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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextInt();
        long m = sc.nextInt();
        String s = sc.next();
        String t = sc.next();
        long max = lcm(n,m);
        long spow = max/n;
        long tpow = max/m;
        for(int i = 0; i < n; i++){
            long index = i*spow;
            if(i == 0 || index % tpow == 0){
                if(s.charAt(i) != t.charAt((int)(index/tpow))){
                    System.out.println(-1);
                    return;
                }
            }else{
                continue;
            }
        }
        System.out.println(max);
    }
    
    private static long gcd(long a, long b){
        while (b > 0){
            long temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }
    
    private static long lcm(long a, long b){
        return a * (b / gcd(a, b));
    }

}