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.
def gcd(x, y):
	if y == 0:
		return x
	return gcd(y, x % y)

for testcase in range(int(input())):
	a, m = list(int(x) for x in input().split(' '))
	m = m // gcd(a, m)
	res = m
	if m % 2 == 0:
		res //= 2
	while m % 2 == 0:
		m //= 2
	i = 3
	while i * i <= m:
		if m % i == 0:
			while m % i == 0:
				m //= i
			res = res // i * (i - 1)
		i += 2
	if m != 1:
		res = res // m * (m - 1)
	print(res)