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)

# encoding:utf-8
import copy
import random
import bisect #bisect_left　これで二部探索の大小検索が行える
import fractions #最小公倍数などはこっち
import math
import sys
import collections

mod = 10**9+7
sys.setrecursionlimit(mod) # 再帰回数上限はでdefault1000

d = collections.deque()
def LI(): return list(map(int, sys.stdin.readline().split()))

N, K = LI()
A = LI()

"""
明るさが一定値を超えると計算しなくて良い
一定？d > math.floort(N/2)
"""

lamps = [[0 for i in range(N)] for j in range(K + 1)]
lamps[0] = A

if K > 15:
    b = [str(N)] * N
    print(" ".join(b))
    sys.exit()

"""
累積和〜
"""
for i in range(K):
    tmps = [0 for i in range(N)]
    for j in range(N):
        w = lamps[i][j]
        tmps[max(0, j - w)] += 1
        r = min(N-1, j + w)
        if r + 1 < N:
            tmps[r + 1] -= 1
    hoge = 0
    for j in range(N):
        hoge += tmps[j]
        lamps[i + 1][j] = hoge
ans = lamps[-1]
ans = map(str, ans)
print(" ".join(ans))