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.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();
        int n = nm[0];
        int m = nm[1];
        var s = Console.ReadLine();
        var t = Console.ReadLine();

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

        if (num == Math.Max(n, m))
        {
            var tmp = Math.Max(n, m);
            if (tmp == n)
            {
                var k = 0;
                while (k < m)
                {
                    if (k == 0)
                    {
                        if (s[k] != t[k])
                        {
                            ans = -1;
                            flag = false;
                            break;
                        }
                    }
                    else
                    {
                        int tmp2 = k * num / m + 1;
                        if (s[tmp2 - 1] != t[k])
                        {
                            ans = -1;
                            flag = false;
                            break;
                        }
                    }
                    k++;
                }
            }
            else
            {
                var k = 0;
                while (k < n)
                {
                    if (k == 0)
                    {
                        if (t[k] != s[k])
                        {
                            ans = -1;
                            flag = false;
                            break;
                        }
                    }
                    else
                    {
                        var tmp2 = k * num / n + 1;
                        if (t[tmp2 - 1] != s[k])
                        {
                            ans = -1;
                            flag = false;
                            break;
                        }
                    }
                    k++;
                }
            }
        }
        else
        {
            ans = num;
        }

        // 出力
        Console.WriteLine(ans);
    }

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

    // ユークリッドの互除法 
    public static int Gcd(int a, int 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;
    }
}