A11335. 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 $k > 1$ . 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.