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: Wrong Answer)

import bisect, collections, copy, heapq, itertools, math, string, sys
input = lambda: sys.stdin.readline().rstrip() 
sys.setrecursionlimit(10**7)
INF = 10**20
def I(): return int(input())
def F(): return float(input())
def S(): return input()
def LI(): return [int(x) for x in input().split()]
def LI_(): return [int(x)-1 for x in input().split()]
def LF(): return [float(x) for x in input().split()]
def LS(): return input().split()

def resolve():
    N, K = LI()
    A = LI()

    # 全部0の最遅ケースでもlog(N)*2くらいで収束する
    for _ in range(min(K, int(2 * math.log(N)) + 1)):
        tmp = [0] * (N + 1)
        b = [0] * (N + 1)
        for i in range(N):
            tmp[max(i - A[i], 0)] += 1
            tmp[min(i + A[i] + 1, N)] -= 1
        for i in range(N):
            b[i+1] = tmp[i] + b[i]
        for i in range(N):
            A[i] = b[i+1] 
        # print(A)

    print(*A)

if __name__ == '__main__':
    resolve()