github.com/captn3m0/codechef.git

---
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---
A balanced parenthesis string is defined as follows:
- The empty string is balanced
- If P is balanced, (P) is also 
- If P and Q are balanced, PQ is also balanced

You are given two even integers $n$ and $k$. Find any balanced paranthesis string of length $n$ that doesn't contain a balanced substring of length $k$, or claim that no such string exists.

### Input
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line containing $n$ and $k$.

### Output
For every testcase, print on a new line, any balanced paranthesis string of length $n$ that doesn't contain a balanced substring of length $k$. If there doesn't exist any such string, print $-1$ instead.

### Constraints 
- $1 \leq T \leq 50000$
- $2 \leq k \leq n \leq 10^5$
- Sum of $n$ over all testcases doesn't exceed $10^5$.
- $n$ and $k$ are both even integers.

### Example Input
```
2
4 2
8 6
```

### Example Output
```
-1
(())(())
```

### Explanation
In the first testcase, the only balanced strings of length $4$ are `(())` and `()()`, both of which contain `()` as a substring.

In the second testcase, `(())(())` is a balanced string that doesn't contain any balanced substring of length $6$.
<aside style='background: #f8f8f8;padding: 10px 15px;'><div>All submissions for this problem are available.</div></aside>