Lamps

AtCoder

IDtokiomarine2020_c

Time2000ms

Memory256MB

Difficulty—

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: $N$ $K$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5 1
1 0 0 1 0

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 $2$.

Input #2

5 2
1 0 0 1 0

Output #2

3 3 4 4 3

API Response (JSON)

{
  "problem": {
    "name": "Lamps",
    "description": {
      "content": "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 bul",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "tokiomarine2020_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ bulbs arranged on a number line, numbered $1$ to $N$ from left to right. Bulb $i$ is at coordinate $i$.\nEach bulb has a non-negative integer parameter called intensity. When there is a bul...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments