CF1998A Find K Distinct Points with Fixed Center

I couldn't think of a good title for this problem, so I decided to learn from LeetCode. — Sun Tzu, The Art of War You are given three integers $ x_c $ , $ y_c $ , and $ k $ ( $ -100 \leq x_c, y_c \leq 100 $ , $ 1 \leq k \leq 1000 $ ). You need to find $ k $ distinct points ( $ x_1, y_1 $ ), ( $ x_2, y_2 $ ), $ \ldots $ , ( $ x_k, y_k $ ), having integer coordinates, on the 2D coordinate plane such that: - their center $ ^{\text{∗}} $ is ( $ x_c, y_c $ ) - $ -10^9 \leq x_i, y_i \leq 10^9 $ for all $ i $ from $ 1 $ to $ k $ It can be proven that at least one set of $ k $ distinct points always exists that satisfies these conditions. $ ^{\text{∗}} $ The center of $ k $ points ( $ x_1, y_1 $ ), ( $ x_2, y_2 $ ), $ \ldots $ , ( $ x_k, y_k $ ) is $ \left( \frac{x_1 + x_2 + \ldots + x_k}{k}, \frac{y_1 + y_2 + \ldots + y_k}{k} \right) $ .

The first line contains $ t $ ( $ 1 \leq t \leq 100 $ ) — the number of test cases. Each test case contains three integers $ x_c $ , $ y_c $ , and $ k $ ( $ -100 \leq x_c, y_c \leq 100 $ , $ 1 \leq k \leq 1000 $ ) — the coordinates of the center and the number of distinct points you must output. It is guaranteed that the sum of $ k $ over all test cases does not exceed $ 1000 $ .

For each test case, output $ k $ lines, the $ i $ -th line containing two space separated integers, $ x_i $ and $ y_i $ , ( $ -10^9 \leq x_i, y_i \leq 10^9 $ ) — denoting the position of the $ i $ -th point. If there are multiple answers, print any of them. It can be shown that a solution always exists under the given constraints.

For the first test case, $ \left( \frac{10}{1}, \frac{10}{1} \right) = (10, 10) $ . For the second test case, $ \left( \frac{-1 + 5 - 4}{3}, \frac{-1 -1 + 2}{3} \right) = (0, 0) $ .