#include <cstdio>
#include <algorithm>
using namespace std;
typedef long long ll;
const int MAX = 200;
const ll INF = 5123456789012345678LL;
int maxLevel;
ll p, q, memo[MAX][2];
ll minGcd(ll a, ll b, int level){
if(a == 0 || b == 0) return 0;
ll &now = a >= b ? memo[level][0] : memo[level][1];
maxLevel = max(maxLevel, level);
if(now != 0) return now;
if(a >= b){
now = minGcd(b, a%b, level+1)+p;
ll count = (a - (a%b))/b;
if((INF - minGcd(a%b, b, level+1))/count > q)
now = min(now, minGcd(a%b, b, level+1) + q*count);
} else {
now = minGcd(b, a, level)+p;
ll count = (b - (b%a))/a;
if((INF - minGcd(a, b%a, level+1))/count > q)
now = min(now, minGcd(a, b%a, level+1) + q*count);
}
return now;
}
void reset(){
for(int i = 0; i <= maxLevel; i++)
memo[i][0] = memo[i][1] = 0;
}
int main(){
int t;
for(scanf("%d", &t); t--;){
ll a, b;
scanf("%lld%lld%lld%lld", &a, &b, &p, &q);
printf("%lld\n", minGcd(a, b, 0));
reset();
}
return 0;
}
