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.List;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.ArrayList;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskD {
    int n, m, k;
    List<Integer>[] g;
    List<Integer> path;
    int[] dist;
    List<Integer> answer;

    boolean rec(int v, int depth) {
        dist[v] = depth;
        path.add(v);
        for (int v2 : g[v])
            if (dist[v2] == -1) {
                if (rec(v2, depth + 1))
                    return true;
            } else if (depth - dist[v2] >= k) {
                for (int i = dist[v2]; i <= depth; i++)
                    answer.add(path.get(i));
                return true;
            }
        path.remove(path.size() - 1);
        return false;
    }

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        n = in.nextInt();
        m = in.nextInt();
        k = in.nextInt();
        g = new ArrayList[n];
        for (int i = 0; i < n; i++)
            g[i] = new ArrayList<Integer>();
        for (int i = 0; i < m; i++) {
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            g[a].add(b);
            g[b].add(a);
        }
        dist = new int[n];
        Arrays.fill(dist, -1);
        path = new ArrayList<Integer>();
        answer = new ArrayList<Integer>();
        for (int i = 0; i < n; i++)
            if (rec(i, 0)) {
                out.println(answer.size());
                for (int x : answer)
                    out.print((x + 1) + " ");
                out.println();
                return;
            }
        throw new RuntimeException();
    }
}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }

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

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
}