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 collections import defaultdict
def totient(n):
    primes = defaultdict(int)
    d = 2
    diver = n
    while d * d <= n:
        while diver % d == 0:
            primes[d] += 1
            diver //= d
        d += 1
    if diver != 1:
        primes[diver] += 1
    tot = 1
    for (p, k) in primes.items():
        tot *= (p - 1) * p**(k - 1)
    return tot

def gcd(a, b):
    while a % b != 0:
        a %= b
        a, b = b, a
    return b

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

