Score : $675$ points

问题陈述

你有两个长度为 $N$ 的序列：$D=(D_1, D_2, \dots, D_N)$ 和 $P=(P_1, P_2, \dots, P_N)$。

按照给定的顺序处理 $Q$ 个查询。每个查询以以下格式给出：

• c x y: 将 $D_c$ 改为 $x$，将 $P_c$ 改为 $y$。然后，解决以下问题并打印答案。

有 $N$ 个工作，编号从 $1$ 到 $N$。 从今天开始（考虑为第 $1$ 天），你将选择并完成一个工作，持续 $N$ 天。 如果你在第 $D_i$ 天或之前完成工作 $i$，你将获得 $P_i$ 的奖励。（如果你在第 $D_i$ 天之前没有完成，你将一无所获。） 通过选择完成工作的最优顺序，找到你可以实现的最大总奖励。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

You are given two sequences of length $N$: $D=(D_1, D_2, \dots, D_N)$ and $P=(P_1, P_2, \dots, P_N)$.

Process $Q$ queries in the order they are given. Each query is given in the following format:

• c x y: Change $D_c$ to $x$ and $P_c$ to $y$. Then, solve the following problem and print the answer.

There are $N$ jobs numbered $1$ to $N$.
Starting from today (consider this as day $1$), you will choose and complete one job per day for $N$ days.
If you complete job $i$ on or before day $D_i$, you will receive a reward of $P_i$. (If you do not complete it by day $D_i$, you get nothing.)
Find the maximum total reward you can achieve by choosing the optimal order of completing the jobs.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq Q \leq 10^5$
• $1 \leq D_i \leq N$
• $1 \leq P_i \leq 10^9$
• $1 \leq c \leq N$
• $1 \leq x \leq N$
• $1 \leq y \leq 10^9$
• All input values are integers.

Input

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

$N$ $Q$

$D_1$ $D_2$ $\dots$ $D_N$

$P_1$ $P_2$ $\dots$ $P_N$

$\mathrm{query}_1$

$\mathrm{query}_2$

$\vdots$

$\mathrm{query}_Q$

Each query is given in the following format.

$c$ $x$ $y$

Output

Print $Q$ lines. The $i$-th line should contain the answer to the $i$-th query.

Sample Input 1

3 2
1 2 3
3 6 3
3 1 4
2 3 9

Sample Output 1

10
13

The first query is as follows:

• Update $D_3$ to $1$ and $P_3$ to $4$. Now, $D = (1, 2, 1)$ and $P = (3, 6, 4)$.
• In the subproblem, one optimal procedure is to complete job $3$ on day $1$, job $2$ on day $2$, and job $1$ on day $3$. The total reward is $10$, so print $10$.

The second query is as follows:

• Update $D_2$ to $3$ and $P_2$ to $9$. Now, $D = (1, 3, 1)$ and $P = (3, 9, 4)$.
• In the subproblem, one optimal procedure is to complete job $3$ on day $1$, job $1$ on day $2$, and job $2$ on day $3$. The total reward is $13$, so print $13$.

Sample Input 2

5 1
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000
1 1 1000000000

Sample Output 2

5000000000

Sample Input 3

10 10
6 2 4 1 5 1 6 6 5 3
45 65 71 52 86 52 48 60 40 98
5 6 5
8 4 34
6 7 83
1 3 21
7 5 85
7 4 51
8 2 81
2 7 54
6 1 5
8 6 30

Sample Output 3

394
379
462
457
459
414
443
479
401
396