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
function howManyTerasu($bulbs, $pos) {
    $count = 0;
    foreach($bulbs as $key => $value) {
        if($pos === $key) {
            $count++;
            continue;
        }
        if($value === 0) {
            continue;
        }
        $from = $key - $value -0.5;
        $to = $key + $value +0.5;
        if($from <= $pos && $pos <= $to) {
            $count++;
        }
    }
    return $count;
}

function sousa(&$bulbs) {
    for($pos = 0;$pos < count($bulbs);$pos++) {
        $newbulbs[$pos] = howManyTerasu($bulbs, $pos);
    }
    $bulbs = $newbulbs;
}

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

foreach ($a as &$value) {
    $value = (int) $value;
}
unset($value);

$bulbs = $a;

for($i=0;$i < $k;$i++) {
    sousa($bulbs);
}

echo implode(' ', $bulbs);