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: Runtime Error)

extern crate core;

use core::cmp::min;
use std::collections::VecDeque;


fn main() {
    let input: Vec<usize> = read_vec();
    let n = input[0];
    let m = input[1];

    let mut edges = vec![Vec::new(); 3 * n];

    for _ in 0..m {
        let input: Vec<usize> = read_vec();
        let input: Vec<usize> = input.iter().map(|x| x - 1).collect();
        let u = input[0];
        let v = input[1];
        edges[3 * u].push(3 * v + 1);
        edges[3 * u + 1].push(3 * v + 2);
        edges[3 * u + 2].push(3 * v);
    }

    let input: Vec<usize> = read_vec();
    let input: Vec<usize> = input.iter().map(|x| 3 * (x - 1)).collect();
    let s = input[0];
    let t = input[1];

    let mut q:VecDeque<(usize, i64)> = VecDeque::new();
    q.push_back((s, 0));
    let mut nodes: Vec<Option<i64>> = vec![None; 3 * n];

    while !q.is_empty() {
        let (cv, count) = q.pop_front().unwrap();    

        if cv == t {
            nodes[cv] = match nodes[cv] {
                Some(v) => Some(min(v, count)),
                None => Some(count),
            }
        } else {
            nodes[cv] = match nodes[cv] {
                Some(v) => Some(min(v, count)),
                None => Some(count),
            };
            if nodes[cv] == Some(count) {
                for u in edges[cv].iter() {
                    q.push_back((*u, count + 1));
                }
            }
        }
    }
    let ans = match nodes[t] {
        Some(v) => v / 3,
        None => -1,
    };
    println!("{:?}", ans);

}


fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}