Mary the Mathematician has a bakery that she founded some years ago, but after all this time she has become bored with always baking the same rectangular and circular cakes. For her next birthday, she wants to bake an irregular cake, which is defined as the area between two "polylines" between x=0 and x=W. These polylines will be called the lower boundary and the upper boundary.
Formally, a polyline is defined by a sequence of points (P_{0}, P_{1}, ..., P_{n}) going from left to right. Consecutive points are connected to form a sequence of line segments, which together make up the polyline.
Today is Mary's birthday and she has baked an irregular cake bounded by two polylines with L points and U points respectively. After singing "Happy Birthday," she wants to make G1 vertical cuts to split the cake into G slices with equal area. She can then share these cake slices with all her guests. However, the irregular cake shape makes this task pretty tricky. Can you help her decide where to make the cuts?
The first line of the input gives the number of test cases, T. T test cases follow. Each test case begins with a line containing four integers: W (the cake's width), L (the number of points on the lower boundary), U (the number of points on the upper boundary) and G (the number of guests at the party).
This is followed by L lines specifying the lower boundary. The ith line contains two integers x_{i} and y_{i}, representing the coordinates of the ith point on the lower boundary. This is followed by U more lines specifying the upper boundary. The jth line here contains two integers x_{j} and y_{j}, representing the coordinates of the jth point on the upper boundary.
For each test case, output G lines. The first line should be "Case #x:" where x is the case number (starting from 1). The next G1 lines should contain the xcoordinates at which cuts must be made, ordered from the leftmost cut to the rightmost cut.
Answers with a relative or absolute error of at most 10^{6} will be considered correct.
1 ≤ T ≤ 100.
1 ≤ W ≤ 1000.
2 ≤ L ≤ 100.
2 ≤ U ≤ 100.
All coordinates will be integers between 1000 and 1000, inclusive.
The xcoordinate of the leftmost point of both boundaries will be 0.
The xcoordinate of the rightmost point of both boundaries will be W.
Points in the same boundary will be sorted increasingly by xcoordinate.
Points in the same boundary will have different xcoordinates.
The lower boundary will always be strictly below the upper boundary for all x between 0 and W, inclusive. (In other words, the lower boundary will have a smaller ycoordinate than the upper boundary at every x position.)
2 ≤ G ≤ 3.
2 ≤ G ≤ 101.
Input 
Output 
2

Case #1:

Points  Correct  Attempted 

7pt  365  378 
7pt  347  365 