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.Diagnostics;
using System.IO;
using System.Linq;

// 解説AC...
namespace AtCoder {
    class Practice {
        static void Main() => CustomMain();

        static void Solve() {
            int n, m;
            ReadMulti(out n, out m);
            var s = ReadString();
            var t = ReadString();

            var g = GCD(n, m);
            var nn = (int) (g / n);
            var mm = (int) (g / m);

            for (int i = 0; i < g; i++) {
                if (s[i * nn] == t[i * mm]) continue;

                WriteAnswer(-1);
                return;
            }

            WriteAnswer(n * m / g);
        }

        static void CustomMain() {
#if DEBUG
            // ファイルからテストケースを読み込む
            global::Common.ChangeStdIn();
            // 時間計測
            var stopwatch = new Stopwatch();
            stopwatch.Start();
#endif
            // 出力高速化
            var streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(streamWriter);
            // 回答
            Solve();
#if DEBUG
            stopwatch.Stop();
            Console.WriteLine(stopwatch.Elapsed);
#endif
            Console.Out.Flush();
        }

        static string ReadString() => Console.ReadLine().Trim();
        static int ReadInt() => int.Parse(ReadString());
        static long ReadLong() => long.Parse(ReadString());
        static float ReadFloat() => float.Parse(ReadString());
        static double ReadDouble => double.Parse(ReadString());

        static string[] ReadStringArray() => ReadString().Split(' ');
        static int[] ReadIntArray() => Array.ConvertAll(ReadString().Split(' '), int.Parse);
        static long[] ReadLongArray() => Array.ConvertAll(ReadString().Split(' '), long.Parse);
        static float[] ReadFloatArray() => Array.ConvertAll(ReadString().Split(' '), float.Parse);
        static double[] ReadDoubleArray() => Array.ConvertAll(ReadString().Split(' '), double.Parse);

        static T TypeConversion<T>(string s) {
            if (typeof(T) == typeof(int)) {
                return (T) Convert.ChangeType(int.Parse(s), typeof(T));
            } else if (typeof(T) == typeof(long)) {
                return (T) Convert.ChangeType(long.Parse(s), typeof(T));
            } else if (typeof(T) == typeof(double)) {
                return (T) Convert.ChangeType(double.Parse(s), typeof(T));
            } else {
                return (T) Convert.ChangeType(s, typeof(T));
            }
        }

        static void ReadMulti<T, U>(out T a, out U b) {
            var str = ReadStringArray();
            a = TypeConversion<T>(str[0]);
            b = TypeConversion<U>(str[1]);
        }

        static void ReadMulti<T, U, V>(out T a, out U b, out V c) {
            var str = ReadStringArray();
            a = TypeConversion<T>(str[0]);
            b = TypeConversion<U>(str[1]);
            c = TypeConversion<V>(str[2]);
        }

        static void WriteAnswer(object ans) => Console.WriteLine(ans);

        static bool IsOdd(long num) {
            return (num & 1) == 1;
        }

        static bool IsEven(long num) {
            return (num & 1) == 0;
        }

        static long GCD(long a, long b) {
            return b != 0 ? GCD(b, a % b) : a;
        }
    }
}