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)

parseInt(x) = parse(Int, x)
parseArray(x::Array{SubString{String}, 1}) = map(parseInt, x)

function main()
  n,k = readline() |> split |> parseArray
  a = zeros(Int, n)
  a = readline() |> split |> parseArray

  for _ in 1:min(k, ceil(Int, 50))
    imos = zeros(Int, n+1)
    for i in 1:n
      d = a[i]
      imos[max(i-d, 1)] += 1
      imos[min(i+d+1, n+1)] += -1
    end
    a = zeros(Int, n)
    c = 0
    for i in 1:n
      c = c+imos[i]
      a[i] = c
    end
  end
  println.(a)
end

main()