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.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Stack;
import java.util.StringTokenizer;


public class CycleInGraph {

	
	 static StringBuilder out = new StringBuilder();
     static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	 static StringTokenizer st;
	 static LinkedList<Integer> arr[];
	 static Stack<Integer> stack = new Stack();
	 static int n,m,k,u,v;
	 static boolean seen[];
	 static boolean flag;
	 static int f = 0;
	 static String ans = "";
	 
		 public static void main(String[]args) throws Throwable{
			 new Thread(null,new Runnable() {
			         
			         public void run() {
			             try {
			                 medo();
			             } catch (NumberFormatException e) {
			                 
			                 e.printStackTrace();
			             } catch (Throwable e) {
							// TODO Auto-generated catch block
							e.printStackTrace();
						} 
			             
			         }
			     },"2",1<<26).start();
			 }
		 
		 public static void medo()throws Throwable{
			 st = new StringTokenizer(br.readLine());
			 n = Integer.parseInt(st.nextToken());
			 m = Integer.parseInt(st.nextToken());
			 k = Integer.parseInt(st.nextToken());
			 arr = new LinkedList[n+1];
			 seen = new boolean[n+1];
			 flag = false;
			 for(int i=0;i<n+1;i++) arr[i] = new LinkedList();
			 for(int i=0;i<m;i++){
				 st = new StringTokenizer(br.readLine());
				 u = Integer.parseInt(st.nextToken());
				 v = Integer.parseInt(st.nextToken());
				 arr[u].add(v);
				 arr[v].add(u);
			 }
			for(int i=1;i<=n;i++){
				Arrays.fill(seen,false);
				dfs(i,k+1,i);
				
				if(stack.size()>k) break;
				
			}
			 
			 out.append(stack.size()+"\n");
			 while(!stack.isEmpty()) out.append(stack.pop()+" ");
			 System.out.print(out);
		 }
		 
		 static void dfs(int i,int k,int s){
			 if(flag) return;
			 if(i==s&&k<=0) {
				 flag = true;
			 }
			
			 if(seen[i]) return;
			 
			 seen[i] = true;
			 stack.push(i);
			 for(Integer u:arr[i]) dfs(u,k-1,s);
			 if(flag==false){
				 while(!stack.isEmpty()){
					 int v = stack.pop();
					 if(v==i) break;
				 }
			 }
		 }
	    
}