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: Runtime Error)

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)
act = np.zeros((N, N),dtype=np.int64)
def loop(N, K, lamps, act):
    init = lamps
    for i in range(K):
        act[:,:] = 0
        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=0)
        # init = s + np.ones(N, dtype=np.int64)
    return init
result = loop(N, K, lamps,act)
ans = list(map(str,result.tolist()))
print(" ".join(ans))