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 LuaJIT (2.0.4) (judge verdict: Wrong Answer)

local n, m = io.read("*n", "*n")
local edge = {}
local edge2 = {}
local edge3 = {}
for i = 1, n do edge2[i] = {} edge3[i] = {} end
for i = 1, m do
  local a, b = io.read("*n", "*n")
  table.insert(edge, {a, b})
  table.insert(edge2[a], b)
  table.insert(edge3[b], a)
end
local len = {}
local inf = 1010
for i = 1, n do len[i] = -inf end
len[1] = 0
local lim = n + 4
for i = 1, lim do
  for j = 1, m do
    local src, dst, c = edge[j][1], edge[j][2], 1
    if len[src] ~= -inf and len[dst] < len[src] + c then
      len[dst] = len[src] + c
      if i == lim then
        len[dst] = inf
      end
    end
  end
end
for i = 1, lim do
  for j = 1, m do
    local src, dst = edge[j][1], edge[j][2]
    if len[src] == inf then
      len[dst] = inf
    end
  end
end
local startpos = 0
local scand = {}
local scflag = {}
local scasked = {}
for i = 1, n do
  if len[i] == inf then
    table.insert(scand, i)
    scflag[i] = true
  else
    scflag[i] = false
  end
  scasked[i] = false
end
while 0 == startpos and 0 < #scand do
  local sc = scand[#scand]
  table.remove(scand)
  scflag[sc] = false
  scasked[sc] = true
  for i = 1, #edge3[sc] do
    local p = edge3[sc][i]
    if scasked[p] then
      startpos = p
      break
    elseif len[p] == inf then
      if not scflag[p] then
        table.insert(scand, p)
        scflag[p] = true
      end
    end
  end
end
if startpos == 0 then
  print(-1)
else
  local tasks = {startpos}
  local asked = {}
  for i = 1, n do
    asked[i] = false
  end
  local done = false
  while 0 < #tasks do
    local src = tasks[#tasks]
    table.remove(tasks)
    asked[src] = true
    while 0 < #edge2[src] do
      local dst = edge2[src][#edge2[src]]
      if dst == startpos then
        table.insert(tasks, src)
        for i = #tasks, 1, -1 do
          if tasks[i] == startpos then
            print(#tasks - i + 1)
            for j = i, #tasks do
              print(tasks[j])
            end
            break
          end
        end
        done = true
      elseif not asked[dst] then
        table.insert(tasks, src)
        table.insert(tasks, dst)
        table.remove(edge2[src])
        break
      else
        table.remove(edge2[src])
      end
      if done then break end
    end
    if done then break end
  end
end