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.

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.

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 $(1,2,\dots,N))$.

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

见题面 Input 部分

见题面 Output 部分