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: Time Limit Exceeded)

use scanner::Scanner;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.read();
    let m: usize = sc.read();
    let gcm = (n * m) / gcd(n, m);

    let s: Vec<char> = sc.read::<String>().chars().collect();
    let t: Vec<char> = sc.read::<String>().chars().collect();

    let s: Vec<_> = s.iter().enumerate().map(|(i, x)| (i * gcm / n + 1, x)).collect();
    let t: Vec<_> = t.iter().enumerate().map(|(i, x)| (i * gcm / m + 1, x)).collect();

    for s_i in s.iter() {
        for t_i in t.iter() {
            if s_i.0 == t_i.0 && s_i.1 != t_i.1 {
                println!("-1");
                return;
            }
        }
    }
    println!("{}", gcm);
}

fn gcd(a: usize, b: usize) -> usize {
    if a % b == 0 {
        b
    } else {
        gcd(b, a % b)
    }
}

mod scanner {
    pub struct Scanner<'a> {
        s: String,
        words: ::std::str::SplitWhitespace<'a>,
    }

    impl<'a> Scanner<'a> {
        pub fn new() -> Scanner<'a> {
            let s = String::new();
            let words = unsafe { ::std::mem::transmute(s.split_whitespace()) };
            Scanner { s: s, words: words }
        }

        pub fn read<T: ::std::str::FromStr>(&mut self) -> T {
            match self.words.next() {
                Some(x) => x.parse().ok().unwrap(),
                None => {
                    self.load();
                    self.read()
                }
            }
        }

        fn load(&mut self) {
            self.s.clear();
            ::std::io::stdin().read_line(&mut self.s).unwrap();
            self.words = unsafe { ::std::mem::transmute(self.s.split_whitespace()) };
        }
    }
}