矩形放置 - المسألة

#4842. 矩形放置

الإحصائيات

تم استخدام هذه المسألة في المسابقات التالية:

Petrozavodsk Summer 2022. Day 5. ZJU Contest 2

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

Grammy 拥有一个包含 $W$ 条竖线和 $H$ 条横线的矩形网格。她想要沿着网格线画出两个互不相交的矩形。其中一个矩形可以完全包含在另一个矩形内部，但这两个矩形在任何点（包括边和角）上都不能相交。

请计算不同矩形画法的数量，结果对 $998\,244\,353$ 取模。当且仅当某个网格边在一种画法中被涂色而在另一种画法中未被涂色时，这两种画法被视为不同。

输入格式

仅一行，包含两个整数 $W$ 和 $H$ ($4 \le W, H \le 10^9$)。

输出格式

输出一个整数，表示不同画法的数量，结果对 $998\,244\,353$ 取模。

样例

样例输入 1

4 5

样例输出 1

样例输入 2

723435135 239873451

样例输出 2

832099301

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