Problem:
Score : 100 points

Problem Statement

In this problem, you should process T testcases.

For each testcase, you are given four integers N, M, A, B.

Calculate \sum_{i = 0}^{N - 1} floor((A \times i + B) / M).

Constraints

1 \leq T \leq 100,000

1 \leq N, M \leq 10^9

0 \leq A, B < M

Input

Input is given from Standard Input in the following format:

T
N_0 M_0 A_0 B_0
N_1 M_1 A_1 B_1
:
N_{T - 1} M_{T - 1} A_{T - 1} B_{T - 1}

Output

Print the answer for each testcase.

Sample Input 1

5
4 10 6 3
6 5 4 3
1 1 0 0
31415 92653 58979 32384
1000000000 1000000000 999999999 999999999

Sample Output 1

3
13
0
314095480
499999999500000000

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

{-# LANGUAGE MultiWayIf #-}

module Main where

import           Control.Monad
import           Control.Monad.Extra
import qualified Data.Array as A
import qualified Data.Array.IO as AIO
import qualified Data.Array.Unboxed as AU
import           Data.Bits
import           Data.Bool
import qualified Data.ByteString as BS
import qualified Data.ByteString.Char8 as BSC8
import           Data.Char
import           Data.Either
import           Data.Function
import qualified Data.Graph.Inductive.Graph as G
import qualified Data.Graph.Inductive.PatriciaTree as G
import qualified Data.Heap as H
import           Data.Int
import           Data.List
import qualified Data.Map.Strict as M
import           Data.Maybe
import           Data.Monoid
import           Data.Ord
import qualified Data.Sequence as SQ
import qualified Data.Set as S
import           Data.Tuple
import qualified Data.Vector as V
import           Data.Vector.Algorithms.Search
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import           Debug.Trace
import           GHC.Base

main = do
  --aN       <- getI
  --[aA, aB] <- getIL
  --aS       <- getLine
  aT <- getI
  replicateM aT
    $ do
      [aN, aM, aA, aB] <- getIL
      print $ aclMathFloorSum aN aM aA aB
  return ()

--雑多系
t :: Int -> (Int, Int)
t x = (x, 1)

i def f t = bool t def $ f t

shiftRCnt k = shiftRCntP k 1

shiftRCntP k c = let nk = shiftR k 1
                 in if nk == 0
                    then c
                    else shiftRCntP nk (c + 1)

myVUmap f vu =
  if vu == VU.empty
  then VU.empty
  else VU.unfoldr
    (\x -> let ret = f $ VU.head x
               tailx = VU.tail x
           in if x == VU.empty
              then Nothing
              else if isLeft ret
                   then Just (either id id ret, tailx)
                   else Just (either id id ret, VU.empty))
    vu

myVUmapM f vu =
  if vu == VU.empty
  then return VU.empty
  else VU.unfoldrM
    (\x -> do
       ret <- f $ VU.head x
       let tailx = VU.tail x
       if x == VU.empty
         then return $ Nothing
         else if isLeft ret
              then return $ Just (either id id ret, tailx)
              else return $ Just (either id id ret, VU.empty))
    vu

myVUmapM_ f vu =
  if vu == VU.empty
  then return ()
  else do
    ret1 <- VU.unfoldrM
      (\x -> do
         ret2 <- f $ VU.head x
         let tailx = VU.tail x
         if x == VU.empty
           then return $ Nothing
           else if isLeft ret2
                then return $ Just (either id id ret2, tailx)
                else return $ Just (either id id ret2, VU.empty))
      vu
    return ()

myVUfor vu f = myVUmap f vu

myVUforM vu f = myVUmapM f vu

myVUforM_ vu f = myVUmapM_ f vu

myVUfoldl f acc vu =
  if vu == VU.empty
  then return acc
  else do
    let ret = f acc (VU.head vu)
    if isLeft ret
      then myVUfoldl f (either id id ret) (VU.tail vu)
      else return $ either id id ret

myVUfoldr f acc vu =
  if vu == VU.empty
  then return acc
  else do
    let ret = f acc (VU.last vu)
    if isLeft ret
      then myVUfoldr f (either id id ret) (VU.init vu)
      else return $ either id id ret

myVUfoldM f acc vu =
  if vu == VU.empty
  then return acc
  else do
    ret <- f acc (VU.head vu)
    if isLeft ret
      then myVUfoldM f (either id id ret) (VU.tail vu)
      else return $ either id id ret

--周りのマス
aroundSquare y x h w =
  [aYX
  | aYX@(aY, aX)
      <- [(y + a, x + b) | a <- [-1 .. 1], b <- [-1 .. 1], abs a + abs b == 1]
  , aY >= 1
  , aY <= h
  , aX >= 1
  , aX <= w]

--入力系
splitReadBSC8 :: BSC8.ByteString -> [Int]
splitReadBSC8 bs = let (bs1, newBs) = BSC8.splitAt 1 bs
                   in if newBs == BSC8.empty
                      then [test $ BSC8.readInt bs1]
                      else test (BSC8.readInt bs1):splitReadBSC8 newBs
  where
    test (Just (i, _)) = i

read2DimChar :: VM.IOVector (VUM.IOVector Char) -> Int -> Int -> IO Char
read2DimChar vec y x = do
  vecY <- VM.read vec y
  VUM.read vecY x

write2DimChar :: VM.IOVector (VUM.IOVector Char) -> Int -> Int -> Char -> IO ()
write2DimChar vec y x t = do
  vecY <- VM.read vec y
  VUM.write vecY x t

readTwoDimVec :: VM.IOVector (VUM.IOVector Int) -> Int -> Int -> IO Int
readTwoDimVec vec y x = do
  vecY <- VM.read vec y
  VUM.read vecY x

writeTwoDimVec :: VM.IOVector (VUM.IOVector Int) -> Int -> Int -> Int -> IO ()
writeTwoDimVec vec y x t = do
  vecY <- VM.read vec y
  VUM.write vecY x t

getVUI :: IO (VU.Vector Int)
getVUI = VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine

getRepVUI :: Int -> IO (VU.Vector Int)
getRepVUI n = VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) . BSC8.unlines
  <$> replicateM n BSC8.getLine

getVS :: IO (V.Vector Char)
getVS = V.fromList <$> getLine

getVUC :: IO (VU.Vector Char)
getVUC = VU.fromList <$> getLine

readI :: BSC8.ByteString -> Int
readI = fst . fromJust . BSC8.readInt

readInteger :: BSC8.ByteString -> Integer
readInteger = fst . fromJust . BSC8.readInteger

readIL :: BSC8.ByteString -> [Int]
readIL = map readI . BSC8.words

readIT2 :: BSC8.ByteString -> (Int, Int)
readIT2 bs = let words = BSC8.words bs
             in (readI $ head words, readI $ last words)

readIT3 :: BSC8.ByteString -> (Int, Int, Int)
readIT3 bs = let words = BSC8.words bs
             in (readI $ words !! 0, readI $ words !! 1, readI $ words !! 2)

getI :: IO Int
getI = readI <$> BSC8.getLine

getInteger :: IO Integer
getInteger = readInteger <$> BSC8.getLine

getIL :: IO [Int]
getIL = readIL <$> BSC8.getLine

getIT2 :: IO (Int, Int)
getIT2 = readIT2 <$> BSC8.getLine

getIT3 :: IO (Int, Int, Int)
getIT3 = readIT3 <$> BSC8.getLine

getIT2Order :: IO (Int, Int)
getIT2Order = getIL
  >>= \x@[xz, xo] -> if xz > xo
                     then return (xo, xz)
                     else return (xz, xo)

getNIS :: Int -> IO [(Int, BSC8.ByteString)]
getNIS 0 = return []
getNIS n = do
  [aFst, aSnd] <- BSC8.words <$> BSC8.getLine
  next <- getNIS (n - 1)
  return ((readI aFst, aSnd):next)

il2Words :: [Int] -> String
il2Words = unwords . map show

il2Lines :: [Int] -> String
il2Lines = unlines . map show

--modNum = 10 ^ 9 + 7
--modulus = 1000000007
modulus = 1000000007

newtype MInt = M Int

instance Num MInt where
  (M a) + (M b) = M $ mod (a + b) modulus

  (M a) - (M b) = M $ mod (a - b) modulus

  (M a) * (M b) = M $ mod (a * b) modulus

  fromInteger a = M $ mod (fromInteger a) modulus

  abs (M a) = undefined

  signum (M a) = undefined

instance Show MInt where
  show (M a) = show (mod a modulus)

int2MInt :: Int -> MInt
int2MInt a = M (mod a modulus)

mInt2Int :: MInt -> Int
mInt2Int (M a) = a

{-
factsMod :: V.Vector MInt
factsMod = V.scanl (\acc x -> M x * acc) 1 $ V.generate 2000000 (+ 1)

factMod :: Int -> MInt
factMod = (factsMod V.!)
-}
factMod :: Int -> MInt
factMod n
  | n == 0 = 1
  | n == 1 = 1
  | otherwise = M n * factMod (n - 1)

factDivMod :: Int -> Int -> MInt
factDivMod n k
  | n == k = M 1
  | otherwise = M n * factDivMod (n - 1) k

powMod :: MInt -> MInt -> MInt
powMod n mK@(M k)
  | k == 0 = M 1
  | k == 1 = n
  | mod k 2 == 0 = powMod (n ^ 2) (M (div k 2))
  | otherwise = n * powMod (n ^ 2) (M (div k 2))

invMod :: MInt -> MInt
invMod (M 0) = error "inverse of 0"
invMod x = powMod x (M (modulus - 2))

{-
combiMod :: Int -> Int -> MInt
combiMod n k
  | n < 0 || k < 0 || k > n = 0
  | otherwise = factMod n * invMod (factMod (n - k)) * invMod (factMod k)
-}
combiMod :: Int -> Int -> MInt
combiMod n k
  | n < 0 || k < 0 || k > n = 0
  | k > n - k = factDivMod n k * invMod (factMod (n - k))
  | otherwise = factDivMod n (n - k) * invMod (factMod k)

combi :: Int -> Int -> Int
combi n k
  | n < 0 || k < 0 || k > n = 0
  | k == n = 1
  | otherwise = div (div (fact n) (fact (n - k))) (fact k)

{-w
primes :: Integral a => [a]
primes = map fromIntegral $ [2, 3] ++ primes'
 where
  primes' = [5] ++ f 1 7 primes'
  f m s (p : ps) = [ n | n <- ns, gcd m n == 1 ] ++ f (m * p) (p * p) ps
    where ns = [ x + y | x <- [s, s + 6 .. p * p - 2], y <- [0, 4] ]

prime n = primes !! n
primes = sieve [2 ..]
sieve (p : xs) = p : sieve [ x | x <- xs, x `mod` p /= 0 ]
-}
fact :: Int -> Int
fact 0 = 1
fact n
  | n > 0 = n * fact (n - 1)

knappsackWDP :: Int -> [(Int, Int)] -> VU.Vector Int
knappsackWDP maxW [] = VU.replicate (maxW + 1) 0
knappsackWDP maxW ((w, v):xs) =
  let tailDP = knappsackWDP maxW xs
  in VU.generate (maxW + 1)
     $ \i -> if w <= i
             then max (tailDP VU.! i) (tailDP VU.! (i - w) + v)
             else tailDP VU.! i

knappsackVDP :: Int -> Int -> Int -> [(Int, Int)] -> VU.Vector Int
knappsackVDP maxW maxV n [] = VU.cons 0 $ VU.replicate (n * maxV) maxW
knappsackVDP maxW maxV n ((w, v):xs) =
  let tailDP = knappsackVDP maxW maxV n xs
  in VU.generate (n * maxV + 1)
     $ \i -> if v <= i
             then min (tailDP VU.! i) (tailDP VU.! (i - v) + w)
             else tailDP VU.! i

knappsackMinVol :: AIO.IOArray (Int, Int) Int
                -> VU.Vector Int
                -> VU.Vector Int
                -> Int
                -> Int
                -> IO Int
knappsackMinVol dp volumeVec valueVec dpSize maxVolume = do
  mapM_
    (\i -> mapM_
       (\v -> do
          let volume = volumeVec VU.! i
              value = valueVec VU.! i
          newdp <- if (v + value) > dpSize
                   then AIO.readArray dp (i, v)
                   else do
                     dpIVm <- AIO.readArray dp (i, v + value)
                     dpIV <- AIO.readArray dp (i, v)
                     return (min (dpIVm - volume) dpIV)
          AIO.writeArray dp (i + 1, v) newdp)
       (reverse [0 .. dpSize]))
    [0 .. VU.length valueVec - 1]
  foldM
    (\acc x -> do
       num <- AIO.readArray dp (VU.length volumeVec, x)
       return
         $ if num <= maxVolume
           then x
           else acc)
    0
    [0 .. dpSize]

lcsTable :: BS.ByteString -> BS.ByteString -> V.Vector (VU.Vector Int)
lcsTable xs ys = V.scanl step (VU.replicate (m + 1) 0) xs'
  where
    n = BS.length xs

    m = BS.length ys

    xs' = V.generate n $ BSC8.index xs :: V.Vector Char

    ys' = VU.generate m $ BSC8.index ys :: VU.Vector Char

    step :: VU.Vector Int -> Char -> VU.Vector Int
    step v x = VU.scanl innerStep 0 (VU.zip3 v (VU.tail v) ys')
      where
        innerStep :: Int -> (Int, Int, Char) -> Int
        innerStep a (b, c, y)
          | x == y = 1 + b
          | otherwise = max a c

{-
main = do
xs <- BS.getLine
ys <- BS.getLine
print $ VU.last $ V.last $ lcsTable xs ys
-}
myFilter :: (a -> Bool) -> [a] -> ([a], [a])
myFilter _pred [] = ([], [])
myFilter pred (x:xs)
  | pred x = let (l, r) = myFilter pred xs
             in (x:l, r)
  | otherwise = let (l, r) = myFilter pred xs
                in (l, x:r)

--UnionFindデータ構造
type UF_PARENT = VUM.IOVector Int

type UF_RANK = VUM.IOVector Int

type UF = (UF_PARENT, UF_RANK)

ufMakeSet :: Int -> IO UF
ufMakeSet n = do
  parent <- VU.thaw $ VU.generate n id
  rank <- VUM.replicate n 0
  return (parent, rank)

ufUnion :: UF -> Int -> Int -> IO ()
ufUnion unionFind@(parents, ranks) x y = do
  xRoot <- ufFind unionFind x
  yRoot <- ufFind unionFind y
  xRootRank <- VUM.read ranks xRoot
  yRootRank <- VUM.read ranks yRoot
  if
    | xRootRank > yRootRank -> VUM.write parents yRoot xRoot
    | xRootRank < yRootRank -> VUM.write parents xRoot yRoot
    | xRoot /= yRoot -> do
      VUM.write parents yRoot xRoot
      VUM.write ranks xRoot (xRootRank + 1)
    | otherwise -> return ()

ufFind :: UF -> Int -> IO Int
ufFind unionFind@(parents, ranks) x = do
  xParent <- VUM.read parents x
  if xParent == x
    then return x
    else do
      xRootParent <- ufFind unionFind xParent
      VUM.write parents x xRootParent
      return xRootParent

--無向グラフ
type UDG = M.Map Int [Int]

list2UDG :: [(Int, Int)] -> M.Map Int [Int]
list2UDG = foldl
  (\acc x -> let lr = M.insertWith (++) (fst x) [snd x] acc
             in M.insertWith (++) (snd x) [fst x] lr)
  M.empty

--有向グラフエッジ情報(コスト付き)
type DGEwC = M.Map Int [(Int, Int, Int)]

--OSA-K法テーブル準備(お酒？)
osaKMethod m = do
  table <- VUM.replicate (m + 1) (0 :: Int) :: IO (VUM.IOVector Int)
  modi table m 2 1 1 (div m 2)
  loopModi table m 3
  VU.freeze table
  where
    loopModi table m x
      | x > m = return ()
      | otherwise = do
        modi table m x 1 2 (div m x)
        loopModi table m (x + 2)

    modi table m x n s nm
      | n > nm = return ()
      | otherwise = do
        let xn = x * n
        target <- VUM.read table xn
        if target == 0
          then do
            VUM.write table xn x
            modi table m x (n + s) s nm
          else if n == 1
               then return ()
               else modi table m x (n + s) s nm

getPrimes osaKTable target = VU.unfoldr
  (\x -> let minPrime = osaKTable VU.! target
             (prime, quo) = if minPrime == 0
                            then (target, 1)
                            else (target, div target minPrime)
         in if x == 1
            then Nothing
            else Just (prime, quo))
  target

--IMOS法1次元用
imosMethodDim1 n lrs = VU.create
  $ do
    table <- VUM.replicate n 0
    VU.mapM_
      (\(l, r) -> do
         VUM.modify table ((+) 1) $ pred l
         if r <= n - 1
           then VUM.modify table ((-) 1) $ r
           else return ())
      lrs
    cumTable <- VUM.replicate n 0
    fTable <- VU.freeze table
    VUM.write cumTable 0 $ bool 1 0 $ even (fTable VU.! 0)
    VU.mapM_
      (\x -> do
         pv <- VUM.read cumTable (x - 1)
         VUM.write cumTable x $ bool 1 0 $ even (pv + fTable VU.! x))
      $ VU.enumFromN 1 (n - 1)
    return cumTable

--ベルマンフォード法 最短経路取得(負数が混じる場合は、まずは、負数閉路があるかどうかを調べる。)
bfMethodShortestPath vn edges = do
  table <- VUM.replicate vn maxInt :: IO (VUM.IOVector Int)
  VUM.write table 0 0
  myVUmapM_
    (\v -> do
       flg <- VU.foldM
         (\acc (from, to, cost) -> do
            fromCost <- VUM.read table $ pred from
            toCost <- VUM.read table $ pred to
            if fromCost /= maxInt && toCost > fromCost + cost
              then do
                VUM.write table (pred to) (fromCost + cost)
                return $ True
              else return $ acc)
         False
         edges
       if flg
         then return $ Left ()
         else return $ Right ())
    $ VU.enumFromN (0 :: Int) (vn - 1)
  VU.freeze table

{-bfMethodShortestPath vn edges = do
  table <- VUM.replicate vn maxInt
  VUM.write table 0 0
  scanLoop table
  VU.freeze table
  where
    scanLoop table = do
      flg <- VU.foldM
        (\acc (from, to, cost) -> do
           fromCost <- VUM.read table $ pred from
           toCost <- VUM.read table $ pred to
           if fromCost /= maxInt && toCost > fromCost + cost
             then do
               VUM.write table (pred to) (fromCost + cost)
               return $ True
             else return $ acc)
        False
        edges
      if flg
        then scanLoop table
        else return ()
-}
--ベルマンフォード法 負数閉路探索
bfMethodFindNegativeLoop vn edges = do
  table <- VUM.replicate vn 0 :: IO (VUM.IOVector Int)
  VU.mapM_
    (\v -> VU.mapM_
       (\(from, to, cost) -> do
          fromCost <- VUM.read table $ pred from
          toCost <- VUM.read table $ pred to
          if toCost > fromCost + cost
            then do
              VUM.write table (pred to) (fromCost + cost)
            else return ())
       edges)
    $ VU.enumFromN (0 :: Int) (vn - 1)
  myVUfoldM
    (\acc (from, to, cost) -> do
       fromCost <- VUM.read table $ pred from
       toCost <- VUM.read table $ pred to
       if toCost > fromCost + cost
         then do
           VUM.write table (pred to) (fromCost + cost)
           return $ Right True
         else return $ Left False)
    False
    edges

--ベルマンフォード法 負数閉路影響調査
bfMethodScanNegativeLoop vn edges = do
  table <- VUM.replicate vn 0 :: IO (VUM.IOVector Int)
  rTable <- VUM.replicate vn False :: IO (VUM.IOVector Bool)
  VU.mapM_
    (\v -> VU.mapM_
       (\(from, to, cost) -> do
          fromCost <- VUM.read table $ pred from
          toCost <- VUM.read table $ pred to
          if toCost > fromCost + cost
            then do
              VUM.write table (pred to) (fromCost + cost)
            else return ())
       edges)
    $ VU.enumFromN (0 :: Int) (vn - 1)
  VU.foldM_
    (\acc (from, to, cost) -> do
       fromCost <- VUM.read table $ pred from
       toCost <- VUM.read table $ pred to
       if toCost > fromCost + cost
         then do
           VUM.write table (pred to) (fromCost + cost)
           VUM.write rTable (pred to) True
           return $ True
         else return $ False)
    False
    edges
  VU.freeze rTable

--DijkstraMethod 壊れてるっぽい
dijkstraMethod :: Int -> DGEwC -> Int -> IO (VU.Vector Int)
dijkstraMethod n edges s = do
  table <- VUM.replicate n maxInt :: IO (VUM.IOVector Int)
  VUM.write table (pred s) 0
  let heap = H.insert (0, s) H.empty
  mfs table heap
  VU.freeze table
  where
    mfs table heap = do
      if heap == H.empty
        then return ()
        else do
          let (hCost, hTo) = H.minimum heap
          toCost <- VUM.read table (pred hTo)
          let toEdges = M.findWithDefault [] hTo edges
          if toCost >= hCost
            then do
              accHeap <- foldM
                (\acc (eFrom, eTo, eCost) -> do
                   totoCost <- VUM.read table (pred eTo)
                   if (totoCost > (toCost + eCost))
                     then do
                       VUM.write table (pred eTo) (toCost + eCost)
                       return $ H.insert (toCost + eCost, eTo) acc
                     else return acc)
                (H.deleteMin heap)
                toEdges
              mfs table accHeap
            else mfs table (H.deleteMin heap)

--BinarySearchっぽいもの 1からmまでのすべての数値をFにいれたとき最初にTrueになる数値を見つける。
binarySearchFirstTrueSerialASC f m =
  binarySearchFirstTrueSerialASCP f 0 (m + 1)

binarySearchFirstTrueSerialASCP f l r =
  let i = l + (div (r - l) 2)
      test = f i
  in if
       | test && i - l == 1 -> i
       | test && i - l /= 1 -> binarySearchFirstTrueSerialASCP f l i
       | not test && r - i == 1 -> r
       | otherwise -> binarySearchFirstTrueSerialASCP f i r

--BinarySearchっぽいもの その２ vuiのすべての数値をFにいれたとき最初にTrueになる数値を見つける。
binarySearchFirstTrueList f vui = let lenl = VU.length vui
                                  in binarySearchFirstTrueListP f vui (-1) lenl

binarySearchFirstTrueListP f vui l r =
  let i = l + (div (r - l) 2)
      test = f (vui VU.! i)
  in if
       | test && i - l == 1 -> i
       | test && i - l /= 1 -> binarySearchFirstTrueListP f vui l i
       | not test && r - i == 1 -> r
       | otherwise -> binarySearchFirstTrueListP f vui i r

--MaxHeap関連
hMaxPoint :: Int
hMaxPoint = 101

hMaximum :: H.Heap Int -> Int
hMaximum h = hMaxPoint - (H.minimum h)

hInsertMax :: Int -> H.Heap Int -> H.Heap Int
hInsertMax x = H.insert (hMaxPoint - x)

hDeleteMax :: H.Heap Int -> H.Heap Int
hDeleteMax = H.deleteMin

----ACL(AtCoder Library)のHaskell移植版(おっさんたたき台Ver.))
---DSU
aclDsuTable n = do
  parentOrSize <- VUM.replicate n (-1)
  return (n, parentOrSize)

aclDsuMerge table@(n, parentOrSize) a b
  | a < 0
    || n <= a = error "aclDsuMerge:aの範囲を見直してください。"
  | b < 0
    || n <= b = error "aclDsuMerge:bの範囲を見直してください。"
  | otherwise = do
    x <- aclDsuLeader table a
    y <- aclDsuLeader table b
    if x == y
      then return x
      else do
        posX <- VUM.read parentOrSize x
        posY <- VUM.read parentOrSize y
        if -posX < -posY
          then do
            VUM.write parentOrSize y (posY + posX)
            VUM.write parentOrSize x y
            return y
          else do
            VUM.write parentOrSize x (posX + posY)
            VUM.write parentOrSize y x
            return x

aclDsuSame table@(n, parentOrSize) a b
  | a < 0
    && n <= a = error "aclDsuSame:aの範囲を見直してください。"
  | b < 0
    && n <= b = error "aclDsuSame:bの範囲を見直してください。"
  | otherwise = do
    x <- aclDsuLeader table a
    y <- aclDsuLeader table b
    return $ x == y

aclDsuLeader table@(n, parentOrSize) a
  | a < 0
    && n <= a = error "aclDsuLeader:aの範囲を見直してください。"
  | otherwise = do
    posA <- VUM.read parentOrSize a
    if posA < 0
      then return a
      else do
        x <- aclDsuLeader table posA
        VUM.write parentOrSize a x
        return x

aclDsuSize table@(n, parentOrSize) a
  | a < 0
    && n <= a = error "aclDsuSize:aの範囲を見直してください。"
  | otherwise = do
    x <- aclDsuLeader table a
    negate <$> VUM.read parentOrSize x

aclDsuGroup table@(n, parentOrSize) = do
  leaderBuf <- VUM.replicate n 0 :: IO (VUM.IOVector Int)
  groupSize <- VUM.replicate n 0 :: IO (VUM.IOVector Int)
  VU.forM_ (VU.enumFromN 0 n)
    $ \i -> do
      leaderI <- aclDsuLeader table i
      VUM.write leaderBuf i leaderI
      VUM.modify groupSize succ leaderI
  resultTmpIndex <- VUM.replicate n 0 :: IO (VUM.IOVector Int)
  resultTmp <- (V.generateM n
                $ \i -> do
                  gs <- VUM.read groupSize i
                  VUM.replicate gs 0 :: IO (VUM.IOVector Int))
  VU.forM_ (VU.enumFromN 0 n)
    $ \i -> do
      leaderI <- VUM.read leaderBuf i
      tmpIndex <- VUM.read resultTmpIndex leaderI
      VUM.write (resultTmp V.! leaderI) tmpIndex i
      VUM.modify resultTmpIndex succ leaderI
  V.mapMaybe id
    <$> (V.mapM
           (\i -> do
              rti <- VU.freeze $ resultTmp V.! i :: IO (VU.Vector Int)
              if rti == VU.empty
                then return Nothing
                else return $ Just rti)
         $ V.enumFromN 0 n)

---Fenwick Tree
aclFenwickTreeData n = do
  ftData <- VUM.replicate n (0)
  return (n, ftData)

--TODO 元のコード読めない。。。これでいいんだろうか。。。
aclFenwickTreeAdd ftData@(n, ft) p x
  | p < 0 || n <= p =
    error "aclFenwickTreeAdd:aの範囲を見直してください。"
  | otherwise = aloop ft (p + 1)
  where
    aloop ft p
      | p > n = return ()
      | otherwise = do
        VUM.modify ft (+ x) (p - 1)
        aloop ft ((p + (p .&. (-p))))

aclFenwickTreeSum ftData@(n, ft) l r
  | l < 0 || l > r || r > n =
    error "aclFenwickTreeSum:l rの範囲を見直してください。"
  | otherwise = (-) <$> psum ft r <*> psum ft l
  where
    psum ft r = aloop ft r 0

    aloop ft r s
      | r <= 0 = return s
      | otherwise = do
        ftr <- VUM.read ft (r - 1)
        aloop ft (r - (r .&. (-r))) (s + ftr)

---Math
--TODO未テスト
aclMathPowMod x n m
  | n < 0 = error "aclMathPowMod:nの範囲を見直してください。"
  | m < 1 = error "aclMathPowMod:mの範囲を見直してください。"
  | otherwise = if m == 1
                then 0
                else aloop n 1 (aclMathInternalSafeMod x m)
  where
    aloop n r y
      | n == 0 = return r
      | otherwise = if (n .&. 1) /= 0
                    then aloop (shiftR n 1) (mul m r y) (mul m y y)
                    else aloop (shiftR n 1) r (mul m y y)

    mul m a b = let im = div (-1) m + 1
                    z = a * b
                    x = shiftR (z * im) 64
                    v = z - x * m
                in if m <= v
                   then v + m
                   else v

--TODO未テスト
aclMathInternalSafeMod x m =
  let nx = mod x m
  in if nx < 0
     then nx + m
     else nx

--TODO未テスト
aclMathInvMod x m
  | m < 1 = error "aclMathInvMod:nの範囲を見直してください。"
  | otherwise =
    let z = aclMathInternalInvGcd x m
    in if fst z == 1
       then error "aclMathInvMod:nの範囲を見直してください。"
       else snd z

--TODO未テスト
aclMathInternalInvGcd a b =
  let na = aclMathInternalSafeMod a b
      (s, t, m0, m1) = aloop b a 0 1
  in if a == 0
     then (b, 0)
     else if m0 < 0
          then (s, m0 + (div b s))
          else (s, m0)
  where
    aloop s t m0 m1
      | t == 0 = (s, t, m0, m1)
      | otherwise = let u = div s t
                    in aloop t (s - t * u) m1 (m0 - m1 * u)

--TODO未テスト
aclMathCrt r m
  | VU.length r /= VU.length m =
    error "aclMathCrt:r mの配列サイズを見直してください。"
  | otherwise = let n = VU.length r
                in aloop r m 0 0 1
  where
    aloop r m i r0 m0
      | i >= VU.length r = (r0, m0)
      | m VU.! i < 1 = error
        "aclMathCrt:mの一番目の要素の値を見直してください。"
      | otherwise = let r1 = aclMathInternalSafeMod (r VU.! i) (m VU.! i)
                        m1 = m VU.! i
                    in if m0 >= m1
                       then amethod r m i r0 r1 m0 m1
                       else amethod r m i r1 r0 m1 m0

    amethod r m i r0 r1 m0 m1 =
      let (g, im) = aclMathInternalInvGcd m0 m1
          u1 = div m1 g
          x = mod (mod (div (r1 - r0) g) u1 * im) u1
          nr0 = r0 + x * m0
          nm0 = m0 * u1
      in if (mod m0 m1) == 0
         then if mod r0 m1 /= r1
              then (0, 0)
              else aloop r m (i + 1) r0 m0
         else if mod (r1 - r0) g /= 0
              then (0, 0)
              else if nr0 < 0
                   then aloop r m (i + 1) (nr0 + nm0) nm0
                   else aloop r m (i + 1) (nr0) nm0

aclMathFloorSum n m a b =
  let (ans1, a1) = am 0 n m a
      (ans2, b1) = bm ans1 n m b
      yMax = div (a1 * n + b1) m
      xMax = yMax * m - b1
  in traceShow [n, m, a, b, a1, b1]
     $ if yMax == 0
       then ans2
       else ans2
         + (n - div (xMax + a1 - 1) a1) * yMax
         + aclMathFloorSum yMax a1 m (mod (a1 - mod xMax a1) a1)
  where
    am ans n m a = if a >= m
                   then (div ((n - 1) * n * (div a m)) 2, mod a m)
                   else (ans, a)

    bm ans n m b = if b >= m
                   then (ans + n * (div b m), mod b m)
                   else (ans, b)