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 7.10.3) (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE CPP                   #-}
{-# LANGUAGE LambdaCase            #-}
{-# LANGUAGE MagicHash             #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE MultiWayIf            #-}
{-# LANGUAGE OverloadedStrings     #-}
{-# LANGUAGE TupleSections         #-}
{-# LANGUAGE TypeFamilies          #-}
{-# LANGUAGE ViewPatterns          #-}

import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.ST
import           Control.Monad.State.Strict
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 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.MutVar
import qualified Data.Set                    as S
import           Data.Tuple
import qualified Data.Vector                 as V
import qualified Data.Vector.Generic         as G
import qualified Data.Vector.Generic.Mutable as GM
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 qualified System.IO                   as IO
import           Unsafe.Coerce

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' lenS lenT z = runST $ do
    uf <- newUnionFind lenT
    let go ((src,dst):es) = do
          merged <- uniteM uf src dst
          if merged
          then go es
          else return (-1)
        go [] = do
            max 0.subtract 1.U.maximum <$> U.mapM (sizeM uf) (U.generate lenT id)
    go $ U.toList edges
  where
    n = lenT
    edges = U.map (\(i, _) -> (i, rem (i + lenS) n))
        . U.filter ((>=lenS).snd)
        . U.indexed
        $ U.slice (lenS + 1) lenT z

rep :: Monad m => Int -> (Int -> m ()) -> m ()
rep n = U.forM_ (U.generate n id)
{-# INLINE rep #-}

zAlgorithm :: B.ByteString -> U.Vector Int
zAlgorithm s = U.create $ do
    let n = B.length s
    z <- UM.replicate n 0
    fix `flip` 1 `flip` 0 $ \loop !start !matchLen -> do
        when (start < n) $ do
            let lcp = matchLen + naiveLCP
                    (B.unsafeDrop matchLen s)
                    (B.unsafeDrop (start + matchLen) s)
            UM.unsafeWrite z start lcp
            if lcp == 0
            then loop (start + 1) lcp
            else do
                flip fix 1 $ \inner !k -> do
                    zk <- UM.unsafeRead z k
                    if k + zk < lcp
                    then do
                        UM.unsafeWrite z (start + k) zk
                        inner (k + 1)
                    else loop (start + k) (lcp - k)
    return z

naiveLCP :: B.ByteString -> B.ByteString -> Int
naiveLCP xs ys = go 0
  where
    !n = B.length xs `min` B.length ys
    go !i
        | i < n, B.unsafeIndex xs i == B.unsafeIndex ys i = go (i + 1)
        | otherwise = i
-------------------------------------------------------------------------------

newtype UnionFind m = UF { parent :: UM.MVector m Int }

newUnionFind :: PrimMonad m => Int -> m (UnionFind (PrimState m))
newUnionFind n = UF <$> UM.replicate n (-1)
{-# INLINE newUnionFind #-}

findM :: PrimMonad m => UnionFind (PrimState m) -> Int -> m Int
findM uf x = go x return
  where
    go !x k = do
        px <- UM.unsafeRead (parent uf) x
        if px < 0
        then k x
        else go px $ \ppx -> do
            UM.unsafeWrite (parent uf) x ppx
            k ppx
{-# INLINE findM #-}

sizeM :: PrimMonad m => UnionFind (PrimState m) -> Int -> m Int
sizeM uf = fix $ \loop x -> do
    px <- UM.unsafeRead (parent uf) x
    if px < 0
    then return $! negate px
    else loop px
{-# INLINE sizeM #-}

uniteM :: PrimMonad m => UnionFind (PrimState m) -> Int -> Int -> m Bool
uniteM uf x y = do
    px <- findM uf x
    py <- findM uf y
    if px == py
    then return False
    else do
        rx <- UM.unsafeRead (parent uf) px
        ry <- UM.unsafeRead (parent uf) py
        if rx < ry
        then do
            UM.unsafeModify (parent uf) (+ry) px
            UM.unsafeWrite (parent uf) py px
        else do
            UM.unsafeModify (parent uf) (+rx) py
            UM.unsafeWrite (parent uf) px py
        return True
{-# INLINE uniteM #-}

equivM :: PrimMonad m => UnionFind (PrimState m) -> Int -> Int -> m Bool
equivM uf x y = (==) `liftM` findM uf x `ap` findM uf y
{-# INLINE equivM #-}

-- | O(n)
countGroupM :: PrimMonad m => UnionFind (PrimState m) -> m Int
countGroupM uf = U.length . U.filter (<0) <$> U.unsafeFreeze (parent uf)
{-# INLINE countGroupM #-}

type Parser a = C.ByteString -> Maybe (a, C.ByteString)

parseInt :: Parser Int
parseInt = C.readInt . C.dropWhile isSpace

parseInt2 :: Parser (Int, Int)
parseInt2 = runStateT $
    (,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)

parseInt3 :: Parser (Int, Int, Int)
parseInt3 = runStateT $
    (,,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)

parseInt4 :: Parser (Int, Int, Int, Int)
parseInt4 = runStateT $
    (,,,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)