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.Collections.Generic;
using System.Linq;


public class A
{
	
	public static void Main()
	{
		string[] args = Console.ReadLine().Split(' ');
		int N = Int32.Parse(args[0]);
		int M = Int32.Parse(args[1]);
		
		string S = Console.ReadLine();
		string T = Console.ReadLine();

		int L = lcm(N,M);
		int LdivN = L/N;
		int LdivM = L/M;
		bool result = true;
		for(int i = 0; i < L; i++)
		{
			if(((i % LdivN) != 0) || ((i % LdivM) != 0))
				continue;
			
			if(S[i/LdivN] != T[i/LdivM])
			{
				result = false;
				break;
			}
		}
		
		Console.WriteLine(result ? L : -1);
	}
	
	
	public static int gcd(int x, int y)
	{
		return ((y == 0) ? x : gcd(y, x%y));
	}
	
	
	public static int lcm(int x, int y)
	{
		return (x * y / gcd(x,y));
	}
	
	
}