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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
	"bufio"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)
func scanInt() int {
	sc.Scan()
	a,_ := strconv.Atoi(sc.Text())
	return a
}

func scanText() string {
	sc.Scan()
	return sc.Text()
}

type vert struct {
	a int
	b int
}

func main() {
	sc.Split(bufio.ScanWords)
	
	n,m := scanInt(),scanInt()
	g := make([][]int, n)
	for i := 0; i < m; i++ {
		u,v := scanInt()-1,scanInt()-1
		g[u] = append(g[u],v)
	}

	s,t := scanInt()-1,scanInt()-1

	g3 := make([][]int, n)
	for i := 0; i < n; i++ {
		g3[i] = append(g3[i], []int{-1,-1,-1}...)
	}

	g3[s][0] = 0

	queue := make([]vert, 0)
	queue = append(queue, vert{s,0})
	for ; len(queue) > 0; {
		a,b := queue[0].a, queue[0].b
		for _, e := range g[a] {
			if g3[e][(b+1)%3] != -1 {
				continue
			}

			g3[e][(b+1)%3] = g3[a][b]+1
			queue = append(queue, vert{e,(b+1)%3})
		}
		queue = queue[1:]
	}

	if g3[t][0] == -1 {
		fmt.Println(-1)
	} else {
		fmt.Println(g3[t][0]/3)
	}

	// fmt.Println(g3)
}