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-mcs 6.8.0.105) (judge verdict: Runtime Error)

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(ReadLine());
        }

        public static long[] Reads()
        {
            return ReadLine().Split().Select(long.Parse).ToArray();
        }

        
         public static long gcd(long x, long y)
        {
            if (x < y) gcd(y, x);
            while (y != 0)
            {
                var z = x;
                x = y;
                y = z % y;
            }
            return x;
        }

        public static long lcm(long x, long y)
        {
            return x*y/ gcd(x, y);
        }

        public static long C(long n, long k)
        {
            long x = 1;
            for (long i = 1; i <= k; i++)
            {
                x *= n - i + 1;
                x /= i;
            }
            return x;
        }
        static void Main(string[] args)
        {
            var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var q = Reads();
            var n = q[0];
            var m = q[1];
            var s = ReadLine().ToArray();
            var t = ReadLine().ToArray();
            var l = lcm(n, m);
            var x = l / n;
            var y = l / m;
            var f = true;
            var ans = new string[l];
            for (int i = 0; i < l; i++)
            {
                if (i % x == 0 && i % y == 0)
                {
                    if (s[i / x] != t[i / y]) f = false;
                    else ans[i] = s[i / x].ToString();
                }
                else if (i % x == 0)
                {
                    ans[i] = s[i / x].ToString();
                }
                else if (i % y == 0)
                {
                    ans[i] = t[i / y].ToString();
                }
                else
                {
                    ans[i] = "i";
                }
            }
            WriteLine(f?l:-1);
           

            Console.Out.Flush();
        }
    }
}