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King Arthur is well known for holding that all knights are equal and for his round table.
There is a central serving platter (did Merlin invent the lazy-susan?) and each knight has a circular trencher to eat from:
Unfortunately, Merlin accidentally called up a pre-shade of George Orwell and Arthur started muttering something like:
… but some knights are more equal than others…
So he asked Merlin to move the center platter away from him a bit so he and his closaest aides could have a bit more room:
Merlin complained that all the trenchers and the serving platter would have to be remade. Arthur, like a good leader said “Deal with it.”
Write a program to help Merlin make the new trenchers and serving platter. To describe the layout we will use a coodinate system with origin at the center of the table, with the x axis pointing to Arthur’s seat and the y axis perpendicular:
Input consists of a single line containing the diameter, D, (8 ≤ D ≤ 30) of the table (in kingly feet), the number, N, (7 ≤ N ≤ 40) of knights to be seated, and the offset, O, 0.1 ≤ O < radius of an original trencher) from the center of the table to the center of the central serving platter (as a decimal number of kingly feet).
The output consists five lines. The first output line gives the radius of the central platter (in kingly feet) to 3 decimal places with center at (-offset, 0). (offset is O from the input.)
The next four lines consist of three space separated floating point values to three decimal places. These values represent the x coordinate of the center of a trencher, the y coordinate of the center of the trencher and the radius of the trencher (all in kingly feet) of Arthur’s trencher and the next three trenchers counter-clockwise from Arthur’s (one set of values for each line of output).
10 11 0.5
2.761 3.631 0.000 1.369 2.703 2.513 1.310 0.572 3.785 1.172 -1.625 3.621 1.031