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.IO;
using System.Linq;
using System.Runtime;
using System.Reflection;
using System.Diagnostics;
using System.Collections.Generic;
using System.Runtime.CompilerServices;
using System.Text;
using System.Text.RegularExpressions;
using static System.Math;

class P
{
    static void Main()
    {
        int[] nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
        string s = Console.ReadLine();
        string t = Console.ReadLine();

        long lcm = Lcm(nm[0], nm[1]);
        Dictionary<long, char> dict = new Dictionary<long, char>();
        long len = lcm / t.Length;
        for (int i = 0; i < t.Length; i++)
        {
            dict.Add(len * i, t[i]);
        }

        len = lcm / s.Length;
        for (int i = 0; i < s.Length; i++)
        {
            if (dict.ContainsKey(len * i))
            {
                if(dict[len * i] != s[i])
                {
                    Console.WriteLine(-1);
                    return;
                }
            }
        }
        Console.WriteLine(lcm);
    }

    static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }

    static long Gcd(long a, long b)
    {
        if (a < b) return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
}