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)

use std::collections::HashMap;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn gcd(a: i32, b:i32) -> i32 {
    if b == 0 {
        return a;
    }
    gcd(b, a % b)
}

fn main() {
    let v = read_vec::<usize>();
    let (n, m) = (v[0], v[1]);
    let s = read::<String>();
    let s = s.chars().collect::<Vec<_>>();
    let t = read::<String>();
    let t = t.chars().collect::<Vec<_>>();

    let gcd_num = gcd(n as i32, m as i32) as usize;
    let x = n * m / gcd_num;
    // println!("{:?}", x);

    let s_indexes = (0..n).map(|i| i * x / n).collect::<Vec<_>>();
    let t_indexes = (0..m).map(|i| (i * x / m, i)).collect::<HashMap<usize, usize>>();

    // println!("{:?}", s_indexes);
    // println!("{:?}", t_indexes);

    let mut success = true;
    for (si, xi) in s_indexes.iter().enumerate() {
        // println!("try {:?}", si);
        if t_indexes.contains_key(&xi) && s[si] != t[t_indexes[xi]] {
            success = false;
            break;
        }
    }

    if success {
        println!("{:?}", x);
    } else {
        println!("-1");
    }
}