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 $3$. #### Notes - A subsequence of a sequence is the result of removing zero or more elements from it and concatenating the remaining elements without changing the order. For example, $(10,30)$ is a subsequence of $(10,20,30)$, while $(20,10)$ is not a subsequence of $(10,20,30)$. - A longest increasing subsequence of a sequence is its strictly increasing subsequence with the greatest length.

Input is given from Standard Input in the following format: > $N \quad M$ #### Constraints - $3 \leq N \leq 1000$ - $3 \leq M \leq 10$ - All values in input are integers.

Print the answer.

***For Sample #1:*** One sequence that satisfies the conditions is $(3,4,1,5)$. On the other hand, $(4,4,1,5)$ do not, because its longest increasing subsequence has the length of 2. ***For Sample #3:*** Find the count modulo $998244353$.

AtCoder [ABC237F]