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.
primes=[True]*1000001
primes[0]=False
primes[1]=False
for i in range(2, 100001):
    if primes[i]:
        for j in range(i*2, 100001, i):
            primes[j]=False
pL=[]
for i in range(2, 100001):
    if primes[i]:pL.append(i)
def fact(n):
    L=[]
    for i in pL:
        if n%i==0:
            while n%i==0:
                L.append(i)
                n//=i
    if n!=1:L.append(n)
    return L
def gcd(a,b):
    while b:
        a,b=b,a%b
    return a
for i in ' '*int(input()):
    a,m=map(int,input().split())
    g=gcd(a,m)
    aa=a//g
    mm=m//g
    L=fact(mm)
    M=[]
    for i in L:
        if i not in M:M.append(i)
    for i in M:
        mm*=(i-1)
        mm//=i
    print(mm)