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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {

			//出力の都度更新をやめる
			var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
			Console.SetOut(sw);


			Ans();

			//更新する
			Console.Out.Flush();
			
		}
	public static void Ans() {


				var inputArray = retreiveLongArray();
				var inputCount = 2;

				// 不正な入力は処理しない
				if (inputArray.Length != inputCount) {
					Console.WriteLine("invalid input");
					return;
				}
				var N = inputArray[0];
				var M = inputArray[1];

				var S = retreiveStringArray()[0].Select(x => x).ToArray();
				var T = retreiveStringArray()[0].Select(x => x).ToArray();

				var L = getLcm(N, M);
				var X = new Dictionary<long, char>();
				for (int i = 0; i < N; i++) {

					var position = i * (L / N);
					if (!X.ContainsKey(position)) {
						X.Add(position, S[i]);
					}

				}

				for (int i = 0; i < M; i++) {

					var position = i * (L / M);
					if (!X.ContainsKey(position)) {
						X.Add(position, T[i]);
					}
					else {
						if (X[position] != T[i]) {
							Console.WriteLine(-1);
							return;
						}
					}

				}
				//答えの出力
				var ans = L;
				Console.WriteLine(ans);

			}

			/// <summary>
			/// スペースで区切られた文字列配列の入力を受け取る
			/// </summary>
			/// <returns></returns>
			private static string[] retreiveStringArray() {
				var inputArray = Console.ReadLine().Split(' ');
				return inputArray;
			}

			/// <summary>
			/// スペースで区切られた整数配列の入力を受け取る
			/// </summary>
			/// <returns></returns>
			private static long[] retreiveLongArray() {
				var inputArray = Console.ReadLine().Split(' ');
				var longArray = inputArray.Select(s => long.Parse(s));
				return longArray.ToArray();
			}


			/// <summary>
			/// 2組みずつの入力データ(数値)からTuppleListを作成する
			/// </summary>
			/// <param name="N"></param>
			/// <returns></returns>
			private static List<Tuple<long, long>> createLongTuppleList(long N) {
				var inpList = new List<Tuple<long, long>>();

				for (int i = 0; i < N; i++) {
					var inp = retreiveLongArray();
					var item1 = inp[0];
					var item2 = inp[1];
					inpList.Add(new Tuple<long, long>(item1, item2));
				}
				return inpList;
			}

			/// <summary>
			/// 最小公倍数を返す
			/// </summary>
			/// <param name="a"></param>
			/// <param name="b"></param>
			/// <returns></returns>
			private static long getLcm(long a, long b) {
				return (a * b / getGcd(a, b));
			}

			/// <summary>
			/// 最大公約数
			/// </summary>
			/// <param name="a"></param>
			/// <param name="b"></param>
			/// <returns></returns>
			private static long getGcd(long a, long b) {
				if (a < b) {
					return getGcd(b, a);
				}
				if (b > 0) {
					return getGcd(b, a % b);
				}
				else {
					return a;
				}
			}
	}
}