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;
using System.Collections.Generic;
using System.IO;
using static System.Console;


namespace atcorder2
{
    class Program
    {
        public static long Read()
        {

            return long.Parse(Console.ReadLine());
        }

        public static long[] Reads()
        {

            return Console.ReadLine().Split().Select(long.Parse).ToArray();
        }

       
        public static long gcd(long a,long b)
        {
            if (a < b) gcd(b, a);
            while (b > 0)
            {
                long z = b;
                b = a % b;
                a = z;
            }
            return a;
        }
        public static long lcm(long a,long b)
        {
            return a * b / gcd(a, b);
        }




        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);


            var nm = Reads();
            var n = nm[0];
            var m = nm[1];
            var s = ReadLine().ToArray();
            var t = ReadLine().ToArray();

            bool f = true;
            long g = lcm(n, m);
            long a = g / n;
            long b = g / m;
            long ab = lcm(a, b);
            long c = 1;

            long i = 0;
            long j = 0;
            f = false;
            while (i < n && j < m)
            {
                if (s[i] != t[j]) f = true;
                i += b;
                j += a;
            }


            WriteLine(f ? -1 : g);
            




            Console.Out.Flush();
        }
    }
}