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.*;
import java.lang.*;
import java.io.*;

public class Solution {
    static int N = 100005;
    static Map<Integer, List<Integer>> map = new HashMap<>();
    static int[] distance = new int[N];
    static List<Integer> list = new ArrayList<>();
    static int n, m, k;
    static boolean foundCycle = false;
    public static void main(String[] args) throws java.lang.Exception {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        sc = new FastReader();
        int test = 1;
        for (int t = 0; t < test; t++) {
            solve();
        }
        out.close();
    }

    private static void solve() {
        map.clear();
        list.clear();
        n = sc.nextInt();
        m = sc.nextInt();
        k = sc.nextInt();
        for (int i = 0; i <= n; i++) {
            map.put(i, new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            int u = sc.nextInt();
            int v = sc.nextInt();
            map.get(u).add(v);
            map.get(v).add(u);
        }
        dfs(1);
    }

    private static void dfs(int node) {
        if (foundCycle) {
            return;
        }
        list.add(node);
        distance[node] = list.size();
        for (int adj : map.get(node)) {
            if (distance[adj] == 0) {
                dfs(adj);
            }else if (!foundCycle && distance[node] - distance[adj] + 1 >= k + 1 && distance[node] - distance[adj] + 1 > 2) {
                // print the cycle
                out.println(distance[node] - distance[adj] + 1);
                for (int i = distance[adj]; i <= distance[node]; i++) {
                    out.print(list.get(i - 1) + " ");
                }
                out.println();
                foundCycle = true;
                return;
            }
        }
        list.remove(list.size() - 1);

    }

    public static FastReader sc;
    public static PrintWriter out;
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}