#include <cstdio>
#include <cmath>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long lint;
lint dp[100];
lint a,b,p,q;
bool calc_valid(lint x, lint y){
double t = log10(x)+log10(y);
return t < 18;
}
lint f(lint x, lint y, int step){
if(x == 0 || y == 0) return 0;
if(x >= y){
if(dp[step]) return dp[step];
if(!calc_valid(q,x/y)) return dp[step] = f(y,x%y,step+1) + p;
else return dp[step] = min(f(y,x%y,step+1) + p,f(x%y,y,step+1) + q*(x/y));
}
else{
if(!calc_valid(q,y/x)) return 5e18;
else return f(x,y%x,step+1) + q * (y/x);
}
}
void solve(){
memset(dp,0,sizeof(dp));
scanf("%lld %lld %lld %lld",&a,&b,&p,&q);
if(a < b) printf("%lld\n",min(p + f(b,a,0),f(a,b,0)));
else printf("%lld\n",f(a,b,0));
}
int main(){
int t;
scanf("%d",&t);
while (t--) {
solve();
}
}
