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D. Count the Arrays
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

• 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 $998244353$.

Examples
Input
3 4

Output
6

Input
3 5

Output
10

Input
42 1337

Output
806066790

Input
100000 200000

Output
707899035

Note

The arrays in the first example are:

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