TG J stress 3

#include <iostream>
#include <cmath>
#include <vector>
#include <queue>
#include <algorithm>
#include <string>
#include <stack>
#include <set>
#include <map>
#define pii pair <int, int>
#define pb(x) push_back(x)
#include <ctime>
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
void cv(vector <int> &v) {
    for (auto x : v) cout << x << ' ';
    cout << "\n";
}

void cvl(vector <ll> &v) {
    for (auto x : v) cout << x << ' ';
    cout << "\n";
}


void cvv(vector <vector <int> > &v) {
    for (auto x : v) cv(x);
    cout << "\n";
}

void cvb(vector <bool> v) {
    for (bool x : v) cout << x << ' ';
    cout << "\n";
}

void cvs(vector <string>  v) {
    for (auto a : v) {
        cout << a << "\n";
    }
}

void cvp(vector <pii> a) {
    for (auto p : a) {
        cout << p.first << ' ' << p.second << "\n";
    }
    cout << "\n";
}

ll a, b, c, d;
bool sh = 0;

ll S(ll a1, ll d, ll n) {
    return (2 * a1 + d * (n - 1)) * n / 2;
}

ll f(ll t) {
    ll res = 1 + (t - 1)  / d;
    if (sh) {
        //cout << "f(" << t << ") = " << res << "\n";
    }
    return res;
}

bool rand_mode = 1;

ll hp(ll t) {
    ll res;
    if (t < 1 + d) {
        res = -a + (t - 1) * b;
        return res;
    }
    ll ft = f(t);
    ll most = ft * (b * c - a);
    ll del;
    ll l, r, m, lid, lend; //look for lid
    ll id = (t - 1) / d + 1;
    l = 0;
    r = id;
    while (l + 1 < r) {
        m = (l + r) / 2;
        if (1 + (m - 1) * d + c > t) {
            r = m;
        } else {
            l = m;
        }
    }
    lid = r;
    /*for (int i = 0; i < 10; ++i) {
        if (1 + i * d + c > t) {
            lid = i;
            break;
        }
    }*/

    //lend = 1 + lid * d + c;
    lend = 1 + (lid - 1) * d + c;

    ll nmb = id - (lid - 1);
    ll start = (lend - t) * nmb * b;
    ll a1 = d * b * (nmb - 1);
    ll step = -d * b;
    del = start + S(a1, step, nmb - 1);
    if (nmb - 1 <= 0) {
        del = 0;
    }
    vector <ll> v = {ft, most, del, id, lid, lend, nmb, start, a1, -step};
    if (rand_mode) {
        cout << "ft = " << ft << "\n";
        cout << "most = " << most << "\n";
        cout << "del = " << del << "\n";
        cout << "id = " << id << "\n";
        cout << "lid = " << lid << "\n";
        cout << "lend = " << lend << "\n";
        cout << "nmb = " << nmb << "\n";
        cout << "start = " << start << "\n";
        cout << "a1 = " << a1 << "\n";
        cout << "step = " << step << "\n";
    }
    if (*min_element(v.begin(), v.end()) < 0) {
        cout << "BAD!!\n";
        exit(0);
    }
    //if ()
    /*if (sh) {
        cout << "ft = " << ft << "\n";
        cout << "ft * (b * c - a) = " << ft * (b * c - a) << "\n";
        cout << "lid = " << lid << "\n";
        cout << "lend = " << lend << "\n\n";

        cout << "nmb = " << nmb << "\n";
        cout << "step = " << step << "\n";
        cout << "a1 = " << a1 << "\n";
        cout << "del = " << del << "\n";
        cout << "id = " << id << "\n";
        //cout << "\n";
    }*/

    res = ft * (b * c - a) - del;
    /*if (res <= 0) {
        cout << "BAD res !!!\n";
        cout << "res = " << res << "\n";
        exit(0);
    }*/
    return res;
}

/*
228 21 11 3


3 1 7 3
*/



void slv() {
    if (!rand_mode) {
        cin >> a >> b >> c >> d;
    } else {
        vector <ll> v = {(ll)1, (ll)1e6};
        a = rand() % 3 + v[rand() % 2];
        b = rand() % 3 + v[rand() % 2];
        c = rand() % 3 + v[rand() % 2];
        d = rand() % 3 + v[rand() % 2];
        cout << "GO\n";
        cout << "a b c d = " << a << ' ' << b << ' ' << c << ' ' << d << "\n";
        if (min(min(a, b), min(c, d)) <= 0) {
            cout << "BAD!!!!\n";
            cout << "a b c d = " << a << ' ' << b << ' ' << c << ' ' << d << "\n";
            exit(0);
        }
    }
    if (a > b * c) {
        cout << -1 << "\n";
        return;
    }
    if (sh) {
        for (ll t = 1; t < 50; ++t) {
            cout << "t = " << 1 + t * d << "\n";
            ll h = hp(1 + t * d);
            cout << "hp = " << h << "\n\n";
        }
    }
    //tehnarnik po t
    /// rt = 1e18 / max(d, b * C - a) - 10
    ll lt = 0, rt = 1e18 / max(d, b * c - a) + 10, t1 = -10, t2 = 100, mn; //still withot noe (t - 1) ::d
    if (sh) {
        //rt = 30;
    }
    while (t1 + 1 != t2) {
        t1 = lt + (rt - lt) / 3;
        t2 = lt + 2 * (rt - lt) / 3;
        if (sh) {
            cout << "lt t1 t2 rt = " << lt << ' ' << t1 << ' ' << t2 << ' ' << rt << "\n";
            cout << "hp(t1) = " << hp(1 + t1 * d) << "\n";
            cout << "hp(t2) = " << hp(1 + t2 * d) << "\n";
        }
        if (hp(1 + t1 * d) < hp(1 + t2 * d)) {
            mn = t1;
            rt = t2;
        } else {
            mn = t2;
            lt = t1;
        }
    }
    if (sh) {
        cout << "mn hp(mn) = " << mn << ' ' << hp(mn) << "\n";
    }
    cout << max(a, -hp(1 + mn * d)) << "\n";
}
/*
3 1 7 3
*/

/*
a b c d = 1000002 3 1000001 1
BAD res !!!
*/

int main() {
    /*ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);*/
    srand(time(0));
    int t = rand();
    if (!sh && !rand_mode) cin >> t;
    int cnt = 0;
    while (cnt < t) {
        cnt++;
        slv();
    }
}