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(a, b)
  a, b = b, a if a > b
  until a == 0
    a, b = b % a, a
  end
  return b
end

def lcm(a, b)
  a*b/gcd(a, b)
end

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

aryS = S.chars
aryT = T.chars

if aryS.size >= aryT.size
  a = aryS
  b = aryT
else
  a = aryT
  b = aryS
end

if N % M == 0 || M % N == 0
  times = a.size / b.size
  i = 0
  is_exist = true
  b.size.times do |j|
    if(a[i] != b[j])
      is_exist = false
    end
    i += times
  end
  if is_exist
    puts a.size
  else
    puts -1
  end
else
  if a[0] == b[0]
    puts lcm(N, M)
  else
    puts -1
  end
end