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;

    class AGC028A
    {
        static void Main(string[] args)
        {
            Method(args);
        }

        static void Method(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int n = int.Parse(input[0]);
            int m = int.Parse(input[1]);

            string s = Console.ReadLine();
            string t = Console.ReadLine();

            int l = Lcm(n, m);

            if(n < m)
            {
                Swap(ref n, ref m);
                Swap(ref s, ref t);
            }
            int ln = l / n;
            int lm = l / m;

            // sとtが同じxの番目に被る時だけ考える
            // 被らないとこは自由にいじれるから関係ない

            for (int i = 0; i < l; i++)
            {
                //Console.WriteLine("{0} {1}", ln, lm);
                // xのl/nとl/mの最大公約数*i+1番目の要素のみを確認
                if (i % (Lcm(ln, lm)) == 0)
                {
                    if (i / (Lcm(ln,lm)) * lm <= n-1 && i / (Lcm(ln, lm)) * ln <= m-1) // ここもおかしい
                    {
                        if (s[i / (Lcm(ln, lm)) * lm] != t[i / (Lcm(ln, lm)) * ln])
                        {
                            Console.WriteLine(-1);
                            return;
                        }
                    }
                }
            }

            Console.WriteLine(l);
        }

        // 最小公倍数
        static int Gcd(int a, int b)
        {
            int c = b;
            do
            {
                c = a % b;
                a = b;
                b = c;
            } while (c > 0);
            return a;
        }

        // 最大公約数
        static int Lcm(int m, int n)
        {
            int g = Gcd(m, n);
            return m * n / g;
        }

        static void Swap<T>(ref T a, ref T b)
        {
            var t = a;
            a = b;
            b = t;
        }
    }