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

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 $$$998244353$$$.

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:

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