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.Scanner;

public class Main {
	public static int gcd(int a, int b) {
		return b > 0 ? gcd(b, a % b) : a;
	}

	public static int lcm(int a, int b) {
		return a * b / gcd(a, b);
	}

	public static void main(String args[]) {

		Scanner sc = new Scanner(System.in);

		String nm = sc.nextLine();
		String[] len = nm.split(" ");

		int n = Integer.parseInt(len[0]);
		int m = Integer.parseInt(len[1]);

		String s = sc.nextLine();
		String t = sc.nextLine();

		for (int i = 0; i < n; i++) {
			if ((m * i) % n == 0) {
				try {
					if (s.charAt(i) != t.charAt((m * i) / n)) {
						System.out.println("-1");
						return;
					}
				} catch (Exception e) {
					System.out.println("-1");
					return;
				}
			}
		}

		System.out.println(lcm(n, m));
		return;
	}
}