Expected Minimum Power

You are given two positive integers $n$ and $x$.

You are going to choose $x$ distinct integers, each between $1$ and $n$, inclusive. The choice will be made uniformly at random. That is, each of the possible $x$-element subsets of the integers $1$ to $n$ is equally likely to be chosen.

Let $S$ be the smallest integer among the $x$ chosen ones. Compute the expected value of $2^S$. In other words, determine the average value of $2$ to the power of $S$, where the average is taken over all possible choices of the $x$ distinct integers.

Input

Two positive integers: $n(1\le n\le 50)$ and $x(1\le x\le n)$.

Output

Print the average value of $2$ to the power of $S$ with $4$ decimal digits.

Examples

In the first test case the only possible situation is that you will choose $(1,2,3,4)$. In this case, the minimum is $1$, and the expected value is $2^1=2$.

In the second test case there are three equally likely scenarios: you will select either $\{1,2\}$ or $\{1,3\}$ or $\{2,3\}$. The corresponding values of $S$ are $1,1$ and $2$ respectively. Thus, the average value of $2^S$ is $(2^1+2^1+2^2)/3=8/3=2.6666666$.