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)

from sys import stdin
from collections import defaultdict as dd
from collections import deque as dq
import itertools as it
from math import sqrt, log, log2
from fractions import Fraction

n, k = map(int, input().split())
intensity = list(map(int, stdin.readline().split()))

count = 0
while count < k:
    totsum = 0
    prefs = [0]*n
    zeros = []
    for i in range(n):
        if intensity[i]!=0:
            l = i - intensity[i]
            r = i + intensity[i] + 1

            prefs[max(l, 0)] += 1
            if r <= n-1: 
                prefs[r] += -1
        else:
            zeros.append(i)
            
    for i in range(1, n):
        prefs[i] += prefs[i-1]
        totsum += prefs[i]
    
    for i in zeros:
        if intensity[i] == 0:
            prefs[i] += 1
            totsum += 1
    
    if totsum == n*k:
        print(*prefs)
        exit()
    
    intensity = prefs
    count += 1

print(*prefs)