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


class Program
{
    static void Main(string[] args)
    {
        // 入力
        int[] nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var n = nm[0];
        var m = nm[1];
        var s = Console.ReadLine();
        var t = Console.ReadLine();

        var ans = 0;
        var flag = true;
        var num = Lcm(n, m);

        char[] c = new char[num];
        for (int i = 0; i < num; i++)
        {
            c[i] = '?';
        }

        //nの判定
        var k = 0;
        while (k < n)
        {
            if (k == 0)
            {
                c[k] = s[k];
            }
            else
            {
                var tmp = k * num / n + 1;
                c[tmp-1] = s[k];
            }
            k++;
        }

        //mの判定
        k = 0;
        while (k < m)
        {
            if (k == 0)
            {
                if (c[k] != t[k])
                {
                    ans = -1;
                    flag = false;
                    break;
                }
            }
            else
            {
                var tmp = k * num / m + 1;
                if (c[tmp-1] != '?' && c[tmp-1] != t[k])
                {
                    ans = -1;
                    flag = false;
                    break;
                }
                else
                {
                    c[tmp-1] = t[k];
                }
            }
            k++;
        }

        if (flag) ans = c.Length;

        // 出力
        Console.WriteLine(ans);
    }

    // 最小公倍数
    public static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }

    // ユークリッドの互除法 
    public static long Gcd(long a, long b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
}