Sequence 2

AtCoder

IDfps_24_d

Time2000ms

Memory256MB

Difficulty—

Consider integer sequences $A=(a_1,a_2,\dots,a_N)$ of length $N$, where each element is a non-negative integer not greater than $M$. Count how many such sequences satisfy the following condition, and output the result modulo $998244353$. * Let $B=(b_1,b_2,\dots,b_N)$ be the sequence obtained by sorting $A$ in ascending order. For every $i$ such that $1 \leq i \leq N-1$, the parity of $b_i$ and $b_{i+1}$ must be different. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq M \leq 2 \times 10^5$ * $N, M$ are integers ## Input The input is given from standard input in the following format: $N$ $M$ [samples]

Samples

Input #1

2 3

Output #1

8

There are $8$ sequences that satisfy the condition:

*   $(0,1)$
*   $(0,3)$
*   $(1,0)$
*   $(1,2)$
*   $(2,1)$
*   $(2,3)$
*   $(3,0)$
*   $(3,2)$

Input #2

12345 67890

Output #2

761484871

API Response (JSON)

{
  "problem": {
    "name": "Sequence 2",
    "description": {
      "content": "Consider integer sequences $A=(a_1,a_2,\\dots,a_N)$ of length $N$, where each element is a non-negative integer not greater than $M$.   Count how many such sequences satisfy the following condition, an",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "fps_24_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider integer sequences $A=(a_1,a_2,\\dots,a_N)$ of length $N$, where each element is a non-negative integer not greater than $M$.  \nCount how many such sequences satisfy the following condition, an...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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