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.util.ArrayList;
import java.util.LinkedList;
import java.util.List;
import java.util.StringTokenizer;

public class Task263D {
    static int n, m, k;
    static boolean[] visited;
    static List<List<Integer>> g;
    static List<Integer> ans = new ArrayList<>();
    static boolean[] inProgress = new boolean[100005];
    static int[] inProgressPathIndex = new int[100005];

    public static void main(String[] args) throws IOException {
        InputScanner is = new InputScanner();

        n = is.nextInt(); // nodes;
        m = is.nextInt(); // edges
        k = is.nextInt(); // cycle

        visited = new boolean[n + 1];
        g = new ArrayList<>(n + 1);
        for (int i = 0; i <= n; i++) g.add(new ArrayList<>());

        int a = 0, b = 0;
        for (int i = 0; i < m; i++) {
            a = is.nextInt();
            b = is.nextInt();
            g.get(a).add(b);
            g.get(b).add(a);
        }
        dfsVisit(a, new LinkedList<>());

        System.out.println(ans.size());
        StringBuffer sb = new StringBuffer();
        for (Integer j : ans) sb.append(j + " ");
        System.out.println(sb);
    }

    static void dfsVisit(int n, LinkedList<Integer> path) {
        path.addLast(n);
        visited[n] = true;
        inProgress[n] = true;
        inProgressPathIndex[n] = path.size()-1;
        for (Integer i : g.get(n)) {
            if (!visited[i]) dfsVisit(i, path);
            else if (inProgress[i] && path.size() - inProgressPathIndex[i] > k && ans.isEmpty()) {
                for (int j = inProgressPathIndex[i]; j < path.size(); j++) ans.add(path.get(j));
            }
        }
        inProgress[n] = false;
        path.removeLast();
    }

    static class InputScanner {
        BufferedReader br;
        StringTokenizer st;

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

        public String next() throws IOException {
            if (st == null || !st.hasMoreTokens()) {
                String line = br.readLine();
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            String next = next();
            return Integer.parseInt(next);
        }

        public long nextLong() throws IOException {
            String next = next();
            return Long.parseLong(next);
        }
    }
}

