#include<bits/stdc++.h>
using namespace std;
int x,y,z,k;
long long dmg(long long a,long long b){
	long long c=min(a/k,b);
	return k*(c*(c+1))/2+(b-c)*a;
}
long long cst(long long a,long long b){
	return 1ll*a*x+b*y;
}
int bsa(int b){
	int l=0,r=z+1;
	while(l+1<r){
		int mid=(l+r)/2;
		if(dmg(mid,b)>=z)r=mid;
		else l=mid;
	}
	return r;
}
int bsb(int a){
	int l=0,r=z+1;
	while(l+1<r){
		int mid=(l+r)/2;
		if(dmg(a,mid)>=z)r=mid;
		else l=mid;
	}
	return r;
}
void solve(){
	cin>>x>>y>>z>>k;
	int l=1,r=z+1;
	while(l+1<r){
		int mid=(l+r)/2;
		if(bsb(mid)<=mid)r=mid;
		else l=mid;
	}
	long long ans=0x3f3f3f3f3f3f3f3f;
	for(int a=1;a<=l;a++){
		int b=bsb(a);
		if(b<=z)ans=min(ans,cst(a,b));
	}
	l=bsb(l);
	for(int b=1;b<=l;b++){
		int a=bsa(b);
		if(a<=z)ans=min(ans,cst(a,b));
	}
	cout<<ans<<"\n";
	return;
}
int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);cout.tie(0);
	int T;
	cin>>T;
	while(T--){
		solve();
	}
	return 0;
}