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 Julia (1.4.0) (judge verdict: Accepted)

const double = Float64
const int = Int64

parseint(x) = parse(int, x)
readint() = map(parseint, split(readline()))

function main()
  N, K = readint()
  A = readint()
  
  B = zeros(int,N)
  Nmax = 0
  for i in 1:K
    B = zeros(int,N)
    for j in 1:N 
      l=max(1,j-A[j])
      r=min(N,j+A[j])
      B[l] += 1
      r+1 <= N && (B[r+1] -=1)
    end
    for j in 2:N
      B[j] += B[j-1]
    end
    s = 0
    for j in 1:N
      if B[j] == N
        s+=1
      end
    end
    if s == N
      for j = 1:N
        print(N," ") 
      end
      println()
      return
    end
    A = B
  end
  for i in 1:N
    print(A[i]," ")
  end
  println()

        
  
end

main()