D. Ascendio or Descendio
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two integers $$$n$$$ and $$$m$$$. Find the number of ways to fill an $$$n\times m$$$ grid with the numbers $$$1, 2, \ldots, n \times m$$$, using each number exactly once, such that the following conditions are satisfied:

  • Every row forms a strictly monotonic$$$^{[5]}$$$ sequence.
  • Every column forms a strictly monotonic sequence.

Count the number of valid fillings, modulo $$$998\,244\,353$$$.

Input

The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 2025$$$).

Output

Output a single integer — the number of valid fillings, modulo $$$998\,244\,353$$$.

Examples
Input
1 1
Output
1
Input
2 1
Output
2
Input
2 2
Output
24
Input
3 2
Output
80
Input
2024 2025
Output
831665454