A. Distance
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Let's denote the Manhattan distance between two points $$$p_1$$$ (with coordinates $$$(x_1, y_1)$$$) and $$$p_2$$$ (with coordinates $$$(x_2, y_2)$$$) as $$$d(p_1, p_2) = |x_1 - x_2| + |y_1 - y_2|$$$. For example, the distance between two points with coordinates $$$(1, 3)$$$ and $$$(4, 2)$$$ is $$$|1 - 4| + |3 - 2| = 4$$$.

You are given two points, $$$A$$$ and $$$B$$$. The point $$$A$$$ has coordinates $$$(0, 0)$$$, the point $$$B$$$ has coordinates $$$(x, y)$$$.

Your goal is to find a point $$$C$$$ such that:

  • both coordinates of $$$C$$$ are non-negative integers;
  • $$$d(A, C) = \dfrac{d(A, B)}{2}$$$ (without any rounding);
  • $$$d(B, C) = \dfrac{d(A, B)}{2}$$$ (without any rounding).

Find any point $$$C$$$ that meets these constraints, or report that no such point exists.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 3000$$$) — the number of test cases.

Each test case consists of one line containing two integers $$$x$$$ and $$$y$$$ ($$$0 \le x, y \le 50$$$) — the coordinates of the point $$$B$$$.

Output

For each test case, print the answer on a separate line as follows:

  • if it is impossible to find a point $$$C$$$ meeting the constraints, print "-1 -1" (without quotes);
  • otherwise, print two non-negative integers not exceeding $$$10^6$$$ — the coordinates of point $$$C$$$ meeting the constraints. If there are multiple answers, print any of them. It can be shown that if any such point exists, it's possible to find a point with coordinates not exceeding $$$10^6$$$ that meets the constraints.
Example
Input
10
49 3
2 50
13 0
0 41
42 0
0 36
13 37
42 16
42 13
0 0
Output
23 3
1 25
-1 -1
-1 -1
21 0
0 18
13 12
25 4
-1 -1
0 0
Note

Explanations for some of the test cases from the example:

  • In the first test case, the point $$$B$$$ has coordinates $$$(49, 3)$$$. If the point $$$C$$$ has coordinates $$$(23, 3)$$$, then the distance from $$$A$$$ to $$$B$$$ is $$$|49 - 0| + |3 - 0| = 52$$$, the distance from $$$A$$$ to $$$C$$$ is $$$|23 - 0| + |3 - 0| = 26$$$, and the distance from $$$B$$$ to $$$C$$$ is $$$|23 - 49| + |3 - 3| = 26$$$.
  • In the second test case, the point $$$B$$$ has coordinates $$$(2, 50)$$$. If the point $$$C$$$ has coordinates $$$(1, 25)$$$, then the distance from $$$A$$$ to $$$B$$$ is $$$|2 - 0| + |50 - 0| = 52$$$, the distance from $$$A$$$ to $$$C$$$ is $$$|1 - 0| + |25 - 0| = 26$$$, and the distance from $$$B$$$ to $$$C$$$ is $$$|1 - 2| + |25 - 50| = 26$$$.
  • In the third and the fourth test cases, it can be shown that no point with integer coordinates meets the constraints.
  • In the fifth test case, the point $$$B$$$ has coordinates $$$(42, 0)$$$. If the point $$$C$$$ has coordinates $$$(21, 0)$$$, then the distance from $$$A$$$ to $$$B$$$ is $$$|42 - 0| + |0 - 0| = 42$$$, the distance from $$$A$$$ to $$$C$$$ is $$$|21 - 0| + |0 - 0| = 21$$$, and the distance from $$$B$$$ to $$$C$$$ is $$$|21 - 42| + |0 - 0| = 21$$$.