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 static java.util.Arrays.fill;

import java.io.*;
import java.util.*;

public class D {

	static void solve() throws IOException {
		int n = nextInt(), edges = nextInt(), k = nextInt();
		List<Integer>[] e = new List[n];
		for (int i = 0; i < n; i++) {
			e[i] = new ArrayList<>();
		}
		for (int i = 0; i < edges; i++) {
			int u = nextInt() - 1;
			int v = nextInt() - 1;
			e[u].add(v);
			e[v].add(u);
		}
		List<Integer> list = new ArrayList<>();
		int[] time = new int[n];
		fill(time, -1);
		int u = 0;
		go: for (int it = 0;; it++) {
			for (int v : e[u]) {
				if (time[v] < 0) {
					time[v] = it;
					list.add(v);
					u = v;
					continue go;
				}
				if (time[u] - time[v] >= k) {
					list.subList(0, time[v]).clear();
					break go;
				}
			}
			throw new AssertionError();
		}
		out.println(list.size());
		for (int i = 0; i < list.size(); i++) {
			if (i > 0) {
				out.print(' ');
			}
			out.print(list.get(i) + 1);
		}
		out.println();
	}

	static BufferedReader br;
	static PrintWriter out;
	static StringTokenizer st;

	public static void main(String[] args) throws Exception {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

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

	static int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	static long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	static double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}
