Problem Statement

Takahashi is a student at Brute Force University (abbreviated: Chokudai).

Meanwhile, his rival Hikuhashi is a student at Speedup University (abbreviated: Sokudai). One day, the two decided to compete to see who could solve a problem faster.

The size of a problem is denoted by $N$. Since Takahashi is a student at Brute Force University, he starts computing by brute force and takes $N^2$ seconds to finish solving the problem. On the other hand, since Hikuhashi is a student at Speedup University, $P$ seconds after seeing the problem he notices that the algorithm called binary search can be used on it, and it then takes him a further $Q*N*log_2 N$ seconds from actually starting to solve the problem until he finishes.

Takahashi wants to beat Hikuhashi, so find the largest $N$ in the range where Takahashi does not finish solving the problem later than Hikuhashi. It is guaranteed that Takahashi can beat Hikuhashi when $N=1$.

(Note): $N$ does not have to be an integer. Also, an error of up to $10^{-5}$ is allowed in the output.

(Added 2020/5/3: Under the constraints, it can be proved that Takahashi does not lose to Hikuhashi when the problem size is at least 1 and at most the N to be found.)

Input

$P\ Q$

$2 \le P \le 10^9$
$1 \le Q \le 10^9$
$P,Q$ are integers.

Output

Find the maximum problem size for which Takahashi does not lose. An absolute or relative error of up to $10^{-5}$ is allowed in the output.

Sample

8 1

4.000000000

7654321 1234567

30706182.561749045