#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef long double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acosl(-1.0); ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 2; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } void solve() { ll n, a, w, k; cin >> n >> a >> w >> k; k--; if (k == 0) { cout << a << "\n"; return; } else if (k == n - 1) { if (w == 0) { if (a < k) { cout << ":(\n"; return; } else { ll ans = (a - k) / (k + 1); cout << ans << "\n"; return; } } else { ll le = -1, ri = w + 1; while (ri - le > 1) { ll x = (le + ri) / 2; ll s = x * (x + 1) / 2; ll rest = a; ll dd = (w - x) / k; ll r = (w - x) % k; if (dd * (dd + 1) / 2 >= s) { ll val = dd * (dd + 1) / 2-s+1; rest -= val * (k - r); } if ((dd + 1) * (dd + 2) / 2 >= s) { ll val = (dd + 1) * (dd + 2) / 2 - s + 1; rest -= val * r; } if (rest < 0) { le = x; } else { ri = x; } } ll x = ri; ll s = x * (x + 1) / 2; ll rest = a; ll dd = (w - x) / k; ll r = (w - x) % k; if (dd * (dd + 1) / 2 >= s) { ll val = dd * (dd + 1) / 2 - s + 1; rest -= val * (k - r); } if ((dd + 1) * (dd + 2) / 2 >= s) { ll val = (dd + 1) * (dd + 2) / 2 - s + 1; rest -= val * r; } ll val1 = dd * (dd + 1) / 2; if (val1 >= s)val1 = s - 1; ll val2 = (dd + 1) * (dd + 2) / 2; if (val2 >= s)val2 = s - 1; ll ans = s; ll dif = s-val2-1; ll m = min(dif, rest); ans += m; rest -= m; dif = val2 - val1; m = min(dif, rest / (r + 1)); ans += m; rest -= m*(r+1); ans += rest / n; cout << ans << "\n"; } } else { if (a >= k) { ll ans = (a - k) / (k + 1); cout << ans << "\n"; return; } else { if (w >= n - k) { cout << -1 << "\n"; return; } else { cout << ":(\n"; return; } } } } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); //init_f(); //init(); //expr(); int t; cin >> t; rep(i, t) solve(); return 0; }