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.*;

class Main{
	
	public static void main(String args[]){

		Scanner sc = new Scanner(System.in);
		long N = sc.nextLong();
		long M = sc.nextLong();

		String A = sc.next();
		String B = sc.next();

		
		long tmp;
		long x=Math.max(N,M);
		long y=Math.min(N,M);
        while ((tmp = x % y) != 0) {
           	x = y;
           	y = tmp;
        }
        long gcd = y;

        long lcm = N*M/gcd;

        boolean f = true;
        outs:for(int n=0;n<N;n++){
        	if(n%(lcm/gcd)!=0) continue;
        	for(int m=0;m<M;m++){
        		if(m%(lcm/gcd)!=0) continue;
        		
        		if(A.charAt(n) != B.charAt(m)){ f = false; break outs;}
        	}
        }
        
       	if(f) System.out.println(lcm);
       	else System.out.println(-1);
		
	}
}