Arboreal Challenge

Our local council discovered that its forest is overrun by invasive pests, and
is considering its options for how to restore natural balance... By fire if
necessary.

Experts insist that the correct plan of action is to set the forest alight,
supposed 'prescribed burning', but you're not quite convinced that the plan is sound without
a clear end. You should calculate the exact time the burn will finish and where, so that we can
verify the blaze is out as soon as possible.

Given that the flames will be lit simultaneously along every edge of the forest
and travel at a rate of  ms through its interior, how long will it
take for the entire forest to be set alight?

The forest has grown in the convenient shape of a simple polygon, with no holes, although
it may or may not be convex and may have any winding order.

figure[!h]
sample1.pdf
sample2.pdf
sample3.pdf
sample4.pdf
Diagrams illustrating sample fires 1, 2, 3, and 4 respectively.
figure

Input
    The first line of input contains two integers , and , where
         () is the speed in ms of the fire, and
         () is the number of vertices in the polygon describing the forest.

    The next  lines each contain two integers,  and  (),
    the coordinates of the  vertex.

Output
    Output the time taken for the entire forest to be set on fire.

    On the next line, output the coordinates of the last point inside the forest to be set alight,
    or any one of them if there are multiple.

    Your answers should have an absolute or relative error of at most .