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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

main=do
    (n:m:_)<-map read.words<$>getLine::IO[Int]
    s<-getLine
    t<-getLine
    print $ solve n m s t
--
solve n m s t = if chk ss tt then l else (-1)
    where
        l = lcm n m
        ss = zip [1,1+l`div`n..] s
        tt = zip [1,1+l`div`m..] t
--
chk (s:ss) [] = True
chk [] (t:tt) = True
chk aa@((a,sa):ss) bb@((b,tb):tt)
    | a < b = chk ss bb
    | a > b = chk aa tt
    | sa == tb = chk ss tt
    | otherwise = False