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.
def GCD(a, b):
    while b:
        a, b = b, a % b
    return a

def factors(n):
    p = 2
    while p * p <= n:
        if n % p == 0:
            while n % p == 0:
                n //= p
            yield p
        else:
            p += 1
    if n > 1:
        yield n

def phi(n):
    result = n
    for p in factors(n):
        result *= (p - 1)
        result //= p
    return result

def solve(a, m):
    return phi(m // GCD(a, m))

if __name__ == '__main__':
    T = int(input())
    for i in range(T):
        print(solve(*map(int, input().split())))
