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: Wrong Answer)

def main():
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))

    for _ in range(min(K,40)):
        e_list_1 = [0] * N
        l_1 = [0] * N
        v = 0
        for i,a in enumerate(A_list):
            l_1[i] = v 
            e_list_1[min(i + a, N-1)] += 1
            v = v + 1 - e_list_1[i]
        
        e_list_2 = [0] * N
        v = 0
        for _i,a in enumerate(A_list[::-1]):
            i = N-1-_i
            A_list[i] = l_1[i] + v + 1
            e_list_2[max(i-a, 0)] += 1
            v = v + 1 - e_list_2[i]
        
    print(*A_list)
if __name__ == "__main__":
    main()