题目描述

You are given $n$ vertical lines with x-coordinates $x_1, x_2, \ldots, x_n$ and weights $a_1, a_2, \ldots, a_n$ and $m$ horizontal lines with y-coordinates $y_1, y_2, \ldots, y_m$ and weights $b_1, b_2, \ldots, b_m$.

Call a rectangle good if and only if all of its four edges lie on the given lines. On this basis, define the cost of a good rectangle as the sum of the costs of its four segments. The cost of a segment is the product of its length and the weight of the line it belongs.

Find the maximum area of good rectangles with cost no more than $c$. Note that the length and the width of the rectangle can be zero, so the answer always exists.

You need to answer $T$ queries with different $c$.

输入格式

The first line contains three integers $n$, $m$ ($2\leq n, m\leq 5\,000$) and $T$ ($1\leq T\leq 100$).

The second line contains $n$ integers $x_1, x_2, \ldots, x_n$ ($1\leq x_1 < x_2 < \ldots < x_n \leq 10 ^ 5$).

The third line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1\leq a_i\leq 10 ^ 7$).

The fourth line contains $m$ integers $y_1, y_2, \ldots, y_m$ ($1\leq y_1 < y_2 < \ldots < y_m \leq 10 ^ 5$).

The fifth line contains $m$ integers $b_1, b_2, \ldots, b_m$ ($1\leq b_i\leq 10 ^ 7$).

Each of the next $T$ lines contains a single integer $c$ ($1\leq c\leq 4\times 10 ^ {12}$), representing a query.

输出格式

For each query, output one line representing the answer.

3 4 20
1 3 4
3 1 2
1 3 4 7
4 2 1 2
1
5
6
7
9
10
11
12
15
16
17
22
23
28
30
35
43
47
49
57

0
0
1
1
1
2
2
3
3
4
4
6
6
9
9
12
12
12
18
18

提示

Source: The 2022 ICPC Asia Xi'an Regional Contest Problem K.

Author: Alex_Wei.