Flipping and Bonus

AtCoder

IDabc261_d

Time2000ms

Memory256MB

Difficulty—

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: $N$ $M$ $X_1$ $X_2$ $\ldots$ $X_N$ $C_1$ $Y_1$ $C_2$ $Y_2$ $\vdots$ $C_M$ $Y_M$ [samples]

Samples

Input #1

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

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.

Input #2

3 2
1000000000 1000000000 1000000000
1 1000000000
3 1000000000

Output #2

5000000000

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

API Response (JSON)

{
  "problem": {
    "name": "Flipping and Bonus",
    "description": {
      "content": "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 t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc261_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi will toss a coin $N$ times. He also has a counter, which initially shows $0$.\nDepending on the result of the $i$\\-th coin toss, the following happens:\n\n*   If it heads: Takahashi increases t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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