Illumination

Description:

Input:

The first line contains three integers $$$d$$$, $$$n$$$ and $$$m$$$ ($$$4 \le d \le 3 \cdot 10^5$$$; $$$1 \le n \le 2 \cdot 10^5$$$; $$$1 \le m \le 16$$$) — the size of the segment, the number of lanterns and the number of points of interest, respectively.

The second line contains $$$n$$$ integers $$$l_1, l_2, \dots, l_n$$$ ($$$1 \le l_i \le d - 1$$$), where $$$l_i$$$ is the coordinate of the $$$i$$$-th lantern.

The third line contains $$$m$$$ integers $$$p_1, p_2, \dots, p_m$$$ ($$$1 \le p_i \le d - 1$$$), where $$$p_i$$$ is the coordinate of the $$$i$$$-th point of interest.

The fourth line contains one integer $$$q$$$ ($$$1 \le q \le 5 \cdot 10^5$$$) — the number of queries.

The fifth line contains $$$q$$$ integers $$$f_1, f_2, \dots, f_q$$$ ($$$1 \le f_i \le d - 1$$$), where $$$f_i$$$ is the integer representing the $$$i$$$-th query.

Additional constraint on the input: during the processing of each query, no coordinate contains more than one object (i. e. there cannot be two or more lanterns with the same coordinate, two or more points of interest with the same coordinate, or a lantern and a point of interest with the same coordinate).

Output:

For each query, print one integer — the answer to it, taken modulo $$$998244353$$$.

Sample Input:

6 1 1
4
3
3
2 1 5

Sample Output:

48
47
47

Sample Input:

6 1 2
4
2 5
2
1 3

Sample Output:

44
46

Sample Input:

20 1 2
11
15 7
1
8

Sample Output:

413

Sample Input:

20 3 5
5 7 18
1 6 3 10 19
5
4 17 15 8 9

Sample Output:

190431
187503
188085
189903
189708