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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.StringTokenizer;


public class round161D {
    static BufferedReader br = new BufferedReader(new InputStreamReader(
            System.in));
    static StringTokenizer st = new StringTokenizer("");
    static int nextInt() throws Exception {
        return Integer.parseInt(next());
    }
    static String next() throws Exception {
        while (true) {
            if (st.hasMoreTokens()) {
                return st.nextToken();
            }
            String s = br.readLine();
            if (s == null) {
                return null;
            }
            st = new StringTokenizer(s);
        }
    }
    static int n, m ,k;
    static ArrayList<Integer> [] graph;
    static ArrayList<Integer> path = new ArrayList<Integer>();
    static boolean [] vis;
    static boolean done = false;
    static int last_node = -1;
    public static void dfs(int idx){        
        if(vis[idx] || done)
            return;
        vis[idx] = true;
        path.add(idx);
        boolean enter = false;
        for(int i = 0 ; i < graph[idx].size() ; ++i){
            int nxt = graph[idx].get(i);
            if(!vis[nxt]){
                enter = true;
                dfs(nxt);
            }
        }
        if(!enter){
            done = true;
            last_node = idx;
        }
    }
    public static void main(String[] args)throws Exception {
        n = nextInt();
        m = nextInt();
        k = nextInt();
        graph = new ArrayList [n + 1];
        vis = new boolean [n + 1];
        for(int i = 0 ; i < n + 1 ; ++i)
            graph[i] = new ArrayList<Integer>();
        for(int i = 0 ; i < m ; ++i){
            int a = nextInt();
            int b = nextInt();
            graph[a].add(b);
            graph[b].add(a);
        }
        dfs(1);
        HashSet<Integer> set = new HashSet<Integer>();
        for(int i = 0 ; i < graph[last_node].size() ; ++i)
            set.add(graph[last_node].get(i));
        boolean start = false;
        int count = 0;
        ArrayList<Integer> cycle = new ArrayList<Integer>();
        for(int i = 0 ; i < path.size() ; ++i){
            if(start){
                ++count;
                cycle.add(path.get(i));
            }
            if(set.contains(path.get(i)) &&  !start){
                start = true;
                count++;
                cycle.add(path.get(i));
            }
        }
        System.out.println(count);
        for(Integer node : cycle)
            System.out.print(node + " ");
    }
}
