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

def phi (n):
    l=[]
    p=[0]*40
    j=0
    i=2
    copy=n
    flag=1
    while(n!=1):
        if (i*i>n and flag==1):
            l.append(n)
            p[len(l)-1]=1
            n=1
            #print (copy,"fuck")
            break
        if (n%i==0):
            if flag ==1:
                l.append(i)
                flag=0
            n=n//i
            p[len(l)-1]+=1
        else:
            flag=1
            i+=1
    ans=1
    for i in range(len(l)):
        ans=ans*(l[i]-1)*((l[i])**(p[i]-1))
    return ans
n=int(input())
for i in range(n):
    a,m=input().split()
    a=int(a)
    m=int(m)
    d=gcd(a,m)
    #print (m//d)
    print(phi(m//d))
