Contest Duration: - (local time) (120 minutes) Back to Home
C - Lamps /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• 1 以上 N 以下の各整数 i に対し、操作時に座標 i を照らしている電球の個数を B_i とする。そして、各電球 i の光の強さを B_i に変更する。

K 回の操作を行った後の各電球の光の強さを求めてください。

### 制約

• 1 \leqq N \leqq 2 \times 10^5
• 1 \leqq K \leqq 2 \times 10^5
• 0 \leqq A_i \leqq N

### 入力

N K
A_1 A_2 \ldots A_N


### 出力

K 回の操作を行った後の電球 i の光の強さ A{'}_i を、以下の形式で標準出力に出力せよ。

A{'}_1 A{'}_2 \ldots A{'}_N


### 入力例 1

5 1
1 0 0 1 0


### 出力例 1

1 2 2 1 2


### 入力例 2

5 2
1 0 0 1 0


### 出力例 2

3 3 4 4 3


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