102613: [AtCoder]ABC261 D - Flipping and Bonus

Problem Statement

Takahashi will toss a coin $N$ times. He also has a counter, which initially shows $0$.

Depending on the result of the $i$-th coin toss, the following happens:

• If it heads: Takahashi increases the counter's value by $1$ and receives $X_i$ yen (Japanese currency).
• If it tails: he resets the counter's value to $0$, without receiving money.

Additionally, there are $M$ kinds of streak bonuses. The $i$-th kind of streak bonus awards $Y_i$ yen each time the counter shows $C_i$.

Find the maximum amount of money that Takahashi can receive.

Constraints

• $1\leq M\leq N\leq 5000$
• $1\leq X_i\leq 10^9$
• $1\leq C_i\leq N$
• $1\leq Y_i\leq 10^9$
• $C_1,C_2,\ldots,C_M$ are all different.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$X_1$ $X_2$ $\ldots$ $X_N$
$C_1$ $Y_1$
$C_2$ $Y_2$
$\vdots$
$C_M$ $Y_M$

Output

Print the maximum amount of money that Takahashi can receive, as an integer.

Sample Input 1

6 3
2 7 1 8 2 8
2 10
3 1
5 5

Sample Output 1

48

If he gets head, head, tail, head, head, head, in this order, the following amounts of money are awarded.

• In the $1$-st coin toss, the coin heads. Change the counter's value from $0$ to $1$ and receive $2$ yen.
• In the $2$-nd coin toss, the coin heads. Change the counter's value from $1$ to $2$ and receive $7$ yen. Additionally, get $10$ yen as a streak bonus.
• In the $3$-rd coin toss, the coin tails. Change the counter's value from $2$ to $0$.
• In the $4$-th coin toss, the coin heads. Change the counter's value from $0$ to $1$ and receive $8$ yen.
• In the $5$-th coin toss, the coin heads. Change the counter's value from $1$ to $2$ and receive $2$ yen. Additionally, get $10$ yen as a streak bonus.
• In the $6$-th coin toss, the coin heads. Change the counter's value from $2$ to $3$ and receive $8$ yen. Additionally, get $1$ yen as a streak bonus.

In this case, Takahashi receives $2+(7+10)+0+8+(2+10)+(8+1)=48$ yen in total, which is the maximum possible.
Note that streak bonuses are awarded any number of times each time the counter shows $C_i$.
As a side note, if he gets head in all $6$ coin tosses, he only receives $2+(7+10)+(1+1)+8+(2+5)+8=44$ yen, which is not the maximum.

Sample Input 2

3 2
1000000000 1000000000 1000000000
1 1000000000
3 1000000000

Sample Output 2

5000000000

Note that the answer may not fit into a $32$-bit integer type.

问题描述

高桥将抛一枚硬币$N$次。 他还有一个计数器，初始值为$0$。

根据第$i$次抛硬币的结果，会发生以下情况：

• 如果是正面：高桥将计数器的值增加$1$，并获得$X_i$日元（日本货币）。
• 如果是反面：他将计数器的值重置为$0$，没有获得金钱。

此外，还有$M$种连胜奖励。第$i$种连胜奖励会在计数器显示$C_i$时，每次奖励$Y_i$日元。

找出高桥可以获得的最大金钱数。

约束条件

• $1\leq M\leq N\leq 5000$
• $1\leq X_i\leq 10^9$
• $1\leq C_i\leq N$
• $1\leq Y_i\leq 10^9$
• $C_1,C_2,\ldots,C_M$都是不同的。
• 输入中的所有值都是整数。

输入

输入以标准输入的以下格式给出：

$N$ $M$
$X_1$ $X_2$ $\ldots$ $X_N$
$C_1$ $Y_1$
$C_2$ $Y_2$
$\vdots$
$C_M$ $Y_M$

输出

打印高桥可以获得的最大金钱数，作为整数。

样例输入1

6 3
2 7 1 8 2 8
2 10
3 1
5 5

样例输出1

48

如果他按照正面，正面，反面，正面，正面，正面的顺序获得硬币，将获得以下金钱数额。

• 在第$1$次抛硬币时，硬币正面朝上。将计数器的值从$0$更改为$1$，并获得$2$日元。
• 在第$2$次抛硬币时，硬币正面朝上。将计数器的值从$1$更改为$2$，并获得$7$日元。此外，获得$10$日元的连胜奖励。
• 在第$3$次抛硬币时，硬币反面朝上。将计数器的值从$2$更改为$0$。
• 在第$4$次抛硬币时，硬币正面朝上。将计数器的值从$0$更改为$1$，并获得$8$日元。
• 在第$5$次抛硬币时，硬币正面朝上。将计数器的值从$1$更改为$2$，并获得$2$日元。此外，获得$10$日元的连胜奖励。
• 在第$6$次抛硬币时，硬币正面朝上。将计数器的值从$2$更改为$3$，并获得$8$日元。此外，获得$1$日元的连胜奖励。

在这种情况下，高桥总共获得了$2+(7+10)+0+8+(2+10)+(8+1)=48$日元，这是可能的最大值。
请注意，每次计数器显示$C_i$时，都可以多次获得连胜奖励。
作为旁注，如果他在所有$6$次抛硬币中都获得正面，则他只获得$2+(7+10)+(1+1)+8+(2+5)+8=44$日元，这不是最大值。

样例输入2

3 2
1000000000 1000000000 1000000000
1 1000000000
3 1000000000

样例输出2

5000000000

请注意，答案可能不适合$32$位整数类型。