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;
using System.Text;

class Program
{
    static void Main(string[] args)
    {
        long[] line = Array.ConvertAll(System.Console.ReadLine().Trim().Split(' '), long.Parse);
        long n = line[0];
        long m = line[1];
        string s = System.Console.ReadLine().Trim();
        string t = System.Console.ReadLine().Trim();

        if (n > m)
        {
            long tmp1;
            string tmp2;

            tmp1 = n;
            n = m;
            m = tmp1;
            tmp2 = s;
            s = t;
            t = tmp2;

        }

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

        System.Console.WriteLine("{0}", Lcm(n, m));

    }

        // 最小公倍数
        static long Lcm(long a, long b)
    {
        return a / Gcd(a, b) * b;
    }

    // 最大公約数
    static long Gcd(long a, long b)
    {
        if (a < b)
            return Gcd(b, a);  // 引数を入替えて自分を呼び出す
        long d = 0;
        do
        {
            d = a % b;
            a = b;
            b = d;
        } while (d != 0);
        return a;
    }

}