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E. 2-Coloring

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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.

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

Input

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

Output

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

Examples

Input

2 2

Output

2

Input

4 3

Output

294

Input

2020 2021

Output

50657649

Note

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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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