Both Mr. Frog and Wallice love running. Wallice missed Mr. Frog’s birthday recently，so he decided to give a belated birthday gift. He quickly found out an idea： he decided to run a closed curve to contain those meaningful buildings. Unfortunately, he only gets a little time left since he is going to attend an important press conference.
Wallice wants to know the maximal number of buildings can be contained in the closed curve. Note that his speed is 1.
The first line contains only one integer T,which indicates the number of test cases.
For each test case, the first line contains an integer N ($1 \leq N \leq 80$), and a double t ($0 \leq l \leq 5000$) indicating the numbers of buildings Wallice cares about and the time he has.
In the following n lines, the i-th line contains two doubles $x_i, y_i (-600 \leq x_i, y_i \leq 600$) indicating the position of the buildings.
For each test case，output one line “Case #x: ans’’，where x is the case number (starting from 1) following with ans indicating the maximum number of buildings Wallice can circled in in limited time.