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.FileInputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	static int Cas;
	static int inf = 0x3f3f3f3f;
	static long lnf = 0x3f3f3f3f3f3f3f3fL;
	static int maxn = (int) (1e5 + 5);
	static int n, m, k;
	static int[] to = new int[maxn*2];
	static int[] next = new int[maxn*2];
	static int[] head = new int[maxn];
	static int cnt;
	static boolean[] vis = new boolean[maxn];
	static int[] path = new int[maxn];
	static int[] depth = new int[maxn];
	static int st, len;

	public static void main(String[] args) throws Exception {
		try {
			System.setIn(new FileInputStream("src\\night13"));
		} catch (Exception e) {

		}

		Scanner cin = new Scanner(System.in);
		while (cin.hasNext()) {
			n = cin.nextInt();
			m = cin.nextInt();
			k = cin.nextInt();
			
			clearGraph();
			for (int i = 0; i < m; ++i) {
				int a = cin.nextInt();
				int b = cin.nextInt();
				addEdge(a, b);
				addEdge(b, a);
			}
			
			Arrays.fill(vis, false);
			
			st = -1;
			vis[1] = true;
			path[0] = 1;
			depth[1] = 0;
			dfs(1, 0);

			System.out.println(len);
			for (int i = 0; i < len; ++i) {
				System.out.print(path[st + i] + " ");
			}
			System.out.println();
		}
		cin.close();
	}

	static void dfs(int u, int dep) {
		for (int i = head[u]; i != -1; i = next[i]) {
			int v = to[i];

			if (!vis[v]) {
				path[dep + 1] = v;
				depth[v] = dep + 1;
				vis[v] = true;
				dfs(v, dep + 1);
				if (st != -1) return;
				vis[v] = false;
				
			} else {
				if (dep + 1 - depth[v] > k) {
					st = depth[v];
					len = dep + 1 - depth[v];
					return;
				}
			}
		}
	}
	
	static void test() {
		for (int i = 1; i <= n; ++i) {
			System.out.print(i + ": ");
			for (int j = head[i]; j != -1; j = next[j]) {
				System.out.print(to[j] + " ");
			}
			System.out.println();
		}
	}
	
	static void clearGraph() {
		Arrays.fill(head, -1);
		cnt = 0;
	}

	static void addEdge(int a, int b) {
		to[cnt] = b;
		next[cnt] = head[a];
		head[a] = cnt++;
	}
}
