One 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:

1. 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).
2. 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 $10^{ - 6}$.

Note

Figure to the second sample