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: Accepted)

require 'pp'
# IS_DEBUG = true
IS_DEBUG = false
def dputs str
	if(IS_DEBUG)
		puts str
	end
end
def dpp str
	if(IS_DEBUG)
		pp str
	end
end
 
def gcd(a,b)
	if(a>b)
		return gcd(b,a)
	end
	if(b%a == 0)
		return a
	else
		return gcd(a,b%a)
	end
end
def lcm(a,b)
	a/gcd(a,b)*b
end
 
MAX_INT = 9999999999999999
 
N,M=gets.chomp.split(' ').map{|n| n.to_i}
S=gets.chomp.split('').map{|n| n}
T=gets.chomp.split('').map{|n| n}
g = gcd(N,M)
nd = N/g
md = M/g
for i in 0..(g-1)
	if(S[i*nd] != T[i*md])
		puts -1
		exit(0)
	end
end
puts lcm(N,M)