Count the Arrays

2000ms

524288K

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 $$$998244353$$$.

3 4

3 5

42 1337

806066790

100000 200000

707899035

The arrays in the first example are:

Informação

Provedor Codeforces

Código CF1312D