South Central USA Regional Programming Contest Problem #3: Polar Explorer

Introduction

You are a intrepid 2-dimensional explorer located at the northern polar reaches of a distant 2-dimensional planet. Unfortunately, you have been assigned to explore the most boring planet in the known universe (due primarily to your lack of social skills and aggressive body odor). Having a perfectly circular surface, your planet holds no surprises for a would-be explorer.

However, you have recently received a distress call from an alien ship which has crash-landed somewhere on the surface of your planet. Unfortunately, you designed your own equipment, and the only information it will give you is an angle (measured from the center of the planet) separating you from the crash site.

Using this information along with how much gasoline is available for your planet-rover (which gets a measley 5 miles per gallon), you have to determine if you can possibly get to the crash site and back without running out of fuel.

Input

Input to this problem will consist of a (non-empty) series of up to 100 data sets. Each data set will be formatted according to the following description, and there will be no blank lines separating data sets.

A single data set has 3 components:
1. Start line - A single line, "START".
2. Input line - A single line, "X Y Z", where:
   X : (1 <= X <= 100) is the radius of your planet in integer miles
   Y : (0 <= Y <= 100) is the amount of gasoline in your planet-rover in integer gallons
   Z : (0 <= Z <= 360) is an angle separating you from the crash site in integer degrees
   
3. End line - A single line, "END".

Following the final data set will be a single line, "ENDOFINPUT".

Take note of the following:
• The circumference of a circle in terms of its radius, r, is known to be 2πr
• Assume that π = 3.14159

START
1 100 0
END
START
10 0 1
END
START
100 50 90
END
START
100 50 270
END
ENDOFINPUT

YES 100
NO 0
NO 250
NO 250