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)

n, m = gets.split(" ").map(&:to_i)
s = gets.chomp.to_s
t = gets.chomp.to_s

lcm = s.size.lcm(t.size)

x = []
y = []

# lcm.times do
#   x.push("")
# end

lcm_s = lcm / s.size
lcm_t = lcm / t.size

lcm_st = lcm_s.lcm(lcm_t)

(lcm_st / lcm_s + 1).times do |num|
  x.push(s[0 + lcm_st / lcm_s * num])
end
# lcm.times do
#   x.push("")
# end

(lcm_st / lcm_t + 1).times do |num|
  y.push(t[0 + lcm_st / lcm_t * num])
end

x.length.times do |num|
  if x[num] != y[num]
    puts "-1"
    exit
  end
end

puts lcm

# lcm_s = lcm / s.size

# s.size.times do |num|
#   x[(1 + lcm_s * num)] = s[num]
# end

# lcm_t = lcm / t.size

# t.size.times do |num|
#   if x[(1 + lcm_t * num)] != "" && x[(1 + lcm_t * num)] != t[num]
#     puts "-1"
#     exit
#   end
# end

# puts lcm