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C. Physical Education Lesson
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$k = 1$$$.

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.

Example
Input
5
10 2
3 1
76 4
100 99
1000000000 500000000
Output
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.