You've got a undirected graph G, consisting of n nodes. We will consider the nodes of the graph indexed by integers from 1 to n. We know that each node of graph G is connected by edges with at least k other nodes of this graph. Your task is to find in the given graph a simple cycle of length of at least k + 1.

A simple cycle of length d (d > 1) in graph G is a sequence of distinct graph nodes v1, v2, ..., vd such, that nodes v1 and vd are connected by an edge of the graph, also for any integer i (1 ≤ i < d) nodes vi and vi + 1 are connected by an edge of the graph.

Input

The first line contains three integers n, m, k (3 ≤ n, m ≤ 105; 2 ≤ k ≤ n - 1) — the number of the nodes of the graph, the number of the graph's edges and the lower limit on the degree of the graph node. Next m lines contain pairs of integers. The i-th line contains integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — the indexes of the graph nodes that are connected by the i-th edge. 

It is guaranteed that the given graph doesn't contain any multiple edges or self-loops. It is guaranteed that each node of the graph is connected by the edges with at least k other nodes of the graph.

Output

In the first line print integer r (r ≥ k + 1) — the length of the found cycle. In the next line print r distinct integers v1, v2, ..., vr (1 ≤ vi ≤ n) — the found simple cycle.

It is guaranteed that the answer exists. If there are multiple correct answers, you are allowed to print any of them.

Examples

Input

3 3 2
1 2
2 3
3 1


Output

3
1 2 3 

Input

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


Output

4
3 4 1 2 
import java.util.List;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.ArrayList;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.Collections;
import java.io.InputStream;

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

class TaskD {
    ArrayList< Integer >[] g;
    ArrayList< Integer > path = new ArrayList<Integer>();
    boolean[] seen;

    void dfs(int u)
    {
        seen[ u ] = true;
        path.add( u );
        for (int v : g[u])
        {
            if ( !seen[ v ] )
            {
                dfs( v );
                break;
            }
        }
    }

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();

        g = new ArrayList[ n ];
        for (int i=0; i<n; i++) g[i] = new ArrayList<Integer>();

        for (int i=0; i<m; i++)
        {
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            g[a].add( b );
            g[b].add( a );
        }

        for (int i=0; i<n; i++) Collections.sort( g[i] );

        seen = new boolean[ n ];
        dfs( 0 );

        int d = path.get( path.size()-1 );
        for (int i=0; i<path.size(); i++)
        {
            if ( Collections.binarySearch( g[ d ], path.get(i) ) >= 0 )
            {
                out.println( path.size() - i );
                for (int j=i; j<path.size(); j++)
                {
                    if ( j > i ) out.print(" ");
                    out.print( path.get(j)+1 );
                }
                out.println();
                return;
            }
        }
    }
}

class InputReader {
    BufferedReader br;
    StringTokenizer st;

    public InputReader(InputStream in)
    {
        br = new BufferedReader(new InputStreamReader(in));
        st = null;
    }

    public String next()
    {
        while (st==null || !st.hasMoreTokens())
        {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return st.nextToken();
    }

    public int nextInt()
    {
        return Integer.parseInt(next());
    }

    }
