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):
	while(y):
		x,y=y,x%y
	return x


def totient(x):
	tot=x
	n=x
	i=1
	prime_factors=[]
	q=2
	while n>1 and q*q<=n:
		if n%q==0:
			prime_factors.append(q)
			while(n%q==0):
				n//=q
			
		q+=1
	
	if n>1:
		prime_factors.append(n)

	for p in prime_factors:
		tot=(tot/p)*(p-1)
	
	return int(tot)


for _ in range(int(input())):
	a,m=map(int,input().split())
	g=gcd(m,a)
	ans=0
	count=0
	prime_factors=[]

	m1=(m)//g

	ans=totient(m1)

	

	print(ans)
			
