Third grader's task

문제

While looking at the kitchen fridge, little boy Tyler noticed magnets with symbols, that can be aligned into a string $ss$.

Tyler likes strings, and especially those that are lexicographically less than string $tt$. After playing with magnets on the fridge he is wondering, how many distinct strings can be composed out of letters of string $ss$ by rearranging them, so that the the resulting string is lexicographically less than string $tt$. Tyler is studying only in the third grade, so he can not answer this question. Help him to calculate the number of permutations of letters of string $ss$, that are lexicographically less than string $tt$.

We call string $xx$ lexicographically less than string $yy$ if one of the followings conditions is fulfilled:

• There exists such position of symbol $mm$ that is presented in both strings, so that before $mm$-th symbol the strings are equal, and the $mm$-th symbol of string $ss$ is less than $mm$-th symbol of string $yy$.
• String $xx$ is the prefix of string $yy$.

Because the answer can be too large, print it modulo $998244353998\backslash ,244\backslash ,353$.

입력

The first line contains two integers $nn$ and $mm$ ($1\le n,m\le 2000001\; \backslash le\; n,\; m\; \backslash le\; 200\backslash ,000$) --- lengths of strings $ss$ and $tt$.

The second line contains $nn$ integers $s_1,s_2,s_3\dots s_{n}s\_1,\; s\_2,\; s\_3\; \backslash ldots\; s\_n$ ($1\le s_i\le 2000001\; \backslash le\; s\_i\; \backslash le\; 200\backslash ,000$) --- symbols of string $ss$.

The third line contains $mm$ integers $t_1,t_2,t_3\dots t_{m}t\_1,\; t\_2,\; t\_3\; \backslash ldots\; t\_m$ ($1\le t_i\le 2000001\; \backslash le\; t\_i\; \backslash le\; 200\backslash ,000$) --- symbols of string $tt$.

출력

Print the single integer --- the number of strings that are lexicographically less than $tt$, that can be composed by rearranging letters of string $ss$ modulo $998244353998\backslash ,244\backslash ,353$.

힌트

In the first sample, we should count strings [1 2 2] and [2 1 2]. String [2 2 1] is lexicographically grater than string [2 1 2 1], so we do not count it.

In the second sample we should count all strings except [4 3 2 1], so the answer is $4!-1=234!\; -\; 1\; =\; 23$.

In the third sample we should count only string [1 1 1 2].

3 4
1 2 2
2 1 2 1

2

4 4
1 2 3 4
4 3 2 1

23

4 3
1 1 1 2
1 1 2

1