Polar Explorer

Time limit1sMemory limit128 MB

Summary

Given planet radius, fuel, and the angle to the crash site, decide if the round trip on the shorter arc fits and report leftover fuel or reachable miles.

Level: Easy2 of 10
Topics: Math, Implementation
Solved: No attempts yet

Problem

You are a two dimensional explorer posted near the north pole of a distant two dimensional planet. The surface of the planet is a perfect circle, so there is no terrain on it to survey.

Then a distress call arrives from an alien ship that has crash landed somewhere on that surface. You built your own equipment, and all it reports is the angle between you and the crash site, measured at the center of the planet.

Your planet rover gets a measly 5 miles per gallon. From that angle and the gasoline you have left, decide whether you can drive to the crash site and back before the tank runs dry.

The rover travels along the surface and takes the shorter of the two arcs, so for an angle of $Z$ degrees the central angle it actually covers is $\min(Z, 360 - Z)$ degrees.

Input

The input holds a series of data sets, at most 100 of them, with no blank line between data sets.

One data set has three parts.

Start line: a single line START
Input line: a single line X Y Z
- $X$ ( $1 \le X \le 100$ ) is the radius of the planet in whole miles
- $Y$ ( $0 \le Y \le 100$ ) is the gasoline left in the rover in whole gallons
- $Z$ ( $0 \le Z \le 360$ ) is the angle between you and the crash site in whole degrees
End line: a single line END

A single line ENDOFINPUT follows the last data set.

The circumference of a circle of radius $r$ is $2 \pi r$ , and $\pi$ is $3.14159$ .

Output

Print one line for each data set.

If the gasoline covers the round trip, print YES X, where $X$ is the fuel left once you are back, written as a whole number of gallons with the fraction dropped.

If the gasoline is not enough, print NO Y, where $Y$ is the distance you can travel on the fuel you have, written as a whole number of miles.

Examples2

Example 1

Input

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

Expected output

YES 100
NO 0
NO 250
NO 250

Example 2

Input

START
100 100 90
END
START
100 100 270
END
START
100 100 180
END
ENDOFINPUT

Expected output

YES 37
YES 37
NO 500