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

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(in, out);
        out.close();
    }
}

class TaskD {
    private ArrayList<Integer>[] graph = new ArrayList[100008];
    private boolean[] visited = new boolean[100008];
    private int[] weight = new int[100008];
    private ArrayList<Integer> path = new ArrayList<Integer>();

    public void solve(InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        for (int i = 0; i < n; i++) {
            graph[i] = new ArrayList<Integer>();
            visited[i] = false;
        }
        for (int i = 0; i < m; i++) {
            int x = in.nextInt() - 1;
            int y = in.nextInt() - 1;
            graph[x].add(y);
            graph[y].add(x);
        }
        dfs(0);
        int node = path.get(path.size() - 1);
        int answer = (int) 1e9;
        for (int i = 0; i < graph[node].size(); i++) {
            answer = Math.min(answer, weight[graph[node].get(i)]);
        }
        out.println(path.size() - answer);
        for (int i = answer; i < path.size(); i++) {
            out.printf("%d ", path.get(i) + 1);
        }
        out.println();
    }

    private void dfs(int t) {
        visited[t] = true;
        weight[t] = path.size();
        path.add(t);
        for (int i = 0; i < graph[t].size(); i++) {
            if (!visited[graph[t].get(i)]) {
                dfs(graph[t].get(i));
                return;
            }
        }
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

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

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