9778: ABC261 —— D - Flipping and Bonus
[Creator : ]
Description
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.
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.
Input
Input is given from Standard Input in the following format:
```
$N$ $M$
$X_1$ $X_2$ $\ldots$ $X_N$
$C_1$ $Y_1$
$C_2$ $Y_2$
$\vdots$
$C_M$ $Y_M$
```
```
$N$ $M$
$X_1$ $X_2$ $\ldots$ $X_N$
$C_1$ $Y_1$
$C_2$ $Y_2$
$\vdots$
$C_M$ $Y_M$
```
Output
Print the maximum amount of money that Takahashi can receive, as an integer.
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.
- $1\leq X_i\leq 10^9$
- $1\leq C_i\leq N$
- $1\leq Y_i\leq 10^9$
- $C_1,C_2,\ldots,C_M$ are all different.
- All values in input are integers.
Sample 1 Input
6 3
2 7 1 8 2 8
2 10
3 1
5 5
Sample 1 Output
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 2 Input
3 2
1000000000 1000000000 1000000000
1 1000000000
3 1000000000
Sample 2 Output
5000000000