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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		const long MOD = 1000000007;
		static void Main(string[] args)
		{
			Scanner cin = new Scanner();
		
			int n = cin.Int();
			int m = cin.Int();
			string s = cin.Next();
			string t = cin.Next();

			if (n == m) {
				bool ok = true;
				for (int i = 0; i < n; i++) {
					if (s[i] != t[i]) {
						ok = false;
						break;
					}
				}

				if (ok) {
					Console.WriteLine(n);
				} else {
					Console.WriteLine(-1);
				}
			} else {
				//  ************************
				//12*-*-*-*-*-*-*-*-*-*-*-*-
				//08*--*--*--*--*--*--*--*--
				long gcd = GCD(n, m);
				long nd = n / gcd;
				long md = m / gcd;
				bool ok = true;
				for (int i = 0; i < gcd; i++) {
					if (s[i * (int)nd] != t[i * (int)md]) {
						ok = false;
						break;
					}
				}

				if (ok) {
					Console.WriteLine(LCM(n, m));
				} else {
					Console.WriteLine(-1);
				}
			}
		}

		public static long GCD(long a, long b)
		{
			if (a > b) {
				if (b == 0) {
					return a;
				}

				return GCD(b, a % b);
			} else {
				if (a == 0) {
					return b;
				}

				return GCD(a, b % a);
			}
		}

		public static long GCD(long[] values)
		{
			if (values.Length == 1) {
				return values[0];
			}

			long gcd = values[0];
			for (int i = 1; i < values.Length; ++i) {
				if (gcd == 1) {
					return gcd;
				}
				gcd = GCD(values[i], gcd);
			}

			return gcd;
		}

		public static long LCM(long a, long b)
		{
			return a / GCD(a, b) * b;
		}

		public static List<long> GetPrimeFactors(long value)
		{
			var factors = new List<long>();
			for (int i = 2; i * i <= value; ++i) {
				if (value % i == 0) {
					factors.Add(i);
					while (value % i == 0) {
						value /= i;
					}
				}
			}

			return factors;
		}
	}

	public class Scanner
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private string[] buf_;
		private int index_;
		
		public Scanner()
		{
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = Console.ReadLine();
			while (st == "") {
				st = Console.ReadLine();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int()
		{
			return int.Parse(Next());
		}
		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long Long()
		{
			return long.Parse(Next());
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double Double()
		{
			return double.Parse(Next());
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}
	}
}