GP 2

AtCoder

IDagc036_c

Time2000ms

Memory256MB

Difficulty—

We have a sequence of $N$ integers: $x=(x_0,x_1,\cdots,x_{N-1})$. Initially, $x_i=0$ for each $i$ ($0 \leq i \leq N-1$). Snuke will perform the following operation **exactly** $M$ times: * Choose two distinct indices $i, j$ ($0 \leq i,j \leq N-1,\ i \neq j$). Then, replace $x_i$ with $x_i+2$ and $x_j$ with $x_j+1$. Find the number of different sequences that can result after $M$ operations. Since it can be enormous, compute the count modulo $998244353$. ## Constraints * $2 \leq N \leq 10^6$ * $1 \leq M \leq 5 \times 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ [samples]

Samples

Input #1

2 2

Output #1

3

After two operations, there are three possible outcomes:

*   $x=(2,4)$
*   $x=(3,3)$
*   $x=(4,2)$

For example, $x=(3,3)$ can result after the following sequence of operations:

*   First, choose $i=0,j=1$, changing $x$ from $(0,0)$ to $(2,1)$.
*   Second, choose $i=1,j=0$, changing $x$ from $(2,1)$ to $(3,3)$.

Input #2

3 2

Output #2

Input #3

10 10

Output #3

211428932

Input #4

100000 50000

Output #4

API Response (JSON)

{
  "problem": {
    "name": "GP 2",
    "description": {
      "content": "We have a sequence of $N$ integers: $x=(x_0,x_1,\\cdots,x_{N-1})$. Initially, $x_i=0$ for each $i$ ($0 \\leq i \\leq N-1$). Snuke will perform the following operation **exactly** $M$ times: *   Choose t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc036_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a sequence of $N$ integers: $x=(x_0,x_1,\\cdots,x_{N-1})$. Initially, $x_i=0$ for each $i$ ($0 \\leq i \\leq N-1$).\nSnuke will perform the following operation **exactly** $M$ times:\n\n*   Choose t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments