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.io.*;
import java.util.*;
import java.text.*;
import java.math.*;

public class Solution {
	private static Scanner input = new Scanner(System.in);
	private static int nodes, edges, minDegree;
	private static ArrayList<ArrayList<Integer>> neighbors;
	private static boolean visited[];
	private static ArrayList<Integer> path;
	
    public static void main(String[] args) {
    	nodes = input.nextInt();
    	edges = input.nextInt();
    	minDegree = input.nextInt();
    	neighbors = initializeArrayListMatrix(nodes + 1);
    	visited = new boolean[nodes + 1];
    	path = new ArrayList<Integer>(nodes + 1);
    	
    	for (int i = 0; i < edges; i++) {
    		int node1 = input.nextInt();
    		int node2 = input.nextInt();
    		
    		neighbors.get(node1).add(node2);
    		neighbors.get(node2).add(node1);
    	}
    	
    	for (int i = 1; i <= nodes; i++) {
    		//System.out.println(i + " " + Arrays.toString(neighbors.get(i).toArray()));
    	}
    	findPath(1);
    	//System.out.println("Longest path: " + Arrays.toString(path.toArray()));
    	int lastNode = path.get(path.size() - 1);
    	int firstNeighborIndex = findFirstNeighbor(lastNode);
    	//System.out.println("First neighbor index: " + firstNeighborIndex);
    	printPathInterval(firstNeighborIndex, path.size() - 1);
    }
    
    private static void findPath(int currentNode) {
    	visited[currentNode] = true;

    	path.add(currentNode);
    	
    	//System.out.println("Current node: " + currentNode);
    	for (int i = 0; i < neighbors.get(currentNode).size(); i++) {
    		int neighbor = neighbors.get(currentNode).get(i);
    		//System.out.print(neighbor + " ");
    		
    		if (!visited[neighbor]) {
    			findPath(neighbor);
    			return;
    		}
    	}
    	//System.out.println();
    }
    
    private static int findFirstNeighbor(int node) {
    	boolean isNodeNeighbor[] = new boolean[nodes + 1];
    	for (int i = 0; i < neighbors.get(node).size(); i++) {
    		int neighbor = neighbors.get(node).get(i);
    		isNodeNeighbor[neighbor] = true;
    	}
    	
    	for (int i = 0; i < path.size(); i++) {
    		if (isNodeNeighbor[path.get(i)])
    			return i;
    	}
    	
    	return -1;
    }
    
    private static void printPathInterval(int fromIndex, int toIndex) {
    	System.out.println(toIndex - fromIndex + 1);
    	
    	for (int i = fromIndex; i <= toIndex; i++) {
    		System.out.print(path.get(i) + " ");
    	}
    }
    
    private static ArrayList<ArrayList<Integer>> initializeArrayListMatrix(int size) {
    	ArrayList<ArrayList<Integer>> res = new ArrayList<ArrayList<Integer>>();
    	
    	for (int i = 0; i <= size; i++)
    		res.add(new ArrayList<Integer>());
    	
    	return res;
    }
}