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.
'''

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''' 
def gcd(a,b):
    if a==0:
        return b 
    elif b==0:
        return a 
    return gcd(b,a%b)
def ph(a):
    i=2 
    ans=a
    while(i*i<=a):
        flag=False
        while(a%i)==0:
            a=a//i 
            flag=True
        if flag:
            ans=ans-ans//i 
        i+=1 
    if a>1:
        ans=ans-ans//a 
    return ans
t=int(input())
for _ in range(t):
    a,b=(int(i) for i in input().split())
    print(ph(b//gcd(a,b)))