C. Physical Education Lessontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIn 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.InputEach 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.OutputFor 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.ExampleInput
510 23 176 4100 991000000000 500000000Output
4
1
9
0
1
NoteIn the first test case, k equals 2, 3, 5, 6 are suitable.An example of settling for these k:  k / №1234567891021212121212312321232125123454321261234565432  In the second test case, k = 2 is suitable.
510 23 176 4100 991000000000 500000000
4 1 9 0 1 
['brute force', 'math', 'number theory', '*1600']