Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Vasily the Bear and Fly

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOne beautiful day Vasily the bear painted 2*m* circles of the same radius *R* on a coordinate plane. Circles with numbers from 1 to *m* had centers at points (2*R* - *R*, 0), (4*R* - *R*, 0), ..., (2*Rm* - *R*, 0), respectively. Circles with numbers from *m* + 1 to 2*m* had centers at points (2*R* - *R*, 2*R*), (4*R* - *R*, 2*R*), ..., (2*Rm* - *R*, 2*R*), respectively.

Naturally, the bear painted the circles for a simple experiment with a fly. The experiment continued for *m*^{2} days. Each day of the experiment got its own unique number from 0 to *m*^{2} - 1, inclusive.

On the day number *i* the following things happened:

- The fly arrived at the coordinate plane at the center of the circle with number ( is the result of dividing number
*x*by number*y*, rounded down to an integer). - The fly went along the coordinate plane to the center of the circle number ( is the remainder after dividing number
*x*by number*y*). The bear noticed that the fly went from the center of circle*v*to the center of circle*u*along the shortest path with all points lying on the border or inside at least one of the 2*m*circles. After the fly reached the center of circle*u*, it flew away in an unknown direction.

Help Vasily, count the average distance the fly went along the coordinate plane during each of these *m*^{2} days.

Input

The first line contains two integers *m*, *R* (1 ≤ *m* ≤ 10^{5}, 1 ≤ *R* ≤ 10).

Output

In a single line print a single real number — the answer to the problem. The answer will be considered correct if its absolute or relative error doesn't exceed 10^{ - 6}.

Examples

Input

1 1

Output

2.0000000000

Input

2 2

Output

5.4142135624

Note

Figure to the second sample

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/21/2019 09:21:26 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|