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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    int N;
    List<Integer>[] adj;
    int K, M;

    void run(FastScanner in, PrintWriter out) {
        N = in.nextInt();
        M = in.nextInt();
        K = in.nextInt();
        adj = new List[N+1];
        pre = new int[N+1];
        for (int i = 1; i <= N; i++) adj[i] = new ArrayList<>();

        while (M-- > 0) {
            int u = in.nextInt();
            int v = in.nextInt();
            adj[u].add(v);
            adj[v].add(u);
        }

        dfs(1, -1);
        out.println(ret.size());
        for (int num : ret) out.print(num + " ");
        out.println();
    }

    int[] pre;
    int preNum = 1;
    LinkedList<Integer> ret = new LinkedList<>();

    int dfs(int u, int p) {
        if (pre[u] != 0) return -1;
        pre[u] = preNum++;

        for (int v : adj[u]) {
            if (v == p) continue;

            int d = dfs(v, u);
            if (d != -1) {
                if (d <= pre[u]) ret.add(u);
                return d;
            }

            if (pre[u]-pre[v]+1 > K) {
                ret.add(u);
                return pre[v];
            }
        }
        return -1;
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

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

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

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}
