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 void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long m = sc.nextLong();
        String s = sc.next();
        String t = sc.next();
        long seki = lcm(n, m);
        long NL = seki / n;
        long ML = seki / m;
        
        int sCount = 0;
        int tCount = 0;
        long ss = 0;
        long tt = 0;
        boolean flag = true;
        for(long i = 0;i < seki;i += Math.min(NL,ML)){
            if(ss == tt){
                if(s.charAt(sCount) != t.charAt(tCount)){
                    flag = false;
                }
                sCount++;
                tCount++;
                ss += NL;
                tt += ML;
            }else if(ss < tt){
                sCount++;
                ss += NL;
            }else{
                tCount ++;
                tt += ML;
            }
            if(ss >= seki)break;
            if(tt >= seki)break;

        }
        if(flag){
            System.out.println(seki);    
        }else{
            System.out.println(-1);
        }
        

    }

    private static long lcm(long m, long n) {
        return m * n / gcd(m, n);
    }

    private static long gcd(long m, long n) {
        if (m < n)
            return gcd(n, m);
        if (n == 0)
            return m;
        return gcd(n, m % n);
    }
}