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 sieve(n):
	prime = [-1]*(n+1)
	for i in range(2,n+1):
		if prime[i]==-1:
			for j in range(i,n+1,i):
				prime[j] = i
	return prime


def totient(n):
	m = n
	primes = []
	i = 1
	while n>1 and i<int(n**0.5)+1:
		if n%i==0 and p[i]==i:
			primes.append(i)
			while n%i==0:
				n = n//i
		i += 1
	if n!=1:
		primes.append(n)
	if len(primes)==0:
		return n-1
	ans = m
	for i in primes:
		ans = ans//i
	for i in primes:
		ans = ans*(i-1)
	return ans

	
p = sieve(100000)
for nt in range(int(input())):
	a,m = map(int,input().split())
	g = math.gcd(a,m)
	m1 = m//g
	print (totient(m1))