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 MAXN = 1e5 + 5;
vector<int> G[MAXN];
int N, M, T, K, L, fup[MAXN], dep[MAXN];
bool vis[MAXN];
vector<int> cyc;
bool check;
bool check2;
void init() {
  for (int i = 0; i < N; i++) vis[i] = false;
  check = false;
  check2 = false;
  L = -1;
}
void dfs(int fro, int par, int d) {
  vis[fro] = true;
  dep[fro] = d;
  fup[fro] = d;
  for (int to : G[fro]) {
    if (to == par || check) continue;
    if (vis[to]) {
      fup[fro] = min(fup[fro], dep[to]);
      int len = d - dep[to] + 1;
      if (len >= K + 1) {
        L = to;
        check = true;
        check2 = true;
        cyc.push_back(fro);
      }
    } else {
      dfs(to, fro, d + 1);
      fup[fro] = min(fup[fro], fup[to]);
      if (check2) {
        cyc.push_back(fro);
        if (fro == L) check2 = false;
      }
    }
  }
}
void input() {
  scanf("%d %d %d", &N, &M, &K);
  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);
  }
}
int main() {
  input();
  init();
  dfs(0, -1, 0);
  printf("%ld\n", cyc.size());
  for (int i = 0; i < cyc.size(); i++) {
    printf("%d ", cyc[i] + 1);
  }
  return 0;
}
