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(x):
    i = 2
    ans = x
    
    while (i * i <= x):
        cnt = 0
        
        while (x % i == 0):
            x //= i
            cnt += 1
            
        if (cnt > 0):
            ans -= ans // i
        
        i += 1
        
    if (x > 1):
        ans -= ans // x
            
    return ans

def solve():
    a, m = map(int, input().split())
    g = math.gcd(a, m)
    ans = 0
    a //= g
    m //= g    
    print(phi(m))

for tt in range(int(input())):
    solve()
