{-# 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

m = 10 ^ 6

main = do
  --aN       <- getI
  --[aA, aB] <- getIL
  --aS       <- getLine
  [aN, aK] <- getIL
  aA <- getVUI
  dTable <- VM.replicateM 60 $ VUM.replicate aN 0
    :: IO (VM.IOVector (VUM.IOVector Int))
  mapM_
    (\v -> do
       d0dTable <- VM.read dTable 0
       VUM.write d0dTable v (aA VU.! v - 1))
    [0 .. aN - 1]
  mapM_
    (\d -> mapM_
       (\v -> do
          ddTable <- VM.read dTable d
          nddTable <- VM.read dTable (d + 1)
          dv <- VUM.read ddTable v
          ddv <- VUM.read ddTable dv
          VUM.write nddTable v ddv)
       [0 .. aN - 1])
    [0 .. 58]
  ans <- (liftM (+ 1))
    $ foldM
      (\acc d -> if (aK .&. (shiftL 1 d)) /= 0
                 then do
                   ddTable <- VM.read dTable d
                   VUM.read ddTable acc
                 else return acc)
      0
      [0 .. 59]
  print ans
  --mapM_ (\x -> VM.read dTable x >>= VU.freeze >>= print) [0 .. 59]
  return ()

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

i def f t = bool t def $ f t

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

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

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)

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

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

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

--UnDirectedGraph(無向グラフ)データ構造
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

--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

--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


{-# LANGUAGE BangPatterns #-}
import Data.Array.Unboxed
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import qualified Data.IntMap as M
readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
type Sym = Array Int Int
main = do
  [n,k] <- map read . words <$> getLine
  a <-  getIntList
  let a' = listArray (1,n) a
  print $ solve n k a' ! 1

dot :: Int -> Sym -> Sym -> Sym
dot n s t = listArray (1,n) $ map (\i ->s ! (t ! i)) [1..n]

solve :: Int -> Int -> Sym -> Sym
solve !n !k !s
  | k == 1 = s
  | odd k = s <> solve n (k-1) s
  | otherwise = t <> t
    where (<>) = dot n
          t = solve n (k `div` 2) s

Global OOD problem IDs are disjoint from train, validation, and in-distribution test problem IDs.

Score: 400 points

Problem Statement

The Kingdom of Takahashi has N towns, numbered 1 through N.

There is one teleporter in each town. The teleporter in Town i (1 \leq i \leq N) sends you to Town A_i.

Takahashi, the king, loves the positive integer K. The selfish king wonders what town he will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Help the king by writing a program that answers this question.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq N

1 \leq K \leq 10^{18}

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \dots A_N

Output

Print the integer representing the town the king will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Sample Input 1

4 5
3 2 4 1

Sample Output 1

4

If we start at Town 1 and use the teleporter 5 times, our travel will be as follows: 1 \to 3 \to 4 \to 1 \to 3 \to 4.

Sample Input 2

6 727202214173249351
6 5 2 5 3 2

Sample Output 2

2

Submitted source-code file size, in bytes.

Execution CPU time reported by official Project CodeNet metadata, in milliseconds.

Peak memory usage reported by official Project CodeNet metadata, in kilobytes.


import qualified Data.Map as M
import Data.Maybe
type Sym a = M.Map a a

main = do
  [n,k] <- map read . words <$> getLine
  a <- map read . words <$> getLine
  let a' = zip [0..n-1] (map (\t -> t-1) a)
  print $ 1 + (Data.Maybe.fromMaybe 0 $ M.lookup 0 $ solve n k (M.fromList a') )

(.^) :: (Ord a) => a -> Sym a -> a
x .^ g = Data.Maybe.fromMaybe x (M.lookup x g) -- if x `notElem` supp (P g), then x is not moved

dot :: Int -> Sym Int -> Sym Int -> Sym Int
dot n sigma tau = M.fromList [(x,x .^ sigma .^ tau) | x <- [0..n]]

solve ::Int -> Int -> Sym Int-> Sym Int
solve n k sigma
  | k == 1 = sigma
  | even k = dot n s s
  | otherwise  = dot n sigma (solve n (k-1) sigma)
    where s = solve n (k `div` 2) sigma


import qualified Data.Map as M
import Data.Maybe
type Sym a = M.Map a a

main = do
  [n,k] <- map read . words <$> getLine
  a <- map read . words <$> getLine
  let a' = zip [0..n] (map (\t -> t-1) a)
  print $ 1 + (Data.Maybe.fromMaybe 0 $ M.lookup 0 $ solve k (M.fromList a') )

(.^) :: (Ord a) => a -> Sym a -> a
x .^ g = Data.Maybe.fromMaybe x (M.lookup x g) -- if x `notElem` supp (P g), then x is not moved

dot ::(Ord a) => Sym a -> Sym a -> Sym a
dot sigma tau = M.fromList [(x,x .^ sigma .^ tau) | x <- M.keys (sigma `M.union` tau)]

solve :: Int -> Sym Int-> Sym Int
solve k sigma
  | k == 1 = sigma
  | even k = s `dot` s
  | otherwise  = sigma `dot` solve (k-1) sigma
    where s = solve (k `div` 2) sigma


import Control.Monad

import qualified Data.Set as S

inputIntList :: IO [Int]
inputIntList = map read . words <$> getLine :: IO[Int]

makeLoopList :: [Int] -> S.Set Int -> Int -> ([Int],[Int])
makeLoopList a st now = do
    if S.member now st
       then ([],[now])
       else do
           let to = a !! now
           let (before_loop, loop) = makeLoopList a (S.insert now st) to
           if (before_loop == [])
                then if (last loop) == now
                        then
                            ([now], loop)
                        else
                            ([], now:loop)
                else (now:before_loop, loop)

main = do
    [n,k] <- inputIntList
    a <- inputIntList
    let (before_loop, loop) = makeLoopList (map (subtract 1) a) S.empty 0
    print $ if length before_loop >= k
               then before_loop !! (k-1)
               else loop !! ((k - (length before_loop)) `mod` (length loop)) + 1


import Data.Maybe
import Data.List
import qualified Data.ByteString.Char8 as BS

readInt = fst . fromJust . BS.readInteger
readIntList = map readInt . BS.words

getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

teleport xs i = xs !! i

teleport_list xs ys i 0 = i : []
teleport_list xs ys i n | index == Nothing = teleport_list xs ys' (teleport xs i - 1) (n - 1)
                        | otherwise = ys'
                        where
                          index = elemIndex i ys
                          ys' = ys ++ [i]

main = do
  [n_g, k_g] <- getIntList
  xs_g <- getIntList
  let xs = map fromIntegral xs_g
  let n = fromIntegral n_g
  let k = fromIntegral k_g
  let teleport_n = teleport_list xs [] 0 n
  let loop_start = fromJust (elemIndex (last teleport_n) teleport_n)
  let loop_end = length teleport_n - 2
  let modulation = loop_end - loop_start + 1
  if k < loop_start then
    putStrLn $ show (teleport_n !! k + 1)
  else do
    let teleport_count = k - loop_start
    let teleport_index = loop_start + teleport_count `mod` modulation
    putStrLn $ show (teleport_n !! teleport_index + 1)


import Data.Maybe
import Data.List
import qualified Data.ByteString.Char8 as BS

readInt = fst . fromJust . BS.readInteger
readIntList = map readInt . BS.words

getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

--teleport :: Num a => [a] -> a -> a
teleport xs i = xs !! i

--teleport_list :: Num a => [a] -> [a] -> a -> a -> [a]
teleport_list xs ys i 0 = i : []
teleport_list xs ys i n | index == Nothing = teleport_list xs ys' (teleport xs i - 1) (n - 1)
                        | otherwise = ys'
                        where
                          index = elemIndex i ys
                          ys' = ys ++ [i]

--get_rep :: Num a => [a] -> a -> [a]
get_rep xs 0 = [0, length(xs) - 1]
get_rep xs n | index == Nothing = get_rep xs (n - 1)
             | otherwise = [search_index, fromJust index + search_index]
             where
               search_index = length xs - n
               remaining = drop (search_index + 1) xs
               index = elemIndex (xs !! search_index) remaining

main = do
  [n_g, k_g] <- getIntList
  xs_g <- getIntList
  let xs = map fromIntegral xs_g
  let n = fromIntegral n_g
  let k = fromIntegral k_g
  let teleport_n = teleport_list xs [] 0 n
  let [loop_start, loop_end] = get_rep teleport_n (length teleport_n)
  let modulation = loop_end - loop_start + 1
  if k < loop_start then
    putStrLn $ show (teleport_n !! (k+1))
  else do
    let teleport_count = k - loop_start
    let teleport_index = loop_start + teleport_count `mod` modulation
    putStrLn $ show (teleport_n !! teleport_index + 1)


import Data.Maybe
import Data.List
import qualified Data.ByteString.Char8 as BS

readInt = fst . fromJust . BS.readInteger
readIntList = map readInt . BS.words

getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

teleport xs i = xs !! i

teleport_list xs i 0 = i : []
teleport_list xs i n = i : teleport_list xs (teleport xs i - 1) (n - 1)

get_rep xs 0 = [0, length(xs) - 1]
get_rep xs n | index == Nothing = get_rep xs (n - 1)
             | otherwise = [search_index, fromJust index + search_index]
             where
               search_index = length xs - n
               remaining = drop (search_index + 1) xs
               index = elemIndex (xs !! search_index) remaining

main = do
  [n_g, k_g] <- getIntList
  xs_g <- getIntList
  let xs = map fromIntegral xs_g
  let n = fromIntegral n_g
  let k = fromIntegral k_g
  let teleport_n = teleport_list xs 0 n
  let [loop_start, loop_end] = get_rep teleport_n (n+1)
  let modulation = loop_end - loop_start + 1
  if k < loop_start then
    putStrLn $ show (teleport_n !! (k+1))
  else do
    let teleport_count = k - loop_start
    let teleport_index = loop_start + teleport_count `mod` modulation
    putStrLn $ show (teleport_n !! teleport_index + 1)


import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import qualified Data.Vector.Unboxed as VU
import qualified Data.IntMap as IM

main :: IO ()
main = do
  [n, k] <- map unsafeTextToInt . T.words <$> T.getLine :: IO [Int]
  as <- VU.map pred . unsafeTextToVectorInt <$> T.getLine :: IO (VU.Vector Int)
  let
    (start, period) = go 0 0 IM.empty :: (Int, Int)
      where
        go :: Int -> Int -> IM.IntMap Int -> (Int, Int)
        go l i m | Just s <- IM.lookup i m = (s, l - s)
                 | otherwise               = go (succ l) (as VU.! i) (IM.insert i l m)
    pos :: Int -> Int
    pos = go 0
      where
        go :: Int -> Int -> Int
        go i 0 = i
        go i l = go (as VU.! i) (pred l)
  print . succ . pos $ if k < start then k else start + (k - start) `mod` period

unsafeTextToVectorInt :: T.Text -> VU.Vector Int
unsafeTextToVectorInt = VU.unfoldr next
  where
    next :: T.Text -> Maybe (Int, T.Text)
    next s | T.null s  = Nothing
           | otherwise = Just . either undefined (T.stripStart <$>) . T.signed T.decimal $ s
{-# INLINE unsafeTextToVectorInt #-}

unsafeTextToInt :: T.Text -> Int
unsafeTextToInt s = case T.signed T.decimal s of
  Right (n, _) -> n
{-# INLINE unsafeTextToInt #-}


--{-# LANGUAGE BangPatterns #-}
--{-# LANGUAGE ScopedTypeVariables #-}
--{-# LANGUAGE FlexibleContexts #-}
--{-# LANGUAGE ViewPatterns #-}
--{-# LANGUAGE OverloadedStrings #-}
--{-# LANGUAGE Strict #-}
--{-# LANGUAGE NumericUnderscores #-}
--{-# LANGUAGE BlockArguments #-}
{-# LANGUAGE MultiWayIf #-}

import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.ByteString.Char8 as BC
import qualified Data.Map as MP
import qualified Data.Set as ST
import qualified Data.Sequence as SQ
import Data.Array
import Data.Array.Unboxed
import Data.Array.ST
import Data.Array.IO
import Data.Maybe
import Data.Ord
import Data.Ratio
import Data.Char
import Data.Bits
import Data.List
import Data.Tuple
import Data.Functor
import Data.IORef
import Data.STRef
import Control.Applicative
import Control.Monad
import Control.Monad.ST
import Control.Monad.State.Strict
import Debug.Trace
import qualified Data.Vector.Algorithms.Merge as VAM
import qualified Data.Heap as HP
import Numeric.Extra
import Data.Tuple.Extra
import Data.List.Extra

--------------------------------------------------------------------------
loop xs table curr i k path = do
    b <- VUM.read table dest
    if i > k
        then return (i,path)
        else do
            if b
                then return (i,path)
                else do
                    VUM.write table dest True
                    loop xs table dest (i+1) k (path SQ.|> curr)
    where
        dest = xs VU.! curr

g sq m =
    case SQ.viewl sq of
        l SQ.:< sq' ->
            if m == 0
                then l
                else g sq' (m-1)

main = do
    [n,k] <- sLineToIntL
    xs <- VU.map (subtract 1) <$> sLineToIntV n
    table <- VUM.replicate (n+1) False :: IO (VUM.IOVector Bool)
    (cnt,path) <- loop xs table 0 (-1) k (SQ.empty)
    let m = (k-cnt) `mod` SQ.length path
        t = g path (m+2)

    print $
        if cnt == k
            then case SQ.viewr path of
                sq SQ.:> r -> r + 1
                _ -> 0
            else
                t + 1
----------------------------------------------------------------------

-- Input Util
int :: IO Int
int = BC.getLine >>= return . bsToInt

double :: IO Double
double = BC.getLine >>= return . bsToDouble

str :: IO String
str = BC.getLine >>= return . BC.unpack

strBS :: IO BC.ByteString
strBS = BC.getLine

-- convert
bsToInt :: BC.ByteString -> Int
bsToInt = fst . fromJust . BC.readInt

bsToDouble :: BC.ByteString -> Double
bsToDouble = read . BC.unpack

bsToIntTuple :: BC.ByteString -> (Int, Int)
bsToIntTuple bs = (a,b)
    where
        Just (a,bs') = parseInt bs
        Just (b,_) = parseInt bs'

bsToIntTriple :: BC.ByteString -> (Int, Int, Int)
bsToIntTriple bs = (a,b,c)
    where
        Just (a,bs') = parseInt bs
        Just (b,bs'') = parseInt bs'
        Just (c,_) = parseInt bs''

parseInt :: BC.ByteString -> Maybe (Int, BC.ByteString)
parseInt = BC.readInt . BC.dropWhile isSpace

-- single line
fromSLineL :: (BC.ByteString -> a) -> IO [a]
fromSLineL f = strBS >>= return . map f . BC.words

-- from single line to List / VU.Vector
sLineToIntL :: IO [Int]
sLineToIntL = fromSLineL bsToInt

sLineToDoubleL :: IO [Double]
sLineToDoubleL = fromSLineL bsToDouble

sLineToStrL :: IO [String]
sLineToStrL = fromSLineL BC.unpack

sLineToStrBSL :: IO [BC.ByteString]
sLineToStrBSL = fromSLineL id

sLineToIntV :: Int -> IO (VU.Vector Int)
sLineToIntV n = BC.getLine >>= return . VU.unfoldrN n parseInt

sLineToDoubleV :: IO (VU.Vector Double)
sLineToDoubleV = BC.getLine >>= return . VU.fromList . map bsToDouble . BC.words

-- multiple lines
fromMLinesL :: Int -> (BC.ByteString -> a) -> IO [a]
fromMLinesL n f = replicateM n (strBS >>= return . f)

fromMLinesV :: VU.Unbox a => Int -> (BC.ByteString -> a) -> IO (VU.Vector a)
fromMLinesV n f = VU.replicateM n (strBS >>= return . f)

-- from multiple lines to List / VU.Vector
mLinesToIntL :: Int -> IO [Int]
mLinesToIntL n = fromMLinesL n bsToInt

mLinesToDoubleL :: Int -> IO [Double]
mLinesToDoubleL n = fromMLinesL n bsToDouble

mLinesToStrL :: Int -> IO [String]
mLinesToStrL n = fromMLinesL n BC.unpack

mLinesToStrBSL :: Int -> IO [BC.ByteString]
mLinesToStrBSL n = fromMLinesL n id

mLinesToTupleL :: Int -> IO [(Int, Int)]
mLinesToTupleL n = fromMLinesL n bsToIntTuple

mLinesToTripleL :: Int -> IO [(Int, Int, Int)]
mLinesToTripleL n = fromMLinesL n bsToIntTriple

mLinesToIntV :: Int -> IO (VU.Vector Int)
mLinesToIntV n = fromMLinesV n bsToInt

mLinesToDoubleV :: Int -> IO (VU.Vector Double)
mLinesToDoubleV n = fromMLinesV n bsToDouble

mLinesToTupleV :: Int -> IO (VU.Vector (Int, Int))
mLinesToTupleV n = fromMLinesV n bsToIntTuple

mLinesToTripleV :: Int -> IO (VU.Vector (Int, Int, Int))
mLinesToTripleV n = fromMLinesV n bsToIntTriple

-- output
yesnoL :: Bool -> IO ()
yesnoL cond
    | cond = putStrLn "Yes"
    | otherwise = putStrLn "No"

yesnoU :: Bool -> IO ()
yesnoU cond
    | cond = putStrLn "YES"
    | otherwise = putStrLn "NO"

-- others
strToChr :: String -> Char
strToChr [x] = x

chrToStr :: Char -> String
chrToStr x = [x]

m1 :: Int -> Int
m1 x = subtract 1 x

toDouble :: Int -> Double
toDouble x = fromIntegral x

toInt :: Double -> Int
toInt x = floor x


import Data.IntMap hiding (map, empty, insert, member)
import Data.IntSet hiding (map, fromList)
import Data.List hiding (insert)
import Data.Maybe

main :: IO ()
main = do
  l1 <- getLine
  l2 <- getLine
  let [n, k] = map read $ words l1 :: [Integer]
      a = fromList $ zip [1..] $ map read $ words l2 :: IntMap Int
      (lroute, loop_start) = g a empty [] 1
      loop_count = fromIntegral $ length lroute
      k' = if k > loop_count then (k - loop_start) `mod` (loop_count - loop_start) else k
      start = if k > loop_count then lroute !! (fromInteger loop_start) else 1
  -- print (loop_start, loop_count, k', start)
  print $ f a k' start

f as 0 x = x
f as 1 x = as ! x
f as k x = f as (k - 1) (as ! x)

g as visited route x = if x `member` visited then (reverse route, fromIntegral $ fromJust $ elemIndex x $ reverse route) else g as (insert x visited) (x:route) next
  where
    next = as ! x


{-# LANGUAGE BangPatterns #-}
import           Control.Exception           (assert)
import           Control.Monad
import           Control.Monad.Primitive
import qualified Control.Monad.ST            as ST
import qualified Data.Array.IO               as IO
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as A
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Foldable
import           Data.List
import qualified Data.Map.Strict             as Map
import           Data.Maybe
import qualified Data.Sequence               as Seq
import qualified Data.Set                    as Set
import qualified Data.Vector                 as VB
import qualified Data.Vector.Mutable         as VBM
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM
import           Debug.Trace

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
getIntVec n = V.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

readInteger = fst . fromJust . BS.readInteger
readIntegerList = map readInteger . BS.words
getInteger = readInteger <$> BS.getLine
getIntegerList = readIntegerList <$> BS.getLine

inf :: Int
inf = 10^18

newUF :: PrimMonad m => Int -> m (VM.MVector (PrimState m) Int)
newUF n = do
  d <- VM.new n
  VM.set d (-1)
  return d

findUF :: PrimMonad m => VM.MVector (PrimState m) Int -> Int -> m Int
findUF d x = do
  dx <- VM.read d x
  if dx < 0
    then return x
    else do dx' <- findUF d dx
            VM.write d x dx'
            return dx'

uniteUF :: PrimMonad m => VM.MVector (PrimState m) Int -> Int -> Int -> m ()
uniteUF d x y = do
  x' <- findUF d x
  y' <- findUF d y
  when (x' /= y') $ do
    let (x'', y'') = if (x' <= y') then (x', y') else (y', x')
    dx <- VM.read d x''
    dy <- VM.read d y''
    VM.write d x'' (dx + dy)
    VM.write d y'' x''
  return ()

sameUF :: PrimMonad m => VM.MVector (PrimState m) Int -> Int -> Int -> m Bool
sameUF d x y = do
  fx <- findUF d x
  fy <- findUF d y
  return $ fx == fy

sizeUF :: PrimMonad m => VM.MVector (PrimState m) Int -> Int -> m Int
sizeUF d x = do
  fx <- findUF d x
  dfx <- VM.read d fx
  return (-dfx)

main = do
  [n, k] <- getIntList
  tas <- getIntList

  uf <- newUF (n+1)

  let as = V.fromList (0:tas)

      getDests :: Int -> [Int] -> IO (Int, V.Vector Int)
      getDests i res = do
        let d = as V.! i
            res' = (d:res)
        same <- sameUF uf 1 d
        if same
          then return (d, V.fromList (reverse res))
          else do uniteUF uf 1 d
                  getDests d res'

  (x, dests) <- getDests 1 [1]

  let Just idx = V.findIndex (== x) dests
      dests' = V.drop idx dests
      m = V.length dests'
      k' = k - idx
      j = k' `mod` m

      ans = if k < (V.length dests)
            then dests V.! (k-1)
            else dests' V.! j

  print ans


{-# LANGUAGE BangPatterns #-}
import           Control.Exception           (assert)
import           Control.Monad
import           Control.Monad.Primitive
import qualified Control.Monad.ST            as ST
import qualified Data.Array.IO               as IO
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as A
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Foldable
import           Data.List
import qualified Data.Map.Strict             as Map
import           Data.Maybe
import qualified Data.Sequence               as Seq
import qualified Data.Set                    as Set
import qualified Data.Vector                 as VB
import qualified Data.Vector.Mutable         as VBM
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM
import           Debug.Trace

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
getIntVec n = V.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

readInteger = fst . fromJust . BS.readInteger
readIntegerList = map readInteger . BS.words
getInteger = readInteger <$> BS.getLine
getIntegerList = readIntegerList <$> BS.getLine

inf :: Int
inf = 10^18

newUF :: PrimMonad m => Int -> m (VM.MVector (PrimState m) Int)
newUF n = do
  d <- VM.new n
  VM.set d (-1)
  return d

findUF :: PrimMonad m => VM.MVector (PrimState m) Int -> Int -> m Int
findUF d x = do
  dx <- VM.read d x
  if dx < 0
    then return x
    else do dx' <- findUF d dx
            VM.write d x dx'
            return dx'

uniteUF :: PrimMonad m => VM.MVector (PrimState m) Int -> Int -> Int -> m ()
uniteUF d x y = do
  x' <- findUF d x
  y' <- findUF d y
  when (x' /= y') $ do
    let (x'', y'') = if (x' <= y') then (x', y') else (y', x')
    dx <- VM.read d x''
    dy <- VM.read d y''
    VM.write d x'' (dx + dy)
    VM.write d y'' x''
  return ()

sameUF :: PrimMonad m => VM.MVector (PrimState m) Int -> Int -> Int -> m Bool
sameUF d x y = do
  fx <- findUF d x
  fy <- findUF d y
  return $ fx == fy

sizeUF :: PrimMonad m => VM.MVector (PrimState m) Int -> Int -> m Int
sizeUF d x = do
  fx <- findUF d x
  dfx <- VM.read d fx
  return (-dfx)

main = do
  [n, k] <- getIntList
  tas <- getIntList

  uf <- newUF (n+1)

  let as = V.fromList (0:tas)

      getDests :: Int -> [Int] -> IO (Int, V.Vector Int)
      getDests i res = do
        let d = as V.! i
            res' = (d:res)
        same <- sameUF uf 1 d
        if same
          then return (d, V.fromList (reverse res))
          else do uniteUF uf 1 d
                  getDests d res'

  (x, dests) <- getDests 1 [1]

  let Just idx = V.findIndex (== x) dests
      dests' = V.drop idx dests
      m = V.length dests'
      k' = k - idx
      j = k' `mod` m

      ans = if k < idx
            then dests V.! (k-1)
            else dests' V.! j

  print ans


module Main where

import           Control.Monad
import           Debug.Trace
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           Data.List
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char
import           Data.Maybe
import           Data.Ord
--import           Data.Vector.Algorithms.Search
import qualified Data.Array                    as A
import qualified Data.Array.Unboxed            as AU
import qualified Data.Array.IO                 as AIO
import qualified Data.Set                      as S
import qualified Data.Map.Strict               as M

main = do
    [aN, aK] <- getIL
    vecA     <- getVUI

    let (rHist, point) = telepwhenloop vecA 1 [1] (S.fromList [1])
    let hist           = reverse rHist
    let histlen        = length hist

    let sp             = searchPoint hist point 0

    let modnum         = mod (aK) (histlen - sp)

    let next = if aK < sp
            then hist !! aK
            else hist !! (sp + (mod (aK - sp) (histlen - sp)))

    print next

searchPoint :: [Int] -> Int -> Int -> Int
searchPoint (x : xs) point n =
    if x == point then n else searchPoint xs point (n + 1)

telepwhenloop :: VU.Vector Int -> Int -> [Int] -> S.Set Int -> ([Int], Int)
telepwhenloop a p hist histset =
    let next = a VU.! (p - 1)
    in  if S.member next histset
            then (hist, next)
            else telepwhenloop a next (next : hist) (S.insert next histset)

fromJustInt :: Maybe Int -> Int
fromJustInt (Just x) = x
fromJustInt Nothing  = 0

getVUI :: IO (VU.Vector Int)
getVUI = VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine
readI :: BSC8.ByteString -> Int
readI = fst . fromJust . BSC8.readInt
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)
getI :: IO Int
getI = readI <$> BSC8.getLine
getIL :: IO [Int]
getIL = readIL <$> BSC8.getLine
get2IT :: IO (Int, Int)
get2IT = readIT2 <$> BSC8.getLine

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)

il2ss :: [Int] -> String
il2ss = unwords . map show

il2sn :: [Int] -> String
il2sn = unlines . map show

modNum = 10 ^ 9 + 7
newtype Mint = M Int
instance Num Mint where
    (M a) + (M b) = M $ mod (a + b) modNum
    (M a) - (M b) = M (a - b)
    (M a) * (M b) = M $ mod (a * b) modNum
    fromInteger a = M $ mod (fromInteger a) modNum
    abs (M a) = M $ abs a
    signum (M a) = M $ signum a
instance Show Mint where
    show (M a) = show (mod a modNum)

int2MInt :: Int -> Mint
int2MInt a = M (mod a modNum)

knappsackMaxVal
    :: AIO.IOArray (Int, Int) Int
    -> VU.Vector Int
    -> VU.Vector Int
    -> Int
    -> IO Int
knappsackMaxVal dp volumeVec valueVec dpSize = do
    mapM_
        (\i -> mapM_
            (\v -> do
                let volume = volumeVec VU.! i
                    value  = valueVec VU.! i
                newdp <- if v < volume
                    then AIO.readArray dp (i, v)
                    else do
                        dpIVm <- AIO.readArray dp (i, v - volume)
                        dpIV  <- AIO.readArray dp (i, v)
                        return (max (dpIVm + value) dpIV)
                AIO.writeArray dp (i + 1, v) newdp
            )
            [0 .. dpSize]
        )
        [0 .. VU.length volumeVec - 1]
    AIO.readArray dp (VU.length volumeVec, dpSize)

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]


{-# LANGUAGE BangPatterns #-}

import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.ByteString.Char8 as C
import Data.List
import Control.Monad
import Control.Arrow
--import Data.Foldable
--import Data.Char
import qualified Data.IntMap.Strict as IM
--import qualified Data.IntSet as IS
-- import Data.Sequence as Sq

r :: Int -> IO (U.Vector Int)
r n = U.unfoldrN n (C.readInt . C.dropWhile (==' ')) <$> C.getLine

r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

main = do
    [n,k] <- r'
    as <- r n
    reach <- U.thaw $ U.replicate n (-1 :: Int)
    (posS,hdS,repS) <- count as reach 0 0
    -- print (posS,hdS,repS)
    let rm =  (k - hdS) `mod` repS
    -- print rm
    print $ succ $ trace as posS rm

count as reach ac pos = do
    h <- UM.read reach pos
    if h == -1
        then do
            UM.write reach pos ac
            count as reach (ac+1) (as U.! pos-1)
        else return (pos,h,ac-h)

trace as pos 0 = pos
trace as pos n = trace as (as U.! pos-1) (n-1)


module Main where

abcd :: String -> (Float, Float, Float, Float)
abcd str =  ( read (head strs)
			, read (head (tail strs))
			, read (head (tail (tail strs)))
			, read (head (tail (tail (tail (strs))))))
	where strs = words str

ans a b c d
	| rsTakahashi < rsAoki = "No"
	| otherwise = "Yes"
	where (rsTakahashi, rsAoki) = (ceiling (a / d) , ceiling (c / b))

main :: IO ()
main = do
	input <- getLine
	let (a, b, c, d) = abcd input
	putStrLn $ ans a b c d

Score : 200 points

Problem Statement

Takahashi and Aoki will have a battle using their monsters.

The health and strength of Takahashi's monster are A and B, respectively, and those of Aoki's monster are C and D, respectively.

The two monsters will take turns attacking, in the order Takahashi's, Aoki's, Takahashi's, Aoki's, ...
Here, an attack decreases the opponent's health by the value equal to the attacker's strength.
The monsters keep attacking until the health of one monster becomes 0 or below. The person with the monster whose health becomes 0 or below loses, and the other person wins.

If Takahashi will win, print Yes; if he will lose, print No.

Constraints

1 \leq A,B,C,D \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

Output

If Takahashi will win, print Yes; if he will lose, print No.

Sample Input 1

10 9 10 10

Sample Output 1

No

First, Takahashi's monster attacks Aoki's monster, whose health is now 10-9=1.

Next, Aoki's monster attacks Takahashi's monster, whose health is now 10-10=0.

Takahashi's monster is the first to have 0 or less health, so Takahashi loses.

Sample Input 2

46 4 40 5

Sample Output 2

Yes


import Control.Applicative
import Data.Bool (bool)

main :: IO ()
main = solve <$> f >>= putStrLn
  where
    f = map read <$> words <$> getLine

solve :: [Int] -> String
solve [a, b, c, d] = bool "No" "Yes" $ f a d >= f c b
  where
    f x y = (x + y - 1) `div` y


{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE Strict #-}
{-# LANGUAGE StrictData #-}
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import Data.Array.Unboxed
import Data.Array.ST
import qualified Data.ByteString.Char8 as BS
import Control.Monad
import Data.List
import Data.Char

main :: IO ()
main = do
    (a,b,c,d) <- (\vec -> (vec VU.! 0, vec VU.! 1, vec VU.! 2, vec VU.! 3)) . VU.unfoldrN 4 (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
    let (xx,zz) = (c `div` b,c `mod` b)
        (yy,ww) = (a `div` d,a `mod` d)
    putStrLn $ if xx < yy then "Yes"
        else if xx == yy && ww /= 0 then "Yes"
        else if xx == yy + 1 && zz == 0 then "Yes"
        else "No"


main = do
  str <- getLine
  let [a,b,c,d] = map read (words str) ::[Int]
  putStrLn $ match (a,b) (c,d) 1

match :: (Int, Int) -> (Int, Int) -> Int -> String
match (a, b) (c, d) n
  | a <= 0    = "No"
  | c <= 0    = "Yes"
  | otherwise = if odd n == True
                  then match (a, b) (c-b, d) (n+1)
                  else match (a-d, b) (c, d) (n+1)


module Main where

import           Control.Monad
import           Debug.Trace
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           Data.List
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char
import           Data.Maybe
import           Data.Ord
import           Data.Vector.Algorithms.Search
import qualified Data.Array                    as A
import qualified Data.Array.Unboxed            as AU
import qualified Data.Array.IO                 as AIO
import qualified Data.Set                      as S

main = do
    [aA, aB, aC, aD] <- getIL

    let s = div aC aB + if mod aC aB == 0 then 0 else 1
    let k = div aA aD + if mod aA aD == 0 then 0 else 1

    putStrLn $if s <= k then "Yes" else "No"

getVUIL :: IO (VU.Vector Int)
getVUIL = VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine
readI :: BSC8.ByteString -> Int
readI = fst . fromJust . BSC8.readInt
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)
getI :: IO Int
getI = readI <$> BSC8.getLine
getIL :: IO [Int]
getIL = readIL <$> BSC8.getLine
getIT2 :: IO (Int, Int)
getIT2 = readIT2 <$> BSC8.getLine

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)

il2ss :: [Int] -> String
il2ss = unwords . map show

il2sn :: [Int] -> String
il2sn = unlines . map show

modNum = 10 ^ 9 + 7
newtype Mint = M Int
instance Num Mint where
    (M a) + (M b) = M $ mod (a + b) modNum
    (M a) - (M b) = M (a - b)
    (M a) * (M b) = M $ mod (a * b) modNum
    fromInteger a = M $ mod (fromInteger a) modNum
    abs (M a) = M $ abs a
    signum (M a) = M $ signum a
instance Show Mint where
    show (M a) = show (mod a modNum)

int2MInt :: Int -> Mint
int2MInt a = M (mod a modNum)


{-# 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
  [a,b,c,d] <- map readInt . words <$> getLine
  putStrLn $ if (c+b-1) `div` b <= (a+d-1) `div` d then "Yes" else "No"
  return ()

#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


import           Control.Monad.ST
import qualified Data.ByteString.Char8        as B
import qualified Data.Vector.Unboxed          as U
import qualified Data.Vector.Algorithms.Radix as U

main :: IO ()
main = do
  [a, b, c, d] <- readInts
  putStrLn $ solve a b c d

solve :: Int -> Int -> Int -> Int -> String
solve a b c d = go a b c d True
  where
    go a b c d taka
      | a <= 0       = "No"
      | c <= 0       = "Yes"
      | taka == True = go a b (c - b) d False
      | otherwise    = go (a - d) b c d True

readInts :: IO [Int]
readInts = map read . words <$> getLine

readIntN :: Int ->  IO (U.Vector Int)
readIntN n = U.unfoldrN n (B.readInt . B.dropWhile ((==) ' ')) <$> B.getLine

radixSort :: U.Vector Int -> U.Vector Int
radixSort xs = runST $ do
  mxs <- U.thaw xs
  U.sort mxs
  U.freeze mxs


{-# LANGUAGE MultiWayIf #-}

module Main where
import           Prelude
import           Control.Monad
import           Data.Monoid
import qualified Data.Array                    as A
import qualified Data.Array.IO                 as AIO
import qualified Data.Array.Unboxed            as AU
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char
import           Data.List
import qualified Data.Map.Strict               as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                      as S
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 qualified Data.Heap                     as H
import qualified Data.Sequence                 as SQ
import qualified Data.Graph.Inductive.PatriciaTree
                                               as G
import qualified Data.Graph.Inductive.Graph    as G
import           Data.Int
import           Data.Bits

main = do
  sBSC8 <- BSC8.getLine
  let iVec    = VU.fromList $ reverse $ splitReadBSC8 sBSC8
  let lenIVec = VU.length iVec
  let dp :: VU.Vector Int
      dp =
        VU.scanl
            (\acc i -> mInt2Int
              ( (int2MInt acc)
              + (int2MInt (iVec VU.! i))
              * (powMod (int2MInt 10) (int2MInt i))
              )
            )
            0
          $ VU.generate lenIVec id
  let zipped = VU.zip dp $ VU.replicate (lenIVec + 1) 1 :: VU.Vector (Int, Int)

  let accumulated = VU.accumulate (+) (VU.replicate 2019 0) zipped

  let filtered    = VU.filter (>= 2) accumulated

  let ret         = VU.sum $ VU.map (mInt2Int.(`combiMod` 2)) filtered

  print ret

{-
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
-}

{-
aroundSquare y x h w =
  [ aYX
  | aYX@(aY, aX) <- [(y - 1, x), (y, x - 1), (y + 1, x), (y, x + 1), (y, x)]
  , aY >= 0
  , aY <= (h - 1)
  , aX >= 0
  , aX <= (w - 1)
  ]
-}

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

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)

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

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

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

p :: Int -> Int
p x = x - 1

--modNum = 10 ^ 9 + 7
--modulus = 1000000007
modulus = 2019

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) = M $ abs a

  signum (M a) = M $ signum a

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 = trace (show [n,k,(fact (n - k)), (fact (k))])
                      $div
                      (div (fact n) (fact (n - k)))
                      (fact k)

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] ]

fact :: Int -> Int
fact 0         = 1
fact n | n > 0 = n * fact (n - 1)

knappsack :: Int -> [(Int, Int)] -> VU.Vector Int
knappsack maxW [] = VU.replicate (maxW + 1) 0
knappsack maxW ((w, v) : xs) =
  let tailDP = knappsack 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

knappsackMaxVal
  :: AIO.IOArray (Int, Int) Int
  -> VU.Vector Int
  -> VU.Vector Int
  -> Int
  -> IO Int
knappsackMaxVal dp volumeVec valueVec dpSize = do
  mapM_
    (\i -> mapM_
      (\v -> do
        let volume = volumeVec VU.! i
            value  = valueVec VU.! i
        newdp <- if v < volume
          then AIO.readArray dp (i, v)
          else do
            dpIVm <- AIO.readArray dp (i, v - volume)
            dpIV  <- AIO.readArray dp (i, v)
            return (max (dpIVm + value) dpIV)
        AIO.writeArray dp (i + 1, v) newdp
      )
      [0 .. dpSize]
    )
    [0 .. VU.length volumeVec - 1]
  AIO.readArray dp (VU.length volumeVec, dpSize)

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)
uf_makeSet :: Int -> IO UF
uf_makeSet n = do
  parent <- VU.thaw $ VU.generate n id
  rank   <- VUM.replicate n 0
  return (parent, rank)
uf_union :: UF -> Int -> Int -> IO ()
uf_union unionFind@(parents, ranks) x y = do
  xRoot     <- uf_find unionFind x
  yRoot     <- uf_find 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 ()

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

--UnDirectedGraph(無向グラフ)データ構造
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

Score : 400 points

Problem Statement

Given is a string S consisting of digits from 1 through 9.

Find the number of pairs of integers (i,j) (1 ≤ i ≤ j ≤ |S|) that satisfy the following condition:

Condition: In base ten, the i-th through j-th characters of S form an integer that is a multiple of 2019.

Constraints

1 ≤ |S| ≤ 200000

S is a string consisting of digits from 1 through 9.

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of pairs of integers (i,j) (1 ≤ i ≤ j ≤ |S|) that satisfy the condition.

Sample Input 1

1817181712114

Sample Output 1

3

Three pairs - (1,5), (5,9), and (9,13) - satisfy the condition.

Sample Input 2

14282668646

Sample Output 2

2

Sample Input 3

2119

Sample Output 3

0

No pairs satisfy the condition.


{-# LANGUAGE MultiWayIf #-}

module Main where
import           Prelude
import           Control.Monad
import           Data.Monoid
import qualified Data.Array                    as A
import qualified Data.Array.IO                 as AIO
import qualified Data.Array.Unboxed            as AU
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char
import           Data.List
import qualified Data.Map.Strict               as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                      as S
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 qualified Data.Heap                     as H
import qualified Data.Sequence                 as SQ
import qualified Data.Graph.Inductive.PatriciaTree
                                               as G
import qualified Data.Graph.Inductive.Graph    as G
import           Data.Int
import           Data.Bits

main = do
  sBSC8 <- BSC8.getLine
  let iVec    = VU.fromList $ reverse $ splitReadBSC8 sBSC8
  let lenIVec = VU.length iVec
  let dp :: VU.Vector Int
      dp =
        VU.scanl
            (\acc i -> mInt2Int
              ( (int2MInt acc)
              + (int2MInt (iVec VU.! i))
              * (powMod (int2MInt 10) (int2MInt i))
              )
            )
            0
          $ VU.generate lenIVec id
  let zipped = VU.zip dp $ VU.replicate (lenIVec + 1) 1 :: VU.Vector (Int, Int)

  let accumulated = VU.accumulate (+) (VU.replicate 2019 0) zipped

  let filtered    = VU.filter (>= 2) accumulated

  let ret         = VU.sum $ VU.map (`combi` 2) filtered

  print ret

{-
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
-}

{-
aroundSquare y x h w =
  [ aYX
  | aYX@(aY, aX) <- [(y - 1, x), (y, x - 1), (y + 1, x), (y, x + 1), (y, x)]
  , aY >= 0
  , aY <= (h - 1)
  , aX >= 0
  , aX <= (w - 1)
  ]
-}

splitReadBSC8 :: BSC8.ByteString -> [Int]
splitReadBSC8 bs =
  let (bs1, newBs) = BSC8.splitAt 1 bs
  in  if newBs == BSC8.empty
        then []
        else (test $ BSC8.readInt bs1) : (splitReadBSC8 newBs)
 where
  test (Just (i, _)) = i
  test Nothing       = 0

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

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)

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

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

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

p :: Int -> Int
p x = x - 1

--modNum = 10 ^ 9 + 7
--modulus = 1000000007
modulus = 2019

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) = M $ abs a

  signum (M a) = M $ signum a

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)

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] ]

fact :: Int -> Int
fact 0         = 1
fact n | n > 0 = n * fact (n - 1)

knappsack :: Int -> [(Int, Int)] -> VU.Vector Int
knappsack maxW [] = VU.replicate (maxW + 1) 0
knappsack maxW ((w, v) : xs) =
  let tailDP = knappsack 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

knappsackMaxVal
  :: AIO.IOArray (Int, Int) Int
  -> VU.Vector Int
  -> VU.Vector Int
  -> Int
  -> IO Int
knappsackMaxVal dp volumeVec valueVec dpSize = do
  mapM_
    (\i -> mapM_
      (\v -> do
        let volume = volumeVec VU.! i
            value  = valueVec VU.! i
        newdp <- if v < volume
          then AIO.readArray dp (i, v)
          else do
            dpIVm <- AIO.readArray dp (i, v - volume)
            dpIV  <- AIO.readArray dp (i, v)
            return (max (dpIVm + value) dpIV)
        AIO.writeArray dp (i + 1, v) newdp
      )
      [0 .. dpSize]
    )
    [0 .. VU.length volumeVec - 1]
  AIO.readArray dp (VU.length volumeVec, dpSize)

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)
uf_makeSet :: Int -> IO UF
uf_makeSet n = do
  parent <- VU.thaw $ VU.generate n id
  rank   <- VUM.replicate n 0
  return (parent, rank)
uf_union :: UF -> Int -> Int -> IO ()
uf_union unionFind@(parents, ranks) x y = do
  xRoot     <- uf_find unionFind x
  yRoot     <- uf_find 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 ()

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

--UnDirectedGraph(無向グラフ)データ構造
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


{-# LANGUAGE MultiWayIf #-}

module Main where
import           Prelude
import           Control.Monad
import           Data.Monoid
import qualified Data.Array                    as A
import qualified Data.Array.IO                 as AIO
import qualified Data.Array.Unboxed            as AU
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char
import           Data.List
import qualified Data.Map.Strict               as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                      as S
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 qualified Data.Heap                     as H
import qualified Data.Sequence                 as SQ
import qualified Data.Graph.Inductive.PatriciaTree
                                               as G
import qualified Data.Graph.Inductive.Graph    as G
import           Data.Int
import           Data.Bits

main = do
  sBSC8 <- BSC8.getLine
  let iVec    = VU.fromList $ reverse $ splitReadBSC8 sBSC8
  let lenIVec = VU.length iVec
  let dp :: VU.Vector Int
      dp =
        VU.scanl (\acc i -> mod (acc + (iVec VU.! i) * (10 ^ i)) 2019) 0
          $ VU.generate lenIVec id
  let zipped = VU.zip dp $ VU.replicate (lenIVec + 1) 1 :: VU.Vector (Int, Int)

  let accumulated = VU.accumulate (+) (VU.replicate 2019 0) zipped

  let filtered    = VU.filter (>= 2) accumulated

  let ret =
        VU.sum $ VU.zipWith (-) filtered (VU.replicate (VU.length filtered) 1)

  print ret

{-
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
-}

{-
aroundSquare y x h w =
  [ aYX
  | aYX@(aY, aX) <- [(y - 1, x), (y, x - 1), (y + 1, x), (y, x + 1), (y, x)]
  , aY >= 0
  , aY <= (h - 1)
  , aX >= 0
  , aX <= (w - 1)
  ]
-}

splitReadBSC8 :: BSC8.ByteString -> [Int]
splitReadBSC8 bs =
  let (bs1, newBs) = BSC8.splitAt 1 bs
  in  if newBs == BSC8.empty
        then []
        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

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)

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

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

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

p :: Int -> Int
p x = x - 1

--modNum = 10 ^ 9 + 7
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) = M $ abs a

  signum (M a) = M $ signum a

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

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

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] ]

fact :: Int -> Int
fact 0         = 1
fact n | n > 0 = n * fact (n - 1)

knappsack :: Int -> [(Int, Int)] -> VU.Vector Int
knappsack maxW [] = VU.replicate (maxW + 1) 0
knappsack maxW ((w, v) : xs) =
  let tailDP = knappsack 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

knappsackMaxVal
  :: AIO.IOArray (Int, Int) Int
  -> VU.Vector Int
  -> VU.Vector Int
  -> Int
  -> IO Int
knappsackMaxVal dp volumeVec valueVec dpSize = do
  mapM_
    (\i -> mapM_
      (\v -> do
        let volume = volumeVec VU.! i
            value  = valueVec VU.! i
        newdp <- if v < volume
          then AIO.readArray dp (i, v)
          else do
            dpIVm <- AIO.readArray dp (i, v - volume)
            dpIV  <- AIO.readArray dp (i, v)
            return (max (dpIVm + value) dpIV)
        AIO.writeArray dp (i + 1, v) newdp
      )
      [0 .. dpSize]
    )
    [0 .. VU.length volumeVec - 1]
  AIO.readArray dp (VU.length volumeVec, dpSize)

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)
uf_makeSet :: Int -> IO UF
uf_makeSet n = do
  parent <- VU.thaw $ VU.generate n id
  rank   <- VUM.replicate n 0
  return (parent, rank)
uf_union :: UF -> Int -> Int -> IO ()
uf_union unionFind@(parents, ranks) x y = do
  xRoot     <- uf_find unionFind x
  yRoot     <- uf_find 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 ()

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

--UnDirectedGraph(無向グラフ)データ構造
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