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 Python (3.8.2) (judge verdict: Wrong Answer)

N, K = map(int, input().split())
As = list(map(int, input().split()))

Bs = [1]*N

for i in range (0, N):
	if As[i] > 0:
		for j in range (max(0, i-As[i]),min(i+As[i]+1, N)):
			Bs[j]+=1
		Bs[i]-=1

Cs = [0]*N

switch = 0

for i in range (0, K-1):
	if switch == 0:
		while sum(Cs) < K*N:
			for j in range (0, N):
				for l in range (max(0, j-Bs[j]),min(j+Bs[j]+1, N)):
					if Cs[l] < N:
						Cs[l]+=1
		Bs = [0]*N
		switch = 1
	else:
		while sum(Bs) < K*N:
			for j in range (0, N):
				for l in range (max(0, j-Cs[j]),min(j+Cs[j]+1, N)):
					if Bs[l] < N:
						Bs[l]+=1
		Cs = [0]*N	
		switch = 0

if switch == 0:
	print(Bs)
else:
	print(Cs)