Collecting Bugs#3858
Ivan is passionate about collecting. Unlike other people who collect stamps, coins, or other material items, he collects software bugs. When Ivan gets a new program, he classifies all possible bugs into categories and notes that the program has subsystems. To call a program disgusting, Ivan must find at least one bug in each subsystem and at least one bug in each category. Each day he discovers exactly one bug in the program and records its category and subsystem in a spreadsheet. Once he achieves this goal, he publishes the table on his homepage and completely forgets about the program.
Two companies, Macrosoft and Microhard, are in fierce competition. Microhard wants to reduce the sales of a Macrosoft program. They hire Ivan to prove that this program is disgusting. However, Ivan faces a challenging task. This new program has subsystems, and finding all types of bugs in each subsystem would take too much time before reaching the goal. Therefore, Ivan and Microhard agreed to use a simpler criterion: Ivan must find at least one bug in each subsystem and at least one bug in each category.
Macrosoft is aware of these plans and wants to estimate how long it will take Ivan to call its program disgusting. This is important because the company will soon release a new version and can adjust its schedule to release it faster. No one will be interested in Ivan's opinion about the reliability of an outdated version.
A bug found in the program can belong to any category with equal probability. Similarly, a bug can be found in any subsystem with equal probability. Any specific bug cannot belong to two different categories or occur simultaneously in two different subsystems. The number of bugs in the program is virtually infinite, so the probability of finding a new bug in some category in some subsystem does not decrease after finding any number of bugs of that category in that subsystem.
Find the expected time (in Ivan's working days) required to call the program disgusting.
The input contains two integers: and (0 < n, s \leq 1000).
Output the expected number of Ivan's working days required to call the program disgusting, accurate to digits after the decimal point.
Example 1