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.
def gcd(a, b):
    if a % b == 0:
        return b
    return gcd(b, a % b)

T = int(raw_input())

def phi(x):
    i = 2
    res = 1
    while i < 123456:
        cnt = 0
        while x % i == 0:
            x /= i
            cnt += 1
        if cnt:
            res *= (i ** (cnt - 1)) * (i - 1)
        if i == 2:
            i += 1
        else:
            i += 2
    if x > 1:
        res *= x - 1
    return res

def solve(a, b):
    g = gcd(a, b)
    a = a / g
    b = b / g
    p = phi(b)
    return p

def brute_force(a, b):
    g = gcd(a, b)
    cnt = 0
    for i in xrange(b):
        if gcd(a + i, b) == g:
            cnt += 1
    return cnt

'''
from random import randint

for i in xrange(10000):
    a, b = randint(1, 10 ** 3), randint(1, 10 ** 3)
    assert solve(a, b) == brute_force(a, b)
'''

for case_ in xrange(T):
    (a, b) = map(int, raw_input().split())
    print solve(a, b)

