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 OCaml (4.02.3) (judge verdict: Wrong Answer)

let rec drop n xs =
  if n = 0
  then xs
  else drop (n - 1) (List.tl xs)

exception Exit of int list

let () = Scanf.scanf "%d %d\n" @@ fun n m ->
  let es = Array.make n [] in
  for i = 0 to m - 1 do
    Scanf.scanf "%d %d\n" @@ fun a b ->
      es.(a - 1) <- b - 1 :: es.(a - 1)
  done;
  let trace = Array.make n None in
  let visited = Array.make n false in
  let rec visit vs v =
    match trace.(v) with
    | Some us -> raise (Exit (drop (List.length us) (List.rev vs)))
    | None ->
        visited.(v) <- true;
        trace.(v) <- Some vs;
        List.iter (fun u -> visit (v :: vs) u) es.(v);
        trace.(v) <- None in
  try
    for v = 0 to n - 1 do
      if not visited.(v) then visit [] v
    done;
    print_endline "-1"
  with Exit vs ->
    Printf.printf "%d\n" (List.length vs);
    List.iter (fun v -> Printf.printf "%d\n" @@ v + 1) vs