Problem:
Score : 300 points

Problem Statement

You are given a string S of length N and another string T of length M.
These strings consist of lowercase English letters.

A string X is called a good string when the following conditions are all met:

Let L be the length of X. L is divisible by both N and M.

Concatenating the 1-st, (\frac{L}{N}+1)-th, (2 \times \frac{L}{N}+1)-th, ..., ((N-1)\times\frac{L}{N}+1)-th characters of X, without changing the order, results in S.

Concatenating the 1-st, (\frac{L}{M}+1)-th, (2 \times \frac{L}{M}+1)-th, ..., ((M-1)\times\frac{L}{M}+1)-th characters of X, without changing the order, results in T.

Determine if there exists a good string. If it exists, find the length of the shortest such string.

Constraints

1 \leq N,M \leq 10^5

S and T consist of lowercase English letters.

|S|=N

|T|=M

Input

Input is given from Standard Input in the following format:

N M
S
T

Output

If a good string does not exist, print -1; if it exists, print the length of the shortest such string.

Sample Input 1

3 2
acp
ae

Sample Output 1

6

For example, the string accept is a good string.
There is no good string shorter than this, so the answer is 6.

Sample Input 2

6 3
abcdef
abc

Sample Output 2

-1

Sample Input 3

15 9
dnsusrayukuaiia
dujrunuma

Sample Output 3

45

Solution in Rust (1.15.1) (judge verdict: Accepted)

// Try AtCoder
// author: Leonardone @ NEETSDKASU

fn main() {
    let mut stdin = String::new();
    std::io::Read::read_to_string(
        &mut std::io::stdin(),
        &mut stdin).unwrap();
    let mut stdin = stdin.split_whitespace();
    let mut get = || stdin.next().unwrap();
    macro_rules! get {
        ($t:ty) => (get().parse::<$t>().unwrap());
        () => (get!(i64));
    }
    
    let n = get!();
    let m = get!();
    let s = get().as_bytes();
    let t = get().as_bytes();
    
    if s[0] != t[0] {
        println!("-1");
        return;
    }
    let gcd = gcd(n, m);
    let lcm = (n / gcd) * (m / gcd) * gcd;
    
    let mut xs = vec![];
    for i in 0..s.len() {
        let j = (lcm / n) as usize * i;
        let c = s[i];
        xs.push((j, c));
    }
    for i in 0..t.len() {
        let j = (lcm / m) as usize * i;
        let mut lp = 0;
        let mut rp = xs.len();
        while lp < rp {
            let hp = (lp + rp) / 2;
            if xs[hp].0 < j {
                lp = hp + 1;
            } else {
                rp = hp;
            }
        }
        if lp < xs.len() && xs[lp].0 == j && xs[lp].1 != t[i] {
            println!("-1");
            return;
        }
    }
    
    println!("{}", lcm);
    
    
}

fn gcd(a: i64, b: i64) -> i64 {
    fn _gcd(x: i64, y: i64) -> i64 {
        if x == 0 { y } else { _gcd(y % x, x) }
    }
    if a < b { _gcd(a, b) } else { _gcd(b, a) }
}