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
T = gets.chomp
Nnum, Mnum,  nmnum = [],[],[]

class Array
  def lcm
    self.inject{|a,b| a.lcm(b)}
  end

  def gcd
    self.inject{|a,b| a.gcd(b)}
  end
end

inc = [N,M].lcm

i = inc
while i <= 100001 do
	N.times do |j|
		Nnum.push(j*(i/N)+1)
	end
	M.times do |k|
		Mnum.push(k*(i/M)+1)
	end	
	#p Nnum, Mnum
	nmnum = Nnum & Mnum
	#番号が1のみ
	if nmnum == [1]
		if S[0] == T[0]
			print("#{i}\n")
			break
		else
			print("-1\n")
			break
		end
	end
	for j in nmnum
		n = ((j-1)*N)/i
		m = ((j-1)*M)/i
		if S[n] != T[m]
			break
		end
		if j == nmnum[-1]
			print("#{i}\n")
			exit
		end
	end
	
	i += inc
	Nnum.clear
	Mnum.clear
	nmnum.clear
end
print("-1\n")