Problem Statement

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.

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.

Input

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

Output

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.