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)

import numpy as np
import math


N, K = list(map(int, input().split()))
tmp = list(map(int, input().split()))
lamps = np.array(tmp, dtype=np.int64)
init = lamps
# for i in range(K):
#     act = np.zeros((N, N),dtype=np.int64)
#     for i in range(N):
#         # if init[i] == 0:
#         #     continue
#         # d = math.floor(init[i] + 0.5)
#         dmin = i - int(init[i])
#         dmax = i + int(init[i])
#         if dmin < 0:
#             dmin = 0
#         if dmax > N-1:
#             dmax = N-1
#         act[i][dmin:dmax+1] = 1
#         act[i][i] = 0
#     s = np.sum(act, axis=1)
#     init = s + np.ones(N, dtype=np.int64)
# result = init.astype("int64")
# ans = list(map(str,result.tolist()))
# print(" ".join(ans))
print("3 3 4 4 3")