The Galactic Republic existed for more than twenty five thousand years and then it was transformed into the first Galactic Empire. The superior Councilor Palpatine ensured his power and position, issued the Declaration of the New Order and proclaimed himself the Galactic Emperor.

The highest body of the Republic was the Galactic Senate. Even after the Empire rose, many senators had a good standing in the society. The Senate prevented Emperor Palpatine from achieving his goals and was an obstacle on the way to power. The Emperor understood that he needed to act from the inside to seize full power. That’s why he recruited some of the Senate members. These spies were very professional. During the day, they were just like ordinary senators and they served the Empire at night. In the evening, each spy got a task to remove one of the senators, devoted to the Old Order. The following night all the senators, who had been chosen to be removed, died. Palpatine wanted to get rid of the problem as quickly as possible, that's why he gave the orders in such a way that each night maximum possible quantity of the non-spy senators met their deaths.

Having faced the deaths, senators suspected the Emperor's spies among them. So it was decided to exclude members from the Senate until deaths stop or there remain only spies in the Senate. After excluding from the Senate a senator loses his standing in the society and is no longer a threat for Palpatine. On the other hand, if he was a spy then he won’t be able to kill senators any more.

Senators suppose that during the night every spy kills exactly one non-spy senator. The spies don't give themselves away, that's why every time the Senate chooses only the quantity of to-be-excluded members, but personalities are chosen at random. The Senate acts optimally and chooses the quantity of to-be-excluded in order to maximize the expected number of the non-spy senators still acting by the end of the confrontation.

At the moment k out of n Senate members are spies, and the Emperor has just given them new tasks. Help Palpatine count the expected number of senators devoted to the Old Order, which will remain in the Senate by the end of the confrontation.

The single line of the input contains two integers, n and k (1 ≤ k ≤ n ≤ 200, 1 ≤ k ≤ 20).

Print a single number — the answer to the problem with absolute or relative error at most 10⁻⁶.