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: Time Limit Exceeded)

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

diff_list = [0 for num in range(n)]
diff_list[0] = a_in[0]
for i in range(1, n):
    diff_list[i] = a_in[i] - a_in[i-1]

itr = k
# if k > 41:
#     itr = 41
for i in range(itr):
    new_list = [0 for num in range(n)]
    d_sum = 0
    for j, d in enumerate(diff_list):
        d_sum += d
        if j-d_sum > 0:
            new_list[j-d_sum] += 1
        else:
            new_list[0] += 1
        if d_sum+j+1 < n:
            new_list[j+d_sum+1] -= 1
    # print(new_list)
    diff_list = new_list.copy()

ans = 0
for d in diff_list:
    ans += d
    print(ans, end= ' ')