2017/quals/progresspie.html

<p>
Some progress bars fill you with anticipation. 
Some are finished before you know it and make you wonder why there was a progress bar at all. 
</p>

<p>
Some progress bars progress at a pleasant, steady rate. 
Some are chaotic, lurching forward and then pausing for long periods.
Some seem to slow down as they go, never quite reaching 100%.
</p>

<p>
Some progress bars are in fact not bars at all, but circles.
</p>

<p>
On your screen is a progress pie, a sort of progress bar that shows its progress as a sector of a circle. 
Envision your screen as a square on the plane with its bottom-left corner at (0, 0), and its upper-right corner at (100, 100).
Every point on the screen is either white or black.
Initially, the progress is 0%, and all points on the screen are white. When the progress percentage, <strong>P</strong>, is greater than 0%, a sector of angle (<strong>P</strong>% * 360) degrees
is colored black, anchored by the line segment from the center of the square to the center of the top side, and proceeding clockwise.
</p>

<img src="{{PHOTO_ID:592385891651966}}" />

<p>
While you wait for the progress pie to fill in, you find yourself thinking about whether certain points would be white or black at different amounts of progress.
</p>


<h3>Input</h3>

<p>
Input begins with an integer <strong>T</strong>, the number of points you're curious about.
For each point, there is a line containing three space-separated integers, <strong>P</strong>,  the amount of progress as a percentage,
and <strong>X</strong> and <strong>Y</strong>, the coordinates of the point.
</p>

<h3>Output</h3>

<p>
For the <strong>i</strong>th point, print a line containing "Case #<strong>i</strong>: " followed by the color of the point, either
"black" or "white".
</p>

<h3>Constraints</h3>

<p>
1 &le; <strong>T</strong> &le; 1,000 <br />
0 &le; <strong>P</strong>, <strong>X</strong>, <strong>Y</strong> &le; 100 <br />
</p>

<p>
Whenever a point (<strong>X</strong>, <strong>Y</strong>) is queried, it's guaranteed that all points within a distance of 10<sup>-6</sup> of 
(<strong>X</strong>, <strong>Y</strong>) are the same color as (<strong>X</strong>, <strong>Y</strong>).
</p>


<h3>Explanation of Sample</h3>

<p>
In the first case all of the points are white, so the point at (55, 55) is of course white. 
</p>

<p>
In the second case, (55, 55) is close to the filled-in sector of the circle, but it's still white. 
</p>

<p>
In the third case, the filled-in sector of the circle now covers (55, 55), coloring it black.
</p>