Let $E$ be a set that consists of all numbers of the form $2^k$ where $k$ is a positive integer less than $x^{x^x}$ and $x=123456789$.

Maija picks one number from $E$ uniformly at random. What is the probability that the first digit of the number is $a$ when the number is written in base $b$?

Input

The only input line contains two integers $a$ and $b$.

Output

Print one line that contains the probability. The difference between your answer and the correct answer has to be less than $10^{-6}$.

Constraints

• $1 \le a < b \le 10$

Example

Input:

3 10

Output:

0.124938737