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 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))) 
   
    return (int)(result) 
      



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

t = int(input())
for T in range(t):
    a, m = [int(x) for x in input().split()]
    g = gcd(a, m)
    count = 0

    count = phi(m // g)
##    if g > 1:
##        count = m // g - 1
##    
##    else:
##        count = phi(m)
##
##    if count == 0:
##        count += 1
    print(count)
