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 math import gcd

def Fenjie(n):
    k = {}
    if (n == 1):
        return {}
    a = 2
    while (n >= 2):
        if (a*a > n):
            if (n in k):
                k[n] += 1
            else:
                k[n] = 1
            break
        b = n%a
        if (b == 0):
            if (a in k):
                k[a] += 1
            else:
                k[a] = 1
            n = n//a
        else:
            a += 1
    return k

def Euler(n):
    if (n == 1):
        return 1
    k = Fenjie(n)
    m = n
    for i in k:
        m = m // i * (i-1)
    return m

t = int(input())
for _ in range(t):
    a, b = map(int, input().split())
    b = b//gcd(a,b)
    print(Euler(b))
    