Rotating Line

There are n points and one line in the 2D plane. Three points can be collinear.
You can rotate the line anti-clockwise, but the rotation centre can be changed every time. The centre must be one of the n points.
Initially the centre is (0, 0) (of course, (0, 0) must be one of the n points), and the line coincides with y axis.
If there is only one point in the line, the line’s rotation centre must be this point.
If the line meets another points, the centre may change to the other point.
If there are k points in this line and the current rotation centre is the p-th point of them (of course, we assume that the k points have already sorted), the next rotation centre will be the (k-p+1)-th point of them.
If p = k – p + 1, we consider that the rotation centre is not changed.
In this problem, you must find the q-th rotation centre’s coordinate.
It is guaranteed that the q-th rotation centre always exists.

The first line contains an integer T (≤100), the number of test cases.
The first line of each test case contains an integer n (1 <= n <= 3000, sum of n over all test cases does not exceed 10000) , the number of points.
The i-th line of the following n lines contains two integers x, y (-100 <= x, y <= 100), the coordinate of the i-th point. One of these n points is (0, 0).
Every two points are different and three points can be collinear.
And the next line contains an integer Q, the number of queries (sum of Q over all test cases does not exceed 10000).
Then Q integers ($q_i$) follow, described above (0 < $q_i $<= 1e9).

Each test case, you must output Q lines and each line contains a pair of integer, the coordinate of qi-th rotation centre.