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.
import math
inp=int(input())
def phi(n) : 
  
    result = n   
    p = 2
    while(p * p<= n) : 
  
        # Check if p is a prime factor. 
        if (n % p == 0) : 
  
            # If yes, then update n and result 
            while (n % p == 0) : 
                n = n // p 
            result = result * (1.0 - (1.0 / (float) (p))) 
        p = p + 1
          
          
    # If n has a prime factor 
    # greater than sqrt(n) 
    # (There can be at-most one 
    # such prime factor) 
    if (n > 1) : 
        result = result * (1.0 - (1.0 / (float)(n))) 
   
    return (int)(result) 

def prm(a):
    for i in range(2,int(math.sqrt(a)+1)):
        if a%i==0:
            return False
    return True
for t in range(inp):
    a,m=map(int,input().split())
    #no=1
    d=math.gcd(a,m)
    big=m/d
    print(phi(big))
