Score: $525$ points

问题描述

给定整数 $X$ 和 $Y$，满足至少一个条件 $X \neq 0$ 或 $Y \neq 0$。

寻找一对整数 $(A, B)$，满足以下所有条件。如果不存在这样的整数对，请报告。

• $-10^{18} \leq A, B \leq 10^{18}$
• 在 $xy$ 平面上以点 $(0, 0), (X, Y), (A, B)$ 为顶点的三角形面积为 $1$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given integers $X$ and $Y$, which satisfy at least one of $X \neq 0$ and $Y \neq 0$.
Find a pair of integers $(A, B)$ that satisfies all of the following conditions. If no such pair exists, report so.

• $-10^{18} \leq A, B \leq 10^{18}$
• The area of the triangle with vertices at points $(0, 0), (X, Y), (A, B)$ on the $xy$-plane is $1$.

Constraints

• $-10^{17} \leq X, Y \leq 10^{17}$
• $(X, Y) \neq (0, 0)$
• $X$ and $Y$ are integers.

Input

The input is given from Standard Input in the following format:

$X$ $Y$

Output

If there is a pair of integers $(A, B)$ that satisfies the conditions, print it in the following format:

$A$ $B$

Otherwise, print -1.

Sample Input 1

3 5

Sample Output 1

1 1

The area of the triangle with vertices at points $(0, 0), (3, 5), (1, 1)$ is $1$. Thus, $(A, B) = (1, 1)$ satisfies the conditions.

Sample Input 2

-2 0

Sample Output 2

0 1

Sample Input 3

8752654402832944 -6857065241301125

Sample Output 3

-1

update @ 2024/3/10 01:33:24