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)

# test sub
parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function solve(N, K, A)
    for _ in 1:K
        tmp = zeros(Int64, N)

        for i in 1:N
            to = maximum([1, i - A[i]])
            en = minimum([N, i + A[i]])
            tmp[to:en] .+= 1
        end
    if A == tmp
        return A
    else
        A = tmp
    end
    end
    return A
end

function print_ans(A)
    for a in A
        print(a, " ")
    end
    println()
end



function main()

N, K = parseMap(split(readline()))

A = parseMap(split(readline()))


if N * K < 10 ^ 6
    print_ans(solve(N, K ,A))
elseif K >= N
    print_ans(fill(N, N))
else
    print_ans(solve(N, 200, A))
end


end

main()