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.io.BufferedReader;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Queue;
public class E980 
{
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException {
            byte[] buf = new byte[10000]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
    
    public static void main(String args[]) throws IOException
    {
        solve();
    }
    static int dp[][]=new int[1000001][20];
    static ArrayList<Integer> g[];
    static void dfs(int parent,int node)
    {
        boolean vis[]=new boolean[1000001];
        Queue<Integer> q=new LinkedList<>();
        vis[node]=true;
        q.add(node);
        while(!q.isEmpty())
        {
            node=q.poll();
            for(int i=0;i<g[node].size();i++)
            {
                int y=g[node].get(i);
                if(!vis[y])
                {
                    vis[y]=true;
                    q.add(y);
                    dp[y][0]=node;
                }
            }
        }
    }
    static void solve() throws IOException
    {
        Reader in=new Reader();
        PrintWriter out=new PrintWriter(System.out);
        int n=in.nextInt();
        int k=in.nextInt();
        g=new ArrayList[n+1];
        for(int i=0;i<=n;i++)
            g[i]=new ArrayList<>();
        for(int i=1;i<n;i++)
        {
            int u=in.nextInt();
            int v=in.nextInt();
            g[u].add(v);
            g[v].add(u);
            
        }
        dfs(0,n);
        for(int i=1;i<20;i++)
            for(int j=1;j<=n;j++)
                dp[j][i]=dp[dp[j][i-1]][i-1];
        k=n-k;
        k--;
        int v[]=new int[n+1];
        v[n]=1;
        v[0]=1;
        for(int i=n-1;i>0;i--)
        {
            if(k==0)
                break;
            if(v[i]==1)
                continue;
            int node=i;
            int lev=0;
            for(int j=19;j>=0;j--)
                if(v[dp[node][j]]==0)
                {
                    lev+=(1<<j);
                    node=dp[node][j];
                }
            while(v[node]==0)
            {
               lev++;
               node=dp[node][0];
            }
            if(k>=lev)
            {
                node=i;
                k-=lev;
                while(v[node]==0)
                {
                    v[node]=1;
                    node=dp[node][0];
                }
            }
        }
        for(int i=1;i<=n;i++)
            if(v[i]==0)
            {
                out.print(i);
                out.print(" ");                
            }
        out.println();
        out.close();
    }

}
