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 Ruby (2.3.3) (judge verdict: Runtime Error)

N, M = gets.chomp.split.map(&:to_i)
S = gets.chomp.chars
T = gets.chomp.chars

def gcd(a, b)
  if (a < b)
    # swap(a, b)
    tmp = a
    a = b
    b = tmp
  end

  if (b == 0)
    return a
  end

  gcd(b, a % b)
end

L = N * M / gcd(N, M)

X = Array.new(L, -1)
LN = L/N
LM = L/M
0.upto(N-1).each do |i|
  X[i * LN] = S[i]
end

def solve
  ans = true
  0.upto(M-1).each do |i|
    if (X[i * LM] == -1) || (X[i * LM] == T[i])
      # OK
    else
      ans = false
      break
    end
  end
  
  if ans
    p L
  else
    p -1
  end
end

solve