Physical Education Lesson
Description
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 $k = 1$.
题面翻译
定义一个 位数列为前 个数是 ，接下来 个数是 ，在接下来 个数是 ，如此循环。
现在你知道这个数列的第 项是 ，求有多少种不同的可能的 。
Input
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.
Output
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.
5
10 2
3 1
76 4
100 99
1000000000 500000000
4
1
9
0
1
Note
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.
相关
在下列比赛中: