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
def phi(n): 
      
    # Initialize result as n 
    result = n;  
  
    # Consider all prime factors 
    # of n and subtract their 
    # multiples from result 
    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 = int(n / p); 
            result -= int(result / 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 -= int(result / n); 
    return result; 
for _ in range(int(input())):
    n,m=map(int,input().split())
    print(phi(m//math.gcd(n,m)))