A9104. Vasily the Bear and Fly

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

The first line contains two integers $m,R$ ( $1<=m<=10^{5}$ , $1<=R<=10$ ).

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 $10^{-6}$ .


Figure to the second sample