Delete 1, 4, 7, ...

AtCoder

IDarc135_f

Time2000ms

Memory256MB

Difficulty—

You are given an integer $N$. On an integer sequence $A = (1, 2, \ldots, N)$, let us do the operation below exactly $K$ times. * Let $n$ be the current number of terms in $A$. For all $i$ such that $1\leq i \leq n$ and $i\equiv 1\pmod{3}$, delete the $i$\-th term of $A$, simultaneously. Find the sum of the terms of $A$ after $K$ operations, modulo $998244353$. ## Constraints * $1\leq N\leq 10^{14}$ * $1\leq K\leq 100$ ## Input Input is given from Standard Input from the following format: $N$ $K$ [samples]

Samples

Input #1

10 2

Output #1

25

*   Initially, we have $A = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)$.
*   After the first operation, we have $A = (2, 3, 5, 6, 8, 9)$.
*   After the second operation, we have $A = (3, 5, 8, 9)$.
*   The sum of the terms here is $3 + 5 + 8 + 9 = 25$.

Input #2

10 10

Output #2

0

*   After the second operation, we have $A = (3, 5, 8, 9)$ (same as Sample Input 1).
*   After the third operation, we have $A = (5, 8)$.
*   After the fourth operation, we have $A = (8)$.
*   After the fifth operation, $A$ is empty.
*   In the sixth and subsequent operations, $A$ remains empty, where the sum of the terms is $0$.

Input #3

10000 10

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Delete 1, 4, 7, ...",
    "description": {
      "content": "You are given an integer $N$. On an integer sequence $A = (1, 2, \\ldots, N)$, let us do the operation below exactly $K$ times. *   Let $n$ be the current number of terms in $A$. For all $i$ such that",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc135_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer $N$. On an integer sequence $A = (1, 2, \\ldots, N)$, let us do the operation below exactly $K$ times.\n\n*   Let $n$ be the current number of terms in $A$. For all $i$ such that...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments