#P1998A. Find K Distinct Points with Fixed Center
Find K Distinct Points with Fixed Center
Description
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.
Input
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 $1000$.
Output
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.
4
10 10 1
0 0 3
-5 -8 8
4 -5 3
10 10
-1 -1
5 -1
-4 2
-6 -7
-5 -7
-4 -7
-4 -8
-4 -9
-5 -9
-6 -9
-6 -8
1000 -1000
-996 995
8 -10
Note
For the first test case, $\left( \frac{10}{1}, \frac{10}{1} \right) = (10, 10)$.
For the second test case, $\left( \frac{-1 + 5 - 4}{3}, \frac{-1 -1 + 2}{3} \right) = (0, 0)$.