Two Histograms

AtCoder

IDagc035_f

Time2000ms

Memory256MB

Difficulty—

We have a square grid with $N$ rows and $M$ columns. Takahashi will write an integer in each of the squares, as follows: * First, write $0$ in every square. * For each $i=1,2,...,N$, choose an integer $k_i$ $(0\leq k_i\leq M)$, and add $1$ to each of the leftmost $k_i$ squares in the $i$\-th row. * For each $j=1,2,...,M$, choose an integer $l_j$ $(0\leq l_j\leq N)$, and add $1$ to each of the topmost $l_j$ squares in the $j$\-th column. Now we have a grid where each square contains $0$, $1$, or $2$. Find the number of different grids that can be made this way, modulo $998244353$. We consider two grids different when there exists a square with different integers. ## Constraints * $1 \leq N,M \leq 5\times 10^5$ * $N$ and $M$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ [samples]

Samples

Input #1

1 2

Output #1

8

Let $(a,b)$ denote the grid where the square to the left contains $a$ and the square to the right contains $b$. Eight grids can be made: $(0,0),(0,1),(1,0),(1,1),(1,2),(2,0),(2,1),$ and $(2,2)$.

Input #2

2 3

Output #2

Input #3

10 7

Output #3

995651918

Input #4

314159 265358

Output #4

70273732

API Response (JSON)

{
  "problem": {
    "name": "Two Histograms",
    "description": {
      "content": "We have a square grid with $N$ rows and $M$ columns. Takahashi will write an integer in each of the squares, as follows: *   First, write $0$ in every square. *   For each $i=1,2,...,N$, choose an in",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc035_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a square grid with $N$ rows and $M$ columns. Takahashi will write an integer in each of the squares, as follows:\n\n*   First, write $0$ in every square.\n*   For each $i=1,2,...,N$, choose an in...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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