A. City

Codeforces

IDCF10247A

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Hi ICPCer, welcome to Xi'an. Being a beautiful ancient city, Xi'an is the capital city of Zhou, Qin, Han, and Tang Dynasties. With a long history, the streets in Xi'an have a grid pattern. Attracted by the streets' structure, Coach _Pang_ would like to conduct his research on them. He draws an $n times m$ grid on the board. The grid consists $n + 1$ vertical line segments and $m + 1$ horizontal line segments. The vertical and horizontal line segments intersect at exactly $(n + 1) times (m + 1)$ points, forming $n times m$ unit squares. We call the $(n + 1) times (m + 1)$ intersections _grid point_s. Output the number of line segments(not only vertical or horizontal) $l$ satisfying the following three conditions: The only line contains two integers $n, m$($1 <= n, m <= 1000$). Print the answer in a single line. ## Input The only line contains two integers $n, m$($1 <= n, m <= 1000$). ## Output Print the answer in a single line. [samples]

**Definitions** Let $ n, m \in \mathbb{Z}^+ $ with $ 1 \leq n, m \leq 1000 $. Consider a grid with $ (n+1) \times (m+1) $ grid points, arranged in a rectangular lattice. **Objective** Count the total number of line segments $ l $ (not restricted to axis-aligned) such that: - Both endpoints of $ l $ are grid points. - The line segment connects two distinct grid points. - The segment lies entirely within the grid (i.e., no restriction on direction beyond endpoint constraints). **Formulation** The number of such line segments is the number of unordered pairs of distinct grid points: $$ \binom{(n+1)(m+1)}{2} $$

API Response (JSON)

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      "content": "Hi ICPCer, welcome to Xi'an.\n\nBeing a beautiful ancient city, Xi'an is the capital city of Zhou, Qin, Han, and Tang Dynasties. With a long history, the streets in Xi'an have a grid pattern. \n\nAttracte...",
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