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: Accepted)

STATUS = Array.new(1010, :unused)
def active?(v); STATUS[v] == :active; end
def activate!(v);  v.tap{ STATUS[v] = :active }; end
def inactivate!(v); v.tap{ STATUS[v] = :used }; end
def used?(v); STATUS[v] != :unused; end
def use!(v); v.tap{ STATUS[v] = :used }; end
def subgraph_include?(v); STATUS[v] == :unused; end
def subgraph_init!(vset); STATUS.fill(:used); vset.each{|v| STATUS[v] = :unused}; end

N,M = gets.split.map(&:to_i)
G = Array.new(N + 1){ [] }
E = M.times.map{ gets.split.map(&:to_i) }
E.each do |from,to|
  G[from] << to
end

def cycle_exists?
  (1 .. N).each do |s|
    next if used?(s)
    stack = [use!(s)]
    cycle = find_cycle(stack)
    return cycle if cycle
  end
  return false
end

def smaller_cycle?(cycle)
  subgraph_init!(cycle)
  
  shortcut = nil
  smaller_not_found = cycle.each_with_index.none? do |from, i|
    to = (i + 1 == cycle.size ? cycle[0] : cycle[i + 1])
    to_ = G[from].find{|t| subgraph_include?(t) && t != to }
    shortcut = [from, to_] if to_
  end
  
  return false if smaller_not_found

  stack = [activate!(shortcut[0]), use!(shortcut[1])]
  find_cycle(stack)
end

def find_cycle(stack)
  until stack.empty?
    u = stack.pop
    
    if active?(u) 
      inactivate!(u)
      next 
    end
    
    stack << activate!(u)
    
    G[u].each do |v|
      if active?(v)
        cycle = stack.select{|r| active?(r) }
                  .drop_while{|r| r != v } 
        return cycle
      end
      used?(v) || stack << use!(v)
    end
  end
  false
end

cycle = cycle_exists?

if !cycle
  puts -1
else
  loop do
    smaller = smaller_cycle?(cycle)
    break if !smaller  
    cycle = smaller
  end
  puts cycle.size
  puts cycle
end