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 sys
from math import gcd
from collections import Counter

reader = (line.rstrip() for line in sys.stdin)
input = reader.__next__
 
t = int(input())
for _ in range(t):
    a, m = map(int, input().split())
    g = gcd(a, m)
    
    m //= g
    
    factorization = Counter()
    while not m & 1:
        factorization[2] += 1
        m >>= 1
    limit = int(m ** 0.5) + 1
    f = 3
    while f < limit and f <= m:
        while m % f == 0:
            factorization[f] += 1
            m //= f
        f += 2
    if m > 1:
        factorization[m] += 1
    
    phi = 1
    for prime, power in factorization.items():
        phi *= (prime - 1) * prime ** (power - 1)
    
    print(phi)
