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:
import sys
sys.setrecursionlimit(10**9)
N,M=map(int,input().split())

graph=[set() for _ in range(N+1)]
for _ in range(M):
  A,B=map(int,input().split())
  graph[A].add(B)
#print(graph)

visited=[False]*(N+1)
def dfs(path):
  global cycle
  u=path[-1]
  
  visited[u]=True  
  for v in graph[u]:
    if visited[v]:
      cycle=list(path+[v])
      return
    else:
      dfs(path+[v])      
    if cycle:
      return    
  visited[u]=False
  
cycle=[]
for i in range(1,N+1):
  dfs([i])
  if cycle:
    break
else:
  print(-1)
  sys.exit(0)
    
#remove prefix  
for i in range(len(cycle)):
  if cycle[i]==cycle[-1]:
    cycle=cycle[i:]
    break
#print(cycle)

cycle_set=set(cycle)
subgraph=[set() for _ in range(N+1)]
for c in cycle_set:
  for v in graph[c]:
    if v in cycle_set:
      subgraph[c].add(v)
#print(subgraph)    

#visited=[False]*(N+1)
ex_path=[]
def dfs2(path,t):
  global ex_path
  u=path[-1]
  if u==t:
    ex_path=path
    return
  
  for v in graph[u]:
    dfs2(path+[v],t)
    if ex_path:
      return

graph=subgraph
while True:
  for i in range(len(cycle)-1):
    u=cycle[i]
    v=cycle[i+1]
    w=-1
    if len(graph[u])>1:
      for x in graph[u]:
        if x!=v:
          w=x
          break
      break
  else:
    print(len(cycle)-1)
    for i in range(len(cycle)-1):
      print(cycle[i])
    sys.exit(0)
    
  #print(u,v,w)
  #w->u
  dfs2([w],u)
  cycle=ex_path+[w]
  #print(cycle)
  cycle_set=set(cycle)
  subgraph=[set() for _ in range(N+1)]
  for c in cycle_set:
    for v in graph[c]:
      if v in cycle_set:
        subgraph[c].add(v)
        
  graph=subgraph