Camel and Oases

AtCoder

IDagc012_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ oases on a number line. The coordinate of the $i$\-th oases from the left is $x_i$. Camel hopes to visit all these oases. Initially, the volume of the hump on his back is $V$. When the volume of the hump is $v$, water of volume at most $v$ can be stored. Water is only supplied at oases. He can get as much water as he can store at a oasis, and the same oasis can be used any number of times. Camel can travel on the line by either walking or jumping: * Walking over a distance of $d$ costs water of volume $d$ from the hump. A walk that leads to a negative amount of stored water cannot be done. * Let $v$ be the amount of water stored at the moment. When $v>0$, Camel can jump to any point on the line of his choice. After this move, the volume of the hump becomes $v/2$ (rounded down to the nearest integer), and the amount of stored water becomes $0$. For each of the oases, determine whether it is possible to start from that oasis and visit all the oases. ## Constraints * $2 ≤ N,V ≤ 2 × 10^5$ * $-10^9 ≤ x_1 < x_2 < ... < x_N ≤ 10^9$ * $V$ and $x_i$ are all integers. ## Input Input is given from Standard Input in the following format: $N$ $V$ $x_1$ $x_2$ $...$ $x_{N}$ [samples]

Samples

Input #1

3 2
1 3 6

Output #1

Possible
Possible
Possible

It is possible to start from the first oasis and visit all the oases, as follows:

*   Walk from the first oasis to the second oasis. The amount of stored water becomes $0$.
*   Get water at the second oasis. The amount of stored water becomes $2$.
*   Jump from the second oasis to the third oasis. The amount of stored water becomes $0$, and the volume of the hump becomes $1$.

Input #2

7 2
-10 -4 -2 0 2 4 10

Output #2

Impossible
Possible
Possible
Possible
Possible
Possible
Impossible

A oasis may be visited any number of times.

Input #3

16 19
-49 -48 -33 -30 -21 -14 0 15 19 23 44 52 80 81 82 84

Output #3

Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Impossible
Impossible
Impossible
Impossible

API Response (JSON)

{
  "problem": {
    "name": "Camel and Oases",
    "description": {
      "content": "There are $N$ oases on a number line. The coordinate of the $i$\\-th oases from the left is $x_i$. Camel hopes to visit all these oases. Initially, the volume of the hump on his back is $V$. When the v",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc012_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ oases on a number line. The coordinate of the $i$\\-th oases from the left is $x_i$.\nCamel hopes to visit all these oases. Initially, the volume of the hump on his back is $V$. When the v...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments