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 = int(n / p); 
            result -= int(result / p); 
        p += 1; 
    if (n > 1): 
        result -= int(result / n); 
    return result
from math import gcd 
for _ in range(int(input())):
	n,m=map(int,input().split())
	print(phi(m//gcd(n,m)))