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)

def gets_nums
    gets.split.map{|x| x.to_i}
end
def light(a,b,n)
    b.fill(0)
    0.upto(n-1) do |i|
        l = [i-a[i],0].max
        r = [i+a[i]+1,n].min
        b[l]+=1
        b[r]-=1
    end
    flag = a[0]==b[0]
    a[0] = b[0]
    1.upto(n-1) do |i|
        b[i] += b[i-1]
        flag &= (a[i]==b[i])
        a[i] = b[i]
    end
    return flag
end
n, k = gets_nums
a = gets_nums
b = Array::new(n+1)
0.upto(k-1) do |i|
    break if light(a,b,n)
end
puts a.join(" ")