CF1312D Count the Arrays

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 $ .

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] $ .