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 Julia (1.4.0) (judge verdict: Time Limit Exceeded)

function main()
    n, k = parse.(Int, split(readline()))
    a = parse.(Int, split(readline()))
    
    h = Int(ceil(log2(n)))+1
    t = Vector{Vector{Int}}(undef, h)
    t[end] = a;
    for i in h-1:-1:1
        t[i] = zeros(Int, Int(ceil(length(t[i+1])/2)))
    end

    for i in 1:k
        p = zeros(Int, length(a))
        for j in 1:n
            p[getrange(j, a[j], n)] .+= 1
        end
        a = p
    end

    for i in a
        print(i," ")
    end
    println()

end

function getrange(i, x, m)
    l = max(1, i-x)
    r = min(i+x, m)
    l:r
end

main()