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.*;
import java.util.*;

import javax.management.RuntimeErrorException;

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {
		InputReader in = new InputReader(System.in);
		int n = in.getInt(), m = in.getInt(), k = in.getInt();
		Node[] graph = new Node[n+1];
		for (int i = 1; i <= n; i++) {
			graph[i] = new Node(i);
		}
		
		for (int i = 0; i < m; i++) {
			int u = in.getInt(), v = in.getInt();
			graph[u].adjacent.add(graph[v]);
			graph[v].adjacent.add(graph[u]);
		}
		
		List<Integer> answer = new ArrayList<>();
		dfs(1, 1, graph, k, answer);
		System.out.println(answer.size());
		for(int v : answer)
		{
			System.out.print(v + " ");
		}
 	}
	
	static boolean done = false;
	static int cycleLength = 0;
	private static int dfs(int v, int status, Node[] G, int k, List<Integer> answer) {
		G[v].status = status;
		for(Node i : G[v].adjacent)
		{
			if(i.status == 0)
			{
				int value = dfs(i.id, status+1, G, k, answer);
				if(value <= status)
					answer.add(v);
				return value;
			}
			if(status - i.status >= k)
			{
				answer.add(v);
				return i.status;
			}
		}
		throw new RuntimeException();
	}

	public static class Node
	{
		public int id, status = 0;
		public List<Node> adjacent = new ArrayList<>();
		public Node previous;
		
		public Node(int i)
		{
			id = i;
		}
		
	}

}

class InputReader {

	private BufferedReader reader;
	private StringTokenizer tokenizer;
	private String delimiters;

	public InputReader(InputStream stream) {
		reader = new BufferedReader(new InputStreamReader(stream));
	}

	public void setDelimiters(String delimiters) {
		this.delimiters = delimiters;
	}

	public void close() throws IOException {
		reader.close();
	}

	private String nextToken() throws IOException {
		if (tokenizer == null)
			tokenizer = new StringTokenizer("");
		while (!tokenizer.hasMoreTokens()) {
			if (delimiters == null)
				tokenizer = new StringTokenizer(reader.readLine());
			else
				tokenizer = new StringTokenizer(reader.readLine(), delimiters);
		}
		return tokenizer.nextToken();
	}

	public int getInt() throws NumberFormatException, IOException {
		return Integer.parseInt(nextToken());
	}

	public long getLong() throws NumberFormatException, IOException {
		return Long.parseLong(nextToken());
	}

	public double getDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextToken());
	}

	public String getNext() throws IOException {
		return nextToken();
	}

	public String getLine() throws IOException {
		tokenizer = null;
		return reader.readLine();
	}
}
