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: Wrong Answer)

use std::io::*;
use std::str::FromStr;


pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed reading char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed parsing")
}

fn lcm(a: u32, b: u32) -> u32 {

    a * b / gcd(a, b)
}

fn gcd(mut a: u32, mut b: u32) -> u32 {

    if a < b {
        return gcd(b, a);
    }
    while b != 0 {

        let rem = a % b;
        a = b;
        b = rem;
    }
    a
}

fn getpos(target: &str, l: u32) -> Vec<(u32, char)> {

    let len = target.len() as u32;
    let mut ret:Vec<(u32, char)> = Vec::new();

    let char_vec:Vec<char> = target.chars().collect();

    for i in 0..len {

        ret.push((i * (l / len), char_vec[i as usize]));
    }
    ret
}


fn main() {

    let n: u32 = read();
    let m: u32 = read();

    let s: String = read();
    let t: String = read();

    let l: u32 = lcm(s.len() as u32, t.len() as u32);

    let mut result: Vec<char> = Vec::new();
    let mut failed = false;

    for x in 0..l {

        result.push(' ');
    }


    for (pos, char) in getpos(s.as_str(), l) {

        result[pos as usize] = char;
    }
    for (pos, char) in getpos(t.as_str(), l) {

        if result[pos as usize] != ' ' && result[pos as usize] != char {
            failed = true;
        }
    }


    if failed {
        println!("-1");

    } else {

        println!("{}", l);
    }

}