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:
from collections import deque
N,M=map(int,input().split())
G=[[] for i in range(N)]
for i in range(M):
	a,b=map(int,input().split())
	G[a-1].append(b-1)
deg=[0 for i in range(N)]
for i in range(N):
	for p in G[i]:
		deg[p]+=1
q=deque(i for i in range(N) if deg[i]==0)
res=[]
while q:
	u=q.popleft()
	res.append(u)
	for v in G[u]:
		deg[v]-=1
		if deg[v]==0:
			q.append(v)
if len(res)==N:
	print(-1)
	exit()
X={i for i in range(N)}
for st in range(N):
	pre=[-1 for i in range(N)]
	q=deque([st])
	flag=0
	while(q):
		r=q.popleft()
		for p in G[r]:
			if pre[p]==-1:
				pre[p]=r
				q.append(p)
			if pre[st]!=-1:
				Y={st}
				tmp=pre[st]
				while(tmp!=st):
					Y.add(tmp)
					tmp=pre[tmp]
				if len(Y)<len(X):
					X={i for i in Y}
				flag=1
				break
		if flag:
			break
print(len(X))
for i in X:
	print(i+1)