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 $j \ge i$).

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 $998244353$.

见题面 Input 部分

见题面 Output 部分

The arrays in the first example are:

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