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 itertools import combinations

# inf = open('input.txt', 'r')
# reader = (line.rstrip() for line in inf)
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)
    
    opt = m // g
    a //= g
    m //= g
    
    ps = []
    if not m & 1:
        ps.append(2)
        while not m & 1:
            m >>= 1
    limit = int(m ** 0.5) + 1
    f = 3
    while f < limit and f <= m:
        if m % f == 0:
            ps.append(f)
            while m % f == 0:
                m //= f
        f += 2
    if m > 1:
        ps.append(m)
    
    ctr = 0
    for w in range(1, len(ps)+1):
        for fs in combinations(ps, w):
            prod = 1
            for f in fs:
                prod *= f
            add = (a + opt - 1) // prod - (a - 1) // prod
            if w & 1:
                ctr += add
            else:
                ctr -= add
    print(opt - ctr)

# inf.close()
