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 Input():
    ans = []
    tem = input().split()
    for it in tem:
        ans.append(int(it))
    return ans
def gcd(x, y):
    if x%y==0:
        return y
    else:
        return gcd(y, x%y)
def eular(x):
    ans = x
    i = 2
    while i*i<=x:
        if x%i==0:
            ans-=(ans//i)
            while x%i==0:
                x=x//i
        i+=1
    if x>1:
        ans-=(ans//x)
    return ans
T = Input()[0]
for tt in range(T):
    n, m = Input()
    yue = gcd(n,m)
    n_, m_ = n//yue, m//yue
    print(eular(m_))
    