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.Text;

namespace atc
{
    class Program
    {
        static void Main(string[] args)
        {
            var bufs = Console.ReadLine().Split();
            var N = int.Parse(bufs[0]);
            var M = int.Parse(bufs[1]);
            var S = Console.ReadLine();
            var T = Console.ReadLine();

            var L = Lcm(N, M);
            var dic = new Dictionary<long, char>();

            //Sを格納
            for (int i = 0; i < N; i++)
            {
                var index = (i * L / N) + 1;
                dic.Add(index, S[i]);
            }

            //TがＳと被るか
            bool hasErr = false;
            for (int i = 0; i < M; i++)
            {
                var index = (i * L / M) + 1;
                if(dic.ContainsKey(index))
                {
                    if (T[i] != dic[index])
                    {
                        //矛盾あり！
                        hasErr = true;
                        break;
                    }
                }
            }

            if(hasErr)
            {
                Console.WriteLine(-1);
            }else
            {
                Console.WriteLine(L);
            }
        }

        static long Lcm(int a, int b)
        {
            return (long)a * b / Gcd(a, b);
        }

        static int Gcd(int a, int b)
        {
            if (a < b)
            {
                return Gcd(b, a);
            }

            while(b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;

        }

    }
}