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 
//package codeforces.contests.cf161;

import java.io.*;
import java.util.ArrayList;
import java.util.List;

public class ProblemD {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(new OutputStreamWriter(System.out));

    int[] readInts() throws IOException {
        String[] strings = reader.readLine().split(" ");
        int[] ints = new int[strings.length];
        for(int i = 0; i < ints.length; i++) {
            ints[i] = Integer.parseInt(strings[i]);
        }
        return ints;
    }

    long[] readLongs() throws IOException {
        String[] strings = reader.readLine().split(" ");
        long[] longs = new long[strings.length];
        for(int i = 0; i < longs.length; i++) {
            longs[i] = Long.parseLong(strings[i]);
        }
        return longs;
    }

    void solve() throws IOException {
        int[] tt = readInts();
        int n = tt[0];
        int m = tt[1];
        int k = tt[2];
        List<ArrayList<Integer>> g = new ArrayList<ArrayList<Integer>>(n + 1);
        for(int i = 0; i <= n; i++) {
            g.add(new ArrayList<Integer>());
        }
        for(int i = 0; i < m; i++) {
            tt = readInts();
            int a = tt[0];
            int b = tt[1];
            g.get(a).add(b);
            g.get(b).add(a);
        }
        int[] time = new int[n + 1];
        int[] seq = new int[n + 1];
        for(int i = 1, t = 1; ; t++) {
            time[i] = t;
            seq[t] = i;
            int u = g.get(i).get(0);
            for(int v: g.get(i)) {
                if(time[v] < time[u]) {
                    u = v;
                }
            }
            if(time[u] == 0) {
                i = u;
                continue;
            }
            writer.println(t - time[u] + 1);
            for(int j = time[u]; j <= t; j++) {
                writer.printf("%d ", seq[j]);
            }
            break;
        }
        writer.flush();
    }

    public static void main(String[] args) throws IOException {
        new ProblemD().solve();
    }
}
