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;
class Program
    {
    	static void Main(string[] args)
    	{
    		// 整数の入力
    		string[] input = Console.ReadLine().Split(' ');
            long[] a = {long.Parse(input[0]), long.Parse(input[1])};

    		string s = Console.ReadLine();
            string t = Console.ReadLine();

    		//出力
            long n = Math.Max(a[0], a[1]), m = Math.Min(a[0], a[1]);
            long big = n; long small = m;
    		while (big % small > 0)
            {
                long buf = big % small;
                big = small;
                small = buf;
            }
            long gcc = small;
            long ret = n * m / gcc;
            for (long i = 0; i < gcc; i++)
            {
                if (s[(int)(a[0] / gcc * i)] != t[(int)(a[1] / gcc * i)])
                {
                    ret = -1;
                    break;
                }
            }
            Console.WriteLine(ret);
        }
    }
    //mcs Main.cs
    //mono Main.exe