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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Iterator;
import java.util.LinkedList;

import static java.lang.Integer.*;
import static java.lang.System.out;
import static java.lang.Math.*;

public class Main {

	static int k;
	static LinkedList<Integer>[] g;
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		
		String inp[] = in.readLine().trim().split("\\s+");
		int n = parseInt(inp[0]),m = parseInt(inp[1]);
		k = parseInt(inp[2]);
		g = new LinkedList[n+1];
		for (int i = 1; i <=n; i++)
		{
			g[i]= new LinkedList<Integer>();
		}
		
		for (int z = m; z>0; z--)
		{
			inp = in.readLine().trim().split("\\s+");
			int a = parseInt(inp[0]),b = parseInt(inp[1]);
			g[a].add(b);
			g[b].add(a);			
		}
		seen = new boolean[n+1];
		seen[1] = true;
		path = new ArrayList<Integer>(k+1);
		path.add(1);
		
		dfs(1,-1);
	}
	
	static boolean[]seen;
	static ArrayList<Integer> path;
	public static boolean dfs(int u,int parent)
	{			
		for (int v: g[u])
		{			
			if (seen[v])
			{				
				if (v!=parent)
				{
					if (path.size()-path.indexOf(v)>k)
					{						
						String sp = "";
						StringBuilder res = new StringBuilder();
						res.append(path.size()-path.indexOf(v));
						res.append("\n");
						for (int i = path.size()-1; i>=path.indexOf(v); i--)
						{
							res.append(sp);
							res.append(path.get(i));
							sp = " ";
						}
						out.println(res.toString());
						return true;						
					}
				}				
			}
			else
			{
				path.add(v);
				seen[v] = true;
				if(dfs(v,u)) return true;
				path.remove(path.size()-1);
				seen[v] = false;
			}
		} 
		return false;
	}
}