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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long N = sc.nextInt();
        long M = sc.nextInt();
        char[] s = sc.next().toCharArray();
        char[] t = sc.next().toCharArray();
        sc.close();
        long lcm = lcm(N, M);
        long n = lcm / N;
        long m = lcm / M;
        boolean success = true;
        for(int i = 0; i < N; i++){
            if((n * i) % m == 0){
                if(s[(int) (i)] != t[(int) (n * i / m)]){
                    success = false;
                    break;
                }
            }
        }

        if(success){
            System.out.println(lcm);
        }else{
            System.out.println(-1);
        }
    }

    private static long gcd(long n, long m){
        if(n < m) return gcd(m, n);
        if(m == 0) return n;
        return gcd(m, n % m);
    }
    private static long lcm(long n, long m){
        return n * m / gcd(n, m);
    }
}