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 codeforces
{
    static int[] d;
    static int[] a;
    static List[] g;
    static boolean done = false;

    static void dfs(int v, int x, int k)
    {
        if (done)
        {
            return;
        }
        if (d[v] > 0)
        {
            if (x - d[v] > k)
            {
                System.out.println(x - d[v]);
                for (int i = d[v]; i < x; i ++)
                {
                    System.out.print(a[i] + " ");
                }
                done = true;
            }
            return;
        }
        d[v] = x;
        for (int i = 0; i < g[v].size(); i ++)
        {
            int cur = (Integer)g[v].get(i);
            a[x + 1] = cur;
            dfs(cur, x + 1, k);
        }
    }

    public static void main(String[] args) throws IOException
    {
        BufferedReader rr = new BufferedReader(new InputStreamReader(System.in));
        String[] s = rr.readLine().split(" ");
        int n = Integer.parseInt(s[0]);
        int m = Integer.parseInt(s[1]);
        int k = Integer.parseInt(s[2]);
        g = new ArrayList[n + 1];
        a = new int[n + 2];
        d = new int[n + 1];
        for (int i = 0; i < n + 1; i ++)
        {
            g[i] = new ArrayList();
        }
        for (int i = 0; i < m; i ++)
        {
            s = rr.readLine().split(" ");
            int x = Integer.parseInt(s[0]);
            int y = Integer.parseInt(s[1]);
            g[x].add(y);
            g[y].add(x);
        }
        Arrays.fill(a, 0);
        Arrays.fill(d, 0);
        for (int i = 1; i < n + 1; i ++)
        {
            if (d[i] == 0)
            {
                a[1] = i;
                dfs(i, 1, k);
            }
        }
    }
}