Parentheses Matrix

A $\textit{parentheses matrix}$ is a matrix where every element is either '(' or ')'. We define the $\textit{goodness}$ of a parentheses matrix as the number of $\textit{balanced}$ rows (from left to right) and columns (from up to down). Note that:

- an empty sequence is balanced;
- if $A$ is balanced, then $(A)$ is also balanced;
- if $A$ and $B$ are balanced, then $AB$ is also balanced.

For example, the following parentheses matrix is a $2 \times 4$ matrix with goodness 3, because the second row, the second column and the fourth column are balanced:

)()(
()()

Now, give you the width and the height of the matrix, please construct a parentheses matrix with maximum goodness.

The first line of input is a single integer $T$ $(1 \leq T \leq 50)$, the number of test cases.

Each test case is a single line of two integers $h, w$ $(1 \leq h, w \leq 200)$, the height and the width of the matrix, respectively.

For each test case, display $h$ lines, denoting the parentheses matrix you construct. Each line should contain exactly $w$ characters, and each character should be either '(' or ')'. If multiple solutions exist, you may print any of them.

3
1 1
2 2
2 3

(
()
)(
(((
)))

2018 Multi-University Training Contest 8