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;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {

            var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var n = input[0];
            var m = input[1];

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

            var gcd = GCD(n, m);
            var ss = n / gcd;
            var tt = m / gcd;
            for (int i = 0; i < gcd; i++)
            {
                if(s[ss * i] != t[tt * i])
                {
                    Console.WriteLine("-1");
                    return;
                }
            }
            Console.WriteLine((long)ss * tt * gcd);
    }


        static int GCD(int x, int y)
        {
            if (x < y) return GCD(y, x);
            var r = x % y;
            if (r == 0) return y;
            return GCD(y, r);
        }

}