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):
    if a == 0:
        return b
    if b == 0:
        return a
    return gcd(b, a % b)

def getPrimeFactors(n):
    factorSet = set()

    factor = 2
    while factor * factor <= n:
        while n % factor == 0:
            factorSet.add(factor)
            n //= factor
        
        factor += 1
    
    if n > 1:
        factorSet.add(n)
    
    return factorSet

def calculateTotient(n):
    for p in getPrimeFactors(n):
        n *= (p - 1)
        n //= p

    return n

n = int(input())
for _ in range(n):
    a, m = [int(i) for i in input().split()]
    print(calculateTotient(m // gcd(a, m)))