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.Scanner;
import static java.lang.System.out;

public class D {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int cantNodos = sc.nextInt();
		int cantAristas = sc.nextInt();
		int minGrado = sc.nextInt();

		ArrayList<ArrayList<Integer>> grafo =
				new ArrayList<ArrayList<Integer>>(cantNodos);

		for (int i = 0; i < cantNodos; i++) {
			grafo.add(i, new ArrayList<Integer>());
		}

		for (int i = 0; i < cantAristas; i++) {
			int n1 = sc.nextInt() - 1;
			int n2 = sc.nextInt() - 1;
			grafo.get(n1).add(n2);
			grafo.get(n2).add(n1);
		}

		sc.close();

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

		camino.add(0);
		int nuevoNodo = 0;

		while (orden[nuevoNodo] == -1) {
			orden[nuevoNodo] = camino.size();
			nuevoNodo =
					getNodoQueNoEsteEnLosUltimosK(grafo, camino, orden,
							minGrado, camino.get(camino.size() - 1));
			camino.add(nuevoNodo);
		}

		camino.subList(0, orden[nuevoNodo]).clear();
		out.println(camino.size());
		
		StringBuilder res = new StringBuilder();
		for (int nodo : camino) {
			res.append(nodo + 1).append(" ");
		}
		res.deleteCharAt(res.length() - 1);
		out.println(res);
	}

	private static Integer getNodoQueNoEsteEnLosUltimosK(
			ArrayList<ArrayList<Integer>> grafo, ArrayList<Integer> camino,
			int[] orden, int minGrado, int nodoActual) {
		int j = -1111;
		for (Integer i : grafo.get(nodoActual)) {
			if (orden[i] == -1 || orden[i] <= camino.size() - minGrado) {
				j = i;
			}
		}
		return j;
	}
}
