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
for _ in range(int(input())):
    x = input().split(' ')
    a = int(x[0])
    m = int(x[1])
    val = gcd(a,m)
    n = m // val
    result = n
    p = 2
    while p*p <= n:
        if n % p == 0:
            while n % p == 0:
                n = n // p
            result = result - int(result/p)
        p = p + 1
    if n > 1:
        result = result - int(result/n)
    print(result)