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
from collections import deque, defaultdict
import copy
import bisect
sys.setrecursionlimit(10 ** 9)
import math
import heapq
from itertools import product, permutations,combinations
import fractions

import sys
def input():
	return sys.stdin.readline().strip()

N, M = list(map(int, input().split()))

graph = [[] for _ in range(N)]

for i in range(M):
	A, B = list(map(int, input().split()))
	A -= 1
	B -= 1
	graph[A].append(B)


for start in range(N):
	parent = [-1] * N
	depth = [0] * N
	que = deque([])
	que.append(start)
	depth[start] = 1
	while len(que) > 0:
		node = que.popleft()
		judge = 0
		if len(graph[node]) > 0:
			for node_next in graph[node]:
				if depth[node_next] == 1:
					judge = 1
				if depth[node_next] == 0:
					depth[node_next] = depth[node] + 1
					que.append(node_next)
					parent[node_next] = node
		if judge == 1:
			last = node
			break
	if judge == 1:
		break


if judge != 1:
	print(-1)
	exit()

node_list = deque([last])
while True:
	loc = parent[node_list[0]]
	if loc == -1:
		break
	else:
		node_list.appendleft(loc)

node_set = set([node_list[0]])


for i in range(1, len(node_list)):
	max_depth = -1
	for edge in graph[node_list[i]]:
		if edge in node_set:
			for j in range(i):
				if edge == node_list[j]:
					max_depth = max(max_depth, j)
	if max_depth >= 0:
		start = max_depth
		end = i
		break
	node_set.add(node_list[i])

#print(node_set, node_list, depth)
print(end + 1 - start)
for node in range(start, end + 1):
	print(node_list[node] + 1)