E. Ethernet
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Mr. Wor's router at home is broken again. After some repairs, he needs to reconnect the Ethernet cables to the router.

It is known that Mr. Wor's router has $$$n$$$ ports, and there are $$$n$$$ Ethernet cables. Then, Mr. Wor will sequentially insert the $$$i$$$-th Ethernet cable to the $$$i$$$-th port, for all $$$i$$$ from $$$1$$$ to $$$n$$$.

However, due to Mr. Wor's mysterious actions, the first $$$m$$$ cables were not inserted into their designated ports, but were inserted into $$$m$$$ ports uniformly at random. For the remaining cables, when cable $$$i$$$ is being inserted, if port $$$i$$$ is not occupied, then cable $$$i$$$ will be inserted into port $$$i$$$. Otherwise, cable $$$i$$$ will be inserted into a randomly chosen unoccupied port.

Mr. Wor wants to know the probability that the last cable, cable $$$n$$$, is plugged into port $$$n$$$.

Input

Only one line contains two integers $$$n,m(1 \leq n \leq 10, 0 \leq m \leq n)$$$, denoting the number of cables and the number of cables which was inserted randomly.

Output

Print the probability in one line. Your answer is considered correct if the relative or absolute error is less than or equal to $$$10^{-6}$$$.

Example
Input
3 1
Output
0.5000000000