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D - Sequence Query

Score : $400$ points

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.

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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.

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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

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 $30$.