Colliding Traffic

For a boat on a small, constrained body of water, other traffic can be a major hazard. The more traffic there is in the same area, the higher the risk of a collision.

Your job is to monitor traffic and help detect likely collisions before they occur. You have sensors that detect the position, direction, and speed of each boat. Assuming the direction and speed remain constant, determine whether any of the boats will collide. Two boats are considered to collide if they come within a given distance of each other.

The first line of input contains a single integer $c$, the number of test cases to follow. Each test case starts with a line containing two numbers, $n$, the number of boats, and $r$, the collision distance. Two boats are considered to collide if they come within $r$ metres of each other. There will be no more than 1000 boats. Each boat is described by a line containing four numbers $x$, $y$, $d$, $s$. The numbers $x$ and $y$ give the current position of the boat as a distance east and north, respectively, from a common origin, and are between $-1000$ and $1000$, inclusive. The lake is small enough to be modelled as a flat surface. The number $d$ gives the direction in which the boat is heading in degrees clockwise from north (so east is $90$ degrees). The number $s$ gives the speed of the boat in metres per second and is between $0.001$ and $1000$. Note that $r$, $x$, $y$, $d$, and $s$ are not necessarily integers. The input data is such that the answer will not change if any of the numbers $x$, $y$, $d$, and $s$ are changed by $10^{-6}$ or less.

For each test case, output a line containing a single integer: the number of seconds, rounded to the nearest second, before any of the boats come within $r$ metres of each other. If none of the boats ever collide, output the line:

No collision.