#define _USE_MATH_DEFINES
#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 = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, 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;

void solve() {
  int n, a, w, k; cin >> n >> a >> w >> k;
  if (k == n) {
    int per = w / n;
    ll ans = -1LL * (per + 1) * (per + 2) / 2;
    if (w % n == 0) {
      if (a < n - 1) {
        if (w == 0) {
          cout << ":(";
        } else {
          cout << min(ans - 1, ans - (per + 1) + a) << '\n';
        }
        return;
      } else {
        a -= n - 1;
      }
    } else {
      int small = w % n;
      if (1LL * small * (per + 1) - 1 <= a) {
        a -= small * (per + 1) - 1;
        ans += per;
      } else if (a < small - 1) {
        cout << min(ans - 1, ans - (per + 2) + a) << '\n';
      } else {
        a -= small - 1;
        int lb = 0, ub = per + 1;
        while (ub - lb > 1) {
          int mid = (lb + ub) >> 1;
          (1LL * mid * small <= a ? lb : ub) = mid;
        }
        cout << ans + lb << '\n';
        return;
      }
    }
    cout << ans + a / n << '\n';
  } else if (a < k - 1) {
    cout << ":(\n";
  } else {
    int lb = 0, ub = a + 1;
    while (ub - lb > 1) {
      int mid = (lb + ub) >> 1;
      (1LL * (mid + 1) * (k - 1) + mid <= a ? lb : ub) = mid;
    }
    cout << lb << '\n';
  }
}

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