You meet two new friends who are twins. The name of the elder twin is $$$A$$$, which consists of $$$N$$$ characters. While the name of the younger twin is $$$B$$$, which consists of $$$M$$$ characters. It is known that $$$N \leq M$$$.

You want to call each of them with a nickname. For the elder twin, you want to pick any permutation of $$$A$$$ as the nickname. For the younger twin, you want to remove exactly $$$M - N$$$ characters from any permutation of $$$B$$$. Denote the nicknames of the elder twin and the younger twin as $$$A'$$$ and $$$B'$$$, respectively.

You want the nicknames to satisfy the following requirement. For each $$$i$$$ that satisfies $$$1 \leq i \leq N$$$, $$$B'_i$$$ must be equal to either $$$A'_i$$$ or the next letter that follows alphabetically after $$$A'_i$$$ (if such a next letter exists).

Determine the number of different pairs of nicknames $$$(A', B')$$$ that satisfy the requirement. Two pairs of nicknames are considered different if at least one of the nicknames are different. As the result might be large, find the answer modulo $$$998\,244\,353$$$.