102603: [AtCoder]ABC260 D - Draw Your Cards

Problem Statement

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:

$N$ $K$
$P_1$ $P_2$ $\dots$ $P_N$

Output

Print $N$ lines.
The $i$-th line ($1 \le i \le N$) should describe the card with the integer $i$ written on it. Specifically,

• if the card with $i$ written on it is eaten in the $x$-th move, print $x$;
• if that card is not eaten in any move, print $-1$.

Sample Input 1

5 2
3 5 2 1 4

Sample 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.

Sample Input 2

5 1
1 2 3 4 5

Sample Output 2

1
2
3
4
5

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

Sample Input 3

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

Sample Output 3

9
9
9
15
15
6
-1
-1
6
-1
-1
-1
-1
6
15