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)

pub struct Poper<'a> {
	iter: std::str::SplitWhitespace<'a>,
}

impl<'a> Poper<'a> {
	pub fn new(iter: std::str::SplitWhitespace) -> Poper {
		Poper { iter: iter }
	}
	pub fn read<T: std::str::FromStr>(&mut self) -> T
	where
		<T as std::str::FromStr>::Err: std::fmt::Debug,
	{
		self.iter.next().unwrap().parse().unwrap()
	}
}

// https://atcoder.jp/contests/abc129/submissions/5849596
const MOD: i64 = 1_000_000_007;
#[derive(Copy, Clone, Hash, Debug)]
struct ModInt {
	x: i64,
}
impl ModInt {
	fn new(x: i64) -> Self {
		ModInt { x: x % MOD }
	}
	fn pow(self, e: i64) -> Self {
		if e == 0 {
			Self::new(1)
		} else if e % 2 == 1 {
			self.pow(e - 1) * self
		} else {
			let y = self.pow(e / 2);
			y * y
		}
	}
	#[allow(dead_code)]
	fn inv(self) -> Self {
		self.pow(MOD - 2)
	}
}
impl<T: Into<ModInt>> std::ops::Add<T> for ModInt {
	type Output = Self;
	fn add(self, other: T) -> Self {
		let other = other.into();
		let sum = self.x + other.x;
		ModInt {
			x: if sum >= MOD { sum - MOD } else { sum },
		}
	}
}
impl<T: Into<ModInt>> std::ops::Sub<T> for ModInt {
	type Output = Self;
	fn sub(self, other: T) -> Self {
		let other = other.into();
		let sum = self.x - other.x;
		ModInt {
			x: if sum < 0 { sum + MOD } else { sum },
		}
	}
}
impl<T: Into<ModInt>> std::ops::Mul<T> for ModInt {
	type Output = Self;
	fn mul(self, other: T) -> Self {
		let other = other.into();
		ModInt {
			x: self.x * other.x % MOD,
		}
	}
}
impl<T: Into<ModInt>> std::ops::Div<T> for ModInt {
	type Output = Self;
	fn div(self, other: T) -> Self {
		let other = other.into();
		self * other.inv()
	}
}
impl From<i64> for ModInt {
	fn from(x: i64) -> Self {
		ModInt::new(x)
	}
}
impl std::fmt::Display for ModInt {
	fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
		self.x.fmt(f)
	}
}
impl<T: Into<ModInt>> std::ops::AddAssign<T> for ModInt {
	fn add_assign(&mut self, other: T) {
		*self = *self + other;
	}
}
impl<T: Into<ModInt>> std::ops::SubAssign<T> for ModInt {
	fn sub_assign(&mut self, other: T) {
		*self = *self - other;
	}
}
impl<T: Into<ModInt>> std::ops::MulAssign<T> for ModInt {
	fn mul_assign(&mut self, other: T) {
		*self = *self * other;
	}
}
impl<T: Into<ModInt>> std::ops::DivAssign<T> for ModInt {
	fn div_assign(&mut self, other: T) {
		*self = *self / other;
	}
}

fn main() {
	let input = {
		use std::io::Read;
		let mut s = String::new();
		std::io::stdin().read_to_string(&mut s).unwrap();
		s
	};
	let mut iter = Poper::new(input.split_whitespace());
	let _: u64 = iter.read();
	let m: u64 = iter.read();

	use std::collections::HashMap;

	let mut map = HashMap::new();
	for _ in 0..m {
		let u: u64 = iter.read();
		let v: u64 = iter.read();
		let l = map.entry(u).or_insert_with(|| vec![]);
		l.push(v);
	}

	let s: u64 = iter.read();
	let t: u64 = iter.read();

	fn reachable(map: &HashMap<u64, Vec<u64>>, start: u64, count: u64) -> Vec<u64> {
		let mut r = vec![];
		if 1 == count {
			if let Some(t) = map.get(&start) {
				for &i in t.iter() {
					r.push(i);
				}
			}
		} else if 0 < count {
			if let Some(t) = map.get(&start) {
				for &i in t.iter() {
					for j in reachable(map, i, count - 1) {
						r.push(j);
					}
				}
			}
		}
		r
	}

	let mut checked = HashMap::new();
	{
		let p = checked.entry(s).or_insert(false);
		*p = true;
	}

	let mut count = 0;

	let mut ps = vec![s];
	loop {
		count += 1;
		let mut ns = vec![];

		for &p in ps.iter() {
			for n in reachable(&map, p, 3) {
				if n == t {
					println!("{}", count);
					return;
				}
				let p = checked.entry(n).or_insert(false);
				if !*p {
					ns.push(n);
					*p = true;
				}
			}
		}

		if ns.is_empty() {
			break;
		}
		ps = ns;
	}

	println!("-1");
}