Count the Arrays

Your task is to calculate the number of arrays such that:

1、each array contains n elements;

2、each element is an integer from 1 to m;

3、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 aj<aj+1, if j<i, and aj>aj+1, if j≥i).

The first line contains two integers n and m (2≤n≤m≤2⋅10^5).

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

3 4

6

3 5

10

42 1337

806066790

100000 200000

707899035

 Note
 
The arrays in the first example are:
 
 
 
 $$$[1, 2, 1]$$$; 
 
 
 $$$[1, 3, 1]$$$; 
 
 
 $$$[1, 4, 1]$$$; 
 
 
 $$$[2, 3, 2]$$$; 
 
 
 $$$[2, 4, 2]$$$; 
 
 
 $$$[3, 4, 3]$$$.