Problem:
Score : 600 points

Problem Statement

Given are two strings s and t consisting of lowercase English letters. Determine if the number of non-negative integers i satisfying the following condition is finite, and find the maximum value of such i if the number is finite.

There exists a non-negative integer j such that the concatenation of i copies of t is a substring of the concatenation of j copies of s.

Notes

A string a is a substring of another string b if and only if there exists an integer x (0 \leq x \leq |b| - |a|) such that, for any y (1 \leq y \leq |a|), a_y = b_{x+y} holds.

We assume that the concatenation of zero copies of any string is the empty string. From the definition above, the empty string is a substring of any string. Thus, for any two strings s and t, i = 0 satisfies the condition in the problem statement.

Constraints

1 \leq |s| \leq 5 \times 10^5

1 \leq |t| \leq 5 \times 10^5

s and t consist of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s
t

Output

If the number of non-negative integers i satisfying the following condition is finite, print the maximum value of such i; if the number is infinite, print -1.

Sample Input 1

abcabab
ab

Sample Output 1

3

The concatenation of three copies of t, ababab, is a substring of the concatenation of two copies of s, abcabababcabab, so i = 3 satisfies the condition.

On the other hand, the concatenation of four copies of t, abababab, is not a substring of the concatenation of any number of copies of s, so i = 4 does not satisfy the condition.

Similarly, any integer greater than 4 does not satisfy the condition, either. Thus, the number of non-negative integers i satisfying the condition is finite, and the maximum value of such i is 3.

Sample Input 2

aa
aaaaaaa

Sample Output 2

-1

For any non-negative integer i, the concatenation of i copies of t is a substring of the concatenation of 4i copies of s. Thus, there are infinitely many non-negative integers i that satisfy the condition.

Sample Input 3

aba
baaab

Sample Output 3

0

As stated in Notes, i = 0 always satisfies the condition.

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns, BinaryLiterals, CPP, DerivingStrategies  #-}
{-# LANGUAGE DerivingVia, FlexibleContexts, FlexibleInstances       #-}
{-# LANGUAGE GeneralizedNewtypeDeriving, KindSignatures, LambdaCase #-}
{-# LANGUAGE MagicHash, MultiParamTypeClasses, MultiWayIf           #-}
{-# LANGUAGE NumericUnderscores, OverloadedStrings, PatternSynonyms #-}
{-# LANGUAGE RankNTypes, RecordWildCards, ScopedTypeVariables       #-}
{-# LANGUAGE StandaloneDeriving, TupleSections, TypeApplications    #-}
{-# LANGUAGE TypeFamilies, TypeInType, UnboxedTuples, ViewPatterns  #-}

import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.Reader
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bifunctor
import           Data.Bool
import qualified Data.ByteString                   as B
import qualified Data.ByteString.Builder           as B
import qualified Data.ByteString.Char8             as C
import qualified Data.ByteString.Internal          as B
import qualified Data.ByteString.Unsafe            as B
import           Data.Char
import qualified Data.Foldable                     as F
import           Data.Function
import           Data.Functor.Identity
import qualified Data.IntMap.Strict                as IM
import qualified Data.IntSet                       as IS
import qualified Data.List                         as L
import qualified Data.Map.Strict                   as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive
import           Data.Proxy
import           Data.Ratio
import           Data.Semigroup
import qualified Data.Set                          as S
import           Data.Tuple
import qualified Data.Vector                       as V
import qualified Data.Vector.Algorithms.Intro      as Intro
import qualified Data.Vector.Fusion.Stream.Monadic as MS
import qualified Data.Vector.Fusion.Bundle.Monadic as MB
import           Data.Vector.Fusion.Util
import qualified Data.Vector.Generic               as G
import qualified Data.Vector.Generic.Mutable       as GM
import qualified Data.Vector.Mutable               as VM
import qualified Data.Vector.Primitive             as P
import qualified Data.Vector.Primitive.Mutable     as PM
import qualified Data.Vector.Unboxed               as U
import qualified Data.Vector.Unboxed.Mutable       as UM
import           Debug.Trace
import           Foreign                           hiding (void)
import           GHC.Exts
import           GHC.TypeLits
import           System.IO
import           Unsafe.Coerce

#define MOD 1000000007

main :: IO ()
main = do
    s <- C.getLine
    t <- C.getLine
    print $ solve t s

solve :: C.ByteString -> C.ByteString -> Int
solve pat text
    | lenT < lenS = solve pat $ C.concat $ replicate (div (lenS + lenT - 1) lenT) text
    | otherwise = solve' lenS lenT $ zAlgorithm $ C.concat [pat, "$", text, text]
  where
    !lenS = C.length pat
    !lenT = C.length text

solve' :: Int -> Int -> U.Vector Int -> Int
solve' lenS lenT z = runST $ do
    uf <- newUnionFind lenT
    merged <- U.mapM (\(src, dst) -> uniteUF uf src dst) edges
    if U.and merged
    then U.foldl' max 0 . U.map (subtract 1.negate) . U.filter (<0)
            <$> freezeUnionFind uf
    else return (-1)
  where
    n = lenT
    edges = U.map (\(i, _) -> (i, rem (i + lenS) n))
        . U.filter ((>=lenS).snd)
        . U.indexed
        $ U.slice (lenS + 1) lenT z

data ZBox = ZBox !Int !Int

zAlgorithm :: B.ByteString -> U.Vector Int
zAlgorithm bs
    | B.null bs = U.empty
    | otherwise = U.create $ do
        let !n = B.length bs
        z <- UM.unsafeNew n
        _ <- MS.foldM'
            (\(ZBox l r) l' -> do
                if r < l'
                then do
                    r' <- maybe n id <$> MS.find
                        (\i -> B.unsafeIndex bs (i - l') /= B.unsafeIndex bs i)
                        (stream l' n)
                    UM.unsafeWrite z l' (r' - l')
                    return (ZBox l' (r' - 1))
                else do
                    zl' <- UM.unsafeRead z (l' - l)
                    if zl' < r - l' + 1
                    then do
                        UM.unsafeWrite z l' zl'
                        return (ZBox l r)
                    else do
                        r' <- maybe n id <$> MS.find
                            (\i -> B.unsafeIndex bs (i - l') /= B.unsafeIndex bs i)
                            (stream r n)
                        UM.unsafeWrite z l' (r' - l')
                        return (ZBox l' (r' - 1))
            ) (ZBox 0 0) (stream 1 n)
        UM.write z 0 n
        return z
-------------------------------------------------------------------------------
-- Utils
-------------------------------------------------------------------------------
rep :: (Monad m) => Int -> (Int -> m ()) -> m ()
rep n = flip MS.mapM_ (stream 0 n)
{-# INLINE rep #-}
rev :: (Monad m) => Int -> (Int -> m ()) -> m ()
rev !n = flip MS.mapM_ (streamR 0 n)
{-# INLINE rev #-}
stream :: (Monad m) => Int -> Int -> MS.Stream m Int
stream !l !r = MS.Stream step l where { step x | x < r = return $ MS.Yield x (x + 1) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] stream #-}
streamR :: (Monad m) => Int -> Int -> MS.Stream m Int
streamR !l !r = MS.Stream step (r - 1) where { step x | x >= l = return $ MS.Yield x (x - 1) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] streamR #-}
stream' :: (Monad m) => Int -> Int -> Int -> MS.Stream m Int
stream' !l !r !d = MS.Stream step l where { step x | x < r = return $ MS.Yield x (x + d) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] stream' #-}
infixl 8 `shiftRL`, `unsafeShiftRL`
shiftRL :: Int -> Int -> Int
shiftRL = unsafeShiftRL
{-# INLINE shiftRL #-}
unsafeShiftRL :: Int -> Int -> Int
unsafeShiftRL (I# x#) (I# i#) = I# (uncheckedIShiftRL# x# i#)
{-# INLINE unsafeShiftRL #-}
type Parser a = StateT C.ByteString Maybe a
runParser :: Parser a -> C.ByteString -> Maybe (a, C.ByteString)
runParser = runStateT
{-# INLINE runParser #-}
int :: Parser Int
int = coerce $ C.readInt . C.dropWhile isSpace
{-# INLINE int #-}
int1 :: Parser Int
int1 = fmap (subtract 1) int
{-# INLINE int1 #-}
char :: Parser Char
char = coerce C.uncons
{-# INLINE char #-}
byte :: Parser Word8
byte = coerce B.uncons
{-# INLINE byte #-}
skipSpaces :: Parser ()
skipSpaces = modify' (C.dropWhile isSpace)
{-# INLINE skipSpaces #-}
lowerBoundM :: (Monad m) => Int -> Int -> (Int -> m Bool) -> m Int
lowerBoundM low high p = go low high where { go !low !high | high <= low = return high | otherwise = p mid >>= bool (go (mid + 1) high) (go low mid) where { mid = low + unsafeShiftRL (high - low) 1}}
{-# INLINE lowerBoundM #-}
upperBoundM :: (Monad m) => Int -> Int -> (Int -> m Bool) -> m Int
upperBoundM low high p = do { flg <- p high; if flg then return high else subtract 1 <$!> lowerBoundM low high (fmap not . p)}
{-# INLINE upperBoundM #-}
lowerBound :: Int -> Int -> (Int -> Bool) -> Int
lowerBound low high p = runIdentity (lowerBoundM low high (return . p))
{-# INLINE lowerBound #-}
upperBound :: Int -> Int -> (Int -> Bool) -> Int
upperBound low high p = runIdentity (upperBoundM low high (return . p))
{-# INLINE upperBound #-}
-------------------------------------------------------------------------------
-- Data.UnionFind
-------------------------------------------------------------------------------
newtype UnionFind s = UF{internalUF :: UM.MVector s Int}
newUnionFind :: PrimMonad m => Int -> m (UnionFind (PrimState m))
newUnionFind n = UF <$> UM.replicate n (-1)
{-# INLINE newUnionFind #-}
freezeUnionFind :: PrimMonad m => UnionFind (PrimState m) -> m (U.Vector Int)
freezeUnionFind = U.unsafeFreeze . internalUF
findUF :: PrimMonad m => UnionFind (PrimState m) -> Int -> m Int
findUF uf x = go x return where { go !x k = do { px <- UM.unsafeRead (internalUF uf) x; if px < 0 then k x else go px $ \ ppx -> do { UM.unsafeWrite (internalUF uf) x ppx; k ppx}}}
{-# INLINE findUF #-}
sizeUF :: PrimMonad m => UnionFind (PrimState m) -> Int -> m Int
sizeUF uf = fix $ \ loop x -> do { px <- UM.unsafeRead (internalUF uf) x; if px < 0 then return $! negate px else loop px}
{-# INLINE sizeUF #-}
uniteUF :: PrimMonad m => UnionFind (PrimState m) -> Int -> Int -> m Bool
uniteUF uf x y = do { px <- findUF uf x; py <- findUF uf y; if px == py then return False else do { rx <- UM.unsafeRead (internalUF uf) px; ry <- UM.unsafeRead (internalUF uf) py; if rx < ry then do { UM.unsafeModify (internalUF uf) (+ ry) px; UM.unsafeWrite (internalUF uf) py px} else do { UM.unsafeModify (internalUF uf) (+ rx) py; UM.unsafeWrite (internalUF uf) px py}; return True}}
{-# INLINE uniteUF #-}
equivUF :: PrimMonad m => UnionFind (PrimState m) -> Int -> Int -> m Bool
equivUF uf x y = (==) `liftM` findUF uf x `ap` findUF uf y
{-# INLINE equivUF #-}
countGroupUF :: PrimMonad m => UnionFind (PrimState m) -> m Int
countGroupUF uf = U.length . U.filter (< 0) <$> freezeUnionFind uf
{-# INLINE countGroupUF #-}