Bessie the brilliant bovine has discovered a new fascination—mathematical magic! One day, while trotting through the fields of Farmer John’s ranch, she stumbles upon two enchanted piles of hay. The first pile contains $a$ bales, and the second pile contains $b$ bales ($1\le a,b\le 10^{18}$).

Next to the hay, half-buried in the dirt, she discovers an ancient scroll. As she unfurls it, glowing letters reveal a prophecy:

To fulfill the decree of the Great Grasslands, the chosen one must transform these two humble hay piles into exactly $c$ and $d$ bales—no more, no less.

Bessie realizes she can only perform the following two spells:

• She can magically conjure new bales to increase the first pile’s size by the amount currently in the second pile.
• She can magically conjure new bales to increase the second pile’s size by the amount currently in the first pile.

For each of $T$ ($1\le T\le 10^4$) independent test cases, output the minimum number of operations needed to fulfill the prophecy, or if it is impossible to do so, output -1.

SAMPLE INPUT:

4
5 3 5 2
5 3 8 19
5 3 19 8
5 3 5 3

SAMPLE OUTPUT:

-1
3
-1
0

In the first test case, it is impossible since $b>d$ initially, but operations can only increase $b$.

In the second test case, initially the two piles have $(5, 3)$ bales. Bessie can first increase the first pile by the amount in the second pile, resulting in $(8, 3)$ bales. Bessie can then increase the second pile by the new amount in the first pile, and do this operation twice, resulting in $(8, 11)$ and finally $(8, 19)$ bales. This matches $c$ and $d$ and is the minimum number of operations to get there.

Note that the third test case has a different answer than the second because $c$ and $d$ are swapped (the order of the piles matters).

In the fourth test case, no operations are necessary.

SAMPLE INPUT:

1
1 1 1 1000000000000000000

SAMPLE OUTPUT:

999999999999999999

Problem credits: Benjamin Qi