Collecting Every Card

A new card set has $C$ different kinds of card. The cards are sold only in booster packs, and each pack holds $N$ cards whose kinds are all different. The contents of a pack are one of the ways to choose $N$ kinds out of the $C$ kinds, and every one of those combinations comes up with the same probability each time you buy a pack.

You buy packs one at a time and keep buying until you own all $C$ kinds. Compute the expected number of packs you buy.

The first line contains the number of test cases $T$. Each of the next $T$ lines contains $C$ and $N$ separated by a space.

Constraints

• $1 \le T \le 100$
• $1 \le N \le C \le 40$

For each test case, print one line in the following format.

Case #x: E

Here $x$ is the test case number starting from 1, and $E$ is the expected number of packs. Round $E$ at the eighth digit after the decimal point and always print exactly seven digits after the decimal point. A whole number prints as $1.0000000$.