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
import sys


def input():
    return sys.stdin.readline().rstrip()


def totient_phi(M):
    ans = M
    V = M
    for i in range(2, M + 1):
        if i * i > M:
            break
        if V % i == 0:
            while V % i == 0:
                V //= i
            ans = ans * (i - 1) // i
    if V > 1:
        ans = ans * (V - 1) // V
    return ans


def slv():
    a, m = map(int, input().split())
    g = gcd(a, m)
    m //= g
    ans = totient_phi(m)
    print(ans)
    return


def main():
    t = int(input())
    for i in range(t):
        slv()
    return


if __name__ == "__main__":
    main()
