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

public class D9 {

	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>[] grafo = new ArrayList[n];
		for (int i = 0; i < n; i++)
			grafo[i] = new ArrayList<Integer>();
		for (int i = 0; i < m; i++) {
			int n1 = sc.nextInt() - 1;
			int n2 = sc.nextInt() - 1;
			grafo[n1].add(n2);
			grafo[n2].add(n1);
		}
		sc.close();

		ArrayList<Integer> camino = new ArrayList<Integer>();
		int[] orden = new int[n];
		Arrays.fill(orden, -1);

		int ordActual = -1;
		int nuevoNodo = 0;
		boolean fin = false;

		while (orden[nuevoNodo] == -1 && !fin) {
			ordActual++;
			camino.add(nuevoNodo);
			orden[nuevoNodo] = ordActual;

			for (int i = 0; i < k; i++) {
				int j = grafo[nuevoNodo].get(i);
				if (orden[j] <= ordActual - k || orden[j] == -1) {
					fin = (orden[j] != -1);
					nuevoNodo = j;
					break;
				}
			}
		}

		camino.subList(0, orden[nuevoNodo]).clear();
		System.out.println(camino.size());

		for (Iterator iterator = camino.iterator(); iterator.hasNext();) {
			System.out.print((Integer) iterator.next() + 1);
			if (iterator.hasNext())
				System.out.print(" ");
		}
	}
}
