You are given two integers a and m. Calculate the number of integers x such that 0 ≤ 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 ≤ T ≤ 50) — the number of test cases.

Next T lines contain test cases — one per line. Each line contains two integers a and m (1 ≤ a < m ≤ 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.
from sys import stdin
from fractions import gcd


def phi(n):
    res, p = n, 2
    while p * p <= n:
        # check p is prime
        if not n % p:
            while not (n % p):
                n //= p
            res -= res // p
        p += 1

    # check other prime
    if n > 1:
        res -= res // n
    return res


rints = lambda: [int(x) for x in stdin.readline().split()]
for _ in range(int(input())):
    a, m = rints()
    g = gcd(a, m)
    a1, m1 = a // g, m // g
    print(phi(m1))
