Background

Original link: https://oier.team/problems/X4C。

Problem Description

Given two integers $a, b$ (possibly negative), you may perform any number of operations (including doing nothing). In each operation, you need to choose one of the following two forms:

• Operation 1: Assign $a$ to the sum of $a$ and $b$, i.e., $a \gets a + b$.
• Operation 2: Assign $b$ to the sum of $a$ and $b$, i.e., $b \gets a + b$.

Your goal is to minimize the absolute value of the difference between $a$ and $b$, $\lvert a-b \rvert$. Output the minimum value.

Input Format

This problem contains multiple test cases.

The first line contains a positive integer $T$, the number of test cases. For each test case:

• One line containing two integers $a, b$.

Output Format

For each test case:

• Output one integer on a single line, the answer.

5
1 1
3 7
-4 1
-5 -8
4 0

0
3
0
3
0

2
-6 9
34 -51

0
0

Hint

[Sample Explanation #1]

For the 1st test case, one feasible plan is: perform no operations, and $\lvert a-b \rvert=0$.

For the 2nd test case, one feasible plan is: first use operation 2, so $b$ is assigned to $10$; then use operation 1, so $a$ is assigned to $13$. At this time, $\lvert a-b \rvert=3$. It can be proven that this is the minimum value achievable.

For the 3rd test case, one feasible plan is: use operation 1 consecutively $5$ times, and $a$ is assigned to $-3,-2,-1,0,1$ in order. At this time, $a$ and $b$ are equal, so $\lvert a-b \rvert=0$.

For the 4th test case, one feasible plan is: perform no operations, and $\lvert a-b \rvert=3$.

For the 5th test case, one feasible plan is: use operation 2, so $b$ is assigned to $4$. At this time, $\lvert a-b \rvert=0$.

[Sample Explanation #2]

For both test cases in this sample, you can first use operation 2 once, then use operation 1 three times, making the absolute difference $0$.

[Constraints]

• Special Property A: $\lvert a \rvert, \lvert b \rvert \le 10$ is guaranteed.
• Special Property B: $a,b \ge 1$ is guaranteed.

For $100\%$ of the testdata, $1 \le T \le 10^5$, $\lvert a \rvert, \lvert b \rvert \le 10^9$.

Translated by ChatGPT 5