Project Euler #197: Investigating the behaviour of a recursively defined sequence

_{This problem is a programming version of Problem 197 from projecteuler.net}

Given is the function ( is the floor-function), the sequence is defined by and .

Find for with given and . Your answer would be considered correct if it has absolute error not more than .

Input Format

Every test file contains two real numbers: and with no more than two digits after decimal point. These numbers are situated in a single line and are separated by a single space.

Constraints

Output Format

Output exactly one real number which is the answer to the problem.

Sample Input 0

0 30

Sample Output 0

1.473849410