AvtoBus

Description:

Input:

The first line contains an integer $$$t$$$ ($$$1 \le t \le 1\,000$$$) — the number of test cases. The following lines contain description of test cases.

The only line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 10^{18}$$$) — the total number of wheels for all buses.

Output:

For each test case print the answer in a single line using the following format.

Print two integers $$$x$$$ and $$$y$$$ ($$$1 \le x \le y$$$) — the minimum and the maximum possible number of buses that can be in the bus fleet.

If there is no suitable number of buses for the given $$$n$$$, print the number $$$-1$$$ as the answer.

Sample Input:

4
4
7
24
998244353998244352

Sample Output:

1 1
-1
4 6
166374058999707392 249561088499561088

Note:

In the first test case the total number of wheels is $$$4$$$. It means that there is the only one bus with two axles in the bus fleet.

In the second test case it's easy to show that there is no suitable number of buses with $$$7$$$ wheels in total.

In the third test case the total number of wheels is $$$24$$$. The following options are possible:

• Four buses with three axles.
• Three buses with two axles and two buses with three axles.
• Six buses with two axles.

So the minimum number of buses is $$$4$$$ and the maximum number of buses is $$$6$$$.