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 Main {

	BufferedReader in;
	StringTokenizer str = null;
	PrintWriter out;

	private String next() throws Exception{
		if (str == null || !str.hasMoreElements())
			str = new StringTokenizer(in.readLine());
		return str.nextToken();
	}
	
	private int nextInt() throws Exception{
		return Integer.parseInt(next());
	}
	
	private long nextLong() throws Exception{
		return Long.parseLong(next());
	}
	
	private double nextDouble() throws Exception{
		return Double.parseDouble(next());
	}
	
	int n,m,k;
	List<Integer> g[];
	boolean used[];
	int []prev, time;

	public void run() throws Exception{
		in =  new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		n = nextInt();
		m = nextInt();
		k = nextInt();
		
		g = new LinkedList[n];
		for(int i=0;i<n;i++)
			g[i] = new LinkedList<Integer>();
		for(int i=0;i<m;i++){
			int x = nextInt()-1;
			int y = nextInt()-1;
			g[x].add(y);
			g[y].add(x);
		}

		used = new boolean[n];
		prev = new int[n];
		prev[0] = -1;
		time = new int[n];

		dfs(0, 1);
	}

	private void dfs(int x, int vtx) {
		used[x] = true;
		time[x] = vtx;
		if (vtx >= k+1) {
			for(int i : g[x]) {
				if (used[i]){
					if (time[x] - time[i] + 1 >= k + 1){
						print(x, i);
					}
				}
			}
		}
		for(int i : g[x]){
			if (!used[i]) {
				prev[i] = x;
				dfs(i, vtx+1);
				prev[i] = -1;
			}
		}
		used[x] = false;
	}

	private void print(int x, int end){
		ArrayList<Integer> ans = new ArrayList<Integer>();
		while(x != end) {
			ans.add(x+1);
			x = prev[x];
		}
		ans.add(x+1);

		out.println(ans.size());
		for(int i : ans){
			out.print(i + " ");
		}
		out.println();
		out.close();
		System.exit(0);
	}
		
	public static void main(String[] args) throws Exception{
		new Main().run();
	}
}
