311059: CF1928C. 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 $k = 1$.
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.
ExampleInput5 10 2 3 1 76 4 100 99 1000000000 500000000Output
4 1 9 0 1Note
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.
Output
输入输出数据格式：
- 输入：第一行是一个整数t，表示测试用例的数量。接下来每行包含两个整数n和x，分别表示Vasya在队伍中的位置和他得到的编号。
- 输出：对于每个测试用例，输出一个整数，表示符合条件的k的数量的个数。
示例输入：
```
5
10 2
3 1
76 4
100 99
1000000000 500000000
```
示例输出：
```
4
1
9
0
1
```
注意：题目中提到k必须大于1，且答案在给定约束下是有限的。题目大意：在体育课上，学生们按照特定的规则排队。每组的第一个人到第k个人分别被编号为1, 2, 3, ..., k，接下来的k-2个人分别被编号为k-1, k-2, ..., 2，然后下一组的k个人再次从1开始编号，如此循环。排队规则每2k-2个位置重复一次。给定一个学生Vasya在队伍中的位置n和他得到的编号x，要求找出所有可能的k的值。 输入输出数据格式： - 输入：第一行是一个整数t，表示测试用例的数量。接下来每行包含两个整数n和x，分别表示Vasya在队伍中的位置和他得到的编号。 - 输出：对于每个测试用例，输出一个整数，表示符合条件的k的数量的个数。 示例输入： ``` 5 10 2 3 1 76 4 100 99 1000000000 500000000 ``` 示例输出： ``` 4 1 9 0 1 ``` 注意：题目中提到k必须大于1，且答案在给定约束下是有限的。