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.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int A = int.Parse(str[0]);
		int B = int.Parse(str[1]);
		string s = Console.ReadLine();
		string t = Console.ReadLine();
		int L = Lcm(A,B);
		int M = A*B;
		int ans = L;
		for(var i=0;i<M/L;i++){
			int a1 = i*A/(M/L);
			int a2 = i*B/(M/L);
			if(s.Substring(a1,1) != t.Substring(a2,1)){
				ans = -1;
				break;
			}
		}
		Console.WriteLine(ans);
	}
	
	public static int Lcm(int a, int b) {
        return a * b / Gcd(a, b);
    }

	public static int Gcd(int a, int b) {
		if (a < b)
			return Gcd(b, a);
		while (b != 0) {
			var r = a % b;
			a = b;
			b = r;
		}
		return a;
	}
}