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,b):
    while a != 0:
        a,b = b % a,a
    return b

def phi(a):
    tmp,ans = a,a
    d = 2
    while d*d <= tmp:
        cnt = 0
        while tmp % d == 0:
            tmp /= d
            cnt += 1
        if cnt > 0:
            ans -= ans/d
        d += 1
    if tmp > 1:
        ans -= ans/tmp
    return int(ans)

for t in range(int(input())):
    a,m = map(int,input().split(" "))
    print(phi(m / gcd(a,m)))


    