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 PYTHON):

Solution:
# -*- coding: utf-8 -*-
import sys
from collections import deque

N,M=map(int, raw_input().split())
al=[ [] for i in range(N+1) ]
edge=[]

for i in range(M):
	a,b=map(int, sys.stdin.readline().split())
	al[a].append(b)
	edge.append((a,b))


def bfs(start,end):
	Visit=[ 0 for _ in range(N+1) ]	#訪問
	d=[ float("inf") for _ in range(N+1)]	#距離
	prev=[ None for _ in range(N+1)]	#経路復元
	d[start]=0
	q=deque()
	q.append(start)
	Visit[start]=1

	while q:
		fro=q.popleft()
		for to in al[fro]:
			if Visit[to]==0:
				Visit[to]=1
				alt=d[fro]+1
				if alt<d[to]:
					d[to]=alt
					prev[to]=fro
				q.append(to)
	return d[end],prev


K=float("inf")
v=[]
start=None
end=None

for x,y in edge:
	kyori,keiro=bfs(y,x)
	if kyori<K:
		K=kyori+1
		v=keiro
		start=y
		end=x

if K==float("inf"):
	print -1
else:
	print K
	print end
	fro=end
	while fro!=start:
		fro=v[fro]
		print fro