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;
const int N = 100000;
int n, m, k;
vector<int> adj[N];
int stkIdx[N];
vector<int> stk;
bool dfs(int u) {
  if (stkIdx[u] != -1) {
    if (stk.size() - stkIdx[u] > k) {
      cout << stk.size() - stkIdx[u] << endl;
      for (cout << stk.back() + 1; stk.back() != u;
           stk.pop_back(), cout << " " << stk.back() + 1)
        ;
      cout << endl;
      return true;
    }
    return false;
  }
  stkIdx[u] = stk.size();
  stk.push_back(u);
  for (int i = 0; i < (int)adj[u].size(); ++i) {
    if (dfs(adj[u][i])) return true;
  }
  stk.pop_back();
  return false;
}
int main() {
  scanf("%d %d %d", &n, &m, &k);
  while (m--) {
    int a, b;
    scanf("%d %d", &a, &b);
    --a;
    --b;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  memset(stkIdx, -1, sizeof stkIdx);
  dfs(0);
  return 0;
}
