The nation of Panel holds an annual show called The Number Games, where each district in the nation will be represented by one contestant.

The nation has n districts numbered from 1 to n, each district has exactly one path connecting it to every other district. The number of fans of a contestant from district i is equal to 2^i.

This year, the president decided to reduce the costs. He wants to remove k contestants from the games. However, the districts of the removed contestants will be furious and will not allow anyone to cross through their districts. 

The president wants to ensure that all remaining contestants are from districts that can be reached from one another. He also wishes to maximize the total number of fans of the participating contestants.

Which contestants should the president remove?

Input

The first line of input contains two integers n and k (1 ≤ k < n ≤ 10^6) — the number of districts in Panel, and the number of contestants the president wishes to remove, respectively.

The next n-1 lines each contains two integers a and b (1 ≤ a, b ≤ n, a ≠ b), that describe a road that connects two different districts a and b in the nation. It is guaranteed that there is exactly one path between every two districts.

Output

Print k space-separated integers: the numbers of the districts of which the contestants should be removed, in increasing order of district number.

Examples

Input

6 3
2 1
2 6
4 2
5 6
2 3


Output

1 3 4


Input

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


Output

1 3 4 5

Note

In the first sample, the maximum possible total number of fans is 2^2 + 2^5 + 2^6 = 100. We can achieve it by removing the contestants of the districts 1, 3, and 4.
import java.math.*;
import java.util.*;
import java.io.*;

public class Main {

    void solve() {
        int n=ni(),k=ni();
        k=n-k;
        g=new int[n+1][];
        int from[]=new int[n-1];
        int to[]=new int[n-1];
        for(int i=1;i<n;i++){
            int a=ni(),b=ni();
            from[i-1]=a; to[i-1]=b;
        }
        g=packU(n,from,to);
        level=new int[n+1];
        parent=new int[n+1];
        dfs(n,-1,0);
        MAXL=log2(n);
        P=new int[n+1][MAXL+1];
        precomput(n);
        boolean include[]=new boolean[n+1];
        include[n]=true;
        int total=1;
        for(int i=n-1;i>=1 && total<k;i--){
            int u=i;
            if(include[i]) continue;
             for(int j=MAXL;j>=0;j--){
                 if(P[u][j]!=-1 && !include[P[u][j]]){
                     u=P[u][j];
                 }
             }
             int d=level[i]-level[u]+1;

            if(total+d<=k){
                //pw.println(i+" "+u);
                total+=d;

                int v=i;
                while(v!=u){
          //          pw.println(v);
                    include[v]=true;
                    v=parent[v];
                }
              //  pw.println(u);

                include[u]=true;
            }
        }
        //pw.println(total);
        for(int i=1;i<=n;i++){
            if(!include[i]) pw.print(i+" ");
        }


    }
    int g[][];
    int level[];
    int parent[];
    int P[][];
    int MAXL;
    static int log2(int v){
        return (int)(Math.log10(v)/Math.log10(2));
    }
    void precomput(int n){
        for(int i=1;i<=n;i++) {
            for(int j=0;j<=MAXL;j++){
                P[i][j]=-1;
            }
        }
        for(int i=1;i<=n;i++) P[i][0]=parent[i];

        for(int j=1;(1<<j)<n;j++){
            for(int i=1;i<=n;i++){
                if(P[i][j-1]!=-1) P[i][j]=P[P[i][j-1]][j-1];

            }
        }

    }


    void dfs(int v,int pr,int l){
        parent[v]=pr;
        level[v]=l;


        for(int u : g[v]){
            if(u!=pr) dfs(u,v,l+1);
        }
    }
    static int[][] packU(int n, int[] from, int[] to) {
        int[][] g = new int[n+1][];
        int[] p = new int[n+1];
        for (int f : from)
            p[f]++;
        for (int t : to)
            p[t]++;
        for (int i = 1; i <= n; i++)
            g[i] = new int[p[i]];
        for (int i = 0; i < from.length; i++) {
            g[from[i]][--p[from[i]]] = to[i];
            g[to[i]][--p[to[i]]] = from[i];
        }
        return g;
    }

    long M=(long)1e9+7;
    InputStream is;
    PrintWriter pw;
    String INPUT = "";
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        pw = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        pw.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }

    public static void main(String[] args) throws Exception { new Main().run(); }

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
}