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 Python (3.8.2) (judge verdict: Wrong Answer)

import sys
import math
input = sys.stdin.readline

def main():
    N, K = map(int, input().split())
    LampList = list(map(int, input().split()))
    
    if math.log(N) <= K:
        LampList = [N for i in range(N)]
        for i in range(N):
            print(LampList[i], end=' ')
    else:
        for i in range(K):
            tmpList = [0 for i in range(N)]
            for p in range(N):
                Start = p - LampList[p]
                Stop = p + LampList[p] + 1
                if Start < 0:
                    Start = 0
                if Stop > N:
                    Stop = N
                for q in range(Start, Stop):
                    tmpList[q] += 1
            
            LampList = tmpList
            if all(elem == N for elem in LampList):
                break
        
        for i in range(N):
            print(LampList[i], end=' ')
    
if __name__ == '__main__':
    main()