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.
t=int(input())

def gcd(a,b):
    while b!=0:
        a,b=b,a%b
    return a

def euler(m):
    x=2
    res=1
    mi=m
    while x*x<=mi:
        cnt=0
        while mi%x==0:
            mi=mi//x
            cnt+=1
        if cnt>0:
            res = res * (x**cnt -x**(cnt-1))
        x+=1
    if mi==1:
        return res
    return res * (mi -1)

def total(a,m):
    d=gcd(a,m)
    if d==1:
        ## we do what?? Idk lol
        ## x such that a+x et m sont premiers entre eux 
        ## nice : if we solve it for d=1, then we are done
        ## so its the number of numbers between a and a+m-1 that are coprime with m
        ## so it's phi(m)
        return(euler(m))
    if d>1:
        return(total(a//d,m//d))
    
    
for _ in range(t):
    a,m=list(map(int,input().split()))
    ##number of x such that gcd(a,m) = gcd(a+x,m)
    print(total(a,m))
