Problem: Given is a directed graph G with N vertices and M edges.
The vertices are numbered 1 to N, and the i-th edge is directed from Vertex A_i to Vertex B_i.
It is guaranteed that the graph contains no self-loops or multiple edges.

Determine whether there exists an induced subgraph (see Notes) of G such that the in-degree and out-degree of every vertex are both 1. If the answer is yes, show one such subgraph.
Here the null graph is not considered as a subgraph.

Constraints

* 1 \leq N \leq 1000
* 0 \leq M \leq 2000
* 1 \leq A_i,B_i \leq N
* A_i \neq B_i
* All pairs (A_i, B_i) are distinct.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
A_1 B_1
A_2 B_2
:
A_M B_M


Output

If there is no induced subgraph of G that satisfies the condition, print `-1`. Otherwise, print an induced subgraph of G that satisfies the condition, in the following format:


K
v_1
v_2
:
v_K


This represents the induced subgraph of G with K vertices whose vertex set is \\{v_1, v_2, \ldots, v_K\\}. (The order of v_1, v_2, \ldots, v_K does not matter.) If there are multiple subgraphs of G that satisfy the condition, printing any of them is accepted.

Examples

Input

4 5
1 2
2 3
2 4
4 1
4 3


Output

3
1
2
4


Input

4 5
1 2
2 3
2 4
1 4
4 3


Output

-1


Input

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2


Output

4
2
3
4
5

Solution (in PYTHON3):

Solution:
# -*- Coding: utf-8 -*-
INF = 1001001001
n, m = map(int, input().split())
 
def bfs(sv, to_list):
  dist = [INF for i in range(n)]
  hist = [-1 for i in range(n)]
  q = []
  dist[sv] = 0
  q.append(sv)
  while len(q) > 0:
    v = q[0]
    del q[0]
    for j in to_list[v]:
      if dist[j] != INF:
        continue
      hist[j] = v
      dist[j] = dist[v] + 1
      q.append(j)
  min_cycle = INF
  min_hist = -1
  for i in range(n):
    if i == sv:
      continue
    for j in to[i]:
      if j == sv:
        if min_cycle > dist[i]:
          min_cycle = dist[i]
          min_hist = i
  res = []
  temp_v = min_hist
  if min_cycle < INF:
    while temp_v > -1:
      res.append(temp_v)
      temp_v = hist[temp_v]
  else:
    res = [1 for i in range(n+1)]
  return res
    
 
to = [[] for i in range(m)]
for i in range(m):
  a, b = map(int, input().split())
  to[a-1].append(b-1)
if len(to) == 0:
  print(-1)
else:  
  c = [bfs(i, to) for i in range(n)]
  ans = [1 for i in range(n+1)]
  for i in range(n):
    if len(ans) > len(c[i]):
      ans = c[i]
  if len(ans) == n + 1:
    print(-1)
  else:
    print(len(ans))
    for v in ans[::-1]:
      print(v+1)