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 math
def phi(n):
	m = n
	factors = set()
	q = 2
	while n>1 and q*q<=n:
		if n % q == 0:
			factors.add(q)
			n //= q
		else:
			q += 1
	if n>1:
		factors.add(n)

	for p in factors:
		m *= p-1
		m //= p

	return m

t = int(input())
for _ in range(t):
	a,b=map(int,input().split())
	g = math.gcd(a,b)
	b//=g
	print(phi(b))