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.
from math import sqrt,gcd
def factors(x):
	t=sqrt(x)
	s=set()
	i=2
	while x>1 and i<=t:
		if x%i==0:
			s.add(i)
			x=x//i
		else:
			i+=1
	if x>1:
		s.add(x)
	return list(s)

for _ in range(int(input())):
	a,b=map(int,input().split())
	b=b//gcd(a,b)
	l=factors(b)
	# print(b)
	# print(l)
	for i in l:
		b=b*(i-1)
		# print(b)
		b=b//i
		# print(b)
	print(b)
