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 
#include <bits/stdc++.h>
int n, m, k, first[100001], edge[200001], next[200001], stk[100001], ans,
    a[100001];
bool solve, hash[100001], hot[100001];
void search(int now, int deep) {
  int i;
  hash[now] = 1;
  a[deep] = now;
  if (hot[now] && deep >= k + 1) {
    solve = 1;
    ans = deep;
    return;
  }
  for (i = first[now]; i; i = next[i]) {
    if (hash[edge[i]]) continue;
    search(edge[i], deep + 1);
    if (solve) break;
  }
  hash[now] = 0;
  return;
}
int main() {
  int i;
  scanf("%d%d%d", &n, &m, &k);
  for (i = 1; i <= m; i++) {
    scanf("%d%d", &edge[(i << 1) - 1], &edge[i << 1]);
    if (first[edge[(i << 1) - 1]] == 0)
      first[edge[(i << 1) - 1]] = i << 1;
    else
      next[stk[edge[(i << 1) - 1]]] = i << 1;
    stk[edge[(i << 1) - 1]] = i << 1;
    if (first[edge[i << 1]] == 0)
      first[edge[i << 1]] = (i << 1) - 1;
    else
      next[stk[edge[i << 1]]] = (i << 1) - 1;
    stk[edge[i << 1]] = (i << 1) - 1;
  }
  for (i = first[1]; i; i = next[i]) hot[edge[i]] = 1;
  search(1, 1);
  printf("%d\n", ans);
  for (i = 1; i <= ans; i++) printf("%d ", a[i]);
  printf("\n");
  return 0;
}
