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.util.*;
import java.io.*;
public class Main {
	static int cnt;
	static ArrayList<Integer>ans;
	static int min;
static void dfs(int idx,int [] pos,ArrayList<Integer>list[]){
		pos[idx] = ++cnt;
		ans.add(idx);
		boolean flag = true;
		for(int temp : list[idx]){
			if(pos[temp] > 0)continue;
			flag = false;
			dfs(temp,pos,list);
			if(min != Integer.MAX_VALUE/2)return;
		}
		if(flag){
			for(int temp : list[idx]){
				min = Math.min(min,pos[temp]);
			}
			return;
		}
	}
public static void main(String [] args)throws Exception{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st = new StringTokenizer(br.readLine());
	int n = Integer.parseInt(st.nextToken());
	int m = Integer.parseInt(st.nextToken());
	int k = Integer.parseInt(st.nextToken());
	ArrayList<Integer>list[] = new ArrayList[n + 1];
	for(int i = 1;i <= n;i++)
		list[i] = new ArrayList<Integer>();
	for(int i = 1;i <= m;i++){
		st = new StringTokenizer(br.readLine());
		int a = Integer.parseInt(st.nextToken());
		int b = Integer.parseInt(st.nextToken());
		list[a].add(b);
		list[b].add(a);
	}
	cnt = -1;
	min = Integer.MAX_VALUE/2;
	ans = new ArrayList<Integer>();
	int pos[] = new int[n + 1];
	dfs(1,pos,list);
	StringBuilder sb = new StringBuilder();
	System.out.println((ans.size() - min));
	for(int i = min;i < ans.size();i++){
		sb.append(ans.get(i) + " ");
	}
	System.out.print(sb);
}
}