AT_arc222_f.Triple Transformation

Consider an operation on a triple $(x,y,z)$ of non-negative integers. In the operation, $(x,y,z)$ is replaced according to the following rules:

• If $y+z<x$: replace with $(x-y-z,\ 2y,\ 2z)$.
• If $x+z<y$: replace with $(2x,\ y-x-z,\ 2z)$.
• If $x+y<z$: replace with $(2x,\ 2y,\ z-x-y)$.
• If none of the above conditions hold: replace with $(y+z-x,\ x+z-y,\ x+y-z)$.

Note that every triple of non-negative integers falls into exactly one of the above four cases.

You are given non-negative integers $A_1, A_2, A_3, B_1, B_2, B_3$. Consider performing the operation on the triple $(A_1,A_2,A_3)$ zero or more times to obtain $(B_1,B_2,B_3)$. Find the minimum number of operations required to do so. If it is impossible to obtain $(B_1,B_2,B_3)$ no matter how many times the operation is performed, output -1.

$T$ test cases are given; solve each of them.

考虑对一个由非负整数构成的三元组 $(x,y,z)$ 进行一种操作。该操作按照以下规则将 $(x,y,z)$ 替换为一个新的三元组：

• 若 $y+z<x$：替换为 $(x-y-z,\ 2y,\ 2z)$；
• 若 $x+z<y$：替换为 $(2x,\ y-x-z,\ 2z)$；
• 若 $x+y<z$：替换为 $(2x,\ 2y,\ z-x-y)$；
• 若以上条件均不满足：替换为 $(y+z-x,\ x+z-y,\ x+y-z)$。

注意：任意一个非负整数三元组必恰好属于上述四种情况之一。

给定非负整数 $A_1, A_2, A_3, B_1, B_2, B_3$。考虑对三元组 $(A_1,A_2,A_3)$ 执行零次或多次该操作，使其变为 $(B_1,B_2,B_3)$。求实现这一目标所需的最少操作次数。若无论执行多少次操作都无法得到 $(B_1,B_2,B_3)$，则输出 -1。

共给出 $T$ 组测试用例，请对每组分别求解。

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

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

Each test case is given in the following format:

$A_1$ $A_2$ $A_3$ $B_1$ $B_2$ $B_3$

输入从标准输入中按以下格式给出：

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

每个测试用例按以下格式给出：

$A_1$ $A_2$ $A_3$ $B_1$ $B_2$ $B_3$

Output one line per test case.

For each test case, output the minimum number of operations required to obtain $(B_1,B_2,B_3)$ by performing the operation on the triple $(A_1,A_2,A_3)$ zero or more times. If it is impossible to obtain $(B_1,B_2,B_3)$ no matter how many times the operation is performed, output -1.

每个测试用例输出一行。

对于每个测试用例，输出通过零次或多次对三元组 $(A_1,A_2,A_3)$ 执行该操作，得到 $(B_1,B_2,B_3)$ 所需的最少操作次数。如果无论执行多少次操作都无法得到 $(B_1,B_2,B_3)$，则输出 -1。

Sample 1 Explanation:
For $(A_1,A_2,A_3)=(2,3,4)$, the triple changes as follows when the operation is repeatedly applied:

• $(2,3,4)\to (5,3,1)\to (1,6,2)\to (2,3,4)\to (5,3,1)\to (1,6,2)\to\cdots$

From this, we can see that the answers to the first three test cases are $0, 1, 2$.

Constraints

• $1\leq T\leq 300$
• $0\leq A_1, A_2, A_3, B_1, B_2, B_3\leq 10^8$
• All input values are integers.

样例 1 解释：
对于 $(A_1,A_2,A_3)=(2,3,4)$，反复应用该操作时，三元组的变化如下：

• $(2,3,4)\to (5,3,1)\to (1,6,2)\to (2,3,4)\to (5,3,1)\to (1,6,2)\to\cdots$

由此可知，前三个测试用例的答案分别为 $0,\ 1,\ 2$。

约束条件

• $1\leq T\leq 300$
• $0\leq A_1, A_2, A_3, B_1, B_2, B_3\leq 10^8$
• 所有输入值均为整数。