Golf

In golf, every hole has a fixed target number of strokes called the par, and almost every score is described relative to that par. Matching the par is a par; one stroke under par is a birdie, and one stroke over par is a bogey. There are also, more rarely, a hole-in-one (the ball goes in with a single stroke), an eagle (2 under par), a double eagle (3 under par) and a double bogey (2 over par). Scores worse than a double bogey have their own names too, but here we assume everyone simply writes them all down as double bogey.

John has just taken up golf and does not know these names yet. On his score card he only wrote the number of strokes he used on each hole, and now he needs those numbers turned into the correct names.

Given the par of a hole and the number of strokes John wrote down, print the proper name of the score. If the number of strokes is 1, always print hole-in-one, even when another description would also fit.

The input consists of several test cases. Each test case is a single line with two integers $p$ and $s$: $p$ is the par of the hole (3, 4, or 5) and $s$ is the number of strokes John used, with $1 \le s < 20$.

The input ends with a line whose $p = 0$; that line must not be processed.

For each test case, first print the hole number as Hole #1, Hole #2, and so on.

On the following line, print the proper name of the score followed by a period, i.e. one of Hole-in-one., Double eagle., Eagle., Birdie., Par., Bogey., or Double Bogey..

Print one blank line between consecutive test cases.