题面翻译

定义一个 $k$ 位数列为前 $k$ 个数是 $1,2,3,\ldots,k$，接下来 $k-2$ 个数是 $k-1,k-2,\ldots,2$，在接下来 $k$ 个数是 $1,2,3,\ldots,k$，如此循环。

现在你知道这个数列的第 $n$ 项是 $x$，求有多少种不同的可能的 $k$。

题目描述

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 $k = 1$ .

输入格式

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.

输出格式

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.

样例 #1

样例输入 #1

5
10 2
3 1
76 4
100 99
1000000000 500000000

样例输出 #1

4
1
9
0
1

提示

注

在第一个测试案例中， $k$ 等于 $2, 3, 5, 6$ 是合适的。

为这些 $k$ 定义的示例：

在第二个测试用例中， $k = 2$ 是合适的。