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;

namespace AtCoder {

    class Pair {

        public int Pos;
        public char Char;
    }

    class Program {
        static int Lcm(int a, int b) {
            return a * b / Gcd(a, b);
        }

        static int Gcd(int a, int b) {
            if (a < b)
                return Gcd(b, a);
            int d = 0;
            do {
                d = a % b;
                a = b;
                b = d;
            } while (d != 0);
            return a;
        }
        static List<Pair> GetPos(string target, int L) {

            var len = target.Length;
            var ret = new List<Pair>();

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

                ret.Add(new Pair { Pos = i * L / len, Char = target[i] });
            }
            return ret;
        }

        static void Main(string[] args) {

            Console.ReadLine();
            var S = Console.ReadLine();
            var T = Console.ReadLine();
            var L = Lcm(S.Length, T.Length);

            var result = new char[L];
            var failed = false;

            foreach(var pos in GetPos(S, L)) {

                result[pos.Pos] = pos.Char;
            }
            foreach (var pos in GetPos(T, L)) {

                var test = pos.Char;
                if(result[pos.Pos] != 0 && result[pos.Pos] != test) {

                    failed = true;
                    break;
                }
            }
            Console.WriteLine(failed ? "-1" : L.ToString());
        }
    }
}