Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.
You are given two integers $$$a$$$ and $$$m$$$. Calculate the number of integers $$$x$$$ such that $$$0 \le x < m$$$ and $$$\gcd(a, m) = \gcd(a + x, m)$$$.
Note: $$$\gcd(a, b)$$$ is the greatest common divisor of $$$a$$$ and $$$b$$$.
Input
The first line contains the single integer $$$T$$$ ($$$1 \le T \le 50$$$) — the number of test cases.
Next $$$T$$$ lines contain test cases — one per line. Each line contains two integers $$$a$$$ and $$$m$$$ ($$$1 \le a < m \le 10^{10}$$$).
Output
Print $$$T$$$ integers — one per test case. For each test case print the number of appropriate $$$x$$$-s.
Example
Input
3
4 9
5 10
42 9999999967
Output
6
1
9999999966
Note
In the first test case appropriate $$$x$$$-s are $$$[0, 1, 3, 4, 6, 7]$$$.
In the second test case the only appropriate $$$x$$$ is $$$0$$$.