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) {
			 
			Scanner sc = new Scanner(System.in);
	 
			long N = sc.nextInt();
			long M = sc.nextInt();
			char[] S = sc.next().toCharArray();
			char[] T = sc.next().toCharArray();
			long g = gcd(N,M);
			long L = (N * M) / g;
			boolean flag = true;
	 
			for(long i = 0;i<g;i++) {
				if(S[(int)(N/g * i)] != T[(int)(M/g *i)]) {
					flag = false;
				}
			}
	 
			if(flag) {
				System.out.println(L);
			}else {
				System.out.println("-1");
			}
		    sc.close();
		}
	 
	 
	    private static long gcd(long m, long n) {
	        if(m < n) return gcd(n, m);
	        if(n == 0) return m;
	        return gcd(n, m % n);
	    }
}