Chance Meeting

AtCoder

IDarc124_f

Time2000ms

Memory256MB

Difficulty—

Given is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\-th row from the top and $j$\-th column from the left. Initially, a camel is on $(1, 1)$, and a cat is on $(H, 1)$. You can send the following four kinds of orders. * `R`: Move the camel on $(i, j)$ to $(i, j+1)$. * `D`: Move the camel on $(i, j)$ to $(i+1, j)$. * `r`: Move the cat on $(i, j)$ to $(i, j+1)$. * `u`: Move the cat on $(i, j)$ to $(i-1, j)$. A sequence of orders satisfying all of the four conditions below is said to be **good**. Find the number of good sequences of orders, modulo $998244353$. 1. The final position of the camel will be $(H, W)$. 2. The final position of the cat will be $(1, W)$. 3. The following will happen exactly once: the camel and the cat are on the same square after an order is processed. 4. Neither the camel nor the cat will leave the grid. ## Constraints * All values in input are integers. * $2 \leq H,W \leq 2 \times 10^{5}$ ## Input Input is given from Standard Input in the following format: $H$ $W$ [samples]

Samples

Input #1

2 2

Output #1

16

*   The good sequences of orders include `DRur`, `DurR`, `RruD`, `RDru`, but not `DRru`, `RRR`.

Input #2

200000 200000

Output #2

412709667

*   Be sure to print the count modulo $998244353$.

API Response (JSON)

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    "name": "Chance Meeting",
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      "content": "Given is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left. Initially, a camel is on $(1, 1)$, and a cat is on $(H, ",
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      "statement_type": "Markdown",
      "content": "Given is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left.\nInitially, a camel is on $(1, 1)$, and a cat is on $(H, ...",
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