Given a ring with $N$ points, labeled $1, 2, \dots, N$. Each time, a segment of length $L$ is used to cover points on the ring. The starting position of the segment is chosen uniformly at random from $1, 2, \dots, N$. Points on the ring can be covered multiple times. What is the expected number of segments required to cover the entire ring?

Input

A single line containing two integers $N$ and $L$ ($1 \le N \le 20, 1 \le L \le N$).

Output

Output a single floating-point number representing the expected number of segments required to cover the entire ring.

Your answer is considered correct if its absolute or relative error does not exceed $10^{-9}$. More precisely, if your answer is $x$ and the standard answer is $y$, your answer will be considered correct if and only if $\frac{|x - y|}{\max(1, |y|)} \le 10^{-9}$.

Examples

Input 1

3 2

Output 1

2.500000000000000