#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

long long mod_inv(long long a, const int m) {
  if ((a %= m) < 0) a += m;
  if (std::gcd(a, m) != 1) return -1;
  long long x = 1;
  for (long long b = m, u = 0; b > 0;) {
    const long long q = a / b;
    std::swap(a -= q * b, b);
    std::swap(x -= q * u, u);
  }
  x %= m;
  return x < 0 ? x + m : x;
}

void solve() {
  ll m; int a, b, k; cin >> m >> a >> b >> k;
  m = max(m / a * a, m / b * b);
  const int g = gcd(a, b);
  if (k > a || k % g > 0) {
    cout << 0 << '\n';
    return;
  }
  m /= g; a /= g; b /= g; k /= g;
  if (a == 1) {
    cout << (k == 1 ? m - 1 : 0) << '\n';
  } else if (k == a) {
    if (m % a > 0) m = m / a * a;
    cout << m / a - 1 - (m / b - m / lcm<ll>(a, b)) << '\n';
  } else {
    ll ans = 0;
    {
      const int md = 1LL * k * mod_inv(b, a) % a;
      const ll r = m / b;
      if (md <= r) ans += (r - md) / a + 1;
    }
    {
      const int md = 1LL * k * mod_inv(a, b) % b;
      const ll r = m / a;
      if (md <= r) ans += (r - md) / b + 1;
    }
    cout << ans << '\n';
  }
}

int main() {
  int t; cin >> t;
  while (t--) solve();
  return 0;
}