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>
using namespace std;
vector<int> edges[100005];
set<int> vert;
bool visted[100005];
int k, printed;
int dfs(int i, int d, int start) {
  visted[i] = true;
  int l = edges[i].size();
  for (int j = 0; j < l; j++) {
    if (d >= k + 1 && edges[i][j] == start) {
      printf("%d\n%d ", d, i);
      return 1;
    }
    if (visted[edges[i][j]] == true) continue;
    if (dfs(edges[i][j], d + 1, start) == 1) {
      printf("%d ", i);
      printed = 1;
      return 1;
    }
  }
  if (printed) return 1;
  return 0;
}
int main() {
  set<int>::iterator it;
  int n, m, temp, temp1;
  scanf("%d%d%d", &n, &m, &k);
  for (int i = 0; i < m; i++) {
    scanf("%d%d", &temp, &temp1);
    vert.insert(temp);
    vert.insert(temp1);
    edges[temp1].push_back(temp);
    edges[temp].push_back(temp1);
  }
  it = vert.begin();
  for (int i = 0; i < n; i++) {
    memset(visted, false, sizeof(visted));
    printed = 0;
    if (dfs(*it, 1, *it)) {
      printf("\n");
      return 0;
    }
    it++;
  }
  return 0;
}
