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# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.ReadLine();

            var strS = Console.ReadLine();
            var strT = Console.ReadLine();

            var lenS = strS.Length;
            var lenT = strT.Length;

            var arrS = strS.ToCharArray();
            var arrT = strT.ToCharArray();

            var lcm = lenS * lenT / Gcd(lenS, lenT);

            if (lenS % lenT == 0)
            {
                for (int i = 0; i < lenT; i++)
                {
                    if (arrT[i] != i * (lenS / lenT))
                    {
                        Console.WriteLine(-1);
                        return;
                    }
                }
            }

            if (lenT % lenS == 0)
            {
                for (int i = 0; i < lenS; i++)
                {
                    if (arrS[i] != i * (lenT / lenS))
                    {
                        Console.WriteLine(-1);
                        return;
                    }
                }
            }


            for (int i = lcm; ; i += lcm)
            {
                var dS = i / lenS;
                var dT = i / lenT;
                var jd = true;
                for (int j = 0; j < lenS; j++)
                {
                    var c = dS * j;
                    if (c / dT >= lenT)
                    {
                        Console.WriteLine(i);
                        return;
                    }
                    if (c % dT == 0 && arrS[j] != arrT[c / dT])
                    {
                        jd = false;
                        break;
                    }
                }
                if (jd)
                {
                    Console.WriteLine(i);
                    return;
                }
            }
        }

        public static int Gcd(int a, int b)
        {
            if (a < b)
                return Gcd(b, a);
            while (b != 0)
            {
                var r = a % b;
                a = b;
                b = r;
            }
            return a;
        }
    }
}