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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;


public class Main {

	/**
	 * @param args
	 * @throws IOException 
	 */
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String input = br.readLine();

		String[] tmpArray = input.split(" ");

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

		String s = br.readLine();
		String t = br.readLine();


		int l = lcm(n, m);
		
		if(l != n && l != m){
			System.out.println(l);
		}
		else {
			if(n > m){
				String tmpS = s;
				s = t;
				t = tmpS;
				
				n = s.length();
				m = t.length();
			}
			
			for(int i = 0; i < n; i++){
				if(s.charAt(i) != t.charAt(i*(m/n))){
					System.out.println(-1);
					return;
				}
			}
			
			System.out.println(l);
		}
	}

	static int gcd(int a, int b){
		int tmp;

		while (a % b != 0)
		{
			tmp = b;
			b = a % b;
			a = tmp;
		}
		return b;
	}

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

	static int lcm(int a, int b){
		int g = gcd(a, b);

		return lcm(a,b,g);
	}

}