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(x, y):
    while y != 0:
        (x, y) = (y, x % y)
    return x
 
def phi(n) : 
    result = n
    p = 2
    while p * p<= n : 
        if n % p == 0 : 
            while n % p == 0 : 
                n = n // p 
            result = result * (1.0 - (1.0 / float(p))) 
        p = p + 1
    if n > 1 : 
        result = result * (1.0 - (1.0 / float(n))) 
    result+=0.1 #to account for rounding errors
    return int(result) 
 
def solve(a,m):
    g=gcd(a,m)
    mPrime=m//g
    return phi(mPrime)
 
t=int(input())
for _ in range(t):
    a,m=[int(x) for x in input().split()]
    print(solve(a,m))