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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;

class MainClass
{
    static void Main()
    {
        var NM = ReadLine().Split().Select(int.Parse).ToArray();
        int N = NM[0], M = NM[1];
        string S = ReadLine();
        string T = ReadLine();

        long g = gcd(N, M);
        long l = lcm(N, M);
        long a = N / g;
        long b = M / g;

        bool frag = true;
        int num = 0;
        for (int i = 0; i < g; i++)
        {
            if (S[(int)a * i] != T[(int)b * i])
                frag = false;
        }
        if (frag)
        {
            WriteLine(l);
        }
        else
        {
            WriteLine(-1);
        }
    }
    static long gcd(long a,long b)
    {
        return a == 0 ? b : gcd(b % a, a);
    }
    static long lcm(long a,long b)
    {
        return a * b / gcd(a, b);
    }
}