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.Linq;
class c
{
    static void Main()
    {
        var nm = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        var s = Console.ReadLine();
        var t = Console.ReadLine();
        if (nm[0] > nm[1])
        {
            nm = nm.OrderBy(_ => _).ToArray();
            var temp = s;
            s = t;
            t = temp;
        }
        long n = nm[0];
        long m = nm[1];
        int now = nm[1] % nm[0];
        while (now != 0)
        {
            nm[1] = nm[0];
            nm[0] = now;
            now = nm[1] % nm[0];
        }
        long gcd = nm[0];
        long lcm = n * m / gcd;
        bool judge = true;
        for (int i = 0; i < gcd; i++)
        {
            if (s[(int)(i * lcm / m)] != t[(int)(i * lcm / n)]) judge = false;
        }
        Console.WriteLine(judge ? lcm : -1);
    }
}