Fractals are really cool mathematical objects. They have a
lot of interesting properties, often including:

fine structure at arbitrarily small scales;

selfsimilarity, i.e., magnified it looks like a copy of
itself;

a simple, recursive definition.
Approximate fractals are found a lot in nature, for example,
in structures such as clouds, snow flakes, mountain ranges, and
river networks.
In this problem, we consider fractals generated by the
following algorithm: we start with a polyline, i.e., a set of
connected line segments. This is what we call a fractal of
depth one (see leftmost picture). To obtain a fractal of depth
two, we replace each line segment with a scaled and rotated
version of the original polyline (see middle picture). By
repetitively replacing the line segments with the polyline, we
obtain fractals of arbitrary depth and very fine structures
arise. The rightmost picture shows a fractal of depth
three.
The complexity of an approximate fractal increases quickly
as its depth increases. We want to know where we end up after
traversing a certain fraction of its length.
Input
The input starts with a single number $c$ $(1
\le c \le 200)$ on one line, the number of test cases.
Then each test case starts with one line with $n$ $(3\le n\le 100)$, the number of
points of the polyline. Then follow $n$ lines with on the $i$th line two integers $x_ i$ and $y_ i$ $(1\, 000\le x_ i,y_ i\le 1\, 000)$,
the consecutive points of the polyline. Next follows one line
with an integer $d$
$(1\le d\le 10)$, the
depth of the fractal. Finally, there is one line with a
floating point number $f$
$(0\le f\le 1)$, the
fraction of the length that is traversed.
The length of each line segment of the polyline is smaller
than the distance between the first point $(x_1,y_1)$ and the last point
$(x_ n,y_ n)$ of the
polyline. The length of the complete polyline is smaller than
twice this distance.
Output
Per test case, the output contains one line with the
coordinate where we end up. Format it as $x$ $y$, with two floating point numbers
$x$ and $y$. The absolute error in both
coordinates should be smaller than $10^{6}$.
Sample Input 1 
Sample Output 1 
1
4
2 2
0 0
0 2
2 2
3
0.75

0.4267766953 2
