1295D · Same GCDs

Problem: 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 Format: 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 Format: Print $T$ integers — one per test case. For each test case print the number of appropriate $x$-s.

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 $0$.