Always Increasing

AtCoder

IDarc210_a

Time2000ms

Memory256MB

Difficulty—

You are given a sequence of positive integers $A=(A_1,A_2,\ldots,A_N)$ of length $N$, and you will perform $Q$ operations on it. For $1\leq q\leq Q$, the $q$\-th operation is given as positive integers $i_q, x_q$ (where $1\leq i_q\leq N$), and it adds $x_q$ to $A_{i_q}$. Your goal is to appropriately determine the initial state of $A$ so that the following condition holds at any point in time (that is, in the initial state and immediately after each operation). * $0<A_1 < A_2 < \cdots < A_N$ holds. When achieving this goal, find the minimum possible sum of elements in the initial state of $A$. ## Constraints * $2\leq N\leq 2\times 10^5$ * $1\leq Q\leq 2\times 10^5$ * $1\leq i_q\leq N$ * $1\leq x_q\leq 10^5$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $Q$ $i_1$ $x_1$ $\vdots$ $i_Q$ $x_Q$ [samples]

Samples

Input #1

4 2
1 2
2 3

Output #1

22

Suppose the initial state of $A$ is $A=(1,4,8,9)$. Then,

*   $A$ immediately after the $1$\-st operation: $A=(3,4,8,9)$
*   $A$ immediately after the $2$\-nd operation: $A=(3,7,8,9)$

and it can be verified that $A$ satisfies the condition at any point in time.
In this case, the sum of elements in the initial state of $A$ is $\displaystyle \sum_{i=1}^NA_i=1+4+8+9=22$.

Input #2

4 2
2 3
1 2

Output #2

Input #3

100000 1
1 100000

Output #3

14999950000

API Response (JSON)

{
  "problem": {
    "name": "Always Increasing",
    "description": {
      "content": "You are given a sequence of positive integers $A=(A_1,A_2,\\ldots,A_N)$ of length $N$, and you will perform $Q$ operations on it. For $1\\leq q\\leq Q$, the $q$\\-th operation is given as positive integer",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc210_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence of positive integers $A=(A_1,A_2,\\ldots,A_N)$ of length $N$, and you will perform $Q$ operations on it. For $1\\leq q\\leq Q$, the $q$\\-th operation is given as positive integer...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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