Draw Your Cards

AtCoder

IDabc260_d

Time2000ms

Memory256MB

Difficulty—

There is a deck consisting of $N$ face-down cards with an integer from $1$ through $N$ written on them. The integer on the $i$\-th card from the top is $P_i$. Using this deck, you will perform $N$ moves, each consisting of the following steps: * Draw the topmost card from the deck. Let $X$ be the integer written on it. * Stack the drawn card, face up, onto the card with the smallest integer among the face-up topmost cards on the table with an integer greater than or equal to $X$ written on them. If there is no such card on the table, put the drawn card on the table, face up, without stacking it onto any card. * Then, if there is a pile consisting of $K$ face-up cards on the table, eat all those cards. The eaten cards all disappear from the table. For each card, find which of the $N$ moves eats it. If the card is not eaten until the end, report that fact. ## Constraints * All values in input are integers. * $1 \le K \le N \le 2 \times 10^5$ * $P$ is a permutation of $(1,2,\dots,N)$ (i.e. a sequence obtained by rearranging $(1,2,\dots,N)$). ## Input Input is given from Standard Input in the following format: $N$ $K$ $P_1$ $P_2$ $\dots$ $P_N$ [samples]

Samples

Input #1

5 2
3 5 2 1 4

Output #1

4
3
3
-1
4

In this input, $P=(3,5,2,1,4)$ and $K=2$.

*   In the $1$\-st move, the card with $3$ written on it is put on the table, face up, without stacked onto any card.
*   In the $2$\-nd move, the card with $5$ written on it is put on the table, face up, without stacked onto any card.
*   In the $3$\-rd move, the card with $2$ written on it is stacked, face up, onto the card with $3$ written on it.
    *   Now there is a pile consisting of $K=2$ face-up cards, on which $2$ and $3$ from the top are written, so these cards are eaten.
*   In the $4$\-th move, the card with $1$ written on it is stacked, face up, onto the card with $5$ written on it.
    *   Now there is a pile consisting of $K=2$ face-up cards, on which $1$ and $5$ from the top are written, so these cards are eaten.
*   In the $5$\-th move, the card with $4$ written on it is put on the table, face up, without stacked onto any card.
*   The card with $4$ written on it was not eaten until the end.

Input #2

5 1
1 2 3 4 5

Output #2

1
2
3
4
5

If $K=1$, every card is eaten immediately after put on the table within a single move.

Input #3

15 3
3 14 15 9 2 6 5 13 1 7 10 11 8 12 4

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Draw Your Cards",
    "description": {
      "content": "There is a deck consisting of $N$ face-down cards with an integer from $1$ through $N$ written on them. The integer on the $i$\\-th card from the top is $P_i$. Using this deck, you will perform $N$ mov",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc260_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a deck consisting of $N$ face-down cards with an integer from $1$ through $N$ written on them. The integer on the $i$\\-th card from the top is $P_i$.\nUsing this deck, you will perform $N$ mov...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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