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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class CFD {
	static List<Integer> ans = new ArrayList<>();

	private static void sport(List<Integer>[] g, int k) {
		int n = g.length;
		int[] m = new int[n];
		Arrays.fill(m, -1);
		dfs(0, new ArrayList<>(), g, k, m, 1);

		System.out.println(ans.size());
		for (Integer integer : ans) {
			System.out.print((integer + 1) + " ");
		}
	}

	static void dfs(int v, List<Integer> curr, List<Integer>[] g, int k, int[] m, int cnt) {
		if (!ans.isEmpty()) {
			return;
		}
		m[v] = cnt;
		curr.add(v);
		for (Integer i : g[v]) {
			if (ans.isEmpty() && m[i] > 0 && cnt - m[i] >= k) {
				boolean f = false;
				for (int j = 0; j < curr.size(); j++) {
					if (!f && curr.get(j).equals(i)) {
						f = true;
					}
					if (f) {
						ans.add(curr.get(j));
					}
				}
				return;
			}
			if (m[i] < 0) {
				dfs(i, curr, g, k, m, cnt + 1);
			}
		}
		curr.remove(curr.size() - 1);
		m[v] = -1;
	}

	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int n = sc.nextInt();
		int m = sc.nextInt();
		int k = sc.nextInt();
		List<Integer>[] g = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			g[i] = new ArrayList<>();
		}
		for (int i = 0; i < m; i++) {
			int a = sc.nextInt() - 1;
			int b = sc.nextInt() - 1;
			g[a].add(b);
			g[b].add(a);
		}
		sport(g, k);
	}

	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		String next() {
			while (!st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				}
				catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long[] readArrayLong(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextLong();
			}
			return a;
		}

		int[] readArrayInt(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}