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)

import qualified Data.ByteString.Char8 as BS
import Data.Maybe
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

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

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

calc :: VU.Vector Int -> VU.Vector Int
calc as = do
  let n = VU.length as
  let base = VU.generate (n + 1) (\x -> 0)
  let ds = VU.imap (\i a -> (max 0 $ i - a, 1)) as VU.++ VU.imap (\i a -> (min n $ i + a + 1, -1)) as
  VU.postscanl' (+) 0 (VU.init (VU.accumulate (+) base ds))

judge :: VU.Vector Int -> Int -> Int -> VU.Vector Int
judge as n 0 = as
judge as n k
  | VU.all (== n) as = as
  | otherwise = judge (calc as) n (k -1)

main = do
  [n, k] <- getIntList
  as <- getIntList
  let as' = VU.fromList as
  let as'' = judge as' n k
  mapM_ putStr (map (\x -> show x ++ " ") (VU.toList as''))