Extension

AtCoder

IDagc046_b

Time2000ms

Memory256MB

Difficulty—

We have a grid with $A$ horizontal rows and $B$ vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation: * Assume that the grid currently has $a$ horizontal rows and $b$ vertical columns. Choose "vertical" or "horizontal". * If we choose "vertical", insert one row at the top of the grid, resulting in an $(a+1) \times b$ grid. * If we choose "horizontal", insert one column at the right end of the grid, resulting in an $a \times (b+1)$ grid. * Then, paint one of the added squares black, and the other squares white. Assume the grid eventually has $C$ horizontal rows and $D$ vertical columns. Find the number of ways in which the squares can be painted in the end, modulo $998244353$. ## Constraints * $1 \leq A \leq C \leq 3000$ * $1 \leq B \leq D \leq 3000$ * $A$, $B$, $C$, and $D$ are integers. ## Input Input is given from Standard Input in the following format: $A$ $B$ $C$ $D$ [samples]

Samples

Input #1

1 1 2 2

Output #1

3

Any two of the three squares other than the bottom-left square can be painted black.

Input #2

2 1 3 4

Output #2

Input #3

31 41 59 265

Output #3

387222020

API Response (JSON)

{
  "problem": {
    "name": "Extension",
    "description": {
      "content": "We have a grid with $A$ horizontal rows and $B$ vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation: *   Assume that the grid currently ha",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc046_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $A$ horizontal rows and $B$ vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:\n\n*   Assume that the grid currently ha...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments