Problem:
Score : 500 points

Problem Statement

Ken loves ken-ken-pa (Japanese version of hopscotch). Today, he will play it on a directed graph G.
G consists of N vertices numbered 1 to N, and M edges. The i-th edge points from Vertex u_i to Vertex v_i.

First, Ken stands on Vertex S. He wants to reach Vertex T by repeating ken-ken-pa. In one ken-ken-pa, he does the following exactly three times: follow an edge pointing from the vertex on which he is standing.

Determine if he can reach Vertex T by repeating ken-ken-pa. If the answer is yes, find the minimum number of ken-ken-pa needed to reach Vertex T. Note that visiting Vertex T in the middle of a ken-ken-pa does not count as reaching Vertex T by repeating ken-ken-pa.

Constraints

2 \leq N \leq 10^5

0 \leq M \leq \min(10^5, N (N-1))

1 \leq u_i, v_i \leq N(1 \leq i \leq M)

u_i \neq v_i (1 \leq i \leq M)

If i \neq j, (u_i, v_i) \neq (u_j, v_j).

1 \leq S, T \leq N

S \neq T

Input

Input is given from Standard Input in the following format:

N M
u_1 v_1
:
u_M v_M
S T

Output

If Ken cannot reach Vertex T from Vertex S by repeating ken-ken-pa, print -1.
If he can, print the minimum number of ken-ken-pa needed to reach vertex T.

Sample Input 1

4 4
1 2
2 3
3 4
4 1
1 3

Sample Output 1

2

Ken can reach Vertex 3 from Vertex 1 in two ken-ken-pa, as follows: 1 \rightarrow 2 \rightarrow 3 \rightarrow 4 in the first ken-ken-pa, then 4 \rightarrow 1 \rightarrow 2 \rightarrow 3 in the second ken-ken-pa. This is the minimum number of ken-ken-pa needed.

Sample Input 2

3 3
1 2
2 3
3 1
1 2

Sample Output 2

-1

Any number of ken-ken-pa will bring Ken back to Vertex 1, so he cannot reach Vertex 2, though he can pass through it in the middle of a ken-ken-pa.

Sample Input 3

2 0
1 2

Sample Output 3

-1

Vertex S and Vertex T may be disconnected.

Sample Input 4

6 8
1 2
2 3
3 4
4 5
5 1
1 4
1 5
4 6
1 6

Sample Output 4

2

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


import qualified Data.Map as Map
import Data.Maybe
import qualified Control.Monad.State as St
import Control.Monad

newtype Env = Env { runEnv :: (Map.Map Int Int, Map.Map Int Int, Map.Map Int Int) }
  deriving (Eq,Show)

kenkenpa' :: Int -> St.State Env Int
kenkenpa' start = do
  env <- St.get
  let (m1,m2,m3) = runEnv env
  case Map.lookup start m1 of
    Nothing -> return (-1)
    Just r1 ->
      case Map.lookup r1 m2 of
        Nothing -> return (-1)
        Just r2 -> 
          case Map.lookup r2 m3 of
            Nothing -> return (-1)
            Just r3 -> do
              St.put . Env $ (Map.delete start m1, Map.delete r1 m2, Map.delete r2 m3)
              return r3

find :: Int -> Int -> Int -> St.State Env Int
find start dest num = do
  r <- kenkenpa' start
  if r == (-1) then return (-1)
  else if r == dest then return num
  else find r dest (num+1)



-- main = do
--   _ <- getLine
--   s <- map  ((\ls -> (head ls,last ls)) . map read . words) . lines <$> getContents :: IO [(Int,Int)]
--   let map = Map.fromList (init s)
--   let (start,dest) = last s
--   -- print $ steps map [start] start dest 0
--   print $ St.evalState (find start dest 1) (Env (map,map,map))

main = do
  m <- last . map read . words <$> getLine :: IO Int
  s <- replicateM m getLine :: IO [String]
  s1 <- map read . words <$> getLine :: IO [Int]
  let (start,dest) = (head s1, last s1)
  let tmp = map ((\ls -> (head ls, last ls)) . map read . words) s
  let map = Map.fromList tmp
  print $ St.evalState (find start dest 1) (Env (map,map,map))