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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.*;

public class cf263d {
  public static void main(String[] args) {
    FastScanner in = new FastScanner(System.in);
    PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    int n = in.nextInt();
    int m = in.nextInt();
    int k = in.nextInt();
    boolean[] seen = new boolean[n];
    HashSet<Integer>[] g = new HashSet[n];
    for(int i=0; i<n; i++) g[i] = new HashSet<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);
    }
    ArrayDeque<Integer> ans = new ArrayDeque<Integer>();
    seen[0] = true;
    ans.add(0);
    int cur = 0;
    boolean ok = true;
    while(ok) {
      ok = false;
      for(int x : g[cur]) {
        if(seen[x]) continue;
        seen[x] = true;
        ok = true;
        ans.add(cur = x);
        break;
      }
    }
    while(!g[ans.peekFirst()].contains(ans.peekLast()))
      ans.pollFirst();
    out.println(ans.size());
    for(int x : ans)
      out.print((x+1)+" ");
    out.close();
  }
  static class FastScanner {
    BufferedReader br;
    StringTokenizer st;
    
    public FastScanner(InputStream in) {
      br = new BufferedReader(new InputStreamReader(in));
      scanLine();
    }
    public void scanLine() {
      try {
        st = new StringTokenizer(br.readLine().trim());
      } catch(Exception e) {
        throw new RuntimeException(e.getMessage());
      }
    }
    public int numTokens() {
      if(!st.hasMoreTokens()) {
        scanLine();
        return numTokens();
      }
      return st.countTokens();
    }
    public String next() {
      if(!st.hasMoreTokens()) {
        scanLine();
        return next();
      }
      return st.nextToken();
    }
    public double nextDouble() {
      return Double.parseDouble(next());
    }
    public long nextLong() {
      return Long.parseLong(next());
    }
    public int nextInt() {
      return Integer.parseInt(next());
    }
  }
}
