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 (1.42.0) (judge verdict: Accepted)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

fn main() {
    input! {
        n:usize, m:usize,
        mut s:Chars,
        mut t:Chars,
    }
    let k = gcd(n as i64, m as i64) as usize;
    let l = n * m / k;
    let mut ok = true;
    if s[0] != t[0] {
        println!("{}", -1);
        return;
    }
    let mut mp = BTreeMap::new();
    for i in 0..n {
        *mp.entry(i * m / k).or_insert('-') = s[i];
    }
    for i in 0..m {
        let ind = i * n / k;
        let v = mp.get(&ind);
        if v != None && v != Some(&t[i]) {
            println!("{}", -1);
            return;
        }
    }
    println!("{}", l);

    pub fn gcd(a: i64, b: i64) -> i64 {
        if b == 0 {
            a
        } else {
            gcd(b, a % b)
        }
    }
}