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 Scala (2.11.7) (judge verdict: Accepted)

import javax.swing.DefaultBoundedRangeModel

import scala.annotation.tailrec

object Main extends App {
  import scala.io.StdIn._

  val Array(n, m) = readLine.trim.split(' ').map(_.toInt)
  val nodes = Array.fill(n){Nil: List[Int]}
  for (_ <- 0 until m) {
    val Array(u, v) = readLine.trim.split(' ').map(_.toInt - 1)
    nodes(u) ::= v
  }
  val Array(s, t) = readLine.trim.split(' ').map(_.toInt - 1)
  val reachable = Array.fill(n){Array.fill(3){-3}}
  reachable(s)(0) = 0
  mark(List(s))
  println(
    reachable(t)(0) / 3
  )
  @tailrec
  def mark(current: List[Int], count: Int = 1): Unit = {
    current match {
      case Nil => ()
      case _ =>
        var next = Nil: List[Int]
        for (c <- current) {
          for (n <- nodes(c) if reachable(n)(count % 3) == -3) {
            reachable(n)(count % 3) = count
            next ::= n
          }
        }
        mark(next, count + 1)
    }
  }
}