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D - Flipping and Bonus

Score : $400$ points

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.

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

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.

3 2
1000000000 1000000000 1000000000
1 1000000000
3 1000000000

5000000000

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