#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
using namespace atcoder;
#define rep(i,n)for (int i = 0; i < int(n); ++i)
#define rrep(i,n)for (int i = int(n)-1; i >= 0; --i)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
template<class T> void chmax(T& a, const T& b) {a = max(a, b);}
template<class T> void chmin(T& a, const T& b) {a = min(a, b);}
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int tt;
    cin >> tt;
    while(tt--) {
        int n, a, w, k;
        cin >> n >> a >> w >> k;
        k--;
        if (k < n - 1) {
            int c = a / (k + 1);
            if (a % (k + 1) == k) {
                cout << c << '\n';
            } else {
                if (c || w) {
                    cout << c - 1 << '\n';
                } else {
                    cout << ":(\n";
                }
            }
            continue;
        }
        if (w == 0 && a < n - 1) {
            cout << ":(\n";
            continue;
        }
        int q = w / n, r = w % n;
        if (r) {
            if (a < r - 1) {
                if (r == 2) {
                    cout << -ll(q + 2) * (q + 3) / 2 + min(q + 2 + q + 1 - 1, a) << '\n';
                } else {
                    cout << -ll(q + 2) * (q + 3) / 2 + min(q + 2 - 1, a) << '\n';
                }
                continue;
            }
            a -= r - 1;
            if (a < ll(q) * r) {
                int t = r / a;
                cout << -ll(q + 1) * (q + 2) / 2 + t << '\n';
                continue;
            }
            a -= ll(q * r);
            int t = a / n;
            cout << -ll(q) * (q + 1) / 2 - 1 + t << '\n';
            continue;
        }
        if (a < n - 1) {
            // q != 0
            if (n == 2) {
                cout << -ll(q + 1) * (q + 2) / 2 + min(q + 1 + q - 1, a) << '\n';
            } else {
                cout << -ll(q + 1) * (q + 2) / 2 + min(q + 1 - 1, a) << '\n';
            }
            continue;
        }
        a -= n - 1;
        int t = a / n;
        cout << -ll(q) * (q + 1) / 2 + t << '\n';
    }
}