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: Time Limit Exceeded)

n, m = gets.chop.split.map(&:to_i)
s = gets.chop
t = gets.chop

l = n.lcm(m)

s_diff = l / n
t_diff = l / m

s_arr = []
t_arr = []

n.times do |i|
  s_arr << i * s_diff + 1
end

m.times do |i|
  t_arr << i * t_diff + 1
end

s_str = s.split('')
t_str = t.split('')

s_is = [0]
t_is = [0]
i = 1
loop do
  s_is << i * t_diff
  i += 1
  if s_is.last >= s_arr.length
    s_is.pop
    break
  end
end
i = 1
loop do
  t_is << i * s_diff
  i += 1
  if t_is.last >= t_arr.length
    t_is.pop
    break
  end
end

# p s_is, t_is

flag = true
s_is.each do |s_i|
  break if !flag
  t_is.each do |t_i|
    if s_arr[s_i] == t_arr[t_i]
      if s_str[s_i] != t_str[t_i]
        flag = false
        break
      end
    end
  end
end

if flag
  puts l
else
  puts '-1'
end