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: Accepted)

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

function main()
	n,k = readline() |> split |> parseMap
	a = readline() |> split |> parseMap
	l = zeros(Int,n)
	r = zeros(Int,n)
	for i in 1:n
		l[i]=max(1,i-a[i])
		r[i]=min(n,i+a[i])
	end
	for i in 1:k
		b = zeros(Int,n)
		for j in 1:n
			b[l[j]]+=1
			if r[j]<n
				b[r[j]+1]-=1
			end
		end
		for j in 2:n
			b[j]+=b[j-1]
		end
		a = copy(b)
		if sum(b)==n*n
			break
		end
		for j in 1:n
			l[j]=max(1,j-a[j])
			r[j]=min(n,j+a[j])
		end
	end
	for i in 1:n-1
		print(a[i]," ")
	end
	println(a[n])
end

main()