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)

import numpy as np
N, K = tuple(int(c) for c in input().split(' '))
A = [0]
A.extend(tuple(int(c) for c in input().split(' ')))
A = np.array(A, dtype=np.int64)

for _ in range(K):
    s = [i for i in range(1, N+1) if A[i] > 0]
    t = [i for i in range(1, N+1) if A[i] == 0]
    B= np.zeros(N+1, dtype=np.int64)
    for i in s:
        lower = max(1, i-A[i])
        upper = min(N, i+A[i])
        #print(i, lower, upper)
        B[lower:upper+1] += 1
    B[t] += 1
    A = B
print(' '.join([str(s) for s in A[1:]]))