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

q = int(input())
for j in range(q):
    a, m = map(int, input().split())
    g = gcd(a, m)
    a //= g
    m //= g
    ans = m
    i = 2
    while i * i <= m:
        if (m % i == 0):
            while (m % i == 0):
                m //= i
            ans -= ans // i
        i += 1
    if m > 1:
        ans -= ans // m
    print(ans)

#gcd(a + x, m) = gcd(m, (a + x) % m)

# (a, m) = (a % m, m)
# (a % m, m) = (a % m, m
