import math

def f(m, a, c):
  if c == 0:
    return max(0, m // a)
  else:
    return max(0, (m + a - c) // a)

def ext_gcd(a, b):
  if b == 1:
    return 0, 1
  q, r = divmod(b, a)
  y, z = ext_gcd(r, a)
  x = z - q * y
  return x, y

def inv_mod(a, m):
  return ext_gcd(a, m)[0] % m

def crt(x1, x2, m1, m2):
  k = (x2 - x1) * inv_mod(m1, m2)
  return (x1 + k * m1) % (m1 * m2)

def solve(m, a, b, k):
  g = math.gcd(a, b)
  if k % g != 0:
    return 0
  m, a, b, k = m // g, a // g, b // g, k // g

  if k > a:
    return 0
  elif k == a:
    cnt_a, cnt_b, cnt_ab = f(m, a, 0), f(m, b, 0), f(m, a * b, 0)
    n = cnt_a + cnt_b - cnt_ab
    cnt_nota = cnt_b - cnt_ab
    x_n = max(m // a * a, m // b * b)
    if x_n % a == 0:
      return (n - 1) - (2 * cnt_nota)
    else:
      return (n - 1) - (2 * cnt_nota - 1)
  else:
    y, z = crt(0, -k, a, b), crt(-k, 0, a, b)
    return f(m - k, a * b, y) + f(m - k, a * b, z)

t = int(input())
for _ in range(t):
  m, a, b, k = map(int, input().split())
  print(solve(m, a, b, k))