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 gcd(a,b) :
    if b==0 : return a
    else : return gcd(b,a%b)

def getphi(x) : 
    y,i=1,2
    while i*i<=x :
        if x%i==0 : 
            y*=i-1;x/=i
            while x%i==0 : y*=i;x/=i
        i+=1
    if x>1 : y*=x-1
    return y

T=int(input())
for o in range(T) : 
    a,m=map(int,input().split())
    print('%d'%(getphi(m/gcd(a,m))))