Find the number of sequences that satisfy all of the conditions below, modulo $998244353$. - The length is $N$. - Each of the elements is an integer between $1$ and $M$ (inclusive). - Its longest increasing subsequence has the length of exactly $3$. ### Constraints - $3 \leq N \leq 1000$ - $3 \leq M \leq 10$ - All values in input are integers.

Input is given from Standard Input in the following format: $N$ $M$

Print the answer.