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.Scanner;

public class Main {
    public static void main(final String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final long n = scanner.nextLong();
        final long m = scanner.nextLong();
        scanner.nextLine();
        final String s = scanner.nextLine();
        final String t = scanner.nextLine();

        final long gcd = getGCD(n, m);

        for (int i = 0; i < gcd; i++) {
            final char a = s.charAt((int)(i * n / gcd));
            final char b = t.charAt((int)(i * m / gcd));

            if (a != b) {
                System.out.println(-1);
                return;
            }
        }

        final long lcm = n * m / gcd;
        System.out.println(lcm);
    }

    private static long getGCD(final long a, final long b) {
        if (b > a) {
            return getGCD(b, a);
        }

        if (b == 0) {
            return a;
        }

        return getGCD(b, a % b);
    }
}