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 main():
    import sys
    from math import gcd, sqrt
    input = sys.stdin.readline

    def f(n, d):
        return n // d

    def prime(n):
        ret = {}
        for d in range(2, int(sqrt(n))+1):
            while n % d == 0:
                ret[d] = 1
                n //= d
        if n > 1:
            ret[n] = 1
        return ret

    for _ in range(int(input())):
        a, m = map(int, input().split())
        k = gcd(a, m)
        p = a // k
        q = m // k
        ans = q
        pr = list(prime(q))
        np = len(pr)
        for i in range(1, 1<<np):
            sign = 0
            d = 1
            for j in range(np):
                if i >> j & 1:
                    sign ^= 1
                    d *= pr[j]
            sign = (-1)**sign
            ans += (f(p+q-1, d) - f(p-1, d))*sign
        print(ans)


if __name__ == '__main__':
    main()
