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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

n,k=gets.split.map(&:to_i)
a=gets.split.map(&:to_i)
#n,k=200000,200000
#a=[0]*200000
t=41
while k>0&&t>0
  b=[]
  l=[0]*n
  c=0
  0.upto(n-1) do |i|
    c+=1
    if i+a[i]<n-1
      l[i+a[i]]+=1
    else
      l[n-1]+=1
    end
    b[i]=c
    c-=l[i]
  end
  l=[0]*n
  c=0
  (n-1).downto(0) do |i|
    if i-a[i]>0
      l[i-a[i]]+=1
    else
      l[0]+=1
    end
    b[i]+=c
    c-=l[i]
    c+=1
  end
  a=b.dup
  k-=1
  t-=1
end
puts a.join(" ")