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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

-- https://github.com/minoki/my-atcoder-solutions
{-# LANGUAGE BangPatterns #-}
import Data.Char (isSpace)
import Data.Int (Int64)
import Data.List (unfoldr)
import Control.Monad
import Control.Monad.ST
import Control.Monad.Except
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.ByteString.Char8 as BS
import qualified Data.IntSet as IntSet
import Data.Monoid
import Data.Foldable

findCycle :: V.Vector IntSet.IntSet -> V.Vector IntSet.IntSet -> Either [Int] ()
findCycle edges edges_to = runST $ runExceptT $ do
  let !n = V.length edges  -- 頂点の個数
  seen <- UM.replicate n (0 :: Int) -- 0: new, 1: DFSの最中, 2: チェック済み
  let dfs !x path = do
        -- x を通る閉路があるかチェックする
        UM.write seen x 1
        forM_ (IntSet.toList $ edges V.! x) $ \y -> do
          -- 辺 (x,y) が存在
          s <- UM.read seen y
          case s of 0 -> dfs y (y : path)
                    1 -> throwError (reverse (y : path)) -- コールスタックのどこかで dfs y が呼ばれている。閉路
                    _ -> return ()
        UM.write seen x 2
  forM_ [0..n-1] $ \x -> do
    s <- UM.read seen x
    when (s == 0) $ dfs x [x]
  return ()

reduceCycle ::  V.Vector IntSet.IntSet -> V.Vector IntSet.IntSet -> [Int] -> [Int]
reduceCycle edges_from edges_to path = do
  let loop :: IntSet.IntSet -> [Int] -> IntSet.IntSet -> [Int] -> Either [Int] [Int]
      loop m (i:ys@(j:_)) seen revAcc = do
        let s1 = IntSet.delete j ((edges_from V.! i) `IntSet.intersection` m)
        case IntSet.maxView s1 of
          Nothing -> loop m ys (IntSet.insert i seen) (i : revAcc)
          Just (j',_) | j' `IntSet.member` seen -> Right (j' : reverse (j' : i : takeWhile (/= j') revAcc))
                      | otherwise -> case dropWhile (/= j') ys of
                                       [] -> error $ show (i,j',ys,seen,revAcc)
                                       ys' -> loop m ys' (IntSet.insert i seen) (i : revAcc)
      loop m [i] seen revAcc = Left (reverse revAcc)
  let loop2 path =  case loop (IntSet.fromList path) path IntSet.empty [] of
        Left result -> result
        Right result -> loop2 result
  loop2 path

main = do
  [n,m] <- unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  edges <- U.replicateM m $ do
    [x,y] <- unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
    return (x-1,y-1)
  let edges_from :: V.Vector IntSet.IntSet
      edges_from = V.create $ do
        vec <- VM.replicate n IntSet.empty
        U.forM_ edges $ \(a,b) ->
          VM.modify vec (IntSet.insert b) a
        return vec
  let edges_to :: V.Vector IntSet.IntSet
      edges_to = V.create $ do
        vec <- VM.replicate n IntSet.empty
        U.forM_ edges $ \(a,b) ->
          VM.modify vec (IntSet.insert a) b
        return vec
  case findCycle edges_from edges_to of
    Right _ -> putStrLn "-1"
    Left path -> do
      let path' = reduceCycle edges_from edges_to path
      print $ length path'
      forM_ path' $ \i -> do
        print (i+1)

foldMap_IntSet :: (Monoid n) => (Int -> n) -> IntSet.IntSet -> n
foldMap_IntSet f set = go set
  where
    go set = case IntSet.splitRoot set of
               [] -> mempty
               [x] -> foldMap f (IntSet.toList x)
               xs -> foldMap go xs

foldMapM_IntSet :: (Monoid n, Monad m) => (Int -> m n) -> IntSet.IntSet -> m n
foldMapM_IntSet f set = go set
  where
    go set = case IntSet.splitRoot set of
               [] -> return mempty
               [x] -> foldlM (\x v -> mappend x <$> f v) mempty (IntSet.toList x)
               xs -> foldlM (\x set' -> mappend x <$> go set') mempty xs