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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class D263 {
    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter pw;

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

    static int nextInt() {
        return Integer.parseInt(nextToken());
    }

    static long nextLong() {
        return Long.parseLong(nextToken());
    }

    static String nextLine() throws IOException {
        return br.readLine();
    }

    static char nextChar() throws IOException {
        return (char) br.read();
    }

    public static void main(String[] args) {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        run();
        pw.close();
    }

    static ArrayList<Integer>[] graf;
    static ArrayList<Integer> ans;

    private static void run() {
        int n = nextInt();
        int m = nextInt();
        k = nextInt();
        graf = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            graf[i] = new ArrayList<>();
        }
        for (int i = 0; i < m; i++) {
            int x = nextInt() - 1;
            int y = nextInt() - 1;
            graf[x].add(y);
            graf[y].add(x);
        }
        used = new boolean[n];
        ans = new ArrayList<>();
        times = new int[n];
        DFS(0, 0);
        ans.add(first);
        pw.println(ans.size());
        for (int i = 0; i < ans.size(); i++) {
            pw.print(ans.get(i) + 1);
            pw.print(" ");
        }
    }

    static boolean[] used;
    static int k;
    static boolean tr = true;
    static int first = -1;
    static int[] times;

    private static void DFS(int v, int kk) {
        used[v] = true;
        times[v] = kk;
        for (int i = 0; i < graf[v].size(); i++) {
            if (!used[graf[v].get(i)]) {
                DFS(graf[v].get(i), kk + 1);
                if (tr) ans.add(graf[v].get(i));
                if (v == first) tr = false;
                k--;
                break;
            }
        }
        if (first == -1) {
            for (int i = 0; i < graf[v].size(); i++) {
                if (times[v] - times[graf[v].get(i)] >= k) {
                    first = graf[v].get(i);
                    break;
                }
            }
        }
    }
}
