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)

use num_integer::gcd;
#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars, Usize1};
use proconio::{fastout, input};
#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        s: Chars,
        t: Chars,
    }
    let gcd = gcd(n, m);
    let l = n * m / gcd;

    let n_p = n / gcd;
    let m_p = m / gcd;
    let mut flag = true;

    for i in 0..gcd {
        if s[i * n_p] != t[i * m_p] {
            flag = false;
            break;
        }
    }
    if flag {
        println!("{}", l);
    } else {
        println!("-1");
    }
}