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: Wrong Answer)

parseInt(x) = parse(Int, x)
parseBigInt(x) = parse(BigInt, x)
parseFloat(x) = parse(Float64, x)
parseBigFloat(x) = parse(BigFloat, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
    n::Int32,k::Int32=parseMap(split(readline()))
    a::Vector{Int32}=parseMap(split(readline()))
    m::Vector{Int}=[0 for i in 1:n]
    if sum(a)==0
        println(join(m," "))
        return
    end
    for _ in 1:k
        flag::Bool=true
        s_m::Vector{Int32}=zeros(Int,n)
        e_m::Vector{Int32}=zeros(Int,n)
        ans::Int=0
        for i in 1:n
            s_m[max(1,i-a[i])]+=1
            e_m[min(n,i+a[i])]+=1
        end
        for i in 1:n
            ans+=s_m[i]
            m[i]=ans
            if m[i]<n
                flag=false
            end
            ans-=e_m[i]
        end
        a=m
        if flag
            break
        end
    end
    println(join(m," "))
end
main()