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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class CycleInTheGraph {

	static int n,m,k;
	static int[] visited;
	static int var;
	static ArrayList<Integer>[] adjacencylist;
	static boolean f=true;
	static ArrayList<Integer> list=new ArrayList<>();
	public static void main(String[] args) {
		
		Scanner sc=new Scanner(System.in);
		n=sc.nextInt();
		m=sc.nextInt();
		k=sc.nextInt();
		adjacencylist=new ArrayList[n+1];
		for(int i=0;i<=n;i++)
		{
			adjacencylist[i]=new ArrayList<>();
		}
		visited=new int[n+1];
		Arrays.fill(visited, -1);
		for(int i=0;i<m;i++)
		{
			int u=sc.nextInt();
			int v=sc.nextInt();
			adjacencylist[u].add(v);
			adjacencylist[v].add(u);
		}
		dfs(1, 1);
	}
	
	public static void  dfs(int vertex,int count)
	{
		visited[vertex]=count;
		for(int i : adjacencylist[vertex])
		{
			if(f)
			if(visited[i]==-1)
			{
				dfs(i, count+1);
				if(var>0)
					{
					System.out.print(vertex+" ");
					var--;
					return;
					}
			}
			else
			{
				if(visited[vertex]-visited[i]>=k)
				{
					var=visited[vertex]-visited[i]+1;
					System.out.println(visited[vertex]-visited[i]+1);
					f=false;
					System.out.print(vertex+" ");
					var--;
					return;
				}
			}
		}
		list.add(vertex);
	}
	
	
	
}
