Ex - Range Harvest Query

AtCoder

IDabc255_h

Time8000ms

Memory256MB

Difficulty—

There are $N$ trees. On Day $0$, each tree bears no fruits. On the morning of Day $1$ and subsequent days, the $i$\-th tree bears $i$ new fruits for each $i = 1, 2, \ldots, N$. Takahashi will perform $Q$ harvesting. For each $i = 1, 2, \ldots, Q$, the $i$\-th harvesting takes place on the night of Day $D_i$, collecting all fruits remaining on the $L_i$\-th through $R_i$\-th trees at that point. For each of the $Q$ harvesting, print the number of fruits Takahashi will collect, modulo $998244353$. ## Constraints * $1 \leq N \leq 10^{18}$ * $1 \leq Q \leq 2 \times 10^5$ * $1 \leq D_1 \lt D_2 \lt \cdots \lt D_Q \leq 10^{18}$ * $1 \leq L_i \leq R_i \leq N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $Q$ $D_1$ $L_1$ $R_1$ $D_2$ $L_2$ $R_2$ $\vdots$ $D_Q$ $L_Q$ $R_Q$ [samples]

Samples

Input #1

Output #1

10
15
50

For each $i = 1, 2, 3, 4, 5$, let $A_i$ be the number of fruits remaining on the $i$\-th tree. Now, we use the sequence $A = (A_1, A_2, A_3, A_4, A_5)$ to represent the numbers of fruits remaining in the trees.

*   On Day $0$, we have $A = (0, 0, 0, 0, 0)$.
*   On the morning of Day $1$, each tree bears new fruits, and we have $A = (1, 2, 3, 4, 5)$.
*   On the morning of Day $2$, each tree bears new fruits, and we have $A = (2, 4, 6, 8, 10)$.
*   On the night of Day $2$, Takahashi performs the $1$\-st harvesting. $4 + 6 = 10$ fruits are collected, and we have $A = (2, 0, 0, 8, 10)$.
*   On the morning of Day $3$, each tree bears new fruits, and we have $A = (3, 2, 3, 12, 15)$.
*   On the night of Day $3$, Takahashi performs the $2$\-nd harvesting. $3 + 12 = 15$ fruits are collected, and we have $A = (3, 2, 0, 0, 15)$.
*   On the morning of Day $4$, each tree bears new fruits, and we have $A = (4, 4, 3, 4, 20)$.
*   On the morning of Day $5$, each tree bears new fruits, and we have $A = (5, 6, 6, 8, 25)$.
*   On the night of Day $5$, Takahashi performs the $3$\-rd harvesting. $5 + 6 + 6 + 8 + 25 = 50$ fruits are collected, and we have $A = (0, 0, 0, 0, 0)$.

Input #2

711741968710511029 1
82803157126515475 516874290286751784 588060532191410838

Output #2

603657470

Be sure to print the numbers modulo $998244353$.

API Response (JSON)

{
  "problem": {
    "name": "Ex - Range Harvest Query",
    "description": {
      "content": "There are $N$ trees. On Day $0$, each tree bears no fruits.   On the morning of Day $1$ and subsequent days, the $i$\\-th tree bears $i$ new fruits for each $i = 1, 2, \\ldots, N$. Takahashi will perfor",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 8000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc255_h"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ trees. On Day $0$, each tree bears no fruits.  \nOn the morning of Day $1$ and subsequent days, the $i$\\-th tree bears $i$ new fruits for each $i = 1, 2, \\ldots, N$.\nTakahashi will perfor...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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