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.
T = int(input())
Ans = []
for i in range(T):
    a, m = map(int, input().split())
    gcd = m
    while a != 0:
        gcd, a = a, gcd % a
    m //= gcd
    temp_1 = m
    temp_2 = 2
    res = m
    while temp_2 * temp_2 <= m:
        if temp_1 % temp_2 == 0:
            res *= (temp_2 - 1)
            res //= temp_2
            while temp_1 % temp_2 == 0:
                temp_1 //= temp_2
        temp_2 += 1
    if temp_1 > 1:
        res *= (temp_1 - 1)
        res //= temp_1
    Ans.append(res)
for k in Ans:
    print(k)