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)

def adjust_light(arr):
    counter = [0] * len(arr)
    is_break = True
    
    for idx in range(0, len(arr)):
        if is_break is True:
            is_break = (arr[idx] == len(arr))
        min = idx - arr[idx]
        if min < 0:
            min = 0
        max = idx + arr[idx]
        if max >= len(arr):
            max = len(arr)-1
        for position in range(min, max+1):
            counter[position] = counter[position] + 1

    return counter, is_break

n, k = list(map(int, input().split(' ')))
arr = list(map(int, input().split(' ')))
for idx in range(0, k):
    arr, is_break = adjust_light(arr)
    if is_break:
        break
print(*arr)