CF1612A Distance

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.

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 $ .

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.

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 $ .