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
input = sys.stdin.buffer.readline

#sys.setrecursionlimit(10**9)
#from functools import lru_cache

def RD(): return input().rstrip().decode()
def II(): return int(input())
def FI(): return int(input())
def MI(): return map(int,input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int,input().split()))
def LF(): return list(map(float,input().split()))
def TI(): return tuple(map(int,input().split()))
# rstrip().decode()

from collections import deque

def main():
	n,m=MI()
	G=[[] for _ in range(n+1)]

	for _ in range(m):
		a,b=MI()
		G[a].append(b)

	A=[10**5]*(n+1)

	for i in range(1,n+1):
		Q=deque([[i,0]])
		D=[-1]*(n+1)
		while Q:
			#print(Q)
			now,d=Q.popleft()
			if now==i and d>0:
				A[i]=d
				break
			for nx in G[now]:
				if D[nx]==-1:
					D[nx]=d+1
					Q.append([nx,d+1])
	#print(A)

	k=min(A)
	#print(k)

	if k==10**5:
		print(-1)
		exit()

	s=A.index(k)
	#print(s)

	A=[]
	Q=deque([[s,0]])
	D=[10**5]*(n+1)

	while Q:
		now,d=Q.pop()
		if now==s and d>0:
			break
		if d==k:
			continue
		A.append(now)
		for nx in G[now]:
			if D[nx]>d+1:
				D[nx]=d+1
				Q.append([nx,d+1])
	D[s]=0

	#print(A)
	#print(D)

	ans=[]
	d=k-1
	for i in reversed(A):
		if D[i]==d:
			ans.append(i)
			d-=1

	print(k)
	print(*ans[::-1],sep="\n")










if __name__ == "__main__":
	main()