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(string[] args)
        {
            Scanner cin = new Scanner();
            int N = cin.Int();
            int M = cin.Int();
            string S = Console.ReadLine();
            string T = Console.ReadLine();

            if(GCD(N, M) == 1)
            {
                if (S[0] == T[0]) Console.WriteLine(LCM(N, M));
                else Console.WriteLine(-1);
            }
            else
            {
                for(int i = 0; i < GCD(N, M); i++)
                {
                    if(S[i * S.Length / GCD(N, M)] != T[i * T.Length / GCD(N, M)])
                    {
                        Console.WriteLine(-1);
                        return;
                    }
                }
                Console.WriteLine(LCM(N, M));
            }
            
            Console.ReadLine();
        }

        static int GCD(int a, int b) //a,bの最大公約数を返す
        {
            if (a < b)
                // 引数を入替えて自分を呼び出す
                return GCD(b, a);
            while (b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }

        static int LCM(int a, int b) //a,bの最小公倍数を返す
        {
            return a / GCD(a, b) * b;
        }
    

        static int BinarySearch<T>(T[] array, T target) where T : IComparable<T> //2分探索
        {
            int min = 0;
            int max = array.Length - 1;

            while (true)
            {
                // 範囲内に見つからなかった
                if (max < min) return -1;
                // 範囲内の中央値と比較する
                int mid = min + (max - min) / 2;
                switch (target.CompareTo(array[mid]))
                {
                    case -1:    // 中央値より小さい
                        max = mid - 1;
                        break;
                    case 1:     // 中央値より大きい
                        min = mid + 1;
                        break;
                    case 0:     // 見つかった
                        return mid;
                }
            }
        }

        static void Swap<T>(ref T a, ref T b)
        {
            T tmp = a;
            a = b;
            b = tmp;
        }
    }

    class Scanner //標準入力
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int Int()
        {
            return int.Parse(next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = Int() + add;
            }
            return Array;
        }

        public long Long()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = Long() + add;
            }
            return Array;
        }

        public double Double()
        {
            return double.Parse(next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = Double() + add;
            }
            return Array;
        }
    }
}