Kevin and Grid

2000ms

262144K

Description:

As Kevin is in BigMan's house, suddenly a trap sends him onto a grid with $$$n$$$ rows and $$$m$$$ columns.

BigMan's trap is configured by two arrays: an array $$$a_1,a_2,\ldots,a_n$$$ and an array $$$b_1,b_2,\ldots,b_m$$$.

In the $$$i$$$-th row there is a heater which heats the row by $$$a_i$$$ degrees, and in the $$$j$$$-th column there is a heater which heats the column by $$$b_j$$$ degrees, so that the temperature of cell $$$(i,j)$$$ is $$$a_i+b_j$$$.

Fortunately, Kevin has a suit with one parameter $$$x$$$ and two modes:

heat resistance. In this mode suit can stand all temperatures greater or equal to $$$x$$$, but freezes as soon as reaches a cell with temperature less than $$$x$$$.
cold resistance. In this mode suit can stand all temperatures less than $$$x$$$, but will burn as soon as reaches a cell with temperature at least $$$x$$$.

Once Kevin lands on a cell the suit automatically turns to cold resistance mode if the cell has temperature less than $$$x$$$, or to heat resistance mode otherwise, and cannot change after that.

We say that two cells are adjacent if they share an edge.

Let a path be a sequence $$$c_1,c_2,\ldots,c_k$$$ of cells such that $$$c_i$$$ and $$$c_{i+1}$$$ are adjacent for $$$1 \leq i \leq k-1$$$.

We say that two cells are connected if there is a path between the two cells consisting only of cells that Kevin can step on.

A connected component is a maximal set of pairwise connected cells.

We say that a connected component is good if Kevin can escape the grid starting from it — when it contains at least one border cell of the grid, and that it's bad otherwise.

To evaluate the situation, Kevin gives a score of $$$1$$$ to each good component and a score of $$$2$$$ for each bad component.

The final score will be the difference between the total score of components with temperatures bigger than or equal to $$$x$$$ and the score of components with temperatures smaller than $$$x$$$.

There are $$$q$$$ possible values of $$$x$$$ that Kevin can use, and for each of them Kevin wants to know the final score.

Help Kevin defeat BigMan!

Input:

The first line contains three integers $$$n$$$,$$$m$$$,$$$q$$$ ($$$1 \leq n,m,q \leq 10^5$$$) – the number of rows, columns, and the number of possible values for $$$x$$$ respectively.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \leq a_i \leq 10^5$$$).

The third line contains $$$m$$$ integers $$$b_1, b_2, \dots, b_m$$$ ($$$1 \leq b_i \leq 10^5$$$).

Each of the next $$$q$$$ lines contains one integer $$$x$$$ ($$$1 \leq x \leq 2 \cdot 10^5$$$).

Output:

Output $$$q$$$ lines, in the $$$i$$$-th line output the answer for the $$$i$$$-th possible value of $$$x$$$ from the input.

Sample Input:

Sample Output:

-1

Sample Input:

Sample Output:

0
1

Note:

In the first example, the score for components with temperature smaller than $$$5$$$ is $$$1+2$$$, and the score for components with temperature at least $$$5$$$ is $$$2$$$. Thus, the final score is $$$2-3=-1$$$.

Informação

Provedor Codeforces

Código CF1392I