#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();
}
}
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