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: Accepted)

using System;
using System.Linq;

namespace agc028_a
{
	class Program
	{
		static void Main(string[] args)
		{
			long[] x = Console.ReadLine().Split().Select(long.Parse).ToArray();
			long gcm = x.Min();
			while (!(x[0] % gcm == 0 && x[1] % gcm == 0)) gcm--;
			string s1 = Console.ReadLine(); string s2 = Console.ReadLine();
			string t1 = ""; string t2 = "";
			for (int i = 0; i < gcm; i++) t1 += s1[(int)(x[0] / gcm) * i];
			for (int i = 0; i < gcm; i++) t2 += s2[(int)(x[1] / gcm) * i];
			Console.WriteLine(t1 == t2 ? x[0] * x[1] / gcm : -1);
		}
	}
}