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,…,k, the next k−2 people have numbers k−1,k−2,…,2, the next k people have numbers 1,2,3,…,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≤t≤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≤x<n≤109) — 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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