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 collections

n,m=map(int,input().split())
g=[[] for _ in range(n+1)]
cand1=set()
cand2=set()
for _ in range(m):
  a,b=map(int,input().split())
  g[a].append(b)
  cand1.add(a)
  cand2.add(b)
cand=cand1&cand2
ans=-1
for i in range(1,n+1):
  if i not in cand:
    continue
  else:
    q=collections.deque()
    q.append((i,[i]))
    checked=[0]*(n+1)
    while len(q)!=0:
      v,chain=q.popleft()
      if v==i and len(chain)!=1:
        ans=chain[:-1]
      for u in g[v]:
        if u not in cand:
          continue
        elif checked[u]==0:
          checked[u]=1
          q.append((u,chain+[u]))
    cand.discard(i)
if ans==-1:
  print(ans)
else:
  print(len(ans))
  for v in ans:
    print(v)