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.
def R(): return map(int, input().split())
def I(): return int(input())
def S(): return str(input())

def L(): return list(R())

from collections import Counter 

import math
import sys

def check(t):
    return [True,False][any(t[i]<t[i+1] for i in range(1,len(t)-1))]

from itertools import permutations

def psi(n):

    n2=n
    factors=[]
    i=1
    while i*i<=n:
        i+=1
        if n%i==0:
            factors.append(i)

            while n%i==0:
                n//=i

    if n>1:
        factors.append(n)

    for p in factors:
        n2*=p-1
        n2//=p

    return n2


for _ in range(I()):
    a,m=R()
    m//=math.gcd(a,m)
    print(psi(m))

