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

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


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

        Console.WriteLine(l);
    } // Main



    /// <summary>
    /// 最小公倍数 least common multiple
    /// aで最小公倍数を割っても、bで最小公倍数を割っても割り切れる一番小さな値
    /// </summary>
    public static long Koubai_Lcm(int a, int b)
    {
        //a,b 2つの値の場合、次の関係が成り立つ   a * b = gcd * lcm
        return (long)a * b / Kouyaku_Gcd(a, b);    //桁あふれをさせないように、最初にlongにキャストする。
    }


    /// <summary>
    /// 最大公約数 Greatest Common Measure
    /// 最大公約数でaを割っても、bを割っても割り切れる一番大きな値
    /// ユークリッドの互除法
    /// </summary>
    public static long Kouyaku_Gcd(int a, int b)
    {
        if (a < b) return Kouyaku_Gcd(b, a); // 引数を入替えて自身を呼び出す

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

        return a;
    }

}     // Class