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 Rust (1.15.1) (judge verdict: Accepted)

use std::collections::VecDeque;

fn solve(uvs: &[(usize, usize)], s: usize, t: usize) -> Option<usize> {
    let mut graph: Vec<Vec<usize>> = vec![Vec::new(); 100001];

    for &(u, v) in uvs {
        graph[u].push(v);
    }

    let mut queue: VecDeque<((usize, usize /* 0,1,2 */), usize /*dist*/)> = VecDeque::new();

    queue.push_back(((s, 0), 0));

    let mut history = vec![false; 100001 * 3];
    history[3 * s] = true;

    while let Some(((next, index), dist)) = queue.pop_front() {
        if (next, index) == (t, 0) {
            return Some(dist / 3);
        }

        for &n in graph[next].iter() {
            let ni = (index + 1) % 3;
            if history[3 * n + ni] == false {
                history[3 * n + ni] = true;
                queue.push_back(((n, ni), dist + 1));
            }
        }
    }

    None
}

#[test]
fn solve_test() {
    assert_eq!(solve(&vec![(1, 2), (2, 3), (3, 4), (4, 1)], 1, 3), Some(2));
    assert_eq!(solve(&vec![(1, 2), (2, 3), (3, 1)], 1, 2), None);
    assert_eq!(solve(&vec![], 1, 2), None);
    assert_eq!(
        solve(
            &vec![
                (1, 2),
                (2, 3),
                (3, 4),
                (4, 5),
                (5, 1),
                (1, 4),
                (1, 5),
                (4, 6)
            ],
            1,
            6
        ),
        Some(2)
    );
}

#[allow(unused_macros)]
macro_rules! parse_line {
    ( $t:ty ) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            iter.next().unwrap().parse::<$t>().unwrap()
        }
    );

    ( $( $t:ty), +) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ( $(iter.next().unwrap().parse::<$t>().unwrap()),* )
        }
    );
}

#[allow(unused_macros)]
macro_rules! read_line {
    () => {{
        let mut line = String::new();
        ::std::io::stdin().read_line(&mut line).unwrap();
        line.pop();
        line
    }};
}

#[allow(unused_macros)]
macro_rules! parse_vec {
    ( $t:ty ) => {{
        let mut line = String::new();
        ::std::io::stdin().read_line(&mut line).unwrap();
        let iter = line.split_whitespace();
        iter.map(|v| v.parse::<$t>().unwrap()).collect::<Vec<_>>()
    }};
}

fn main() {
    let (n, m) = parse_line!(usize, usize);
    let uvs = (0..m)
        .map(|_| parse_line!(usize, usize))
        .collect::<Vec<_>>();

    let (s, t) = parse_line!(usize, usize);

    println!(
        "{}",
        if let Some(n) = solve(&uvs, s, t) {
            n as isize
        } else {
            -1
        }
    );
}