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.ArrayList;
import java.util.Scanner;

// http://codeforces.com/contest/263/problem/D
public class CycleinGraph {

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int m = s.nextInt();
        int k = s.nextInt();
        ArrayList<ArrayList<Integer>> g = new ArrayList<ArrayList<Integer>>();
        for (int i = 0; i <= n; i++) {
            g.add(new ArrayList<Integer>());
        }
        for (int i = 0; i < m; i++) {
            int a = s.nextInt();
            int b = s.nextInt();
            g.get(a).add(b);
            g.get(b).add(a);
        }
        s.close();
        boolean[] visited = new boolean[n + 1];
        boolean[] good = new boolean[n + 1];
        int[] list = new int[n + 1];
        list[0] = 1;
        visited[1] = true;
        int match = dfs(g, list, 0, visited, good, 1, k);
        StringBuilder sb = new StringBuilder();
        int pos = 0;
        for (; pos <= n; pos++) {
            if (list[pos] == match) {
                break;
            }
        }
        int cnt = 0;
        for (; pos <= n && list[pos] > 0; pos++, cnt++) {
            sb.append(list[pos] + " ");
        }
        System.out.println(cnt);
        System.out.println(sb);
    }

    static int dfs(ArrayList<ArrayList<Integer>> g, int[] list, int pos, boolean[] visited,
            boolean[] good, int cur, int needed) {
        for (Integer next : g.get(cur)) {
            if (good[next]) {
                return next;
            }
            if (!visited[next]) {
                if (pos - needed + 1 >= 0) {
                    good[list[pos - needed + 1]] = true;
                }
                visited[next] = true;
                list[pos + 1] = next;
                return dfs(g, list, pos + 1, visited, good, next, needed);
            }
        }
        return -1;
    }

}
