{"problem":{"name":"[ICPC 2020 Shanghai R] Sky Garden","description":{"content":"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, Pro","description_type":"Markdown"},"platform":"Luogu","limit":{"time_limit":1000,"memory_limit":1048576},"difficulty":{"LuoguStyle":"P4"},"is_remote":true,"is_sync":true,"sync_url":null,"sign":"LGP9827"},"statements":[{"statement_type":"Markdown","content":"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.\n\nOn 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 $i$.\n\nMeanwhile, 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.\n\nLet $Q$ 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.\n\nFor 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 $\\{a, b\\}\\subseteq P$. \n\n## Input\n\nThe only line contains two integers $n,m~(1\\le n,m\\le 500)$.\n\n## Output\n\nOutput one number -- the sum of the distances between every pair of points in $P$.\n\nYour answer is considered correct if its absolute or relative error does not exceed $10^{-6}$.\n\n[samples]\n\n## Note\n\n![](https://cdn.luogu.com.cn/upload/image_hosting/81sxvtcp.png)\n\n$dis(p_1, p_2)=dis(p_2, p_3)=dis(p_3, p_4)=dis(p_1, p_4)=\\frac{\\pi}{2}$\n\n$dis(p_1, p_5)=dis(p_2, p_5)=dis(p_3, p_5)=dis(p_4, p_5)=1$\n\n$dis(p_1, p_3)=dis(p_2, p_4)=2$","is_translate":false,"language":"English"}],"meta":{"iden":"LGP9827","tags":["动态规划 DP","数学","2020","上海","Special Judge","O2优化","ICPC"],"sample_group":[["1 2","14.2831853072"],["2 3","175.4159265359"]],"created_at":"2026-03-03 11:09:25"}}