Problem Statement

There are variables $a_1,a_2,a_3$. Initially, $(a_1,a_2,a_3) = (B_1,B_2,B_3)$. You may now perform the following operation any number of times.

• Choose distinct integers $i,j \in \{1,2,3\}$. Simultaneously replace $a_i,a_j$ with $a_i - \min(a_i,A_j - a_j),a_j + \min(a_i,A_j - a_j)$.

Your goal is to make $(a_1,a_2,a_3) = (C_1,C_2,C_3)$. Determine whether this is possible, and if it is possible, find the minimum number of operations required to achieve the goal.

A total of $T$ test cases are given.

Constraints

• $1 \le T \le 10^4$
• $A_i \ge 1$
• $A_1 + A_2 + A_3 \le 10^{18}$
• $0 \le B_i,C_i \le A_i$
• $B_1 + B_2 + B_3 = C_1 + C_2 + C_3$
• All input values are integers.

Input

The input is given in the following format. Here, $\text{case}_i$ is the $i$-th test case.

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

Each test case is given in the following format.

$A_1 \ A_2 \ A_3$
$B_1 \ B_2 \ B_3$
$C_1 \ C_2 \ C_3$

Output

Output $T$ lines.

On the $i$-th line, for $\text{case}_i$, output $-1$ if it is impossible to achieve the goal, and otherwise output the minimum number of operations required.

Sample

4
3 2 1
3 0 0
1 1 1
3 2 2
3 0 0
1 1 1
499999999999999999 250000000000000000 249999999999999999
499999999999999999 0 0
374999999999999999 125000000000000000 0
400000000000000000 300000000000000000 200000000000000000
400000000000000000 0 0
0 200000000000000001 199999999999999999

2
-1
499999999999999998
-1