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::io;
use std::io::Read;

fn main() {
    // inputs
    let mut stdin = io::stdin();
    let mut lines_str = String::new();
    let _ = stdin.read_to_string(&mut lines_str);
    let mut lines = lines_str.lines();
    let mut l1 = lines.next().expect("").split_whitespace();
    let n :usize = l1.next().expect("").trim().parse().unwrap();
    let m :usize = l1.next().expect("").trim().parse().unwrap();
    let s :Vec<char> = lines.next().expect("").trim().to_string().chars().collect();
    let t :Vec<char> = lines.next().expect("").trim().to_string().chars().collect();

    let d = gcd(n,m);
    let l = n * (m / d);
    //check
    for i in 0..d {
        if s[i * (n / d)] != t[i * (m / d)] {
            println!("-1");
            return;
        }
    }

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

fn gcd(x :usize, y :usize) -> usize {
    if x == 0 {
        return y;
    }
    if y == 0 {
        return x;
    }
    if x > y {
        return gcd(y, x-y);
    } else {
        return gcd(x, y-x);
    }
}