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.
import sys
range = xrange
input = raw_input

def gcd(a,b):
    while a:
        a,b = b%a, a
    return b

t = int(input())
for _ in range(t):
    a,m = [int(x) for x in input().split()]

    g = gcd(a,m)
    a //= g
    m //= g

    prodder = m
    p = 2
    while p * p <= m:
        if m % p == 0:
            prodder -= prodder//p
            while m % p == 0:
                m //= p
        p += 1
    if m > 1:
        prodder -= prodder//m

    print prodder
