Black and White Stones

AtCoder

IDabc256_g

Time2000ms

Memory256MB

Difficulty—

There is a regular $N$\-gon with side length $D$. Starting from a vertex, we place black or white stones on the circumference at intervals of $1$. As a result, each edge of the $N$\-gon will have $(D+1)$ stones on it, for a total of $ND$ stones. How many ways are there to place stones so that all edges have the same number of white stones on them? Find the count modulo $998244353$. ## Constraints * $3 \leq N \leq 10^{12}$ * $1 \leq D \leq 10^4$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $D$ [samples]

Samples

Input #1

3 2

Output #1

10

There are $10$ ways, as follows:
![image](https://img.atcoder.jp/abc256/ba2bebe9d374f281e2b44e36231abae2.png)

Input #2

299792458 3141

Output #2

138897974

Find the count modulo $998244353$.

API Response (JSON)

{
  "problem": {
    "name": "Black and White Stones",
    "description": {
      "content": "There is a regular $N$\\-gon with side length $D$. Starting from a vertex, we place black or white stones on the circumference at intervals of $1$. As a result, each edge of the $N$\\-gon will have $(D+",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc256_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a regular $N$\\-gon with side length $D$.\nStarting from a vertex, we place black or white stones on the circumference at intervals of $1$. As a result, each edge of the $N$\\-gon will have $(D+...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments