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;

namespace _158
{
  class Program
  {
    static void Main(string[] args)
    {
      var scan = new Scanner();

      var A = scan.nextInt();
      var B = scan.nextInt();
      var C = scan.nextInt();

      var e = (A + B + 1) > C ? C : (A + B + 1);

      Console.WriteLine(B + e);
    }
  }

  class Scanner
  {
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
      s = new string[0];
      i = 0;
    }

    public string next()
    {
      if (i < s.Length) return s[i++];
      string st = Console.ReadLine();
      while (st == "") st = Console.ReadLine();
      s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
      if (s.Length == 0) return next();
      i = 0;
      return s[i++];
    }

    public int nextInt()
    {
      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] = nextInt() + add;
      }
      return Array;
    }

    public long nextLong()
    {
      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] = nextLong() + add;
      }
      return Array;
    }

    public double nextDouble()
    {
      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] = nextDouble() + add;
      }
      return Array;
    }
  }

}