Score : $500$ points

问题描述

Takahashi 持有一个整数 $x$。初始时，$x = 0$。

有 $N$ 个操作。第 $i$ 个操作 $(1 \leq i \leq N)$ 由两个整数 $t_i$ 和 $y_i$ 表示，如下所示：

• 若 $t_i = 1$，则将 $x$ 替换为 $y_i$。
• 若 $t_i = 2$，则将 $x$ 替换为 $x + y_i$。

Takahashi 可以跳过任意从 $0$ 到 $K$（包括 $0$ 和 $K$）的若干个操作。当他按照原顺序仅执行剩余的操作一次时，找出 $x$ 的最大可能最终值。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi has an integer $x$. Initially, $x = 0$.

There are $N$ operations. The $i$-th operation $(1 \leq i \leq N)$ is represented by two integers $t_i$ and $y_i$ as follows:

• If $t_i = 1$, replace $x$ with $y_i$.
• If $t_i = 2$, replace $x$ with $x + y_i$.

Takahashi may skip any number between $0$ and $K$ (inclusive) of the operations. When he performs the remaining operations once each without changing the order, find the maximum possible final value of $x$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq K \leq N$
• $t_i \in \{1,2\} \, (1 \leq i \leq N)$
• $|y_i| \leq 10^9 \, (1 \leq i \leq N)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

$t_1$ $y_1$

$\vdots$

$t_N$ $y_N$

Output

Print the answer.

Sample Input 1

5 1
2 4
2 -3
1 2
2 1
2 -3

Sample Output 1

3

If he skips the $5$-th operation, $x$ changes as $0 \rightarrow 4 \rightarrow 1 \rightarrow 2 \rightarrow 3$, so $x$ results in $3$. This is the maximum.

Sample Input 2

1 0
2 -1000000000

Sample Output 2

-1000000000

Sample Input 3

10 3
2 3
2 -1
1 4
2 -1
2 5
2 -9
2 2
1 -6
2 5
2 -3

Sample Output 3

15

update @ 2024/3/10 10:39:20