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 calc(A)
    B=zeros(Int32,N)
    let i=1
        #println("A=$A")
        while i<=N
            #xmin=ceil(Int64, i-A[i]-0.5)
            #xmax=floor(Int64, i+A[i]+0.5)
            if A[i]==N
                B .+=1
                i += 1
                continue
            else
                xmin=i-A[i]
                xmax=i+A[i]
                if xmin >= 1
                    j=xmin
                else
                    xmin=1
                end
                if xmax > N
                    xmax = N
                end

                B[xmin:xmax] .+= 1
                #=while j<=xmax
                    B[j] += 1
                    j += 1
                end=#
                i += 1
            end
        end
        #println("B=$B")
        B
    end
end

tmp=readline()
N,K=parse.(Int32,split(tmp))
tmp=readline()
#A=zeros(Int32,(N,K))
#A[1:end,1]=parse.(Int32,split(tmp))
#println("$N,$K,$A")
A=parse.(Int32,split(tmp))
let kl=1
    while kl<=K
        B=calc(A)
        A .= B
#=        let i=1
            while i<=N
                A[i]=B[i]=#
                if kl==K
                    print.(A," ")
                end
#=                i += 1
            end
        end=#
        kl+=1
    end
end