#include<bits/stdc++.h>

using namespace std;

using ll = long long;
using ld = long double;

using pii = pair<int, int>;
using pll = pair<long long, long long>;

#define pb push_back
#define ins insert
#define fi first
#define se second
#define btpc __builtin_popcount
#define btclz __builtin_clz

#define sz(x) (int)(x.size());
#define all(x) x.begin(), x.end()
#define debug(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

int d4x[4] = {1, 0, -1, 0}; int d4y[4] = {0, 1, 0, -1};
int d8x[8] = {0, 1, 1, 1, 0, -1, -1, -1};
int d8y[8] = {1, 1, 0, -1, -1, -1, 0, 1};

template<class X, class Y>
    bool minimize(X &x, const Y &y) {
        if (x > y)
        {
            x = y;
            return true;
        }
        return false;
    }
template<class X, class Y>
    bool maximize(X &x, const Y &y) {
        if (x < y)
        {
            x = y;
            return true;
        }
        return false;
    }

const int MOD = 1e9 + 7; //998244353

/* Author : Le Ngoc Bao Anh, A5K37 Le Quy Don High School for Gifted Student, Da Nang */

/*       University of Wollongong       */

const long long INF = 1e18;
const int N = 1e5 + 10;

pll calc(ll x, ll y, ll z, ll k, ll p) {
	ll cycle = (p / k);
	ll d = 0;
	ll cost = 0;
	cost += cycle * k * x + y * cycle;
	d = cycle * k;
	p %= k;
	z -= k * cycle * (cycle + 1) / 2;

	d += p;
	cost += p * x;

	ll t = 0;
	if(z > 0) {
		t = (z + d - 1) / d;
		cost += y * t;
	}

	return {cost, t};
}

void BaoJiaoPisu() {
	ll x, y, z, k; cin >> x >> y >> z >> k;

	ll ans = INF;
	for(int i = 1; i <= 10000; i++) {
		ans = min(ans, calc(x, y, z, k, i).fi);
	}

	for(int i = 0; i <= 10000; i++) {
		ll l = 1, r = z;
		while(l <= r) {
			ll mid = (l + r) >> 1;
			pll cur = calc(x, y, z, k, mid);
			ans = min(ans, cur.fi);
			if(cur.se > i) {
				l = mid + 1;
			} else {
				r = mid - 1;
			}
		}	
	}

	cout << ans << '\n';
}

int main()
{
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    #ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #else 
    //online
    #endif

    int tc = 1, ddd = 0;
    cin >> tc;
    while(tc--) {
        //ddd++;
        //cout << "Case #" << ddd << ": ";
        BaoJiaoPisu();
    }
}