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: Time Limit Exceeded)

using System;
using System.Collections.Generic;

namespace AtCoder.AGC028
{
    class a
    {
        static long Gcd(long x, long y)
        {
            long r = 0;
            while ((r = x % y) != 0)
            {
                x = y;
                y = r;
            }
            return y;
        }

        static long Lcm(long x, long y)
        {
            return (x * y / Gcd(x, y));
        }

        static void Main(string[] args)
        {
            var line = Console.ReadLine().Trim();
            var spl = line.Split(' ');
            var N = int.Parse(spl[0]);
            var M = int.Parse(spl[1]);
            var S = Console.ReadLine().Trim();
            var T = Console.ReadLine().Trim();
            var lm = Lcm(N, M);
            for (long i = Math.Max(N, M); i <= lm; ++i)
            {
                if(i % N == 0 && i % M == 0)
                {
                    bool flg = true;
                    var str = new char[i];
                    for(var j = 0; j < N; ++j)
                    {
                        str[j * (i / N)] = S[j];
                    }
                    for(var j = 0; j < M; ++j)
                    {
                        if(str[j * (i / M)] != '\0' && str[j * (i / M)] != T[j])
                        {
                            flg = false;
                            break;
                        }
                        else
                        {
                            str[j * (i / M)] = T[j];
                        }
                    }
                    if (flg)
                    {
                        Console.WriteLine(i);
                        return;
                    }
                }
            }
            Console.WriteLine(-1);
        }
    }
}