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.*;

public class D {
	
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int k = sc.nextInt();
		
		ArrayList<Integer>[] e = new ArrayList[n];
		for(int i=0;i<n;i++)
			e[i] = new ArrayList<Integer>();
		for(int i=0;i<m;i++){
			int n1 = sc.nextInt()-1;
			int n2 = sc.nextInt()-1;
			e[n1].add(n2);
			e[n2].add(n1);
		}
		sc.close();
		
		int center = 0;
		int[] time = new int[n];
		Arrays.fill(time, -1);
		ArrayList<Integer> res = new ArrayList<>();
		res.add(center);
		time[0] = 0;
		out: for(int it = 1;it<m;it++){
			for(Integer v:e[center]){
				if(time[v]<0){
					time[v] = it;
					res.add(v);
					center = v;
					continue out;
				}
				if(-time[v]+time[center]>=k){
					res.subList(0, time[v]).clear();
					break out;
				}
			}
		}
		System.out.println(res.size());
		for(int i=0, len = res.size();i<len;i++){
			System.out.print((1+res.get(i))+" ");
		}
	}
}
