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)

N, M = gets.chomp.split(" ").map(&:to_i)
V = Hash.new{|h, k| h[k] = Array.new}
M.times{|i|
  a, b = gets.chomp.split(" ").map(&:to_i)
  V[a] << b
}

def dfs
  lst = T[-1]
  V[lst].each{|v|
    if T.include?(v) then
      wk = T.index(v)
      (wk...T.size).each{|i| A << T[i]}
      A.all?{|a| V[a].select{|v| A.include?(v)}.size == 1} ? break : A.clear
    end
    next if C[v]
    T << v
    C[v] = true
    dfs
    T.pop
    break if not A.empty?
  }
end

T = []
A = []
C = Array.new(N + 1, false)
(1..N).each{|n|
  next if C[n]
  C[n] = true
  T << n
  dfs
  T.pop
  break if not A.empty?
}

if A.empty? then
  puts -1
else
  puts A.size
  puts A.join("\n")
end