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

问题描述

有一个由$N$张牌组成的牌堆，每张牌的正面都写有一个从1到$N$的整数。在牌堆顶部的第$i$张牌上写的数字是$P_i$。

使用这个牌堆，你将进行$N$次操作，每次操作包含以下步骤：

• 从牌堆顶部抽取一张牌。设该牌上写的数字为$X$。
• 将抽取的牌正面朝上放在桌子上一张牌的顶部，这张牌需要满足以下条件：它是最顶部的一张牌，且牌面上的数字大于等于$X$，并且在所有满足条件的牌中，这张牌的数字最小。如果没有满足条件的牌在桌子上，将抽取的牌放在桌子上，正面朝上，不放在任何牌的顶部。
• 然后，如果桌子上有一叠由$K$张牌组成的牌堆，将这叠牌吃掉。被吃掉的牌都会从桌子上消失。

对于每张牌，找出它在$N$次操作中哪一次被吃掉。如果它在任何一次操作中都没有被吃掉，报告这一事实。

约束

• 输入中的所有值都是整数。
• $1 \le K \le N \le 2 \times 10^5$
• $P$是序列$(1,2,\dots,N)$的排列（即通过重新排列$(1,2,\dots,N)$得到的序列）。

输入

从标准输入给出输入，格式如下：

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

输出

打印$N$行。
第$i$行（$1 \le i \le N$）应该描述写有数字$i$的牌。具体来说，

• 如果写有数字$i$的牌在第$x$次操作中被吃掉，打印$x$；
• 如果这张牌在任何操作中都没有被吃掉，打印$-1$。

样例输入1

5 2
3 5 2 1 4

样例输出1

4
3
3
-1
4

在这个输入中，$P=(3,5,2,1,4)$，$K=2$。

• 在第1次操作中，写有数字3的牌被放在桌子上，正面朝上，不放在任何牌的顶部。
• 在第2次操作中，写有数字5的牌被放在桌子上，正面朝上，不放在任何牌的顶部。
• 在第3次操作中，写有数字2的牌被放在写有数字3的牌的顶部，正面朝上。现在有一叠由$K=2$张牌组成的牌堆，最上面两张牌的数字是2和3，所以这些牌被吃掉了。
• 在第4次操作中，写有数字1的牌被放在写有数字5的牌的顶部，正面朝上。现在有一叠由$K=2$张牌组成的牌堆，最上面两张牌的数字是1和5，所以这些牌被吃掉了。
• 在第5次操作中，写有数字4的牌被放在桌子上，正面朝上，不放在任何牌的顶部。
• 写有数字4的牌在最后没有被吃掉。

样例输入2

5 1
1 2 3 4 5

样例输出2

1
2
3
4
5

如果$K=1$，那么每张牌在被放在桌子上后，在一次操作中就会立即被吃掉。

样例输入3

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

样例输出3

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