102876: [AtCoder]ABC287 G - Balance Update Query

Problem Statement

Takahashi has $10^{100}$ cards of each of $N$ kinds. Initially, the score and quota of the $i$-th kind of card are set to $a_i$ and $b_i$, respectively.

Given $Q$ queries in the following formats, process them in order.

• 1 x y: set the score of the $x$-th kind of card to $y$.
• 2 x y: set the quota of the $x$-th kind of card to $y$.
• 3 x: if one can choose $x$ cards subject to the following condition, print the maximum possible sum of the scores of the chosen cards; print -1 otherwise.
  • The number of chosen cards of each kind does not exceed its quota.

Constraints

• $1 \leq N,Q \leq 2 \times 10^5$
• $0 \leq a_i \leq 10^9$
• $0 \leq b_i \leq 10^4$
• For each query of the $1$-st kind, $1 \leq x \leq N$ and $0 \leq y \leq 10^9$.
• For each query of the $2$-nd kind, $1 \leq x \leq N$ and $0 \leq y \leq 10^4$.
• For each query of the $3$-rd kind, $1 \leq x \leq 10^9$.
• There is at least one query of the $3$-rd kind.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format, where $\mathrm{query}_i$ denotes the $i$-th query:

$N$
$a_1$ $b_1$
$\vdots$
$a_N$ $b_N$
$Q$
$\mathrm{query}_1$
$\vdots$
$\mathrm{query}_Q$

Output

Print $M$ lines, where $M$ is the number of queries of the $3$-rd kind.
The $i$-th line should contain the response to the $i$-th such query.

Sample Input 1

3
1 1
2 2
3 3
7
3 4
1 1 10
3 4
2 1 0
2 3 0
3 4
3 2

Sample Output 1

11
19
-1
4

For the first query of the $3$-rd kind, you can choose one card of the $2$-nd kind and three cards of the $3$-rd kind for a total score of $11$, which is the maximum.
For the second such query, you can choose one card of the $1$-st kind and three cards of the $3$-rd kind for a total score of $19$, which is the maximum.
For the third such query, you cannot choose four cards, so -1 should be printed.
For the fourth such query, you can choose two cards of the $2$-nd kind for a total score of $4$, which is the maximum.

问题描述

高桥持有$N$种各$10^{100}$张的卡。初始时，第$i$种卡的分数和配额分别为$a_i$和$b_i$。

根据以下格式的$Q$个查询，按顺序处理它们。

• 1 x y：将第$x$种卡的分数设置为$y$。
• 2 x y：将第$x$种卡的配额设置为$y$。
• 3 x：如果可以选择满足以下条件的$x$张卡，则打印所选卡的分数之和的最大可能值；否则打印-1。
  • 每种卡所选的数量不超过其配额。

约束

• $1 \leq N,Q \leq 2 \times 10^5$
• $0 \leq a_i \leq 10^9$
• $0 \leq b_i \leq 10^4$
• 对于每种类型的第1个查询，$1 \leq x \leq N$，$0 \leq y \leq 10^9$。
• 对于每种类型的第2个查询，$1 \leq x \leq N$，$0 \leq y \leq 10^4$。
• 对于每种类型的第3个查询，$1 \leq x \leq 10^9$。
• 至少有一个第3种类型的查询。
• 输入中的所有值都是整数。

输入

输入以以下格式从标准输入给出，其中$\mathrm{query}_i$表示第$i$个查询：

$N$
$a_1$ $b_1$
$\vdots$
$a_N$ $b_N$
$Q$
$\mathrm{query}_1$
$\vdots$
$\mathrm{query}_Q$

输出

打印$M$行，其中$M$是第3种类型的查询的数量。
第$i$行应包含对第$i$个此类查询的响应。

样例输入1

3
1 1
2 2
3 3
7
3 4
1 1 10
3 4
2 1 0
2 3 0
3 4
3 2

样例输出1

11
19
-1
4

对于第3种类型的第一个查询，你可以选择第2种卡1张和第3种卡3张，总分为11，这是最大的。
对于第二个此类查询，你可以选择第1种卡1张和第3种卡3张，总分为19，这是最大的。
对于第三个此类查询，你不能选择4张卡，所以应打印-1。
对于第四个此类查询，你可以选择第2种卡2张，总分为4，这是最大的。