String nextLine() {
                int c = snext();
                while (isSpaceChar(c))
                    c = snext();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = snext();
                } while (!isEndOfLine(c));
                return res.toString();
            }
    
            public boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }
    
            private boolean isEndOfLine(int c) {
                return c == '\n' || c == '\r' || c == -1;
            }
    
            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }
        class Pair{
            int le;
            int p;
            Pair(int leaves,int parent){
                le=leaves;
                p=parent;
            }
        }