Problem 2. Transforming Pairs

USACO 2025 February Contest, Platinum

Answer $Q$ ($1\le Q\le 10^5$) independent queries each of the following form:

You are given four integers $a,b,c,d$ ($-10^{18}\le a,b,c,d\le 10^{18}$). In one operation you can either do $a\mathrel{+}=b$, or $b\mathrel{+}=a$. Determine the minimum number of operations to transform $(a,b)$ into $(c,d)$, or if it is impossible to do so, output $-1$.

INPUT FORMAT (input arrives from the terminal / stdin):

The first line contains $Q$.

The next $Q$ lines each contain four integers $a,b,c,d$.

OUTPUT FORMAT (print output to the terminal / stdout):

The answer for each query on a separate line.

SAMPLE INPUT:

4
5 -3 -1 -3
5 3 5 2
5 3 8 19
5 3 5 3

SAMPLE OUTPUT:

2
-1
3
0

First query: $(5,-3)\to (2,-3)\to (-1,-3)$

Second query: Impossible.

Third query: $(5,3) \to (8, 3) \to (8, 11) \to (8, 19)$

Fourth query: No operations necessary.

SCORING: Input 2: $|a|, |b|, |c|,|d|\le 10$Input 3: $a,b\ge 0$Input 4: $a \geq 0 \geq b$Input 5: $a \leq 0 \leq b$Input 6: $a,b\le 0$Input 7: $c,d\ge 0$Input 8: $c \geq 0 \geq d$Input 9: $c \leq 0 \leq d$Input 10: $c,d\le 0$Inputs 11-14: $Q \leq 10^3$Inputs 15-19: No additional constraints.

Problem credits: Benjamin Qi