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 $$$k = 1$$$.

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 $$$x$$$ ($$$1 \le x \lt n \le 10^9$$$) — 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.

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.

Idx	Name	Rating
A	Rectangle Cutting	800
B	Equalize	1200
C	Physical Education Lesson	1600
D	Lonely Mountain Dungeons	1900
E	Modular Sequence	2300
F	Digital Patterns	2900

Codeforces Round 924 (Div. 2)