Problem:
Score : 600 points

Problem Statement

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.

Notes

For a directed graph G = (V, E), we call a directed graph G' = (V', E') satisfying the following conditions an induced subgraph of G:

V' is a (non-empty) subset of V.

E' is the set of all the edges in E that have both endpoints in V'.

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.

Sample Input 1

4 5
1 2
2 3
2 4
4 1
4 3

Sample Output 1

3
1
2
4

The induced subgraph of G whose vertex set is \{1, 2, 4\} has the edge set \{(1, 2), (2, 4), (4, 1)\}. The in-degree and out-degree of every vertex in this graph are both 1.

Sample Input 2

4 5
1 2
2 3
2 4
1 4
4 3

Sample Output 2

-1

There is no induced subgraph of G that satisfies the condition.

Sample Input 3

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2

Sample Output 3

4
2
3
4
5

Solution in PyPy3 (2.4.0) (judge verdict: Wrong Answer)


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

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


if judge == 0:
	print(-1)
	exit()

ans = [last]
#print(last_list, last, deep)
while True:
	x = parent[ans[-1]]
	if x == -1:
		break
	elif x in last_list:
		ans.append(x)
		break
	else:
		ans.append(x)
print(len(ans))
for i in range(len(ans)):
	print(ans[i] + 1)