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.

Input is given from Standard Input in the following format:

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

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 $-1$.

-   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 $(1,2,\dots,N)$).

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.

1
2
3
4
5

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