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.util.*;
import java.io.*;
//import java.text.*;

public class Main{
    final long mod = (long)1e9+7, IINF = (long)1e19;
    final int MAX = (int)1e5+1, MX = (int)1e7+1, INF = (int)1e9;
//    DecimalFormat df = new DecimalFormat("0.00000000");
    final double EPS = 1e-8;
    FastReader in;
    PrintWriter out;
    boolean multipleTC = false;

    public static void main(String[] args) throws Exception{new Main().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 = 20;
    void solve(int TC){
        int n = ni(), k = ni();
        int[][] g = new int[n][], edge = new int[n-1][2];
        int[] cnt = new int[n];
        for(int i = 0; i< n-1; i++){
            edge[i] = new int[]{ni()-1, ni()-1};
            cnt[edge[i][0]]++;
            cnt[edge[i][1]]++;
        }
        for(int i = 0; i< n; i++)g[i] = new int[cnt[i]];
        for(int i = 0; i< n-1; i++){
            g[edge[i][0]][--cnt[edge[i][0]]] = edge[i][1];
            g[edge[i][1]][--cnt[edge[i][1]]] = edge[i][0];
        }
        int[][] par = new int[B][n];int[] dep = new int[n];
        for(int b = 0; b< B; b++)for(int i = 0; i< n; i++)par[b][i] = -1;
        dfs(g,par,dep,n-1);
        for(int b = 1; b< B; b++)for(int i = 0; i< n; i++)if(par[b-1][i]!=-1)par[b][i] = par[b-1][par[b-1][i]];
        boolean[] inc = new boolean[n];
        inc[n-1] = true;
        int count = 1;
        for(int i = n-2; i>= 0; i--){
            if(inc[i])continue;
            int u = i,cn = 1;
            for(int b = B-1; b>=0; b--){
                if(par[b][u]==-1 || inc[par[b][u]])continue;
                u = par[b][u];
            }
            cn = dep[i]-dep[u]+1;
            if(count+cn<= n-k){
                u = i;
                int v = 0;
                while(!inc[u]){
                    inc[u] = true;
                    u = par[0][u];
                    v++;
                }
                count+=v;
            }
        }
        for(int i = 0; i< n; i++)if(!inc[i])p((i+1)+" ");
    }
    
    void dfs(int[][] g, int[][] par,int[] dep, int u){
        for(int v:g[u]){
            if(v==par[0][u])continue;
            par[0][v] = u;
            dep[v] = dep[u]+1;
            dfs(g,par,dep,v);
        }
    }

    void dfs(int i){
        
    }
    
    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;
    }

    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;
        }
    }
}