Count the Arrays

求满足如下条件的长度为 $n$ 的序列 $a$ 的个数： - $\forall 1 \leq i \leq n$，都有 $1 \leq a_i \leq m$。 - $a$ 中存在且仅存在一对相同的元素 - 存在一个位置 $p$，使得 $a_1 \sim a_p$ 为严格单增序列，$a_p \sim a_n$ 为严格单减序列。即 $\forall 0 < j < p$，都有 $a_{j} < a_{j + 1}$，且 $\forall p \leq j < n$，都有 $a_j > a_{j + 1}$。 $2 \leq n\le m \leq 2 \times 10^5$。 答案对 $998,244,353$ 取模。

Your task is to calculate the number of arrays such that: - each array contains $ n $ elements; - each element is an integer from $ 1 $ to $ m $ ; - for each array, there is exactly one pair of equal elements; - for each array $ a $ , there exists an index $ i $ such that the array is strictly ascending before the $ i $ -th element and strictly descending after it (formally, it means that $ a_j < a_{j + 1} $ , if $ j < i $ , and $ a_j > a_{j + 1} $ , if $ j \ge i $ ).

The first line contains two integers $ n $ and $ m $ ( $ 2 \le n \le m \le 2 \cdot 10^5 $ ).

Print one integer — the number of arrays that meet all of the aforementioned conditions, taken modulo $ 998244353 $ .

3 4

6

3 5

10

42 1337

806066790

100000 200000

707899035

The arrays in the first example are: - $ [1, 2, 1] $ ; - $ [1, 3, 1] $ ; - $ [1, 4, 1] $ ; - $ [2, 3, 2] $ ; - $ [2, 4, 2] $ ; - $ [3, 4, 3] $ .