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 PyPy3 (7.3.0) (judge verdict: Accepted)

n, k = map(int, input().split())
A = list(map(int, input().split()))


def query(lamps):
    start_list = []
    end_list = []
    for idx, power in enumerate(lamps):
        start, end = idx - power, idx + power
        start_list.append(start)
        end_list.append(end)

    start_list.sort(reverse=True)
    end_list.sort(reverse=True)

    now = 0
    for idx in range(n):
        while start_list and start_list[-1] <= idx:
            start_list.pop()
            now += 1

        while end_list and end_list[-1] < idx:
            end_list.pop()
            now -= 1

        lamps[idx] = now


def full_check(counts, full):
    for count in counts:
        if count == full:
            continue
        else:
            return False

    return True


for _ in range(k):
    query(A)
    if full_check(A, n):
        break

print(*A)