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.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Scanner;


public class D {
	public boolean dfs(boolean[] visited, ArrayList<Integer> path, int current){
		boolean found = false;
		for(int n: neighbours[current]){
			if( !visited[n] ){
				found = true;
				visited[n] = true;
				if( dfs(visited, path, n) ){
					path.add( current );
					return true;
				}
			}
		}
		if(!found) {
			path.add( current );
			return true;
		}
		return false;
	}
	
	ArrayList<Integer>[] neighbours;
	
	public void solve(){
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));		
		Scanner sc = new Scanner(System.in);		
		int N = sc.nextInt();
		int M = sc.nextInt();
		int K = sc.nextInt();
		
		neighbours = new ArrayList[N];
		for(int i = 0; i < N; i++){
			neighbours[i] = new ArrayList<Integer>();
		}
		for(int i = 0; i < M; i++){
			int n1 = sc.nextInt()-1;
			int n2 = sc.nextInt()-1;
			neighbours[n1].add(n2);
			neighbours[n2].add(n1);
		}
		
		ArrayList<Integer> path = new ArrayList<Integer>();
		boolean[] visited = new boolean[N];
		visited[0] = true;
		dfs( visited, path, 0);
		
//		for(int i = 0; i < path.size(); i++){
//			System.out.println( path.get(i) );
//		}
		for(int i = path.size()-1; i > 0; i--){
			if( neighbours[path.get(0)].contains(path.get(i)) ){
				out.println( i+1 );
				for(int j = i; j >= 0; j--){
					out.print( (path.get(j)+1) + " ");
				}
				break;
			}			
		}
		out.close();
	}
	
	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		new D().solve();
	}

}
