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
t = int(input())
 
def phi(n):
	res = n
	i = 2
	while i*i<=n:
		if n%i==0:
			res/=i
			res*=(i-1)
 
			while n%i==0:
				n/=i
		i+=1
	
	if n>1:
		res/=n
		res*=(n-1)
 
	return int(res)
 
while t:
	a,m = list(map(int,input().split()))
	g = math.gcd(a,m)
	print(phi(m//g))
	t-=1