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;
void Get(int &Ret) {
  char CH;
  bool FL = 0;
  for (; CH = getchar(), CH < '0' || CH > '9';)
    if (CH == '-') FL = 1;
  for (Ret = CH - '0'; CH = getchar(), CH >= '0' && CH <= '9';
       Ret = Ret * 10 + CH - '0')
    ;
  FL && (Ret = -Ret);
}
void Get(long long &Ret) {
  char CH;
  bool FL = 0;
  for (; CH = getchar(), CH < '0' || CH > '9';)
    if (CH == '-') FL = 1;
  for (Ret = CH - '0'; CH = getchar(), CH >= '0' && CH <= '9';
       Ret = Ret * 10 + CH - '0')
    ;
  FL && (Ret = -Ret);
}
const int MAXN = 220000;
struct node {
  int v;
  node *next;
};
node Edge[MAXN * 2];
node *Ecnt = &Edge[0];
node *adj[MAXN];
inline void addedge(int u, int v) {
  node *p = ++Ecnt;
  p->v = v;
  p->next = adj[u];
  adj[u] = p;
}
int n, m, cnt;
void Read() {
  Get(n);
  Get(m);
  Get(cnt);
  int i;
  for (i = 1; i <= m; i++) {
    int u, v;
    Get(u);
    Get(v);
    addedge(u, v);
    addedge(v, u);
  }
  for (i = 1; i <= n; i++) addedge(0, i);
}
bool vis[MAXN];
int path[MAXN];
int dep[MAXN];
void Print(int a, int d) {
  int i;
  printf("%d\n", d - a + 1);
  for (i = a; i < d; i++) printf("%d ", path[i]);
  printf("%d\n", path[d]);
}
void DFS(int u, int d) {
  path[d] = u;
  vis[u] = true;
  dep[u] = d;
  vector<int> rec;
  for (node *p = adj[u]; p; p = p->next) {
    if (vis[p->v] == false)
      rec.push_back(p->v);
    else if (d - dep[p->v] + 1 >= cnt + 1) {
      Print(dep[p->v], d);
      exit(0);
    }
  }
  int len = rec.size();
  for (int i = 0; i < len; i++) DFS(rec[i], d + 1);
  vis[u] = false;
}
int main() {
  Read();
  DFS(0, 0);
  return 0;
}
