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: Time Limit Exceeded)

### 解答
N, K = map(int, input().split())
A = list(map(int, input().split()))

#B = [0]*N                                 # 記録用のリスト

for k in range(K):                        # 以降の操作をK回繰り返す
  B = [0]*N 
  for i in range(N):                      # 各電球によって照らされる範囲を考える
    start = max(0, i-A[i])                # 始点のインデックスは0かi-A[i]
    end = min(N, i+A[i]+1)                # 終点のインデックスはNかi+A[i]+1
    B[start] += 1                         # 始点に+1を記録する
    if end <= N - 1:
      B[end] -= 1                         # 終点に電球が存在する場合は-1を記録する
  bmin = B[0] 
  for i in range(1, N):                   # 累積和の計算
    B[i] = B[i-1] + B[i]
    bmin = min(B[i], bmin)
  A = B                                   # AをBで更新してつぎのループへ 
  if bmin == N:                        # すべての電球がN個の電球に照らされるタイミングでbreakする
    break

print(*A)                                 # リストAの中身を順に表示