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):
    l=[]
    i=2
    pro=n
    while(i*i<=n):
        if(n%i==0):
            l.append(i)
            while(n%i==0):
                n=n//i
        i+=1
    if(n!=1):
        l.append(n)
    for  i in l:
        pro=(pro//i)*(i-1)
    return pro
def gcd(a,b):
    if(a%b==0):
        return b
    return gcd(b,a%b)
t=int(input())
for you in range(t):
    l=input().split()
    a=int(l[0])
    m=int(l[1])
    k=m//gcd(a,m)
    print(phi(k))
