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.*;
import java.util.*;

public class Main {
	static int MAXN = (int)2e5 + 5;
	static int []list = new int[MAXN];
	static int sz = 0;
	static int []used = new int[MAXN];
	static int k;
	static int []g = new int[MAXN];
	static int []edge = new int[2 * MAXN];
	static int [] next = new int[2 * MAXN];
	static int [] pos = new int[2 * MAXN];
	static int INF = (int)1e9;

	static void DFS(int node) {
		list[sz] = node;
		pos[node] = sz;
		used[node] = 1;
		sz++;
		int x = g[node];
		int early = INF;
		int idx = -1;
		int v = -1;
		//System.out.println("here node = " + node);
		
		while(x != -1) {
			//System.out.println("here here x = " + edge[x]);
			if (used[edge[x]] == 0) {
				v = edge[x];
			} else {
				if (pos[edge[x]] < early) {
					early = pos[edge[x]];
					idx = edge[x];
				}
			}
			x = next[x];
		}

		//System.out.println("early = " + early + ", idx = " + idx);
		if (sz - early > k) {
			list[sz] = idx;
		} else {
			DFS(v);
		}
		return;
	}

    public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		k = sc.nextInt();
		int prox = 0;

		for (int i = 1; i <= n; i++) {
			g[i] = -1;
			used[i] = 0;
			pos[i] = INF;
		}
		for (int i = 0; i < m; i++) {
			int a = sc.nextInt();
			int b = sc.nextInt();

			next[prox] = g[a];
			edge[prox] = b;
			g[a] = prox++;
			next[prox] = g[b];
			edge[prox] = a;
			g[b] = prox++;
		}

		DFS(1);
		int start = -1;
		for (int i = sz - 1; i >= 0; i--) {
			if (list[i] == list[sz]) {
				start = i;
				break;
			}
		}
		System.out.println(sz - start);
		for (int i = start; i < sz; i++) {
			if (i != start) {
				System.out.print(" ");
			}
			System.out.print(list[i]);
		}
			
		System.out.println("");
    }
}
// 1506711360430
