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: Accepted)

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.WriteLine(solve());
            return;
        }

        private static long solve()
        {
            Console.ReadLine();
            var strS = Console.ReadLine();
            var strT = Console.ReadLine();

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

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

            if (lenS < lenT)
            {
                lenS = strT.Length;
                lenT = strS.Length;

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

            long gcm = Gcd(lenS, lenT);
            long lcm = lenS / Gcd(lenS, lenT) * lenT;

            //if (gcm == 1) return lcm;

            for (long i = 0; i < lenT; i++)
            {
                if (i * lenS / gcm >= lenS || i * lenT / gcm >= lenT) break;
                if (arrS[i * lenS / gcm] != arrT[i * lenT / gcm]) return -1;
            }
            return lcm;
        }

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