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: Wrong Answer)

def gcd(lhs, rhs)
  return lhs if rhs == 0
  return gcd(rhs, lhs) if lhs < rhs

  mod = lhs % rhs
  div = lhs / rhs

  return gcd(rhs, mod)
end

s_length, t_length = gets.split.map(&:to_i)
s = gets.chomp
t = gets.chomp

gcd_res = gcd(s_length, t_length)
x_length = s_length * t_length / gcd_res

ok = true
(x_length / gcd_res).times do |i|
  if s[i * s_length / gcd_res] != t[i * t_length / gcd_res]
    ok = false
    break
  end
end

if ok
  puts x_length
else
  puts -1
end