Codeforces Round 924 (Div. 2) |
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Finished |
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.
510 23 176 4100 991000000000 500000000
4 1 9 0 1
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.
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