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.
'''input
1
37 102
'''
import math
def totient(x):
	i=2
	ans = x
	while i*i<=x:
		if x%i==0:
			ans = (ans*(i-1))//i
			while x%i==0:
				x//=i
		i+=1
	if x>1:
		ans = (ans*(x-1))//x
	return ans
def solve():
	a,m = map(int,input().split())
	g = math.gcd(a,m)
	m//=g
	print(totient(m))
	return 
t = 1
t = int(input())
while t>0:
	t-=1
	solve()