题目描述

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 $\ge i).$

中文题目

求满足如下条件的数列个数，答案对$998244353$取模： 长度为$n$ 每个元素值域为$1$到$m$ 有且仅有一对相等的元素 存在下标$i$，满足$a_1<· · ·<a_{i−1}<a_i >a_{i+1}>· · ·>a_n$ 数据范围：$n,m≤2×10^5$

输入描述

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

输出描述

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

样例

3 4

6

3 5

10

42 1337

806066790

100000 200000

707899035

提示

The arrays in the first example are:

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