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: Wrong Answer)

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

namespace AtCoder
{
    class Program
    {



        static void Main()
        {
            IO io = new IO();
            Func func = new Func();

            //ここから


            int[] str = io.ReadLineToIntArray();
            int n = str[0];
            int m = str[1];

            int ans = 0;

            string s = io.ReadLineToString();
            string t = io.ReadLineToString();

            int gcd = func.Gcd(n, m);
            int hoge = 0;
            for (int i = 0; i < gcd; i++)
            {
                if (s[(n / gcd * i)] != t[(m / gcd * i)])
                {
                    hoge++;
                }
            }
            ans = hoge == 0 ? func.Lcm(n, m) : -1;



            //ここまで
            Console.Write(ans);
            Console.ReadKey();
        }
    }

    //関数
    public class Func
    {
        public void Swap<T>(ref T a,ref T b)
        {
            T temp;
            temp = a;
            a = b;
            b = temp;
        }

        public int Gcd(int a,int b)
        {
            if (a == b)
            {
                return a;
            }

            if (a > b)
            {
                a = a % b;
            }
            else
            {
                b = b % a;
            }

            if (a == 0)
            {
                return b;
            }
            if (b == 0)
            {
                return a;
            }
            return Gcd(a, b);

        }

        public int Lcm(int a,int b)
        {
            int gcd = Gcd(a, b);
            return a * b / gcd;
        }
    }

    //IOを担う関数群
    public class IO
    {
        //stringの入力
        public string ReadLineToString()
        {
            return Console.ReadLine();
        }

        //intの入力
        public int ReadLineToInt()
        {
            return int.Parse(Console.ReadLine());
        }

        //空白区切りの複数の文字列の入力をstring[]にして返す
        public string[] ReadLineToStringArray()
        {
            return Console.ReadLine().Split(' ').ToArray();
        }


        //空白区切りの複数の整数の入力をint[]にして返す
        public int[] ReadLineToIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        //空白区切りの複数の文字列の入力をList<string>で受け取る
        public List<string> ReadLineToStringList()
        {
            return Console.ReadLine().Split(' ').ToList();
        }

        //空白区切りの複数の整数の入力をList<int>で受け取る
        public List<int> ReadLineToIntList()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToList();
        }
    }

}