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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;


public class R161qDCyclesInGraph {

	static ArrayList<Integer> g[],ans;
	static int vis[],parent[];
	static boolean cycleFound;
	
	@SuppressWarnings("unchecked")
	public static void main(String args[] ) throws Exception {
		   
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    PrintWriter w = new PrintWriter(System.out);
	    
	    StringTokenizer st1 = new StringTokenizer(br.readLine());
	    int n = ip(st1.nextToken());
		int m = ip(st1.nextToken());
	    //int k = ip(st1.nextToken());
	          
	    g = new ArrayList[n];
	    for(int i=0;i<n;i++)
			g[i] = new ArrayList<Integer>();
		
	    for(int i=0;i<m;i++){
			StringTokenizer st = new StringTokenizer(br.readLine());
			int u = ip(st.nextToken()) - 1;
			int v = ip(st.nextToken()) - 1;
			g[u].add(v);
			g[v].add(u);
		}
	    
	    vis = new int[n];
	    Arrays.fill(vis, -1);
	    cycleFound = false;
	    
	    parent = new int[n];
	    
	    for(int i=0;i<n && !cycleFound;i++){
	    	if(vis[i] == -1){
	    		vis[i] = 1;
	    		parent[i] = -1;
	    		dfs(i);
	    	}
	    }
	    
	    w.println(ans.size());
	    for(int v : ans)
	    	w.print((v+1) + " ");
	    w.println();
	    
	    w.close(); 
	}
	
	public static void dfs(int curr){

		if(cycleFound)	return;
		
		boolean found = false;
		int s = g[curr].size();
		for(int j=0;j<s;j++){
			int nxt = g[curr].get(j);
			if(vis[nxt] == -1){
				vis[nxt] = vis[curr] + 1;
				parent[nxt] = curr;
				dfs(nxt);
				found = true;
			}
		}
		
		if(!found){
			cycleFound = true;
			int min = g[curr].get(0);
			for(int j=0;j<s;j++){
				int nxt = g[curr].get(j);
				if(vis[nxt] < vis[min])
					min = nxt;
			}
			
			ans = new ArrayList<Integer>();
			while(curr != parent[min]){
				ans.add(curr);
				curr = parent[curr];
			}
			
		}
	}
	
	public static int ip(String s){
		return Integer.parseInt(s);
	}
}
