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 factor(x):
	factors = set()

	f = 2

	while f * f <= x:
		while x % f == 0:
			factors.add(f)
			x //= f

		f += 1

	if x > 1:
		factors.add(x)

	return factors

for _ in range(int(input())):
	a, m = map(int, input().split())

	g = gcd(a, m)

	a //= g
	m //= g

	# now just find such that 0 <= x < m & gcd(a + x, m) = 1
	# how many numbers in [a, a + m) are coprime to m

	f = list(factor(m))

	tot = 0

	for i in range(1, 2 ** len(f)):
		mul = 1

		bc = -1

		for j in range(len(f)):
			if i & (1 << j):
				mul *= f[j]
				bc = -bc

		tot += bc * (m // mul + (a % mul < (a + m - 1) % mul))

	print(m - tot)