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.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.Map.Entry;
import java.util.function.Function;
import java.util.function.Supplier;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

public class Solutions {
	static PrintWriter out = new PrintWriter(System.out);
	static Scanner in = new Scanner();
	static int n, m, k, last_cycle, start_cycle;
	static ArrayList<Integer> adj[];
	static int par[], depth[];

	public static void main(String[] test) throws NumberFormatException, IOException {
		n = in.nextInt();
		m = in.nextInt();
		k = in.nextInt();
		adj = new ArrayList[n];
		par = new int[n];
		depth = new int[n];
		Arrays.fill(depth, -1);
		Arrays.fill(par, 0);
		for (int i = 0; i < n; i++) {
			adj[i] = new ArrayList<>();
		}
		for (int i = 0; i < m; i++) {
			int u = in.nextInt() - 1;
			int v = in.nextInt() - 1;
			adj[u].add(v);
			adj[v].add(u);
		}
		par[0] = -1;
		depth[0] = 0;
		int ret = dfs(0);
		// out.println(ret);
		out.println(Math.abs(depth[ret] - depth[last_cycle]) + 1);
		while (true) {
			out.print((ret + 1) + " ");
			if (ret == last_cycle) {
				break;
			}
			ret = par[ret];
		}
		out.flush();
		out.close();
	}

	static int dfs(int s) {
		for (Integer u : adj[s]) {
			if (depth[u] == -1) {
				depth[u] = depth[s] + 1;
				par[u] = s;
				int ret = dfs(u);
				if (ret != -1) {
					return ret;
				}
			} else if (u != par[s] && Math.abs(depth[u] - depth[s]) + 1 >= k + 1) {
				last_cycle = u;
				// out.println("s last " + s + " " + last_cycle);
				return s;

			}
		}
		return -1;
	}

	static class Scanner {// Fast I/O
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		Scanner(String file) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(file));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

	}

}
