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)

n, k = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)
k.times do
    sum = Array.new(n + 1, 0)
    a.each_with_index do |a, i|
        if i - a < 0
            s = 0
        else
            s = i - a
        end
        if i + a + 1 >= n
            t = n
        else
            t = i + a + 1
        end
        sum[s] += 1
        sum[t] -= 1
    end
    sum.each_with_index do |s, i|
        if i == 0
            a[i] = s
        elsif i < n
            a[i] = a[i-1] + s
        end
    end
    break if a.all?{|aa| aa == n}
end
puts a * " "