M. Delivery
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Mazen challenged his brother Amir to solve this problem. Mazen loves consecutive ranges.

Given a number $$$x$$$, is there a range from $$$l$$$ to $$$r$$$ (inclusive) such that $$$\sum_{i= l}^{r} i = x$$$ where $$$(r < x)$$$.

If a range exists, output the $$$l$$$ and $$$r$$$ of such a range, otherwise output -1.

Input

The first line contains a single integer $$$t$$$ $$$(1 \le t \le 10^3)$$$ - the number of test cases.

The only line of each test case contains one integer $$$x$$$ $$$(1 \le x \le 2.10^9)$$$

Output

For each test case, If there is no valid range, output -1.

Otherwise, print 2 integers $$$l,r$$$ $$$(1 \le l < r < x)$$$ - indicates the range. If there are multiple solutions, output any.

Example
Input
3
4
9
88
Output
-1
4 5
3 13