CF1503E.2-Coloring

There is a grid with $n$ rows and $m$ columns. Every cell of the grid should be colored either blue or yellow.

A coloring of the grid is called stupid if every row has exactly one segment of blue cells and every column has exactly one segment of yellow cells.

In other words, every row must have at least one blue cell, and all blue cells in a row must be consecutive. Similarly, every column must have at least one yellow cell, and all yellow cells in a column must be consecutive.

An example of a stupid coloring.

Examples of clever colorings. The first coloring is missing a blue cell in the second row, and the second coloring has two yellow segments in the second column.

How many stupid colorings of the grid are there? Two colorings are considered different if there is some cell that is colored differently.

有一个 $n$ 行 $m$ 列的网格。网格中的每个单元格必须被染成蓝色或黄色。

若一个网格染色方案满足：每一行恰好包含一段连续的蓝色单元格，且每一列恰好包含一段连续的黄色单元格，则称其为“愚蠢的”（stupid）染色方案。

换言之，每一行必须至少有一个蓝色单元格，且该行中所有蓝色单元格必须彼此相邻（即构成一个连续区间）；同理，每一列必须至少有一个黄色单元格，且该列中所有黄色单元格也必须彼此相邻。

一个“愚蠢的”染色方案示例。

一些“聪明的”（clever）染色方案示例。第一个方案中第二行缺少蓝色单元格；第二个方案中第二列含有两段黄色单元格。

该网格共有多少种“愚蠢的”染色方案？若两个染色方案在某个单元格上的颜色不同，则认为它们是不同的染色方案。

The only line contains two integers $n$, $m$ ($1\le n, m\le 2021$).

唯一的一行包含两个整数 $n$、$m$（$1\le n, m\le 2021$）。

Output a single integer — the number of stupid colorings modulo $998244353$.

输出一个整数——愚蠢染色方案的数量对 $998244353$ 取模的结果。

In the first test case, these are the only two stupid $2\times 2$ colorings.

在第一个测试用例中，仅有以下两种愚蠢的 $2\times 2$ 染色方案。