Count the Arrays
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 $j \ge i$).
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 $998244353$.
Input
The first line contains two integers $n$ and $m$ ($2 \le n \le m \le 2 \cdot 10^5$).
Output
Print one integer — the number of arrays that meet all of the aforementioned conditions, taken modulo $998244353$.
Samples
3 4
6
3 5
10
42 1337
806066790
100000 200000
707899035
Note
The arrays in the first example are:
- $[1, 2, 1]$;
- $[1, 3, 1]$;
- $[1, 4, 1]$;
- $[2, 3, 2]$;
- $[2, 4, 2]$;
- $[3, 4, 3]$.