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: Runtime Error)

import sys
input = sys.stdin.readline
import numpy as np


def nextLights(A, D):
    Lights = D
    i = 1
    for a in A:
        line = np.ones(a*2+1, dtype = int)
        Lights[i-1, n+i-a:n+i+a+1] = line
        i+=1
    Lights = Lights[:, n+1:2*n+1]
    Next_A = np.sum(Lights, axis=0)
    return Next_A


n, k = map(int, input().split())
A = [int(a) for a in input().split()]

D = np.zeros((n, 3*n+2), dtype = int)

if k >= n+1:
    print((str(n)+" ")*n)
else:
    for i in range(k):
        Next_A = nextLights(A, D)
        A = Next_A
    L=[str(a) for a in A]
    L=" ".join(L)
    print(L)