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)

def gcd(a,b)
    return a if b == 0
    gcd(b,a%b)
end

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

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

ss={}
tt={}
l = lcm(n,m)
0.upto(s.size-1) do |i|
    ss[i*l/s.size]  = i
end
0.upto(t.size-1) do |i|
    tt[i*l/t.size] = i
end


ss.each do |k, v|
    if tt.has_key?(k)
        if s[ss[k]] != t[tt[k]]
            puts -1
            exit
        end
    end
end
puts l