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;
using namespace std;
void chekarre(int* arr, int n) {
  cout << "[";
  for (int i = 0; i < n; i++) cout << arr[i] << " ";
  cout << "]" << endl;
}
int n, m, x, y, k;
vector<int> vec[100009];
int done = 0;
vector<int> ans;
stack<int> s;
int flag[100009] = {0};
int dfs(int x, int len) {
  for (int i = 0; i < vec[x].size(); i++) {
    if (flag[vec[x][i]] == 0) {
      flag[vec[x][i]] = len;
      s.push(vec[x][i]);
      dfs(vec[x][i], len + 1);
    } else {
      if (flag[x] - flag[vec[x][i]] >= k) {
        cout << flag[x] - flag[vec[x][i]] + 1 << endl;
        while (s.top() != vec[x][i]) {
          cout << s.top() << " ";
          s.pop();
        }
        cout << vec[x][i];
        exit(0);
      }
    }
  }
}
int solve() {
  dfs(1, 2);
  cout << "-1";
  return 1;
}
bool input() {
  scanf("%d", &n);
  scanf("%d", &m);
  scanf("%d", &k);
  for (int i = 0; i < m; i++) {
    scanf("%d", &x);
    scanf("%d", &y);
    vec[x].push_back(y);
    vec[y].push_back(x);
  }
  return true;
}
int main() {
  int T = 1;
  for (int testnum = 1; testnum <= T; testnum++) {
    if (!input()) break;
    solve();
  }
  return 0;
}
