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 gcd
from sys import stdout
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
print = stdout.write

primes = []
n = 10**5+1
mark = [True]*(n)
for i in range(2,n):
	if mark[i]:
		primes.append(i)
		for j in range(i, n, i): mark[j] = False

del mark

for _ in range(int(input())):	
	a, m = map(int, input().split())
	m //= gcd(a, m)
	ans = m
	for i in primes:
		if m==1: break
		if m%i == 0:
			ans -= ans//i
			while m%i == 0: m //= i
	else: ans -= ans//m
	print(str(ans) + '\n')