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)

import Data.Maybe (fromMaybe)
import Control.Exception (assert)

{-
S と T の重なるところは整数倍しても同じなので、最小公倍数かそうでないか。
-}

main :: IO ()
main = do
  [n, m] <- map read . words <$> getLine
  s <- getLine
  t <- getLine
  let
    result = assert (length s == n && length t == m) $ f n m s t
  print $ fromMaybe (-1) result


f :: Int -> Int -> String -> String -> Maybe Int
f n m s t = if s' == t' then Just lcm' else Nothing
  where
    gcd' = gcd n m
    lcm' = lcm n m
    s' = everyN (n `div` gcd') s
    t' = everyN (m `div` gcd') t

everyN :: Int -> [a] -> [a]
everyN n xs | n < 1 = xs
everyN _ [] = []
everyN n (x:xs) = x : everyN n (drop (n - 1) xs)