{"problem":{"name":"[ICPC 2024 Xi'an I] Triangle","description":{"content":"There are three points $A(a, 0)$, $B(0, b)$, $C(0, 0)$ in the plane rectangular coordinate system. Define the size of triangle $ABC$ as the number of squares that belong to it.                For inte","description_type":"Markdown"},"platform":"Luogu","limit":{"time_limit":1000,"memory_limit":524288},"difficulty":{"LuoguStyle":"P3"},"is_remote":true,"is_sync":true,"sync_url":null,"sign":"LGP10562"},"statements":[{"statement_type":"Markdown","content":"There are three points $A(a, 0)$, $B(0, b)$, $C(0, 0)$ in the plane rectangular coordinate system. Define the size of triangle $ABC$ as the number of squares that belong to it.\n    \n    \n    \nFor integers $x,y$, one square is defined by four points $(x, y)$, $(x + 1, y)$, $(x, y + 1)$, $(x + 1, y + 1)$. We consider a square to belong to a triangle if half or more of it is inside the triangle.\n    \n    \n    \nFor example, when $a = 8, b = 6$, the size of triangle $ABC$ will be $24$. The image below shows which squares are counted in the triangle.\n\n![](https://cdn.luogu.com.cn/upload/image_hosting/3fnqi74y.png)\n\n## Input\n\n    \nThe first and only line contains two integers $a\\ (1\\le a\\le 10^6)$ and $b\\ (1\\le b\\le 10^6)$.\n\n## Output\n\nPrint an integer: the size of triangle $ABC$.\n    \n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"LGP10562","tags":["2024","O2优化","ICPC","西安"],"sample_group":[["6 8","24"],["5 5\n","15"],["1 999999","500000"]],"created_at":"2026-03-03 11:09:25"}}