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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using E = System.Linq.Enumerable;
using System.IO.Pipes;

class Program
{
    static char[] abc = "abcdefghijklmnopqrstuvwxyz".ToCharArray();
    static long mod = 1000000007;

    static long X1;
    static long Y1;
    static long R;
    static long X2;
    static long Y2;
    static long X3;
    static long Y3;
    static void Main(string[] args)
    {
        //var S = Console.ReadLine();
        //var A = long.Parse(Console.ReadLine());
        var NM = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var N = NM[0];
        var M = NM[1];
        var S = Console.ReadLine();
        var T = Console.ReadLine();
        
        var LCM = Lcm(N,M);
        long ans = LCM;
        if (N <= LCM || M <= LCM)
        {
            ans = -1;
        }
        else
        {
            var tmp = new char[LCM];
            for (int i = 0; i < tmp.Length; i++)
            {
                tmp[i] = '@';
            }

            for (long i = 0; i < N; i += (LCM / N))
            {
                tmp[i] = S[(int)i];
            }

            for (long i = 0; i < M; i += (LCM / M))
            {
                if (tmp[i] != '@' && tmp[i] != T[(int)i])
                {
                    ans = -1;
                    break;
                }
            }
        }
        

        Console.WriteLine(ans);
        
    }

    public static long Gcd(long a, long b)
    {
        var x = 0L;

        while (true)
        {
            // 割り切れたら
            if (a % b == 0)
            {
                return b;
            }
            else
            {
                x = a % b;
                a = b;
                b = x;

            }
        }

    }
    // 最小公倍数
    public static long Lcm(long a, long b)
    {
        var x = Gcd(a, b);

        return a * b / x;
    }



}