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.LinkedList;
import java.util.Scanner;

/**
 * Created with IntelliJ IDEA.
 * Author   : Dylan
 * Date     : 2013-07-22
 * Time     : 15:58
 * Project  : Cycle in Graph
 */
public class Main {
    static Node[] graph;
    static boolean[] visited;
    static int[] depth;
    static int k;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        k = in.nextInt();
        graph = new Node[n + 1];
        for(int i = 1; i <= n; i++) {
            graph[i] = new Node();
        }
        int x, y;
        for(int i = 0; i < m; i++) {
            x = in.nextInt();
            y = in.nextInt();
            graph[x].next.add(y);
            graph[y].next.add(x);
        }
        visited = new boolean[n + 1];
        depth = new int[n + 1];
        if(dfs(1, 1) == 1)
            System.out.println(1);
    }

    static int dfs(int x, int d) {
        visited[x] = true;
        depth[x] = d;
        for(int i : graph[x].next) {
            if(!visited[i]) {
                int t = dfs(i, d + 1);
                if(t > 0) {
                    System.out.print(i + " ");
                    if(t == i) return -1;
                    else return t;
                }
                if(t == -1) return -1;
            } else {
                if(d - depth[i] >= k) {
                    System.out.println(d - depth[i] + 1);
                    return i;
                }
            }
        }
        visited[x] = false;
        return 0;
    }
}

class Node {
    LinkedList<Integer> next;

    Node() {
        next = new LinkedList<Integer>();
    }
}