AT_abc459_g.Golf 2

You are given integers $A, B, X, Y$.

A piece is placed on a two-dimensional plane. Initially, the piece is at coordinates $(0, 0)$.

You can perform the following operation zero or more times:

• Let $(x, y)$ be the current coordinates of the piece. Move the piece to coordinates $(x', y')$ satisfying one of the following conditions:
  • $|x - x'| = A$ and $|y - y'| = B$
  • $|x - x'| = B$ and $|y - y'| = A$

Determine whether it is possible to move the piece to coordinates $(X, Y)$, and if so, find the minimum number of operations required.

You are given $T$ test cases; solve each.

给你整数 $A, B, X, Y$。

一个棋子被放置在二维平面上，初始时位于坐标 $(0, 0)$ 处。

你可以执行以下操作零次或多次：

• 设棋子当前坐标为 $(x, y)$，将其移动至满足以下任一条件的坐标 $(x', y')$：
  • $|x - x'| = A$ 且 $|y - y'| = B$
  • $|x - x'| = B$ 且 $|y - y'| = A$

判断是否能将棋子移动到坐标 $(X, Y)$；若可以，求出所需的最少操作次数。

你将得到 $T$ 组测试用例，请对每组分别求解。

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

$T$
$\text{case}_1$
$\text{case}_2$
$\vdots$
$\text{case}_T$

The $i$-th $(1 \le i \le T)$ test case $\text{case}_i$ is given in the following format:

$A$ $B$ $X$ $Y$

输入从标准输入中按以下格式给出：

$T$
$\text{case}_1$
$\text{case}_2$
$\vdots$
$\text{case}_T$

第 $i$ 个 $(1 \le i \le T)$ 测试用例 $\text{case}_i$ 按以下格式给出：

$A$ $B$ $X$ $Y$

Output the answers for the test cases in order, separated by newlines.

For each test case, if it is possible to move the piece to coordinates $(X, Y)$, output the minimum number of operations required; otherwise, output $-1$.

按顺序输出各测试用例的答案，答案之间用换行符分隔。

对于每个测试用例，若能将棋子移动到坐标 $(X, Y)$，则输出所需的最少操作次数；否则输出 $-1$。

Sample 1 Explanation:
Consider the first test case.

By moving the piece from $(0, 0)$ to $(1, 2)$, then to $(-1, 1)$, then to $(1, 0)$ in order, the piece can be moved to coordinates $(1, 0)$ in three operations.

It is impossible to move the piece to coordinates $(1, 0)$ in fewer than three operations, so output $3$ on the first line.

Constraints

• $1 \le T \le 2 \times 10^5$
• $1 \le A < B \le 10^6$
• $0 \le X, Y \le 10^6$
• All input values are integers.

样例 1 解释：
考虑第一个测试用例。

按顺序将棋子从 $(0, 0)$ 移动到 $(1, 2)$，再移动到 $(-1, 1)$，最后移动到 $(1, 0)$，共需三步操作，即可将棋子移至坐标 $(1, 0)$。

无法在少于三步操作内将棋子移至坐标 $(1, 0)$，因此第一行输出 $3$。

约束条件

• $1 \le T \le 2 \times 10^5$
• $1 \le A < B \le 10^6$
• $0 \le X, Y \le 10^6$
• 所有输入值均为整数。