Problem:
Score : 500 points

Problem Statement

We have N bulbs arranged on a number line, numbered 1 to N from left to right.
Bulb i is at coordinate i.

Each bulb has a non-negative integer parameter called intensity.
When there is a bulb of intensity d at coordinate x, the bulb illuminates the segment from coordinate x-d-0.5 to x+d+0.5.
Initially, the intensity of Bulb i is A_i. We will now do the following operation K times in a row:

For each integer i between 1 and N (inclusive), let B_i be the number of bulbs illuminating coordinate i. Then, change the intensity of each bulb i to B_i.

Find the intensity of each bulb after the K operations.

Constraints

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

1 \leq K \leq 2 \times 10^5

0 \leq A_i \leq N

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \ldots A_N

Output

Print the intensity A{'}_i of each bulb i after the K operations to Standard Output in the following format:

A{'}_1 A{'}_2 \ldots A{'}_N

Sample Input 1

5 1
1 0 0 1 0

Sample Output 1

1 2 2 1 2

Initially, only Bulb 1 illuminates coordinate 1, so the intensity of Bulb 1 becomes 1 after the operation.
Similarly, the bulbs initially illuminating coordinate 2 are Bulb 1 and 2, so the intensity of Bulb 2 becomes 2.

Sample Input 2

5 2
1 0 0 1 0

Sample Output 2

3 3 4 4 3

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

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE MultiWayIf #-}


import Control.Arrow
import Control.Concurrent
import Control.Monad
import qualified Data.ByteString.Char8 as C
import Data.Complex
import Data.Function
import Data.Function.HT
import qualified Data.IntMap.Strict as IM
import qualified Data.IntSet as IS
import Data.List
import Data.Ord
import qualified Data.Sequence as Sq
import Data.Vector.Algorithms.Search
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import Debug.Trace


------------------
-- #   Read   # --
------------------

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 :: IO ()
main = do
    [n,k] <- r'
    as <- r n
    
    res <- ((min k 100) `timesM` solve)  as
    putStrLn $ unwords $ map show $ U.toList res


f 0 = 0
f n = f (n-1) * 2 + 1

solve :: -- Int -> -- (UM.Vector Int, UM.Vector Int) ->
            U.Vector Int -> IO (U.Vector Int)
solve v = do
    let on  = U.imap (\i a -> max 1 ((i+1)-a)) v
        off = U.imap (\i a -> min (U.length v) (i+1+a)) v

    -- print on
    -- print off

    onI <- UM.replicate (U.length v) 0 :: IO (UM.IOVector Int)
    offI <- UM.replicate (U.length v) 0 :: IO (UM.IOVector Int)
    U.forM_ on  (\i -> UM.modify onI  succ (i-1) )
    U.forM_ off (\i -> UM.modify offI succ (i-1) )
    onIF <- U.freeze onI
    offIF <- U.freeze offI
    let difs = U.zipWith (-) (U.tail onIF) offIF
    return $ U.scanl' (+) (U.head onIF) difs

timesM 0 f x = return x
timesM n f x = do
    r <- f x
    timesM (n-1) f r