USACO 2025 February Contest, Platinum
Problem 2. Transforming Pairs
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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