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 functools import reduce
from itertools import combinations
from operator import mul


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


def primes(n):
    p = []
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            p.append(i)
            while n % i == 0:
                n = n // i
        if i > n:
            break
    if n>1:
        p.append(n)
    return p


def copr(n, k, p=None):
    if p is None:
        p = primes(n)
    res = 0
    for c in range(1, len(p) + 1):
        sig = 1 if c % 2 else -1
        for v in combinations(p, c):
            res += sig * (k // reduce(mul, v))
    return k-res


def go():
    a, m = map(int, input().split())
    g = gcd(a, m)
    a = a // g
    m = m // g
    p = primes(m)
    return copr(m,m,p) #-copr(m,a,p)


T = int(input())
for _ in range(T):
    print(go())

#
# for a,b in ((10,5), (5,10), (72,71), (72,12), (72,64)):
#     print (a,b,gcd(a,b))

# print(primes(10 ** 10 - 2))
# print ('----')
# print (copr(10,2))