Problem Statement

A Kadomatsu sequence is defined as follows: when 3 integers are arranged as $A$, $B$, $C$ from left to right,
all the values are distinct and the second largest integer among $A$, $B$, $C$ is either $A$ or $C$.
In particular, in this problem, $A$, $B$, $C$ of a Kadomatsu sequence must be positive integers.

3 positive integers $A$, $B$, $C$ are given in this order from left to right.
Perform the following 3 operations any number of times to make a Kadomatsu sequence at the minimum cost.

・At cost $X$, subtract 1 from the positive integers $A$ and $B$.
・At cost $Y$, subtract 1 from the positive integers $B$ and $C$.
・At cost $Z$, subtract 1 from the positive integers $A$ and $C$.

※Note that in this problem, multiple queries are given in a single test case.

Input

$T$
$A_1$ $B_1$ $C_1$ $X_1$ $Y_1$ $Z_1$
$A_2$ $B_2$ $C_2$ $X_2$ $Y_2$ $Z_2$
$ \vdots\ $
$A_T$ $B_T$ $C_T$ $X_T$ $Y_T$ $Z_T$

$T$ is the number of given sets of 6 positive integers $A$, $B$, $C$, $X$, $Y$, $Z$. $1 \le T \le 10000 = 10^4$.
$A_i$, $B_i$, $C_i$ are the $i$-th given positive integers $A$, $B$, $C$. $1 \le A_i,B_i,C_i \le 1000000000 = 10^9$.
$X_i$, $Y_i$, $Z_i$ are the costs $X$, $Y$, $Z$ in the $i$-th case. $1 \le X_i,Y_i,Z_i \le 1000000000 = 10^9$.

Output

On the $i$-th line, output the answer for the $i$-th $A_i$, $B_i$, $C_i$, $X_i$, $Y_i$, $Z_i$.
If a Kadomatsu sequence cannot be made, output -1.

Sample

1
2 4 2 2 1 1

1

3
1 3 2 1 2 3
1 2 3 1 2 3
3 3 3 1 2 3

0
-1
-1