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.*;
import java.io.*;
public class A {

	
	public static void main(String[] args) throws IOException {
		Scanner sc=new Scanner(System.in);
		PrintWriter pw=new PrintWriter (System.out);
		int n=sc.nextInt(),m=sc.nextInt(),k=sc.nextInt();
		ArrayList<Integer> []adj=new ArrayList[n];
		for(int i=0;i<n;i++)
			adj[i]=new ArrayList();
		
		while(m-->0)
		{
			int u=sc.nextInt()-1,v=sc.nextInt()-1;
			adj[u].add(v);
			adj[v].add(u);
		}
		boolean []visited=new boolean[n];
		int []d=new int [n];
		Arrays.fill(d, n+n);
		visited[0]=true;
		d[0]=0;
		int u=0;
		ArrayList<Integer> path=new ArrayList();
		int ans=0;
		StringBuilder sb=new StringBuilder();
		out: while(true)
		{
			path.add(u);
			for(int v:adj[u])
				if(d[u]-d[v]>=k)
				{
					
					
					
					boolean start=false;
					for(int x:path)
					{
						if(x==v)
							start=true;
						if(start) {
							ans++;
							sb.append((x+1)+" ");
						}
						if(x==u)
							start=false;
					}
					break out;
				}
				for(int v:adj[u])
					if(!visited[v])
					{
						d[v]=d[u]+1;
						visited[v]=true;
						u=v;
						break;
						
					}
			
		}
		
		pw.println(ans);
		pw.println(sb);
		
		
		pw.close();
		
		
	}
	static class Scanner {
        StringTokenizer st;
        BufferedReader br;
 
        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }
 
        public Scanner(FileReader s) {
            br = new BufferedReader(s);
        }
 
        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
 
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
 
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
 
        public String nextLine() throws IOException { return br.readLine();}
        public boolean ready() throws IOException {return br.ready();}
        public double nextDouble() throws IOException {return Double.parseDouble(next());}
       
    }

}
