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 static System.Console;

class Program
{
    static void Main()
    {
        var nm = ReadLine().Split().Select(long.Parse).ToArray();
        var lcm = Lcm(nm[0], nm[1]);
        var dic = new Dictionary<long, char>();
        var s = ReadLine();
        for (int i = 0; i < nm[0]; i++)
        {
            dic[lcm / nm[0] * i] = s[i];
        }
        var t = ReadLine();
        for (int i = 0; i < nm[1]; i++)
        {
            if (dic.ContainsKey(lcm / nm[1] * i) && dic[lcm / nm[1] * i] != t[i])
            {
                WriteLine(-1);
                return;
            }
        }
        WriteLine(lcm);
    }
    static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }
    static long Gcd(long a, long b)
    {
        if (b == 0) return a;
        return Gcd(b, a % b);
    }
}