407853: GYM102900 I Sky Garden

Prof. Du and Prof. Pang plan to build a sky garden near the city of Allin. In the garden, there will be a plant maze consisting of straight and circular roads.

On the blueprint of the plant maze, Prof. Du draws $$$n$$$ circles indicating the circular roads. All of them have center $$$(0, 0)$$$. The radius of the $$$i$$$-th circle is $$$i$$$.

Meanwhile, Prof. Pang draws $$$m$$$ lines on the blueprint indicating the straight roads. All of the lines pass through $$$(0, 0)$$$. Each circle is divided into $$$2m$$$ parts with equal lengths by these lines.

Let $$$Q$$$ be the set of the $$$n+m$$$ roads. Let $$$P$$$ be the set of all intersections of two different roads in $$$Q$$$. Note that each circular road and each straight road have two intersections.

For two different points $$$a\in P$$$ and $$$b\in P$$$, we define $$$dis(\{a, b\})$$$ to be the shortest distance one needs to walk from $$$a$$$ to $$$b$$$ along the roads. Please calculate the sum of $$$dis(\{a, b\})$$$ for all $$$\{a, b\}\subseteq P$$$.

The only line contains two integers $$$n,m~(1\le n,m\le 500)$$$.

Output one number – the sum of the distances between every pair of points in $$$P$$$.

Your answer is considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$.

1 2

14.2831853072

2 3

175.4159265359

$$$dis(p_1, p_2)=dis(p_2, p_3)=dis(p_3, p_4)=dis(p_1, p_4)=\frac{\pi}{2}$$$

$$$dis(p_1, p_5)=dis(p_2, p_5)=dis(p_3, p_5)=dis(p_4, p_5)=1$$$

$$$dis(p_1, p_3)=dis(p_2, p_4)=2$$$