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 $\left( \frac{x_1 + x_2 + \ldots + x_k}{k}, \frac{y_1 + y_2 + \ldots + y_k}{k} \right)$.

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.

Note

For the first test case, $\left( \frac{10}{1}, \frac{10}{1} \right) = (10, 10)$.

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