Description:
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 $$$j \ge i$$$).
Input Format:
The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le m \le 2 \cdot 10^5$$$).
Output Format:
Print one integer — the number of arrays that meet all of the aforementioned conditions, taken modulo $$$998244353$$$.
Note:
The arrays in the first example are:
- $$$[1, 2, 1]$$$;
- $$$[1, 3, 1]$$$;
- $$$[1, 4, 1]$$$;
- $$$[2, 3, 2]$$$;
- $$$[2, 4, 2]$$$;
- $$$[3, 4, 3]$$$.