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
fscanf(STDIN, "%d %d", $n, $k);
$as = explode(' ', trim(fgets(STDIN)));

for ($i=0; $i < $k; $i++) {
  $cnts = array_fill(0, $n, array());
  foreach ($as as $p => $a) {
    $start = $a*(-1) < $n*(-1) ? $n*(-1) : $a*(-1);
    $end = $a > $n ? $n : $a;
    for ($ii=$start; $ii <= $end; $ii++) {
      if (isset($cnts[$p+$ii])) {
        $cnts[$p+$ii][] = $a;
      }
    }
  }

  $check = 0;
  for ($j=0; $j < $n; $j++) {
    $as[$j] = count($cnts[$j]);

    if ($as[$j] == $n) {
      $check++;
    }
  }

  if ($check == $n) {
    break;
  }
  // echo implode(' ', $as).'-'.PHP_EOL;
}

echo implode(' ', $as);