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.
from math import gcd


def solve(n):
    ans = n
    i = 2
    while i ** 2 <= n:
        if not n % i:
            while not n % i:
                n //= i
            ans -= ans // i
        i += 1
    if n > 1:
        ans -= ans // n
    return ans


def main():
    for _ in range(int(input())):
        a, m = map(int, input().split())
        a = gcd(a, m)
        n = m // gcd(a, m)
        print(solve(m // gcd(a, m)))


main()
