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;

//https://beta.atcoder.jp/contests/agc028/tasks/agc028_a

public class Program_AGC028_A // ←Class名変更！！
{
    public static void Main(string[] args)
    {
        var st = Console.ReadLine();
        var s = Console.ReadLine();
        var t = Console.ReadLine();

        var l = Lcm(s.Length, t.Length);
        var x = new Dictionary<long, char>();

        for (int i = 0; i < s.Length; i++)
        {
            var pos = i * (l / s.Length) + 1;
            x[pos] = s[i];
        }


        for (int i = 0; i < t.Length; i++)
        {
            var pos = i * (l / t.Length) + 1;
            if (x.ContainsKey(pos))
            {
                if (x[pos] != t[i])
                {
                    Console.WriteLine(-1);
                    return;

                }
            }
        }

        Console.WriteLine(l);
    } // Main



    // 最小公倍数 least common multiple 
    //public static long Lcm(int a, int b)
    //{
    //    return a * b / Gcd(a, b);
    //}

    // ユークリッドの互除法 
    //public static int Gcd(int a, int b)
    //{
    //    if (a < b)  return Gcd(b, a); // 引数を入替えて自分を呼び出す

    //    while (b != 0)
    //    {
    //        var temp = a % b;
    //        a = b;
    //        b = temp;
    //    }

    //    return a;
    //}





    static long Gcd(long a, long b)
    {
        var small = Math.Min(a, b);
        var big = Math.Max(a, b);

        if (small > 0)
        {
            return Gcd(small, big % small);
        }
        else
        {
            return big;
        }


        //if (a < b)
        //{
        //    return Gcd(b, a);
        //}
        //else
        //{
        //    if (b > 0)
        //    {
        //        return Gcd(b, a % b);
        //    }
        //    else
        //    {
        //        return a;
        //    }
        //}

        //return (a < b) ? Gcd(b, a)
        //     : (b > 0) ? Gcd(b, a % b)
        //               : a;
    }

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


    static long gcd(long a, long b)
    {
        long c = Math.Max(a, b) % Math.Min(a, b);
        b = Math.Min(a, b);
        while (c != 0)
        {
            a = b % c;
            b = c;
            c = a;
        }
        return b;
    }

}     // Class