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 (long)a * b / Gcd(a, b) ;
        //return (long)(a  / Gcd(a, b)) * (long)b;    //桁あふれをさせないために早めに割る。
    }

    //ユークリッドの互除法
    public static long 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;
    }

}     // Class