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 Ruby (2.3.3) (judge verdict: Wrong Answer)

lines = []
while line = gets
    lines << line.chomp.split(' ').map(&:to_i)
end

N = lines[0][0]
M = lines[0][1]

access = []
for i in 1..N do
  access[i-1] = []
end
for i in 1..M do
  from = lines[i][0]
  to = lines[i][1]
  access[from-1].push(to)
end

checked = []
num_checked = 0
for i in 1..N do
  checked[i-1] = false
end

boucle = false
while num_checked < N do
  visited = []
  path_to = []
  for i in 1..N do
    visited[i-1] = false
    path_to[i-1] = []
  end
  for i in 1..N do
    if checked[i-1] == false then
      target = [i]
      break
    end
  end
  while target != [] do
    next_target = []
    target.each do |i|
      visited[i-1] = true
      if checked[i-1] == false then
        checked[i-1] = true
        num_checked += 1
      end
      access[i-1].each do |j|
        path_to[i-1].each do |k|
          path_to[j-1].push(k)
        end
        path_to[j-1].push(i)
        next_target.push(j)
        if visited[j-1] then
          boucle = true
          puts path_to[j-1].length
          puts path_to[j-1]
          next_target = []
          num_checked = N
          break
        end
      end
      if boucle then
        break
      end
    end
    target = next_target
  end
end
    
if boucle == false then
  puts -1
end