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)

import sys
n,k = map(int,input().split())
ls = list(map(int,input().split()))
if n >17 and k >n/2:
    for q in range(len(ls)):
        print(len(ls),end=" ")
    sys.exit()
if k >= len(ls):
    for q in range(len(ls)):
        print(len(ls),end=" ")
    sys.exit()
for _ in range(k):
    new = [0]*n
    for i in range(n):
        p = 0
        for l in range(1,max(n-i,i+1)):
            if i+l >= 0 and i+l <n:
                if ls[i+l] >= l:
                    p += 1
            if i-l >= 0 and i-l <n:
                if ls[i-l] >= l:
                    p += 1
        new[i] = p+1
    ls = new
print(*ls)