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.*;
public final class Cycle161
{ static ArrayList<Integer>[] arr;
	static ArrayList<Integer> cycle;
	static int[] dis;
	static int k,ans=0;
	static boolean cycleFound;
	static int[] edgeTo;
	public static void main(String[] args) {
		Scanner br=new Scanner(System.in);
		int n=br.nextInt();
	 	int m=br.nextInt();
		k=br.nextInt();
		arr=new ArrayList[n+1];
		dis=new int[n+1];
		edgeTo=new int[n+1];
		
		for(int i=0;i<=n;i++)
			arr[i]=new ArrayList<Integer>();
		for(int i=1;i<=m;i++)
		{
			int x=br.nextInt();
			int y=br.nextInt();
			arr[x].add(y);
			arr[y].add(x);
		}
		Arrays.fill(dis,-1);
		for(int i=1;i<=n;i++)
		{	
			
			if(dis[i]==-1 && !cycleFound)
			{
				dis[i] = 1;
	    		edgeTo[i] = -1;
	    		dfs(i);
	    	}
			else
				break;
		}
		System.out.println(cycle.size());
		for(Integer i:cycle)
			System.out.print(i+" ");

	}
	public static void dfs(int v)
	{
		 
		 if(cycleFound)
		 	return;
		 boolean found=false;
		 int s = arr[v].size();
        for (int w :arr[v])
         {   
         	if (dis[w]==-1) 
               	{
               	edgeTo[w] = v;
               	dis[w]=dis[v]+1;
                dfs(w);
                found=true;
            	}
        }
            if(!found )
            {
            	cycleFound = true;
				int min = arr[v].get(0);
				for(int j=0;j<s;j++)
				{
				int nxt = arr[v].get(j);
				if(dis[nxt] < dis[min])
					min = nxt;
				}
				cycle=new ArrayList<Integer>();
            	while(v != edgeTo[min]){
				cycle.add(v);
				v = edgeTo[v];
			}
            	
            }
        
        
        return;
            
	}
}