C. Physical Education Lesson
brute force; math; number theory
In a well-known school, a physical education lesson took place. As usual, everyone was lined up and asked to settle in ""the first–\(k\)-th"" position.As is known, settling in ""the first–\(k\)-th"" position occurs as follows: the first \(k\) people have numbers \(1, 2, 3, \ldots, k\), the next \(k - 2\) people have numbers \(k - 1, k - 2, \ldots, 2\), the next \(k\) people have numbers \(1, 2, 3, \ldots, k\), and so on. Thus, the settling repeats every \(2k - 2\) positions. Examples of settling are given in the ""Note"" section.The boy Vasya constantly forgets everything. For example, he forgot the number \(k\) described above. But he remembers the position he occupied in the line, as well as the number he received during the settling. Help Vasya understand how many natural numbers \(k\) fit under the given constraints.Note that the settling exists if and only if \(k > 1\). In particular, this means that the settling does not exist for \(k = 1\).
Each test consists of multiple test cases. The first line contains a single integer \(t\) (\(1 \leq t \leq 100\)) — the number of test cases. This is followed by the description of the test cases.The only line of each test case contains two integers \(n\) and \(x\) (\(1 \le x < n \le 10^9\)) — Vasya's position in the line and the number Vasya received during the settling.
For each test case, output a single integer — the number of different \(k\) that fit under the given constraints.It can be proven that under the given constraints, the answer is finite.
In the first test case, \(k\) equals \(2, 3, 5, 6\) are suitable.An example of settling for these \(k\): \(k\) / №\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(2\)\(1\)\(2\)\(1\)\(2\)\(1\)\(2\)\(1\)\(2\)\(1\)\(2\)\(3\)\(1\)\(2\)\(3\)\(2\)\(1\)\(2\)\(3\)\(2\)\(1\)\(2\)\(5\)\(1\)\(2\)\(3\)\(4\)\(5\)\(4\)\(3\)\(2\)\(1\)\(2\)\(6\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(5\)\(4\)\(3\)\(2\) In the second test case, \(k = 2\) is suitable.