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 = list(map(int,input().split()))
if((n+3)//2+1 <= k):
    c = [str(n)]*n
else:
    for i in range(k):
        b = [0]*n
        p = 0
        for j in range(n):
            if(a[j] == n):
                p += 1
            else:
                for k in range(max(0,j-a[j]),min(n-1,j+a[j])+1):
                    b[k] += 1
        if(p == n):
            c = [str(n)]*n
            break
        else:
            for k in range(n):
                b[k] += p
            a = b
    c = [str(a) for a in b]
print(' '.join(c))