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.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Stack;
import java.util.StringTokenizer;

public class D {
    static BufferedReader br = new BufferedReader(new InputStreamReader(
            System.in));
    static StringTokenizer st = new StringTokenizer("");

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

    static String next() throws Exception {
        while (true) {
            if (st.hasMoreTokens()) {
                return st.nextToken();
            }
            String s = br.readLine();
            if (s == null) {
                return null;
            }
            st = new StringTokenizer(s);
        }
    }

    static int k;
    static int[] depth;
    static boolean[] vis;
    static ArrayList<Integer>[] graph;
    static Stack<Integer> stack;
    static boolean found = false;
    static PrintWriter out;

    public static void dfs(int cur, int parent,int d) {
        if(found) return;
        if(vis[cur]){
            if(d-depth[cur]>k){
                found=true;
                out.println(d-depth[cur]);
                while(stack.peek()!=cur){
                    out.print((stack.pop()+1)+" ");
                }
                out.println(stack.pop()+1);
            }
            return;
        }
        vis[cur]=true;
        depth[cur]=d;
        stack.push(cur);
        for(Integer ii:graph[cur]){
            if(ii!=parent){
                dfs(ii,cur,d+1);
            }
        }
        if(found) return;
        stack.pop();
    }

    public static void main(String[] args) throws Exception {
        out = new PrintWriter(System.out);
        int n = nextInt();
        int m = nextInt();
        k = nextInt();
        depth = new int[n];
        vis = new boolean[n];
        graph = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            graph[i] = new ArrayList<Integer>();
        }
        for (int i = 0; i < m; i++) {
            int s = nextInt() - 1;
            int d = nextInt() - 1;
            graph[s].add(d);
            graph[d].add(s);
        }
        stack=new Stack<Integer>();
        for (int i = 0; i < n; i++) {
            if (!vis[i] && !found) {
                dfs(i, -1,0);
            }
        }
        out.flush();
    }
}