#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, x, n) for (int i = x; i <= n; i++)
#define rep3(i, x, n) for (int i = x; i >= n; i--)
#define each(e, v) for (auto &e : v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
const int MOD = 1000000007;
// const int MOD = 998244353;

int main() {
    int T;
    cin >> T;

    while (T--) {
        ll N, A, W, K;
        cin >> N >> A >> W >> K;

        if (K <= N - 1) {
            if (A >= K - 1) {
                cout << (A + 1) / K - 1 << '\n';
                continue;
            } else {
                if (W <= N - K) {
                    cout << ":(\n";
                    continue;
                } else {
                    cout << "-1\n";
                }
            }
        } else {
            ll ans = INF;
            if (W > 0) {
                ll X = (W - 1) / N, Y = (W + N - 2) / N;
                ll L = (W - 1) % N;
                if (L == 0) L = N;
                ll Z = Y + 1;
                X = X * (X + 1) / 2, Y = Y * (Y + 1) / 2, Z = Z * (Z + 1) / 2;
                ll D1 = Z - Y, D2 = Y - X;
                if (A < D1 - 1) {
                    chmin(ans, Z - A);
                } else {
                    ll B = A - (D1 - 1);
                    if (B < D2 * L) {
                        chmin(ans, Y + 1 - B / L);
                    } else {
                        ll C = B - D2 * L;
                        chmin(ans, X + 1 - C / N);
                    }
                }
            }
            {
                ll X = W / N, Y = (W + N - 1) / N;
                X = X * (X + 1) / 2, Y = Y * (Y + 1) / 2;
                ll L = W % N;
                if (L == 0) L = N;
                ll D = Y - X;
                if (A >= L - 1) {
                    ll B = A - (L - 1);
                    if (B < (D - 1) * L) {
                        chmin(ans, Y - B / L);
                    } else {
                        ll C = B - (D - 1) * L;
                        chmin(ans, X + 1 - C / N);
                    }
                }
            }
            if (ans == INF) {
                cout << ":(\n";
            } else {
                cout << -ans << '\n';
            }
        }
    }
}