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)

my $N = 0;
my $K = 0;
while(<STDIN>)
{
  chomp $_;
  my @cols = split(" ", $_);
  if($cnt == 0) {
  	$N = $cols[0];
  	$K = $cols[1];
  }elsif($cnt == 1) {
  	my @As = @cols;
  	for(my $i=0; $i < $K; $i++) {
        my @Bs;
        for(my $x=0; $x < $N; $x++) { push @Bs, 0; }
  		for(my $j=1; $j <= $N; $j++) {
  			my $d = $As[$j-1];
  			my $min = $j - $d - 0.5;
  			my $max = $j + $d + 0.5;
  			for(my $k=1; $k <= int($max); $k++) {
  		        if($min <= $k && $k <= $max) { $Bs[$k-1] += 1; }
  			}
  		}
        @As = @Bs;
  	}
  	my $line = "";
  	for(my $x=0; $x < $N; $x++) {
  		if($x > 0) { $line .= " "; }
  		$line .= $As[$x];
  	}
  	print $line;
  }
  $cnt++;
}