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: Wrong Answer)

import java.util.*;

public class Main{

    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        
        int N = sc.nextInt();
        int M = sc.nextInt();
        String S = sc.next();
        String T = sc.next();
        sc.close();

        long L = (long)(N*M)/gcd(N, M);

        int n = N/gcd(N, M);
        int m = M/gcd(N, M);

        for(int k = 0; k < gcd(N, M); k++){
            if(S.charAt(k*n) == T.charAt(k*m))
                continue;
            else {
                System.out.println(-1);
                return;
            }
        }
        System.out.println(L);
    }

    static int gcd(int n, int m){
        if(n < m)
            return gcd(m, n);
        else{
            if(m == 0)
                return n;
            else
                return gcd(m, n%m);
        }
    }
}