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.*;
import java.io.*;

public class CycleInGraph {
	public static void main(String[] args) throws IOException {
		rd = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(System.out);
		st = new StringTokenizer(rd.readLine());
		n = Integer.parseInt(st.nextToken());
		m = Integer.parseInt(st.nextToken());
		k = Integer.parseInt(st.nextToken());
		g = new ArrayList[n+1];
		for(int i=0; i<g.length; i++) g[i] = new ArrayList<Integer>();
		for(int i=0; i<m; i++){
			st = new StringTokenizer(rd.readLine());
			int a = Integer.parseInt(st.nextToken()), b = Integer.parseInt(st.nextToken());
			g[a].add(b);
			g[b].add(a);
		}
		HashMap<Integer, Integer> usedVertices = new HashMap<Integer, Integer>();
		ArrayList<Integer> path = new ArrayList<Integer>();
		int currentVertex = 1;
		usedVertices.put(currentVertex, 0);
		path.add(currentVertex);
		while(true){
			int next = addAnyNeighbour(currentVertex, usedVertices);
			if(next==-1) break;
			path.add(next);
			usedVertices.put(next, usedVertices.get(currentVertex)+1);
			currentVertex = next;
		}
		int firstIndex = getFirstOccuringNeighbour(currentVertex, usedVertices);
		int ind = usedVertices.get(g[currentVertex].get(firstIndex));
		int len = path.size()-ind+1;
		pw.println(len-1);
		for(int i=ind; i<path.size(); i++) pw.print(path.get(i)+" ");
		pw.println();
		pw.flush();
	}
	
	static int getFirstOccuringNeighbour(int vertex, HashMap<Integer, Integer> usedVertices){
		int ans = 0;
		for(int i=1; i<g[vertex].size(); i++){
			int to = g[vertex].get(i);
			if(usedVertices.get(to)<usedVertices.get(g[vertex].get(ans)))
				ans = i;
		}
		return ans;
	}
	
	static int addAnyNeighbour(int vertex, HashMap<Integer, Integer> usedVertices){
		for(int i=0; i<g[vertex].size(); i++){
			int to = g[vertex].get(i);
			if(usedVertices.containsKey(to)) continue;
			return to;
		}
		return -1;
	}
	
	
	static int n, m, k;
	
	static StringTokenizer st;
	
	static ArrayList<Integer>[] g;
	
	static BufferedReader rd;
	
	static PrintWriter pw;
	
}
