You are working as a guide on a tour bus for retired people,
and today you have taken your regular Nordic seniors to The
Gate of Heavenly Peace. You let them have a lunch break where
they could do whatever they like. Now you have to get them back
to the bus, but they are all walking in random directions. You
try to intersect them, and send them straight back to the bus.
Minimize the time before the last person is in the bus. You
will always be able to run faster than any of the tour guests,
and they walk with constant speed, no matter what you tell
them. The seniors walk in straight lines, and the only way of
changing their direction is to give them promises of camphor
candy. A senior will neither stop at nor enter the bus before
given such a promise.
Input
There are a number of test cases (at most $10$) consisting of: A line with an
integer $1 \leq n \leq 8$,
the number of people on the tour. A line with an floating point
number $1 < v \leq
100$, your maximum speed (you start in the bus at the
origin). Then follow $n$
lines, each containing four floating point numbers $x_ i$ $y_ i$ $v_ i$ $a_ i$, the starting coordinates
($10^6 \leq x_ i, y_ i \leq
10^6$), speed ($1 \leq v_
i < 100$) and direction ($0 \leq a_ i < 2 \pi $) of each of
the tour guests.
The input is terminated by a case with $n = 0$, which should not be
processed. All floating point numbers in the input will be
written in standard decimal notation, and have no more than
$6$ digits.
Output
For each test case, print a line with the time it takes
before everybody is back in the bus (the origin). Round the
answer to the nearest integer. The answer will never be larger
than $10^6$.
Sample Input 1 
Sample Output 1 
1
50.0
125.0 175.0 25.0 1.96
3
100.0
40.0 25.0 20.0 5.95
185.0 195.0 6.0 2.35
30.0 80.0 23.0 2.76
0

20
51
