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.*;
import java.math.BigInteger;

public class Solution {

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st;
	
	String nextToken() throws Exception {
		while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}
	
	int nextInt() throws Exception {
		return Integer.parseInt(nextToken());
	}
	
	long nextLong() throws Exception {
		return Long.parseLong(nextToken());
	}
	
	class Edge {
		int e;
		Edge next;
		Edge(int q, Edge n) {
			e = q; next = n;
		}
	}
	
	void solve() throws Exception {
		int n = nextInt();
		int m = nextInt();
		int k = nextInt();
		Edge[] a = new Edge[n + 1];
		for (int i = 0; i < m; i++) {
			int q = nextInt();
			int w = nextInt();
			a[q] = new Edge(w, a[q]);
			a[w] = new Edge(q, a[w]);
		}
		Set<Integer> s = new TreeSet<Integer>();
		int[] ans = new int[n];
		ans[0] = 1;
		s.add(1);
		int j = 0;
		int end = -1;
		for (int i = 1; i < n; i++) {
			ans[i] = -1;
			for (Edge r = a[ans[i - 1]]; r != null; r = r.next) {
				if (!s.contains(r.e)) {
					ans[i] = r.e;
					s.add(r.e);
					break;
				}
			}
			if (ans[i] == -1) {
				end = i - 1;
				break;
			}
		}
		if (end == -1) end = n - 1;
		TreeSet<Integer> f = new TreeSet<Integer>();
		for (Edge r = a[ans[end]]; r != null; r = r.next) {
			f.add(r.e);
		}
		j = 0;
		while (!f.contains(ans[j])) j++;
		out.println(end - j + 1);
		for (int i = j; i <= end; i++) out.print(ans[i] + " ");
	}
	
	void run() {
		try {
			Locale.setDefault(Locale.US);
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			solve();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		} finally {
			out.close();
		}
	}
	
	public static void main(String[] args) {
		new Solution().run();
	}

}