A14715 | Distance
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题目描述
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.
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.
输入格式
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 $B$ .
Each test case consists of one line containing two integers $x$ and $y$ ( $0 \le x, y \le 50$ ) — the coordinates of the point $B$ .
输出格式
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.
- 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.
输入输出样例
输入 #1
10 49 3 2 50 13 0 0 41 42 0 0 36 13 37 42 16 42 13 0 0
输出 #1
23 3 1 25 -1 -1 -1 -1 21 0 0 18 13 12 25 4 -1 -1 0 0
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 $|21 - 42| + |0 - 0| = 21$ .
- 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 $|21 - 42| + |0 - 0| = 21$ .
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评测结果：Accepted