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.*;
import java.util.*;

public class Main {

    static BufferedReader br;
    static PrintWriter out;
    static StringTokenizer st;
    
    static int k;
    static ArrayList<Integer>[] g;
    static boolean[] used;
    static int[] d;
    static int[] p;
    
    static boolean dfs(int v, int depth){
        used[v] = true; 
        d[v] = depth;
        for(int i = 0; i < g[v].size(); i++){
            int to = g[v].get(i);
            if(!used[to]){
                p[to] = v;
                if(dfs(to, depth + 1)){
                    return true;
                }
            }else{
                int cl = Math.abs(d[v] - d[to]) + 1;
                if(cl >= k + 1){
                    p[to] = v;
                    out.println(cl);
                    for(int u = v; u != to; u = p[u]){
                        out.print((u + 1) + " ");
                    }
                    out.print((to + 1) + " ");
                    return true;
                }
            }
        }
        return false;
    }
    
    static void solve() throws Exception {
        int n = nextInt();
        int m = nextInt();
        k = nextInt();
        g = new ArrayList[n];
        p = new int[n];
        d = new int[n];
        used = new boolean[n];
        for(int i = 0; i < n; i++){
            g[i] = new ArrayList<Integer>();
        }
        for(int i = 0; i < m; i++){
            int u = nextInt() - 1;
            int v = nextInt() - 1;
            g[u].add(v);
            g[v].add(u);
        }
        for(int i = 0; i < n; i++){
            if(!used[i]){
                if(dfs(i, 0)){
                    return;
                }
            }
        }
    }

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

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

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

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

    public static void main(String[] args) {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new PrintStream(System.out));
            solve();
            out.close();
            br.close();
        } catch (Throwable t) {
            t.printStackTrace();
        }
    }

}