Problem:
Score : 500 points

Problem Statement

There are N blocks arranged in a row. Let us paint these blocks.

We will consider two ways to paint the blocks different if and only if there is a block painted in different colors in those two ways.

Find the number of ways to paint the blocks under the following conditions:

For each block, use one of the M colors, Color 1 through Color M, to paint it. It is not mandatory to use all the colors.

There may be at most K pairs of adjacent blocks that are painted in the same color.

Since the count may be enormous, print it modulo 998244353.

Constraints

All values in input are integers.

1 \leq N, M \leq 2 \times 10^5

0 \leq K \leq N - 1

Input

Input is given from Standard Input in the following format:

N M K

Output

Print the answer.

Sample Input 1

3 2 1

Sample Output 1

6

The following ways to paint the blocks satisfy the conditions: 112, 121, 122, 211, 212, and 221. Here, digits represent the colors of the blocks.

Sample Input 2

100 100 0

Sample Output 2

73074801

Sample Input 3

60522 114575 7559

Sample Output 3

479519525

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

{-# LANGUAGE
  ScopedTypeVariables, BangPatterns, TupleSections, ExplicitForAll,
  LambdaCase, MultiWayIf, Unsafe, RecordWildCards, FlexibleContexts, CPP,
  NoMonomorphismRestriction, GADTs, PatternGuards, MagicHash, UnboxedTuples,
  RankNTypes, EmptyDataDecls, EmptyCase, ViewPatterns, PolyKinds,
  TypeFamilies, OverloadedStrings, FlexibleInstances, UndecidableInstances,
  DefaultSignatures, GeneralizedNewtypeDeriving, StandaloneDeriving,
  DeriveGeneric, DeriveFunctor, DeriveDataTypeable, DeriveFoldable,
  DeriveTraversable, DeriveDataTypeable, FlexibleInstances,
  MultiParamTypeClasses, TypeApplications #-}
{-# OPTIONS_GHC -O2 #-}

#define PHASE_FUSED [1]
#define PHASE_INNER [0]
#define INLINE_FUSED INLINE PHASE_FUSED
#define INLINE_INNER INLINE PHASE_INNER

import Prelude
import Data.Bits
import Data.List
import Data.Maybe
import Data.Tuple
import Data.Ord
import Data.Int
import Data.Word
import Data.Char
import Data.Ratio
import Data.Function
import Data.STRef
import Data.IORef
import Data.Monoid
import Data.Functor
import Data.Functor.Identity
import Data.Data
import Data.Typeable
import GHC.Generics
import System.IO
import System.IO.Unsafe (unsafeDupablePerformIO, unsafePerformIO)
import Control.Arrow
import Control.Applicative
import Control.Monad
import Control.Monad.Primitive
import Control.Monad.State.Strict
import Control.Monad.ST
import Control.Monad.ST.Lazy (strictToLazyST, lazyToStrictST)
import qualified Control.Monad.ST.Lazy as STL
-- import Control.Monad.ST.Safe
import Control.DeepSeq
import Data.Coerce
import qualified Data.ByteString as BSW
import qualified Data.ByteString.Char8 as BS
import qualified Data.ByteString.Lazy as BSLW
import qualified Data.ByteString.Lazy.Char8 as BSL
import qualified Data.ByteString.Builder as BSB
import qualified Data.ByteString.Unsafe as BSU
import qualified Data.ByteString.Internal as BSU
import Data.IntMap (IntMap)
import qualified Data.IntMap.Strict as IMS
import qualified Data.IntMap.Lazy as IML
import Data.IntSet (IntSet)
import qualified Data.IntSet as IS
import qualified Data.Sequence as Seq
import Data.Sequence (Seq)
import qualified Data.Array.IArray as A
import qualified Data.Array.MArray.Safe as A
import qualified Data.Array.MArray as A
import Data.Array (Array)
import Data.Array.Unboxed (UArray)
import Data.Array.IArray (IArray)
import Data.Array.MArray.Safe (MArray)
import Data.Array.IO.Safe (IOArray, IOUArray)
import Data.Array.ST.Safe (STArray, STUArray, runSTArray, runSTUArray)
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.Vector.Storable as VS
import qualified Data.Vector.Storable.Mutable as VSM
import qualified Data.Vector.Primitive as VP
import qualified Data.Vector.Primitive.Mutable as VPM
import qualified Data.Vector.Generic as VG
import qualified Data.Vector.Generic.Mutable as VGM
import qualified Data.Vector.Fusion.Bundle.Monadic as VFBM
import qualified Data.Vector.Fusion.Bundle as VFB
import qualified Data.Vector.Fusion.Stream.Monadic as VFSM
import qualified Data.Vector.Fusion.Bundle.Size as VFBS
import qualified Data.Vector.Fusion.Util as VFU
import qualified Data.Vector.Algorithms.Intro as VAIT
import qualified Data.Attoparsec.ByteString.Char8 as Atto
import Debug.Trace
import Unsafe.Coerce
import Foreign.ForeignPtr
import GHC.Exts (build, Int(..), Int#,
                 (+#), (*#), (-#), (<#), (>=#), (==#), quotRemInt#,
                 remInt#, uncheckedIShiftRL#, andI#, orI#,
                isTrue#, Addr#, Ptr(..))

main :: IO ()
main = do
  [n,m,k] <- map readInt . words <$> getLine
  print $ VU.sum $ VU.generate (k+1) $ \ !c ->
    remF (fromIntegral m) * remF (fromIntegral (m-1))^(n-c-1) * comb (n-1) c 
  return ()

comb :: Int -> Int -> RemF
comb n k | n < 0 || k < 0 || k > n = 0
         | otherwise = facto n * factoInv (n-k) * factoInv k


factos :: VU.Vector RemF
factos = VU.scanl' (*) 1 $ VU.map Rem $ VU.tail
         $ VU.generate 200001 fromIntegral
factoInvs :: VU.Vector RemF
factoInvs = VG.unstreamR $ VG.stream $ VU.scanl' (*) (recip $ VU.last factos) $
  VU.map (Rem . fromIntegral) $ VU.generate 200000 (200000-)

facto :: Int -> RemF
{-# INLINE facto #-}
facto = (factos VU.!)
factoInv :: Int -> RemF
{-# INLINE factoInv #-}
factoInv = (factoInvs VU.!)

data FixedModulus

instance HasWord32 FixedModulus where
  {-# INLINE CONLIKE word32Val #-}
  word32Val = const 998244353

type RemF = Rem FixedModulus

pxyF :: Proxy FixedModulus
pxyF = Proxy
remF :: Word32 -> RemF
{-# INLINE CONLIKE remF #-}
remF = Rem

newtype Magic r = Magic (forall (m :: *). HasWord32 m => Proxy m -> r)

{-# INLINE reifyWord32 #-}
reifyWord32 :: forall a. Word32 ->
  (forall (m :: *). HasWord32 m => Proxy m -> a) -> a
reifyWord32 v f = unsafeCoerce (Magic f :: Magic a) (const v) Proxy

newtype Rem m = Rem {unRem :: Word32} deriving (Eq)

withTypeArgOf :: c a -> d a -> c a
{-# INLINE CONLIKE withTypeArgOf #-}
withTypeArgOf = const

proxyFor :: c a -> Proxy a
{-# INLINE CONLIKE proxyFor #-}
proxyFor = const Proxy

withProxy :: (Proxy m -> c m) -> c m
{-# INLINE withProxy #-}
withProxy f = f Proxy

remP :: Proxy m -> Word32 -> Rem m
{-# INLINE CONLIKE remP #-}
remP = const Rem

{-# INLINE modulus32 #-}
modulus32 :: HasWord32 m => Rem m -> Word32
modulus32 x = word32Val $ proxyFor x

class HasWord32 m where
  word32Val :: Proxy m -> Word32

instance Show (Rem m) where
  {-# INLINE showsPrec #-}
  showsPrec = coerce `asTypeOf` (\f p (Rem v) -> f p v) $ showsPrec

negRem :: HasWord32 m => Rem m -> Rem m
{-# INLINE negRem #-}
negRem x0@(Rem x)
  | x == 0 = Rem 0
  | otherwise = Rem $ modulus32 x0 - x

addRem, subRem, multRem
  :: HasWord32 m => Rem m -> Rem m -> Rem m
{-# INLINE subRem #-}
subRem x0@(Rem x) (Rem y) = Rem $ x-y + if x < y then modulus32 x0 else 0
{-# INLINE addRem #-}
addRem x0@(Rem x) (Rem y) = Rem $ x-negy + if x < negy then m else 0
  where m = modulus32 x0; negy = m-y
{-# INLINE multRem #-}
multRem x0@(Rem x) (Rem y)
  = Rem $ toW32 $ (toW64 x * toW64 y) `rem` toW64 (modulus32 x0)

{-# INLINE fromIntegerRem #-}
fromIntegerRem :: (HasWord32 m) => Integer -> Rem m
fromIntegerRem x = withProxy $ Rem . fromInteger . mod x . toInteger . word32Val

{-# INLINE signumRem #-}
signumRem :: (HasWord32 m) => Rem m -> Rem m
signumRem = (\case True -> Rem 0; False -> Rem 1) . (== Rem 0)

instance HasWord32 m => Num (Rem m) where
  {-# INLINE negate #-}
  negate = negRem
  {-# INLINE (-) #-}
  (-) = subRem
  {-# INLINE (+) #-}
  (+) = addRem
  {-# INLINE (*) #-}
  (*) = multRem
  {-# INLINE fromInteger #-}
  fromInteger = fromIntegerRem
  {-# INLINE abs #-}
  abs = id
  {-# INLINE signum #-}
  signum = signumRem

recipRem :: HasWord32 m => Rem m -> Rem m
{-# INLINE recipRem #-}
recipRem = \x -> x ^ (modulus32 x - 2)

-- works only for primes
instance HasWord32 m => Fractional (Rem m) where
  {-# INLINE recip #-}
  recip = recipRem
  fromRational q = fromInteger (numerator q) / fromInteger (denominator q)

newtype instance VU.Vector (Rem m)
  = VRem { unVRem :: VU.Vector Word32 }
newtype instance VUM.MVector s (Rem m)
  = VMRem { unVMRem :: VUM.MVector s Word32 }
instance VUM.Unbox (Rem m)

instance VGM.MVector VUM.MVector (Rem m) where
  {-# INLINE basicLength #-}
  basicLength = coerce `asTypeOf` (. unVMRem) $ VGM.basicLength
  {-# INLINE basicUnsafeSlice #-}
  basicUnsafeSlice
    = coerce `asTypeOf` (\f x y (VMRem v) -> VMRem $ f x y v)
      $ VGM.basicUnsafeSlice
  {-# INLINE basicOverlaps #-}
  basicOverlaps = coerce `asTypeOf` (`on` unVMRem) $ VGM.basicOverlaps
  {-# INLINE basicUnsafeNew #-}
  basicUnsafeNew = fmap (coerce `asTypeOf` VMRem) . VGM.basicUnsafeNew
  {-# INLINE basicInitialize #-}
  basicInitialize = coerce `asTypeOf` (. unVMRem) $ VGM.basicInitialize
  {-# INLINE basicUnsafeReplicate #-}
  basicUnsafeReplicate !n
    = fmap (coerce `asTypeOf` VMRem) . VGM.basicUnsafeReplicate n
    . unRem
  {-# INLINE basicUnsafeRead #-}
  basicUnsafeRead (VMRem v) i = coerce `asTypeOf` Rem <$>
                                VGM.basicUnsafeRead v i
  {-# INLINE basicUnsafeWrite #-}
  basicUnsafeWrite = coerce `asTypeOf` (\f (VMRem v) n (Rem x) -> f v n x)
                     $ VGM.basicUnsafeWrite
  {-# INLINE basicClear #-}
  basicClear = coerce `asTypeOf` (. unVMRem) $ VGM.basicClear
  {-# INLINE basicSet #-}
  basicSet = coerce `asTypeOf` (\f (VMRem v) (Rem x) -> f v x) $ VGM.basicSet
  {-# INLINE basicUnsafeCopy #-}
  basicUnsafeCopy = coerce `asTypeOf` (`on` unVMRem) $ VGM.basicUnsafeCopy
  {-# INLINE basicUnsafeMove #-}
  basicUnsafeMove = coerce `asTypeOf` (`on` unVMRem) $ VGM.basicUnsafeMove
  {-# INLINE basicUnsafeGrow #-}
  basicUnsafeGrow (VMRem v) !n
    = fmap (coerce `asTypeOf` VMRem) $ VGM.basicUnsafeGrow v n

instance VG.Vector VU.Vector (Rem m) where
  {-# INLINE basicUnsafeFreeze #-}
  basicUnsafeFreeze (VMRem v)
    = (coerce `asTypeOf` VRem) <$> VG.basicUnsafeFreeze v
  {-# INLINE basicUnsafeThaw #-}
  basicUnsafeThaw (VRem v)
    = (coerce `asTypeOf` VMRem) <$> VG.basicUnsafeThaw v
  {-# INLINE basicLength #-}
  basicLength = coerce `asTypeOf` (. unVRem) $ VG.basicLength
  {-# INLINE basicUnsafeSlice #-}
  basicUnsafeSlice
    = coerce `asTypeOf` (\f i l (VRem v) -> VRem $ f i l v)
      $ VG.basicUnsafeSlice
  {-# INLINE basicUnsafeIndexM #-}
  basicUnsafeIndexM (VRem !v) !i = coerce <$> VG.basicUnsafeIndexM v i
  {-# INLINE basicUnsafeCopy #-}
  basicUnsafeCopy
    = coerce `asTypeOf` (\f (VMRem mv) (VRem v) -> f mv v)
      $ VG.basicUnsafeCopy
  {-# INLINE elemseq #-}
  elemseq = const seq



#define IL(f) {-# INLINE f #-}; f

IL(putBuilder) = BSB.hPutBuilder stdout

printVecInLines, printVecInSpcSepLn ::
  (VG.Vector v a, ShowAsBuilder a) => v a -> IO ()
IL(printVecInLines) = putBuilder . v2BLines
IL(printVecInSpcSepLn) = putBuilder . v2BSpcSepLn

class ShowAsBuilder a where
  showAsBuilder :: a -> BSB.Builder
  default showAsBuilder :: (Show a) => a -> BSB.Builder
  IL(showAsBuilder) = BSB.string8 . show

-- Inconsistent with show
instance (ShowAsBuilder a, VG.Vector v a) => ShowAsBuilder (v a) where
  IL(showAsBuilder) = v2BSpcSep

#define INS(t,f) instance ShowAsBuilder t where { IL(showAsBuilder)=f }
INS(Int,BSB.intDec)
INS(Int8,BSB.int8Dec)
INS(Int16,BSB.int16Dec)
INS(Int32,BSB.int32Dec)
INS(Int64,BSB.int64Dec)
INS(Word,BSB.wordDec)
INS(Word8,BSB.word8Dec)
INS(Word16,BSB.word16Dec)
INS(Word32,BSB.word32Dec)
INS(Word64,BSB.word64Dec)
INS(Integer,BSB.integerDec)
INS(Float,BSB.floatDec)
INS(Double,BSB.doubleDec)
-- INS(String,BSB.string8) -- Inconsistent with Show
-- INS(BS.ByteString,BSB.byteString) -- Inconsistent with Show
-- INS(BSL.ByteString,BSB.lazyByteString) -- Inconsisitent with Show
#undef INS

-- Inconsistent with Show
instance (ShowAsBuilder a, ShowAsBuilder b) => ShowAsBuilder (a,b) where
  IL(showAsBuilder) = showTupAsBuilder
instance (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c) =>
  ShowAsBuilder (a,b,c) where
  IL(showAsBuilder) = showTup3AsBuilder
instance (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c, ShowAsBuilder d) =>
  ShowAsBuilder (a,b,c,d) where
  IL(showAsBuilder) = showTup4AsBuilder

IL(showTupAsBuilderWith)
  :: (a -> BSB.Builder) -> (b -> BSB.Builder) -> (a,b) -> BSB.Builder
showTupAsBuilderWith showA showB
  = \(a,b) -> (showA a <>) $ BSB.char7 ' ' <> showB b
IL(showTupAsBuilder) :: (ShowAsBuilder a, ShowAsBuilder b)
  => (a,b) -> BSB.Builder
showTupAsBuilder = showTupAsBuilderWith showAsBuilder showAsBuilder 

IL(showTup3AsBuilderWith) :: (a -> BSB.Builder) -> (b -> BSB.Builder) ->
  (c -> BSB.Builder) -> (a,b,c) -> BSB.Builder
showTup3AsBuilderWith showA showB showC
  = \(a,b,c) -> (showA a <>) $ (BSB.char7 ' ' <>) $ (showB b <>)
                $ (BSB.char7 ' ' <>) $ showC c
IL(showTup3AsBuilder) :: (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c)
  => (a,b,c) -> BSB.Builder
showTup3AsBuilder
  = showTup3AsBuilderWith showAsBuilder showAsBuilder showAsBuilder

IL(showTup4AsBuilderWith) :: (a -> BSB.Builder) -> (b -> BSB.Builder) ->
  (c -> BSB.Builder) -> (d -> BSB.Builder) -> (a,b,c,d) -> BSB.Builder
showTup4AsBuilderWith showA showB showC showD
  = \(a,b,c,d) -> (showA a <>) $ (BSB.char7 ' ' <>)
                  $ showTup3AsBuilderWith showB showC showD (b,c,d)
IL(showTup4AsBuilder) ::
  (ShowAsBuilder a, ShowAsBuilder b, ShowAsBuilder c, ShowAsBuilder d) =>
  (a,b,c,d) -> BSB.Builder
showTup4AsBuilder = showTup4AsBuilderWith showAsBuilder showAsBuilder
                    showAsBuilder showAsBuilder

v2BSpcSepLn, v2BSpcSep, v2BConcat, v2BLines ::
  (VG.Vector v a, ShowAsBuilder a)
  => v a -> BSB.Builder
IL(v2BSpcSepLn) = v2BSpcSepLnWith showAsBuilder
IL(v2BSpcSep) = v2BSpcSepWith showAsBuilder
IL(v2BConcat) = v2BConcatWith showAsBuilder
IL(v2BLines) = v2BLinesWith showAsBuilder


v2BSpcSepLnWith, v2BSpcSepWith, v2BConcatWith, v2BLinesWith ::
  (VG.Vector v a)
  => (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
IL(v2BSpcSepLnWith) = v2BSpcSepPostfWith $ BS.singleton '\n'
IL(v2BSpcSepWith) = v2BSpcSepPostfWith BS.empty
IL(v2BConcatWith) showFct = VG.foldr ((<>) . showFct) mempty
IL(v2BLinesWith) showFct
  = VG.foldr (\ a -> (showFct a <>) . (BSB.char7 '\n' <>)) mempty


v2BSpcSepPostf :: (VG.Vector v a, ShowAsBuilder a)
  => BS.ByteString -- ^ postfix
  -> v a -> BSB.Builder
IL(v2BSpcSepPostf) = (`v2BSpcSepPostfWith` showAsBuilder)

v2BSpcSepPostfWith :: (VG.Vector v a)
  => BS.ByteString -- ^ postfix
  -> (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
IL(v2BSpcSepPostfWith) = vecToBuilder BS.empty $ BS.singleton ' '

IL(vecToBuilder) :: (VG.Vector v a)
  => BS.ByteString -- ^ prefix
  -> BS.ByteString -- ^ separator
  -> BS.ByteString -- ^ postfix
  -> (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
vecToBuilder !prefix !separator !postfix
  = vecToBuilder_ (BSB.byteString prefix)
                  (BSB.byteString separator)
                  (BSB.byteString postfix)


IL(vecToBuilder_) :: (VG.Vector v a)
  => BSB.Builder -- ^ prefix
  -> BSB.Builder -- ^ separator
  -> BSB.Builder -- ^ postfix
  -> (a -> BSB.Builder) -- ^ show function
  -> v a -> BSB.Builder
vecToBuilder_ !prefix !separator !postfix showFct = \vec -> prefix <>
  VG.foldr
  (\ a rest !prefx -> prefx <> (showFct a <> rest separator))
  (const postfix) vec mempty

IL(evalVals) :: [a] -> [a]
evalVals xs = build $ \c n -> foldr (c $!) n xs
IL(forceVals) :: (NFData a) => [a] -> [a]
forceVals xs = build $ \c n -> foldr (c $!!) n xs

IL(readLnWith) :: StateT BS.ByteString Maybe a -> IO a
readLnWith parser = fromJust . evalStateT parser <$> BS.getLine
IL(readContentWith) :: StateT BSL.ByteString Maybe a -> IO a
readContentWith parser = fromJust . evalStateT parser <$> BSL.getContents

IL(getVecGLn) :: (VG.Vector v a) =>
  Int -> StateT BS.ByteString Maybe a -> IO (v a)
getVecGLn n s = VG.unfoldrN n (runStateT s) <$> BS.getLine
IL(getVecGRest) :: (VG.Vector v a) =>
  Int -> StateT BSL.ByteString Maybe a -> IO (v a)
getVecGRest n s = VG.unfoldrN n (runStateT s) <$> BSL.getContents
IL(getVecLn) :: Int -> StateT BS.ByteString Maybe a -> IO (V.Vector a)
getVecLn = getVecGLn
IL(getVecRest) :: Int -> StateT BSL.ByteString Maybe a -> IO (V.Vector a)
getVecRest = getVecGRest
IL(getVecULn) :: (VU.Unbox a) =>
  Int -> StateT BS.ByteString Maybe a -> IO (VU.Vector a)
getVecULn = getVecGLn
IL(getVecURest) :: (VU.Unbox a) =>
  Int -> StateT BSL.ByteString Maybe a -> IO (VU.Vector a)
getVecURest = getVecGRest

IL(rIntL) :: StateT BSL.ByteString Maybe Int
rIntL = skipSpecialL $ StateT BSL.readInt
IL(rIntS) :: StateT BS.ByteString Maybe Int
rIntS = skipSpecialS $ StateT BS.readInt
IL(rStrL) :: (MonadState BSL.ByteString m) => m BS.ByteString
rStrL = skipSpecialL $ BSL.toStrict <$> state (BSL.span (>='!'))
IL(rStrS) :: (MonadState BS.ByteString m) => m BS.ByteString
rStrS = skipSpecialS $ state $ BS.span (>='!')
IL(rCharL) :: StateT BSL.ByteString Maybe Char
rCharL = StateT BSL.uncons
IL(rCharS) :: StateT BS.ByteString Maybe Char
rCharS = StateT BS.uncons
IL(dropSpecialL) :: (MonadState BSL.ByteString m) => m ()
dropSpecialL = modify $ BSL.dropWhile (<'!')
IL(dropSpecialS) :: (MonadState BS.ByteString m) => m ()
dropSpecialS = modify $ BS.dropWhile (<'!')
IL(skipSpecialL) :: (MonadState BSL.ByteString m) => m a -> m a
skipSpecialL = (dropSpecialL *>)
IL(skipSpecialS) :: (MonadState BS.ByteString m) => m a -> m a
skipSpecialS = (dropSpecialS *>)

IL(linToMat) :: (VG.Vector v a) => Int -> Int -> v a -> V.Vector (v a)
linToMat h w lvec = vEvalElemsId $ V.generate h (\i -> VG.slice (i*w) w lvec)

IL(mLinToMat) :: (VGM.MVector v a) => Int -> Int -> v s a -> V.Vector (v s a)
mLinToMat h w lvec = vEvalElemsId $ V.generate h (\i -> VGM.slice (i*w) w lvec)
  
IL(unsafeAddrToSVec) :: Int -> Addr# -> VS.Vector Word8
unsafeAddrToSVec n addr
  = (`VS.unsafeFromForeignPtr0` n)
    $ unsafeDupablePerformIO
    $ newForeignPtr_ $ Ptr addr

IL(vEvalElemsId) :: (VG.Vector v a) => v a -> v a
vEvalElemsId = vMapFoldl (\ !_ !x -> (x,())) ()

IL(vEvalElems) :: (VG.Vector v a) => v a -> ()
vEvalElems = VG.foldl' (\ !_ !_ -> ()) () 

IL(vMapFoldl) :: (VG.Vector v b, VG.Vector v c) =>
  (a -> b -> (c,a)) -> a -> v b -> v c
vMapFoldl f a
  = VG.unstream . VFB.inplace (streamMapFoldl f a) id . VG.stream

streamMapFoldl :: (Functor m) =>
  (a -> b -> (c,a)) -> a -> VFSM.Stream m b -> VFSM.Stream m c
{-# INLINE_FUSED streamMapFoldl #-}
streamMapFoldl f a (VFSM.Stream step s) = VFSM.Stream step1 (a,s)
  where
    {-# INLINE_INNER step1 #-}
    step1 (a0,s0) =  (<$> step s0) $ \r -> case r of
      VFSM.Yield b s1 -> case f a0 b of (c,a1) -> VFSM.Yield c (a1,s1)
      VFSM.Skip    s1 -> VFSM.Skip (a0,s1)
      VFSM.Done       -> VFSM.Done

IL(svecToBS) :: VS.Vector Word8 -> BS.ByteString
svecToBS vec = BSU.fromForeignPtr ptr 0 len
  where (ptr, len) = VS.unsafeToForeignPtr0 vec


unlessM, whenM :: (Monad m) => m Bool -> m () -> m ()
IL(whenM) = (. flip when) . (>>=)
IL(unlessM) = (. flip unless) . (>>=)

IL(wrA) = A.writeArray
IL(rdA) = A.readArray
IL(mdA) = \arr f !i -> do
  ai <- rdA arr i
  let fai = f ai 
  wrA arr i fai
  return (ai,fai)
{-# INLINE mdA' #-}
mdA' = \arr f !i -> do
  !ai <- rdA arr i
  let !fai = f ai
  wrA arr i fai
  return (ai,fai)
IL(swapA) = \arr !i !j -> do
  ai <- rdA arr i
  wrA arr i =<< rdA arr j
  wrA arr j ai

#define D(f,r,d)\
  IL(f) :: Integral a=>a->d; f=fromIntegral;\
  IL(r) :: String->d; r=read
#define C(f,r,g,h,d) D(f,r,d);\
  g,h :: RealFrac a=>a->d; IL(g)=floor; IL(h)=ceiling
C(_toInteger_,readInteger,floorInteger,ceilInteger,Integer)
C(toInt,readInt,floorInt,ceilInt,Int)
C(toI8,readI8,floorI8,ceilI8,Int8)
C(toI16,readI16,floorI16,ceilI16,Int16)
C(toI32,readI32,floorI32,ceilI32,Int32)
C(toI64,readI64,floorI64,ceilI64,Int64)
C(toWord,readWord,floorWord,ceilWord,Word)
C(toW8,readW8,floorW8,ceilW8,Word8)
C(toW16,readW16,floorW16,ceilW16,Word16)
C(toW32,readW32,floorW32,ceilW32,Word32)
C(toW64,readW64,floorW64,ceilW64,Word64)
D(toDouble,readDouble,Double)
D(toFloat,readFloat,Float)
#undef D
#undef C

#define TS(f,a,m,init)\
  IL(f) :: forall e i s. (C(a,m) A.Ix i) => (i,i) -> init m (a i e); f
#define N(f,g,h,a,m)\
  TS(f,a,m,e->)=A.newArray;\
  TS(g,a,m,)=A.newArray_;\
  TS(h,a,m,[e]->)=A.newListArray
#define C(a,m)
N(newIOA,newIOA_,newIOAL,IOArray,IO)
N(newSTA,newSTA_,newSTAL,STArray s,ST s)
#undef C
#define C(a,m) MArray (a) e (m), 
N(newIOUA,newIOUA_,newIOUAL,IOUArray,IO)
N(newSTUA,newSTUA_,newSTUAL,STUArray s,ST s)
#undef C
#undef N
#undef TS

#undef IL