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: Time Limit Exceeded)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{min, max};
use std::collections::{HashSet, BinaryHeap};

fn main() {
    input!{
        n: usize,
        m: usize,
        es: [(usize1, usize1); m],
        s: usize1,
        t: usize1
    }
    let mut g: Vec<Vec<usize>> = vec![vec![]; n];
    for &(u, v) in &es {
        g[u].push(v);
    }
    let mut g2: Vec<Vec<usize>> = vec![vec![]; n];
    for i in 0..n {
        g2[i] = dfs(i, &g, 3).iter().cloned().collect();
    }
    if let Some(ans) = dijkstra(s, t, &g2) {
        println!("{}", ans);
    } else {
        println!("-1");
    }
}

fn dfs(v: usize, g: &Vec<Vec<usize>>, d: usize) -> HashSet<usize> {
    if d == 0 {
        return [v].iter().cloned().collect();
    }
    let mut set = HashSet::new();
    for &c in &g[v] {
        set = set.union(&dfs(c, g, d - 1)).cloned().collect();
    }
    set
}


use std::cmp::Ordering;

#[derive(Debug, PartialEq, Eq)]
struct DijkstraState {
    v: usize,
    w: usize
}

impl Ord for DijkstraState {
    fn cmp(&self, other: &Self) -> Ordering {
        other.w.cmp(&self.w)
    }
}

impl PartialOrd for DijkstraState {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

fn dijkstra(s: usize, t: usize, g: &Vec<Vec<usize>>) -> Option<usize> {
    let n = g.len();
    let mut prev = vec![usize::max_value(); n];
    let mut pq = BinaryHeap::new();
    pq.push(DijkstraState{v: s, w: 0});
    prev[s] = 0;
    while let Some(s) = pq.pop() {
        if prev[s.v] < s.w {
            continue;
        }
        if s.v == t {
            return Some(s.w);
        }
        for &v in &g[s.v] {
            if prev[v] > s.w + 1 {
                prev[v] = s.w + 1;
                pq.push(DijkstraState{v: v, w: s.w + 1});
            }
        }
    }
    None
}