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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 2010-2018 Mike Mirzayanov

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