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: Time Limit Exceeded)


# いもす法の利用
import copy 
N,K=map(int,(input().split()))
A=list(map(int,(input().split())))
B= [0 for _ in range(N)]
for i in range(K):
  B= [0 for _ in range(N)]
  C=0
  for j in A:

    if(C-j<0):
      left=0
      B[left]+=1
    else:
      left=C-j
      B[left]+=1
    if(C+j+1>=N):
      right=N-1
    else:
      right=C+j+1
      B[right]-=1

    C+=1
  
  ruiseki = [0] * N  # 累積和用リスト
  ruiseki[0] = B[0]
  for m in range(N):
      ruiseki[m] = ruiseki[m-1] + B[m]
  A = copy.copy(ruiseki)
  if(i==100):
    break
print(*ruiseki)