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 *
from collections import *
t = int(input())
for y in range(t):
	a,m = map(int,input().split())
	g = gcd(a,m)
	m1 = m//g
	i = 2
	ans = m1
	while(i*i <= m1):
		if(m1%i == 0):
			ans //= i
			ans *= (i-1)
		while(m1%i == 0): m1 //= i
		i += 1
	if(m1 > 1):
		ans //= m1
		ans *= (m1-1)
	print(ans)