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(a, b):
	while(b != 0):
		c = a % b
		a = b
		b = c
	return a

def totient(n):
	i = 2
	ret = n
	while i * i <= n:
		if (n % i) == 0:
			while (n % i) == 0:
				n //= i
			ret = ret * (i - 1) // i
		i += 1
	if n > 1:
		ret = ret * (n - 1) // n
	return ret

tc = int(input())
for _ in range(tc):
	a, m = map(int, input().split())
	d = gcd(a, m)
	v = m // d
	ans = totient(v)
	print(ans)