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: Runtime Error)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        char[] s = sc.next().toCharArray();
        char[] t = sc.next().toCharArray();
        int len = (int)lcm((long)s.length,(long)t.length);
        char[] ans = new char[len];
        Arrays.fill(ans, '0');
        int spow = len/n;
        for(int i = 0; i < s.length; i++){
            ans[spow*i] = s[i];
        }
        int tpow = (int)(len/m);
        for(int i = 0; i < t.length; i++){
            if(ans[tpow*i] != '0' && ans[tpow*i] != t[i]){
                System.out.println(-1);
                return;
            }
        }
        System.out.println(len);
    }
    
    private static long gcd(long a, long b){
        while (b > 0)
        {
            long temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }
    
    private static long lcm(long a, long b){
        return a * (b / gcd(a, b));
    }
}