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: Time Limit Exceeded)



def gcm(a, b)
	if a > b
		a, b = [b, a]
	end
	mod = b % a
	if mod ==0
		return a
	else
		return gcm(mod, a)
	end
end

def lcm(a, b)
	g = gcm(a, b)
	return g * (a / g) * (b / g)
end

N, M = gets.strip.split(/ /).collect{|n| n.to_i}
S = gets.strip.each_char.collect{|c| c.ord}
T = gets.strip.each_char.collect{|c| c.ord}

def check(cm)
	k1 = cm / N
	k2 = cm / M
	
	l = lcm(k1, k2)
	
	d1 = l / k1
	d2 = l / k2

	cm2 = 0
	while cm2 < cm
		if S[cm2 / k1] != T[cm2 / k2]
			return false
		end
		
		cm2 += l
	end
	
	return true
end

if N == M
	if S == T
		puts N
	else
		puts -1
	end
else
	nm = N * M
	l = lcm(N, M)
	cm = l
	while true
		if check(cm)
			puts cm
			break
		end
		cm += l
		if cm > nm
			puts -1
			break
		end
	end
end