L. Triangle hole
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You have an equilateral triangle with a height of $$$H$$$. You'll perform $$$K$$$ operations on it, in each operation the following is performed:

  1. Divide the triangle into four equilateral triangles, as shown in the figure below.
  2. Then, take the triangle in the middle and discard the rest.

dividing to 4 equal triangles

Now, you're interested in finding the area of the triangle after $$$K$$$ steps. Can you do that?

Input

The first and only line contains two integers $$$H$$$ and $$$K$$$ $$$(1 \le H \le 10^9$$$ , $$$0 \le K \le 10^5)$$$ — representing the initial height of the triangle, and the number of operations, respectively.

Output

Print a single number, the area of the triangle after $$$K$$$ steps.

Your answer will be accepted if the absolute or relative error does not exceed $$$10^{-4}$$$

Examples
Input
10 2
Output
3.608439
Input
5 0
Output
14.433757