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 math import gcd

def phi(n):
    m = n
    factors = set()
    q = 2

    while n > 1 and q * q <= n:
        if n % q == 0:
            factors.add(q)
            n //= q
        else:
            q += 1
    if n > 1:
        factors.add(n)

    for p in factors:
        m *= p - 1
        m //= p
    return m

for _ in range(int(input())):
    a, m = map(int, input().split())
    m //= gcd(a, m)
    print(phi(m))
