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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class D {
    static int n, m, k;
    static int[] d;
    static int[] p;
    static ArrayList<Integer>[] adj;

    public static void main(String[] args) throws IOException {
        InputReader in = new InputReader();
        n = in.nextInt();
        m = in.nextInt();
        k = in.nextInt();
        d = new int[n];
        p = new int[n];
        for(int i = 0 ; i < n;i++)
            p[i]=i;
        Arrays.fill(d, -1);
        adj = new ArrayList[n];
        for (int i = 0; i < n; i++)
            adj[i] = new ArrayList<Integer>();
        for (int i = 0; i < m; i++) {
            int a = in.nextInt()-1;
            int b = in.nextInt()-1;
            adj[a].add(b);
            adj[b].add(a);
        }
        for (int i = 0; i < n; i++)
            if (d[i] == -1&&!done)
                dfs(i, 1,-1);
    }
    static boolean done = false;
    public static void dfs(int i, int dist,int pr) {
        if(done)return;
        if (d[i] == -1) {
            d[i] = dist;
            p[i]=pr;
            for(int nxt : adj[i]){
                if(nxt==p[i])continue;
                dfs(nxt,dist+1,i);
            }
        }else{
            int tot = dist-d[i];
            if(tot>=k+1){
                p[i]=pr;
                StringBuilder sb = new StringBuilder();
                System.out.println(tot);
                int cur = i;
                while(tot>0){
                    sb.append((cur+1)+" ");
                    cur = p[cur];
                    tot--;
                }
                System.out.println(sb);
                done = true;
            }
        }
    }

    static class InputReader {
        BufferedReader in;
        StringTokenizer st;

        public InputReader() throws IOException {
            in = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer(in.readLine());
        }

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

        public String next() throws IOException {
            while (!st.hasMoreElements())
                st = new StringTokenizer(in.readLine());
            return st.nextToken();
        }

        public int nextInt() throws NumberFormatException, IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws NumberFormatException, IOException {
            return Long.parseLong(next());
        }
    }
}