Stop. Otherwise...

AtCoder

IDarc102_c

Time2000ms

Memory256MB

Difficulty—

Takahashi throws $N$ dice, each having $K$ sides with all integers from $1$ to $K$. The dice are NOT pairwise distinguishable. For each $i=2,3,...,2K$, find the following value modulo $998244353$: * The number of combinations of $N$ sides shown by the dice such that the sum of no two different sides is $i$. Note that the dice are NOT distinguishable, that is, two combinations are considered different when there exists an integer $k$ such that the number of dice showing $k$ is different in those two. ## Constraints * $1 \leq K \leq 2000$ * $2 \leq N \leq 2000$ * $K$ and $N$ are integers. ## Input Input is given from Standard Input in the following format: $K$ $N$ [samples]

Samples

Input #1

3 3

Output #1

7
7
4
7
7

*   For $i=2$, the combinations $(1,2,2),(1,2,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3)$ satisfy the condition, so the answer is $7$.
*   For $i=3$, the combinations $(1,1,1),(1,1,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3)$ satisfy the condition, so the answer is $7$.
*   For $i=4$, the combinations $(1,1,1),(1,1,2),(2,3,3),(3,3,3)$ satisfy the condition, so the answer is $4$.

Input #2

4 5

Output #2

Input #3

6 1000

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Stop. Otherwise...",
    "description": {
      "content": "Takahashi throws $N$ dice, each having $K$ sides with all integers from $1$ to $K$. The dice are NOT pairwise distinguishable. For each $i=2,3,...,2K$, find the following value modulo $998244353$: * ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc102_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi throws $N$ dice, each having $K$ sides with all integers from $1$ to $K$. The dice are NOT pairwise distinguishable. For each $i=2,3,...,2K$, find the following value modulo $998244353$:\n\n* ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments