Twin Friends

문제

You meet two new friends who are twins. The name of the elder twin is $AA$, which consists of $NN$ characters. While the name of the younger twin is $BB$, which consists of $MM$ characters. It is known that N ≤ M.

You want to call each of them with a nickname. For the elder twin, you want to pick any permutation of $AA$ as the nickname. For the younger twin, you want to remove exactly $M-NM\; -\; N$ characters from any permutation of $BB$. Denote the nicknames of the elder twin and the younger twin as $A^{\mathrm{\prime }}A\text{'}$ and $B^{\mathrm{\prime }}B\text{'}$, respectively.

You want the nicknames to satisfy the following requirement. For each i that satisfies 1 ≤ i ≤ N, $B_i^{\mathrm{\prime }}B\text{'}\_i$ must be equal to either $A_i^{\mathrm{\prime }}A\text{'}\_i$ or the next letter that follows alphabetically after $A_i^{\mathrm{\prime }}A\text{'}\_i$ (if such a next letter exists).

Determine the number of different pairs of nicknames $(A^{\mathrm{\prime }},B^{\mathrm{\prime }})(A\text{'}\; ,\; B\text{'}\; )$ 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 $998244353998\backslash ,\; 244\backslash ,\; 353$.

입력

The first line consists of two integers $NN$ $MM$ (1 ≤ N ≤ M ≤ 200\, 000).

The second line consists of a string $AA$ of length $NN$.

The third line consists of a string $BB$ of length $MM$.

All strings consist of only upper-case letters.

출력

Output a single integer representing number of different pairs $(A^{\mathrm{\prime }},B^{\mathrm{\prime }})(A\text{'}\; ,\; B\text{'}\; )$ that satisfy the requirement, modulo $998244353998\backslash ,\; 244\backslash ,\; 353$.

3 4
AMA
ANAB

9

5 8
BINUS
BINANUSA

120

15 30
BINUSUNIVERSITY
BINANUSANTARAUNIVERSITYJAKARTA

151362308

4 4
UDIN
ASEP

0