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 INF = 1000 * 1000 * 1000;
const long long INF64 = ((long long)INF) * INF;
const double PI = acos(-1.0);
template <typename T>
inline T sqr(T x) {
  return x * x;
}
int n, m, k, d;
vector<vector<int> > g;
int st[100500], r[100500], y[100500];
bool used[100500];
void dfs(int u) {
  used[u] = true;
  st[d] = u;
  r[u] = d;
  ++d;
  int sz = g[u].size();
  for (int i = 0; i < sz; ++i) {
    int v = g[u][i];
    if (used[v]) {
      if (d - r[v] > k) {
        cout << d - r[v] << endl;
        for (int i = r[v]; i < d; ++i) printf("%d ", st[i] + 1);
        exit(0);
      }
    } else
      dfs(v);
  }
  --d;
}
int main() {
  srand(time(0));
  scanf("%d %d %d", &n, &m, &k);
  g.resize(n);
  for (int i = 0; i < m; ++i) {
    int u, v;
    scanf("%d %d", &u, &v);
    --u;
    --v;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  for (int i = 0; i < n; ++i) random_shuffle(g[i].begin(), g[i].end());
  for (int i = 0; i < n; ++i) y[i] = i;
  random_shuffle(y, y + n);
  for (int i = 0; i < n; ++i)
    if (!used[y[i]]) dfs(y[i]);
  for (;;)
    ;
  return 0;
}
