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 Control.Arrow
import Data.List
import qualified Data.ByteString.Char8 as B
import Control.Monad

main :: IO ()
main = breads >>= main'
    where
        main' [n, m] = replicateM 2 B.getLine >>= print . solve n m 

solve :: Int -> Int -> [B.ByteString] -> Int
solve n m [ss, ts] = check 0
    where
        check x
            | s >= n || t >= m = l
            | B.index ss s == B.index ts t = check $ x + 1 
            | otherwise = -1
            where
                s = i * x
                t = j * x
        l = lcm n m 
        i = l `div` m
        j = l `div` n 
        

breads :: IO [Int]
breads = unfoldr (\s -> second (maybe B.empty snd . B.uncons) <$> B.readInt s) <$> B.getLine