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 math
t = int(input())
def gcd(a,b):
    mn = min(a,b)
    mx = max(a,b)
    if mx%mn == 0:
        return mn
    else:
        return gcd(mx%mn,mn)
for i in range(t):
    a,m = map(int, input().strip().split())
    g = gcd(a,m)
    m = m/g
    n = m
    primeFactors = {}
    if m == 1:
       print(1)
    else:
        highest = math.floor(math.sqrt(m))
        for i in range(2,highest+1):
            while m%i == 0:
                primeFactors[i] = True
                m = m/i
        if m != 1:
            primeFactors[m] = True
        for key in primeFactors.keys():
            n = n*(key-1)/key
        if len(primeFactors.keys()) == 0:
            print(int(n-1))
        else:
            print(int(n))