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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Diagnostics.CodeAnalysis;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using System.Xml.Schema;

namespace Contest
{
    class Scanner
    {
        private string[] line = new string[0];
        private int index = 0;
        public string Next()
        {
            if (line.Length <= index)
            {
                line = Console.ReadLine().Split(' ');
                index = 0;
            }
            var res = line[index];
            index++;
            return res;
        }
        public int NextInt()
        {
            return int.Parse(Next());
        }
        public long NextLong()
        {
            return long.Parse(Next());
        }
        public ulong NextUlong()
        {
            return ulong.Parse(Next());
        }
        public string[] Array()
        {
            line = Console.ReadLine().Split(' ');
            index = line.Length;
            return line;
        }
        public int[] IntArray()
        {
            var array = Array();
            var result = new int[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = int.Parse(array[i]);
            }

            return result;
        }
        public long[] LongArray()
        {
            var array = Array();
            var result = new long[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = long.Parse(array[i]);
            }

            return result;
        }
    }

    struct S
    {
        public int X, Y, H;
    }

    class Program
    {
        private int N, M;
        private string S, T;
        private void Scan()
        {
            var sc = new Scanner();
            N = sc.NextInt();
            M = sc.NextInt();

            S = sc.Next();
            T = sc.Next();
        }

        public void Solve()
        {
            Scan();
            long lcm = LCM(N, M);
            if (S == T)
            {
                Console.WriteLine(N);
                return;
            }
            if (S[0] != T[0])
            {
                Console.WriteLine(-1);
                return;
            }
            if (N == lcm)
            {
                int t = N;
                N = M;
                M = t;
                string tt = S;
                S = T;
                T = tt;
            }
            if (M == lcm)
            {
                for (int i = 0; i < N; i++)
                {
                    if (S[i] != T[i * (M / N)])
                    {
                        Console.WriteLine(-1);
                        return;
                    }
                }
            }


            Console.WriteLine(lcm);
        }


        public long LCM(long a, long b)
        {
            return a * b / GCD(a, b);
        }

        public long GCD(long a, long b)
        {
            while (b > 0)
            {
                var r = b;
                b = a % b;
                a = r;
            }
            return a;
        }

        static void Main() => new Program().Solve();
    }
}