CF1928C.Physical Education Lesson

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 $k \gt 1$. In particular, this means that the settling does not exist for $k = 1$.

在一所有名的学校里，进行了一节体育课。和往常一样，所有人排成一列，并被要求按“第1–$k$号”方式站位。

众所周知，“第1–$k$号”站位规则如下：前 $k$ 个人编号分别为 $1, 2, 3, \ldots, k$；接下来的 $k - 2$ 个人编号分别为 $k - 1, k - 2, \ldots, 2$；再接下来的 $k$ 个人编号又为 $1, 2, 3, \ldots, k$；依此类推。因此，整个编号模式每 $2k - 2$ 个位置重复一次。站位方式的具体示例见“注”部分。

男孩瓦夏总是忘事。例如，他就忘了上述的数 $k$。但他记得自己在队列中的位置，以及站位时所分配到的编号。请帮助瓦夏确定：有多少个正整数 $k$ 满足给定的约束条件。

注意：“第1–$k$号”站位方式仅当 $k > 1$ 时存在。特别地，这意味着当 $k = 1$ 时该站位方式不存在。

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 $x$ ($1 \le x \lt n \le 10^9$) — Vasya's position in the line and the number Vasya received during the settling.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 100$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例仅有一行，包含两个整数 $n$ 和 $x$（$1 \le x \lt n \le 10^9$），分别表示瓦西娅在队列中的位置以及他在分配过程中得到的编号。

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.

对于每个测试用例，输出一个整数——满足给定约束条件的不同 $k$ 的个数。

可以证明，在给定约束条件下，答案是有限的。

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.

在第一个测试用例中，$k = 2, 3, 5, 6$ 是合适的。

这些 $k$ 值对应的示例方案如下：

$k$ / 编号

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$2$

$1$

$2$

$1$

$2$

$1$

$2$

$1$

$2$

$1$

$2$

$3$

$1$

$2$

$3$

$2$

$1$

$2$

$3$

$2$

$1$

$2$

$5$

$1$

$2$

$3$

$4$

$5$

$4$

$3$

$2$

$1$

$2$

$6$

$1$

$2$

$3$

$4$

$5$

$6$

$5$

$4$

$3$

$2$

在第二个测试用例中，$k = 2$ 是合适的。