#include <stdio.h>
#include <algorithm>
#include <map>
using namespace std;
long long a,b,p,q,l;
int t;
std::map<int, long long> chk[100000];
long long go(long long a, long long b)
{
if (a == 0 || b == 0) return 0;
if (a == b) return p < q ? p : q;
unsigned int h = a*b+a*3+b;
long long &r = chk[t][h];
if (r) return r;
r = p + go(b,a%b);
if (a > b){
long long d = a / b, e = q * d;
if (d <= l) r = min(r, e+go(a-b*d,b));
}
else{
long long d = b / a, e = q * d;
if (d <= l) r = min(r, e+go(a,b-a*d));
}
return r;
}
int main()
{
int T; scanf ("%d",&T); while (T--){
scanf ("%lld %lld %lld %lld",&a,&b,&p,&q);
l = 1e18 / q;
printf ("%lld\n",go(a,b));
t++;
}
return 0;
}
