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: Time Limit Exceeded)

n, k = gets.split.map(&:to_i)
nums = gets.split.map(&:to_i)
zeros = Array.new(n + 1, 0)
previous = nums
k.times do |i|
  after = zeros.dup
  previous.each_with_index do |num, index|
    min = index - num
    min = 0 if min < 0
    max = index + num
    max = n - 1 if max > n - 1
    after[min] += 1
    after[max + 1] -= 1
  end
  minimum = n
  prev = after[0]
  (1...n).each do |i|
    cur = after[i]
    next if cur == n
    before = cur
    cur += prev
    minimum = cur if minimum > cur
    cur = n if cur > n
    after[i] = cur unless before == cur
    prev = cur
  end
  after.delete_at(-1)
  previous = after
  break if minimum == n
end

previous[0] = n if previous.first > n
puts previous.join(' ')