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