区间不等查询 - Problema

#6323. 区间不等查询

Estadísticas

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

给定两个正整数 $N$ 和 $M$。

计算满足以下条件的 $(0, 1, \dots, NM - 1)$ 的排列 $P = (P_0, P_1, \dots, P_{NM-1})$ 的数量，结果对 $998244353$ 取模：

对于所有满足 $0 \le i < NM$ 的整数 $i$，都有 $\lfloor \frac{i}{M} \rfloor \neq \lfloor \frac{P_i}{M} \rfloor$。

输入

输入通过标准输入给出，格式如下：

$N \ M$

输入中的所有值均为整数。
$2 \le N \le 1000$
$1 \le M \le 1000$

输出

输出答案。

样例

输入 1

2 2

输出 1

输入 2

5 1

输出 2

输入 3

167 91

输出 3

284830080

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