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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = ReadArrayLong();
            var N = input[0];
            var M = input[1];
            var S = Read();
            var T = Read();
            var L = Lcm(N, M);
            var Sn = new int[L];
            var Tn = new int[L];
            for (int i = 1; i < N; i++) Sn[i * (L / N)] = i;
            for (int i = 1; i < M; i++) Tn[i * (L / M)] = i;
            if (S[0] != T[0]) { Console.WriteLine(-1); return; }
            for (long i = 1; i < L; i++)
            {
                if (Sn[i] != 0 && Tn[i] != 0)
                {
                    if (S[Sn[i]] != T[Tn[i]])
                    {
                        Console.WriteLine(-1);
                        return;
                    }
                }
            }

            Console.WriteLine(L);
            Console.ReadLine();
        }

        static long Gcd(long a, long b) { if (b == 0) return a; return Gcd(b, a % b); }
        static long Lcm(long a, long b) { return a / Gcd(a, b) * b; }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}