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.lang.*;
import java.math.*;
import java.io.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;

public class D{
	// Scanner sc=new Scanner(System.in);
	BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

	int INF=1<<28;
	double EPS=1e-9;

	int n, k;
	HashSet<Integer>[] es;

	void run(){
		try{
			String[] ss=br.readLine().split(" ");
			n=Integer.parseInt(ss[0]);
			int m=Integer.parseInt(ss[1]);
			k=Integer.parseInt(ss[2]);
			es=new HashSet[n];
			for(int i=0; i<n; i++){
				es[i]=new HashSet<Integer>();
			}
			for(int i=0; i<m; i++){
				ss=br.readLine().split(" ");
				int a=Integer.parseInt(ss[0])-1;
				int b=Integer.parseInt(ss[1])-1;
				es[a].add(b);
				es[b].add(a);
			}
			solve();
		}catch(Exception e){}
	}

	void solve(){
		int[] vs=new int[n];
		int[] pos=new int[n];
		fill(pos, -1);
		vs[0]=0;
		pos[0]=0;
		for(int t=1;; t++){
			int v=vs[t-1];
			for(int u : es[v]){
				if(pos[u]>=0){
					int cycle=t-pos[u];
					if(cycle>=k+1){
						StringBuilder sb=new StringBuilder();
						sb.append(cycle).append('\n');
						for(int i=pos[u]; i<t; i++){
							sb.append(vs[i]+1).append(' ');
						}
						println(sb.toString());
						return;
					}
				}else{
					vs[t]=u;
					break;
				}
			}
			pos[vs[t]]=t;
		}
	}

	void println(String s){
		System.out.println(s);
	}

	void print(String s){
		System.out.print(s);
	}

	void debug(Object... os){
		System.err.println(Arrays.deepToString(os));
	}

	public static void main(String[] args){
		Locale.setDefault(Locale.US);
		new D().run();
	}
}
