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.
t = input()

def phi(v):
	res = v
	i  = 2
	while i*i <= v:
		if v%i == 0:
			res = res/i*(i-1)
		while v%i == 0:
			v /= i
		i += 1
	if v>1:
		res = res/v*(v-1)
	return res
def gcd(a,b):
	if a%b == 0:
		return b
	return gcd(b,a%b)

for _ in range(t):
	a,m = map(int,raw_input().split(" "))
	g = gcd(a,m)
	print phi(m/g)