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 *
from math import gcd
from collections import *
def isValid(n):
    if n <= 0: return 0
    if n - int(n) != 0: return 0
    return 1
def mu(n):
    if n == 1:
        return 1
    elif isDivisibleBySquare(n):
        return 0
    else:
        return (-1) ** numberOfFactors(n)
def isDivisibleBySquare(n):
    if n % 2 == 0:
        n = n / 2
    if n % 2 == 0:
        return True
    for i in range(3, int(n ** 0.5) + 1):
        if n % i == 0:
            n //= i
        if n % i == 0:
            return True
    return False
def factorGenerator(n):
    r = []
    while n % 2 == 0:
        n //= 2
        r.append(2)
    i = 3
    while i * i <= n:
        while n % i == 0:
            n //= i
            r.append(i)
        i += 2
    if n != 1:
        r.append(n)
    return r
def numberOfFactors(n):
    return len(factorGenerator(n))
def divisors(n):
    return set(reduce(list.__add__,
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))

def calc(m, n):
    # Calculate number of integers in [1, m] coprime to n
    s = 0
    for d in sorted(list(set(divisors(n)))):
        s += mu(d) * (m // d)
    return s

n = int(input())
for _ in range(n):
    a, m = map(int, input().split())
    g = gcd(a, m)
    # print (calc(a, m))
    print (calc((m + a - 1) // g, m // g) - calc((a - 1) // g, m // g))
    # print (sum(gcd(a, m) == gcd(a + x, m) for x in range(m)))