Score : $400$ points

问题描述

我们有一个空的序列 $A$。
给定 $Q$ 个查询，按照顺序处理它们。
每个查询属于以下三种类型之一。

• 1 x ：将 $x$ 插入到 $A$ 中。

• 2 x k ：在 $A$ 中小于等于 $x$ 的元素中，输出第 $k$ 大的值。 （$k$ 不超过 $\bf{5}$）
  如果 $A$ 中小于等于 $x$ 的元素少于 $k$ 个，则输出 -1。

• 3 x k ：在 $A$ 中大于等于 $x$ 的元素中，输出第 $k$ 小的值。 （$k$ 不超过 $\bf{5}$）
  如果 $A$ 中大于等于 $x$ 的元素少于 $k$ 个，则输出 -1。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

We have an empty sequence $A$.
Given $Q$ queries, process them in order.
Each query is of one of the following three types.

• 1 x : Insert $x$ to $A$.

• 2 x k : Among the elements of $A$ that are less than or equal to $x$, print the $k$-th largest value. ($k$ is no more than $\bf{5}$)
  If there are less than $k$ elements of $A$ that are less than or equal to $x$, then print -1.

• 3 x k : Among the elements of $A$ that are greater than or equal to $x$, print the $k$-th smallest value. ($k$ is no more than $\bf{5}$)
  If there are less than $k$ elements of $A$ that are greater than or equal to $x$, then print -1.

Constraints

• $1\leq Q \leq 2\times 10^5$
• $1\leq x\leq 10^{18}$
• $1\leq k\leq 5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$Q$

$\text{query}_1$

$\text{query}_2$

$\vdots$

$\text{query}_Q$

In the $i$-th query $\text{query}_i$, the type of query $c_i$ (which is either $1, 2$, or $3$) is given first.

If $c_i=1$, then $x$ is additionally given; if $c_i=2, 3$, then $x$ and $k$ are additionally given.

In other words, each query is given in one of the following three formats:

$1$ $x$

$2$ $x$ $k$

$3$ $x$ $k$

Output

Print $q$ lines, where $q$ is the number of queries such that $c_i=2,3$.
The $j$-th line $(1\leq j\leq q)$ should contain the answer for the $j$-th such query.

Sample Input 1

11
1 20
1 10
1 30
1 20
3 15 1
3 15 2
3 15 3
3 15 4
2 100 5
1 1
2 100 5

Sample Output 1

20
20
30
-1
-1
1

After $\text{query}_{1,2,3,4}$ have been processed, we have $A=(20,10,30,20)$.

For $\text{query}_{5,6,7}$, the elements of $A$ greater than or equal to $15$ are $(20,30,20)$.
The $1$-st smallest value of them is $20$; the $2$-nd is $20$; the $3$-rd is $30$.

update @ 2024/3/10 10:23:31