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 Perl (5.26.1) (judge verdict: Time Limit Exceeded)

use strict;
use warnings;

my ($n, $k) = glob <>;
my @a = glob <>;

print join ' ' , @{operation(\@a, $k, 0)};

sub operation {
    my ($lights, $k, $count) = @_;
    my @range_diff = map { 0 } (0..$n-1);

    for my $pos (0..$n-1) {
        my $min = ($pos - $lights->[$pos] >= 0) ? $pos - $lights->[$pos] : 0;
        ++$range_diff[$min];

        if ($pos + $lights->[$pos] + 1 <= $n-1) {
            --$range_diff[$pos + $lights->[$pos] + 1];
        }
    }
    for my $pos (1..$n-1) {
        $range_diff[$pos] += $range_diff[$pos-1];
    }

    return ($k-1 == 0 || $count >= 50) ? \@range_diff : operation(\@range_diff, $k-1, $count+1);
}