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: Time Limit Exceeded)

solve _ _ _ [] _ = True
solve _ _ _ _ [] = True
solve l n m (cs:s) (ct:t)
  | condS && condT && cs /= ct = False
  | otherwise = solve (l-1) n m (if condS then s else cs:s) (if condT then t else ct:t)
  where condS = l `mod` n == 0
        condT = l `mod` m == 0

main :: IO ()
main = do
  [n,m] <- map read.words <$> getLine :: IO [Int]
  s <- getLine :: IO String
  t <- getLine :: IO String
  let l = lcm n m
  if solve l (l`div`n) (l`div`m) s t
    then print l
    else print (-1)