CF336B.Vasily the Bear and Fly

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.

一个美好的日子里，维克多熊在坐标平面上画了 $2m$ 个半径均为 $R$ 的圆。编号为 $1$ 到 $m$ 的圆，其中心坐标分别为 $(2R - R,\, 0)$、$(4R - R,\, 0)$、…、$(2Rm - R,\, 0)$；编号为 $m+1$ 到 $2m$ 的圆，其中心坐标分别为 $(2R - R,\, 2R)$、$(4R - R,\, 2R)$、…、$(2Rm - R,\, 2R)$。

显然，熊画这些圆是为了进行一项关于一只苍蝇的简单实验。该实验持续了 $m^2$ 天。实验中的每一天被赋予一个从 $0$ 到 $m^2 - 1$（含）的唯一编号。

在编号为 $i$ 的这一天，发生以下事件：

1. 苍蝇抵达坐标平面，落点为编号为 $\left\lfloor \frac{i}{m} \right\rfloor + 1$ 的圆的圆心（其中 $\left\lfloor \frac{x}{y} \right\rfloor$ 表示将 $x$ 除以 $y$ 后向下取整所得的整数）。
2. 苍蝇沿坐标平面飞向编号为 $i \bmod m + 1$ 的圆的圆心（其中 $x \bmod y$ 表示 $x$ 除以 $y$ 后所得的余数）。熊注意到：苍蝇从编号为 $v$ 的圆的圆心出发，沿最短路径飞至编号为 $u$ 的圆的圆心，且该路径上所有点均位于至少一个（共 $2m$ 个）圆的边界上或内部。苍蝇抵达编号为 $u$ 的圆的圆心后，便朝未知方向飞离。

请帮助维克多计算：在这 $m^2$ 天中，苍蝇每天在坐标平面上飞行的平均距离。

The first line contains two integers m, R (1 ≤ m ≤ 105, 1 ≤ R ≤ 10).

第一行包含两个整数 $m$ 和 $R$（$1 \leq m \leq 10^5$，$1 \leq R \leq 10$）。

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.

在一行中输出一个实数——该问题的答案。若答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。

Figure to the second sample

第二个样例对应的图