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 gcdcalc(a,m):
    if m%a==0:
        return a
    return gcdcalc(m%a,a)
def gcdnumber(m):
    temp=m
    ans=m
    d=2
    cnt=0
    while d*d<=temp:
        if temp%d==0:
            ans=ans-ans//d
            while temp%d==0:
                temp=temp//d
            cnt=1
        d+=1
    if temp>0 and temp!=1:
        ans=ans-ans//temp
    return ans
if __name__=='__main__':
    t=int(input())
    l=[]
    for i in range(t):
        a,m=map(int,input().strip().split())
        gcd=gcdcalc(a,m)
        ans=gcdnumber(m//gcd)
        l.append(ans)
    for i in l:
        print(i)
