Gardens

AtCoder

IDabc235_g

Time3000ms

Memory256MB

Difficulty—

Takahashi has $A$ apple seedlings, $B$ banana seedlings, and $C$ cherry seedlings. Seedlings of the same kind cannot be distinguished. He will plant these seedlings in his $N$ gardens so that all of the following conditions are satisfied. * At least one seedling must be planted in every garden. * It is not allowed to plant two or more seedlings of the same kind in the same garden. * It is not necessary to plant all seedlings he has. How many ways are there to plant seedlings to satisfy the conditions? Find the count modulo $998244353$. Two ways are distinguished when there is a garden with different sets of seedlings planted in these two ways. ## Constraints * $1 \leq N \leq 5 \times 10^6$ * $0 \leq A \leq N$ * $0 \leq B \leq N$ * $0 \leq C \leq N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A$ $B$ $C$ [samples]

Samples

Input #1

2 2 1 1

Output #1

21

As illustrated below, there are $21$ ways to plant seedlings to satisfy the conditions.  
(The two frames arranged vertically are the gardens. $A, B, C$ stand for apple, banana, cherry, respectively.)
![image](https://img.atcoder.jp/ghi/30cbec3c4cc587889e3c37933da06c3f.png)

Input #2

2 0 0 0

Output #2

0

There may be no way to plant seedlings to satisfy the conditions.

Input #3

2 0 2 2

Output #3

Input #4

100 12 34 56

Output #4

769445780

Input #5

5000000 2521993 2967363 3802088

Output #5

264705492

API Response (JSON)

{
  "problem": {
    "name": "Gardens",
    "description": {
      "content": "Takahashi has $A$ apple seedlings, $B$ banana seedlings, and $C$ cherry seedlings. Seedlings of the same kind cannot be distinguished.   He will plant these seedlings in his $N$ gardens so that all of",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc235_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has $A$ apple seedlings, $B$ banana seedlings, and $C$ cherry seedlings. Seedlings of the same kind cannot be distinguished.  \nHe will plant these seedlings in his $N$ gardens so that all of...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments