Colorful Blocks

AtCoder

IDabc167_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ blocks arranged in a row. Let us paint these blocks. We will consider two ways to paint the blocks different if and only if there is a block painted in different colors in those two ways. Find the number of ways to paint the blocks under the following conditions: * For each block, use one of the $M$ colors, Color $1$ through Color $M$, to paint it. It is not mandatory to use all the colors. * There may be at most $K$ pairs of adjacent blocks that are painted in the same color. Since the count may be enormous, print it modulo $998244353$. ## Constraints * All values in input are integers. * $1 \leq N, M \leq 2 \times 10^5$ * $0 \leq K \leq N - 1$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $K$ [samples]

Samples

Input #1

3 2 1

Output #1

6

The following ways to paint the blocks satisfy the conditions: `112`, `121`, `122`, `211`, `212`, and `221`. Here, digits represent the colors of the blocks.

Input #2

100 100 0

Output #2

73074801

Input #3

60522 114575 7559

Output #3

479519525

API Response (JSON)

{
  "problem": {
    "name": "Colorful Blocks",
    "description": {
      "content": "There are $N$ blocks arranged in a row. Let us paint these blocks. We will consider two ways to paint the blocks different if and only if there is a block painted in different colors in those two ways",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc167_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ blocks arranged in a row. Let us paint these blocks.\nWe will consider two ways to paint the blocks different if and only if there is a block painted in different colors in those two ways...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments