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.*;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();
		char[] S = sc.next().toCharArray();
		char[] T = sc.next().toCharArray();
		if(S[0]!=T[0]){
			System.out.println("-1");
			System.out.flush();
			return;
		}
		int gcd = getGCD(N, M);
		int lcm = (N * M)/gcd;
		int n = M/gcd;
		int m = N/gcd;
		for(long i=0; i<lcm; i+=n){
			if(i%m==0 && S[(int)(i/n)]!=T[(int)(i/m)]){
				System.out.println("-1");
				System.out.flush();
				return;
			}
		}
		System.out.println(lcm);
	}
	private static int getGCD(int m, int n) {
        if(m < n){return getGCD(n, m);}
        if(n == 0){return m;}
        return getGCD(n, m%n);
    }
}