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
NK = list(map(int, input().split()))
A = list(map(int, input().split()))

lamp = []
for i in range(len(A)):
    lamp.append(A[i])


def operation(lampList):
    tmpList = [0] * len(lampList)
    allList = [1] * len(lampList)

    for i in range(len(lampList)):
        l = lampList[i] + 1
        if ((l > NK[0] - i) and (l > i)):
            tmpList = np.array(tmpList) + np.array(allList)
        else:
            tmpList[i] += 1
            for j in range(1, l):
                if (i - j >= 0):
                    tmpList[i - j] += 1
                if (i + j < NK[0]):
                    tmpList[i + j] += 1
    return tmpList

for i in range(NK[1]):
    lamp = operation(lamp)

L=[str(a if a < NK[0] else NK[0]) for a in lamp]
L=" ".join(L)
print(L)