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: Accepted)

import numpy as np
from numba import njit
import sys
# import copy
# def input(): return sys.stdin.readline().rstrip()
# input = sys.stdin.readline
input = sys.stdin.buffer.readline
# sys.setrecursionlimit(10 ** 7)

N, K = map(int, input().split())
# A = np.array(list(map(int, (input().split()))))
A = np.array(input().split(), dtype=np.int64)
# A = list(map(int, (input().split())))
# nd = np.zeros((N,N), dtype=bool)
# print(*A)

# @njit('(i8[::1],)', cache=True)
@njit(cache=True)
def loop(A):
    for i in range(K):
        # cnt = [0]*N
        cnt = np.zeros_like(A)
        for j, x in enumerate(A):
            # nd[j, max(j-A[j],0):min(j+A[j]+1,N)] = True
            l = max(j-x,0)
            r = min(j+x+1,N)
            cnt[l] += 1
            if r<N:
                cnt[r] -= 1
            # for k in range(max(j-A[j],0), min(j+A[j]+1,N)):
            #     cnt[k] += 1
        # print(nd)
        # A = np.count_nonzero(nd, axis=0)
        # print(cnt)
        A = np.cumsum(cnt)
        if A[0] == A[N-1] == N:
            break
        # print(*A)
    return A

A = loop(A)
print(*A)