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.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class D3 {

	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();

		boolean estaEnUltimosK[] = new boolean[n];
		boolean estaEnElCamino[] = new boolean[n];

		for (int i = 0; i < estaEnUltimosK.length; i++) {
			estaEnUltimosK[i] = false;
		}

		Queue<Integer> ultimosK = new LinkedList<Integer>();

		ArrayList<Integer> camino = new ArrayList<Integer>();
		camino.add(0);
		estaEnUltimosK[0] = true;
		estaEnElCamino[0] = true;
		ultimosK.add(0);

		int nuevoNodo;

		while (true) {
			int i = 0;
			nuevoNodo = grafo[camino.get(camino.size() - 1)].get(i);

			while (estaEnUltimosK[nuevoNodo]) {
				i++;
				nuevoNodo = grafo[camino.get(camino.size() - 1)].get(i);
			}

			if (estaEnElCamino[nuevoNodo]) {
				break;
			} else {
				camino.add(nuevoNodo);
				if (ultimosK.size() == k) {
					estaEnUltimosK[ultimosK.poll()] = false;
				}
				ultimosK.add(nuevoNodo);
				estaEnUltimosK[nuevoNodo] = true;
				estaEnElCamino[nuevoNodo] = true;
			}
		}

		int i = 0;
		while (camino.get(i) != nuevoNodo)
			i++;

		System.out.println(camino.size() - i);

		while (i < camino.size()) {
			System.out.print(camino.get(i) + 1);
			i++;
			if (i != camino.size())
				System.out.print(" ");
		}

		System.out.println("");
	}

}
