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

MX = 100000

prime = [2]
def sieve():
    mark = [True for i in range(MX)]
    for i in range(3,MX,2):
        if (mark[i]):
            prime.append(i)
            for j in range(i*i,MX,i):
                mark[j] = False

def phi(N):
    ph = N
    for p in prime:
        if (N%p == 0):
            ph //= p
            ph *= p-1
            while (N%p == 0):
                N //= p
    if (N > 1):
        ph //= N
        ph *= N-1
    return ph
        
sieve()
T = int(input())
for cs in range(T):
    a, m = map(int,input().split())
    print(phi(m//gcd(a,m)))
