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 Ruby (2.7.1) (judge verdict: Runtime Error)

#!/usr/bin/env ruby

N, K = gets.chomp.split.map(&:to_i)
lights = gets.chomp.split.map(&:to_i)

if K >= N
  puts Array.new(N, N).join(' ')
  exit
end

# 1回目
tmp = Array.new(N, 0)

lights.each_with_index do |a, i|
  1.upto(a) do |j|
    tmp[i-j] += 1 if i-j >= 0
    tmp[i+j] += 1 if i+j < N
  end

  tmp[i] += 1
end

lights = tmp

# 2回目
if K >= 2
  tmp = Array.new(N, 0)

  lights.each_with_index do |a, i|
    1.upto(a) do |j|
      tmp[i-j] += 1 if i-j >= 0
      tmp[i+j] += 1 if i+j < N
    end

    tmp[i] += 1
  end

  changes = Hash.new
  N.times do |i|
    change = tmp[i] - lights[i]
    changes[i] = change if change > 0
  end

  lights = tmp

  # 3回目以降
  (K-2).times do
    hash = Hash.new { 0 }

    loop do
      i, change = changes.shift

      break unless i

      a = lights[i]

      change.times do |j|
        d = a - j

        if i-d >= 0
          lights[i-d] += 1
          hasj[i-d] += 1
        end

        if i+d < N
          lights[i+d] += 1
          hash[i+d] += 1
        end
      end
    end

    changes = hash
  end
end

puts lights.join(' ')