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 mcd(a,b):
    while(b != 0):
        c = a % b
        a = b
        b = c
    return a

def primeFactors(n):
    factores=[]
    if  n%2==0:
        exp=0
        while n%2 ==0:
            exp+=1
            n//=2
        factores.append((2,exp))
    i=3
    while(i*i<=n):
        if(n%i==0):
            exp=0
            while n%i ==0:
                exp+=1
                n//=i
            factores.append((i,exp))    
        i+=2 
    if n > 2:
        factores.append((n,1))
    return factores
def Phi(n):
    phi=1
    for fact in primeFactors(n):
        phi*=(fact[0]**(fact[1]-1))*(fact[0]-1)
    return phi

for _ in range(int(input())):
    a,m = map(int,input().split())
    print(Phi(m//(mcd(a,m))))