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 (2.7.1) (judge verdict: Runtime Error)

n, m = gets.split.map(&:to_i)
S = gets.chomp
T = gets.chomp
if S[0] != T[0]
  puts '-1'
  exit
end

c = n.lcm(m)
i = 1
loop do
  d = c * i
  x = Array.new(d, '*')
  y_n = d / n
  a = [1]
  (1..n-1).each do |j|
    a << j * y_n + 1
  end
  b = [1]
  y_m = d / m
  (1..m-1).each do |j|
    b << j * y_m + 1
  end
  a.each_with_index{|j, k| x[j-1] = S[k]}
  flag = true
  b.each_with_index do |j, k|
    next if x[j-1] == '*' || x[j-1] == T[k]
     flag = false
  end
  if flag
    puts d
    exit
  end

  i += 1
  break if i > 1000
end
puts '-1'