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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php
  list($n, $k) = array_map('intval', explode(" ", trim(fgets(STDIN))));

  $a = array_map('intval', explode(" ", trim(fgets(STDIN))));

  $loop = min($k, 200);
  for ($h=0; $h<$loop; $h++) {
    $x = array_fill(0, $n+1, 0);
    for ($i=0; $i<$n; $i++) {
      $l = max($i-$a[$i], 0);
      $r = min($i+$a[$i]+1, $n);
      $x[$l]++;
      $x[$r]--;
    }
    $a[0]=$x[0];
    for ($i=1; $i<$n; $i++) {
      $a[$i]=$a[$i-1]+$x[$i];
    }
  }

  echo implode(" ", $a);