FreeCell Statistics
Submit Solution(Code Jam Page)


I played D (D > 0) games of FreeCell today. Each game of FreeCell ends in one of two ways -- I either win, or I lose. I've been playing for many years, and have so far played G games in total (obviously, GD).

At the end of the day, I look at the game statistics to see how well I have played. It turns out that I have won exactly PD percent of the D games today, and exactly PG percent of G total games I had ever played. Miraculously, there is no rounding necessary -- both percentages are exact! Unfortunately, I don't remember the exact number of games that I have played today (D), or the exact number of games that I have played in total (G). I do know that I could not have played more than N games today (DN).

Are the percentages displayed possible, or is the game statistics calculator broken?


The first line of the input gives the number of test cases, T. T lines follow. Each line contains 3 integers -- N, PD and PG.


For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is either "Possible" or "Broken".


0 ≤ PD ≤ 100;
0 ≤ PG ≤ 100.

Small dataset

1 ≤ T ≤ 100;
1 ≤ N ≤ 10.

Large dataset

1 ≤ T ≤ 2000;
1 ≤ N ≤ 1015.



1 100 50
10 10 100
9 80 56
Case #1: Possible
Case #2: Broken
Case #3: Possible

In Case #3, I could have played 5 games today (D = 5) and 25 games in total (G = 25), and won 4 games today (80% of 5) and 14 games in total (56% of 25).

Points Correct Attempted
6pt 3079 4262
14pt 2181 2997

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