A13345. Count the Arrays

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 $998244353$ .

The arrays in the first example are:

- $[1, 2, 1]$ ;
- $[1, 3, 1]$ ;
- $[1, 4, 1]$ ;
- $[2, 3, 2]$ ;
- $[2, 4, 2]$ ;
- $[3, 4, 3]$ .