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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn dfs(
    cur_step: usize,
    cur_pos: usize,
    edges: &Vec<Vec<usize>>,
    checked: &mut Vec<HashSet<usize>>,
    dest: &mut Vec<usize>,
) {
    checked[cur_step].insert(cur_pos);
    if cur_step == 2 {
        for &to in edges[cur_pos].iter() {
            // checked[2].insert(to);
            dest.push(to);
        }
        return;
    }
    for &to in edges[cur_pos].iter() {
        if checked[cur_step + 1].contains(&to) {
            continue;
        }
        // checked[cur_step + 1].insert(to);
        dfs(cur_step + 1, to, edges, checked, dest);
    }
}
fn main() {
    let v = read_vec::<usize>();
    let (n, m) = (v[0], v[1]);
    let mut rev_edges = vec![vec![]; n];

    for _ in 0..m {
        let v = read_vec::<usize>();
        let (a, b) = (v[0] - 1, v[1] - 1);
        rev_edges[b].push(a); // enable b from a
    }

    let v = read_vec::<usize>();
    let (s, t) = (v[0] - 1, v[1] - 1);

    let mut checked = vec![HashSet::new(); 3];
    let mut que = VecDeque::new();
    que.push_back((t, 0));

    while let Some((cur_pos, cycle)) = que.pop_front() {
        // debug!(checked);
        if cur_pos == s {
            println!("{}", cycle);
            return;
        }
        let mut dest = vec![];
        if checked[0].contains(&cur_pos) {
            continue;
        }
        dfs(0, cur_pos, &rev_edges, &mut checked, &mut dest);
        for d in dest {
            que.push_back((d, cycle + 1));
        }
    }
    println!("-1");
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}