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::collections::HashMap;

fn gcd(a: usize, b: usize) -> usize {
  // Use Euclid's algorithm
  let mut m = a;
  let mut n = b;
  while m != 0 {
    let temp = m;
    m = n % temp;
    n = temp;
  }
  n
}

fn lcm(a: usize, b: usize) -> usize {
  // should not have to recalculate abs
  (a * b) / gcd(a, b)
}

pub fn good_string(s: &str, t: &str) -> Option<usize> {
  let n = s.len();
  let m = t.len();
  let l = lcm(n, m);
  let mut check: HashMap<usize, char> = HashMap::new();
  for (i, (s, t)) in s.chars().zip(t.chars()).enumerate() {
    let s_position = i * l / n + 1;
    let t_position = i * l / m + 1;

    {
      let v = check.entry(s_position).or_insert(s);
      if *v != s {
        return None;
      }
    }

    let v = check.entry(t_position).or_insert(t);
    if *v != t {
      return None;
    }
  }
  Some(l)
}

fn main() {
    let mut ignore = String::new();
    let mut s = String::new();
    let mut t = String::new();

    io::stdin().read_line(&mut ignore);
    io::stdin().read_line(&mut s);
    io::stdin().read_line(&mut t);

    match good_string(&s.trim(), &t.trim()) {
        None => println!("-1"),
        Some(r) => println!("{}", r),
    }
}