407803: GYM102896 E Easy Measurements

Edward was tasked to measure the pumping rate of two water pumps. To do so, he used the pumps to pump water into a water tank and checked how much water was pumped into the tank in a specific time.

He found out that the first pump pumps $$$a$$$ liters of water in $$$b$$$ seconds, and the second pump pumps $$$c$$$ liters of water in $$$d$$$ seconds. He also discovered that when both pumps are used at the same time, together they pump $$$b$$$ liters of water in $$$d$$$ seconds.

Unfortunately, Edward has spilled some water on his records, so now he can't recover the values $$$a$$$ and $$$c$$$. However, he remembers that these values were positive integers. Now he wonders how many ways are there to choose the values $$$a$$$ and $$$c$$$ that are consistent with his measurements.

The first line contains an integer $$$n$$$ ($$$1\le n\le1000$$$) — the number of test cases.

Each of the next $$$n$$$ lines contains two integers $$$b$$$ and $$$d$$$ ($$$1\le b,d\le10^9$$$).

For each test case, output a single integer — the number of ways to choose $$$a$$$ and $$$c$$$. Output each answer on a separate line.

3
9 6
40 60
60 40

4
13
29

In the first test case, the possible values are $$$a=3$$$, $$$c=7$$$; $$$a=6$$$, $$$c=5$$$; $$$a=9$$$, $$$c=3$$$; and $$$a=12$$$, $$$c=1$$$.