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.*;

public class Main {

    static List<Integer> a[];
    static boolean[] marked;
    static int k, count = 0, start = -1, edgeTo[], distTo[];
    static List<Integer> list;
    static int size = 1 ;
    static StringBuilder sb = new StringBuilder();
    static void dfs(int cur, int prev){
        if(size>1)
            return;
        marked[cur] = true;
        if(prev == -1)
            distTo[cur] = 0;
        else
            distTo[cur] = distTo[prev] + 1;
        for (Integer next : a[cur]) {
            if(size!=1)
                return;
            if(marked[next]){
                if(prev != next){
                    if(distTo[cur] - distTo[next] >= k){
                        for (int x = cur; x != next; x = edgeTo[x]) {
                            size++;
                            sb.append((x+1)+" ");
                        }
                        sb.append(next+1);
                        return ;
                    }
                }
            }
            else{
                edgeTo[next] = cur;
                dfs(next, cur);
            }
        }
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        k = in.nextInt();

        a = new ArrayList[n];
        edgeTo = new int[n];
        distTo = new int[n];
        marked = new boolean[n];
        for (int i = 0; i < n; i++) {
            a[i] = new ArrayList<>();
        }

        for (int i = 0; i < m; i++) {
            int x = in.nextInt();
            int y = in.nextInt();
            a[x - 1].add(y - 1);
            a[y - 1].add(x - 1);
        }

        dfs(0,  -1);
        System.out.println(size);
        System.out.println(sb);
    }
}