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.Arrays;
import java.util.Iterator;
import java.util.Scanner;

public class D {

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

      ArrayList<Integer>[] grafo = new ArrayList[n];
      for (int i = 0; i < n; i++)
         grafo[i] = new ArrayList<Integer>();
      for (int i = 0; i < m; i++) {
         int n1 = sc.nextInt() - 1;
         int n2 = sc.nextInt() - 1;
         grafo[n1].add(n2);
         grafo[n2].add(n1);
      }
      sc.close();

      ArrayList<Integer> camino = new ArrayList<Integer>();
      int[] orden = new int[n];
      Arrays.fill(orden, -1);

      int ordActual = -1;
      int nuevoNodo = 0;
      boolean fin = false;

      while (orden[nuevoNodo] == -1 && !fin) {
         ordActual++;
         camino.add(nuevoNodo);
         orden[nuevoNodo] = ordActual;

         for (int i = 0; i < k; i++) {
            int j = grafo[nuevoNodo].get(i);
            if (orden[j] <= ordActual - k || orden[j] == -1) {
               fin = (orden[j] != -1);
               nuevoNodo = j;
               break;
            }
         }
      }

      camino.subList(0, orden[nuevoNodo]).clear();
      System.out.println(camino.size());

      for (Iterator iterator = camino.iterator(); iterator.hasNext();) {
         System.out.print((Integer) iterator.next() + 1);
         if (iterator.hasNext())
            System.out.print(" ");
      }
   }
}