#include <unordered_set>
#include <unordered_map>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
long long dp[200][200];
long long a, b, p, q;
const long long INF = 1000000ll * 1000000ll * 500000ll;
unordered_set<long long> nodes;
unordered_map<long long, int> hash_;
void preproc(long long a, long long b)
{
nodes.insert(a);
nodes.insert(b);
if(a == 0 || b == 0) return;
preproc(b, a % b);
}
long long getAns(long long a, long long b)
{
if(a == 0 || b == 0) return 0;
int i1 = hash_[a], i2 = hash_[b];
long long &ret = dp[i1][i2];
if(ret != -1) return ret;
ret = p + getAns(b, a % b);
if(a >= b)
{
long long howMany = a / b;
if(howMany <= ret / (double)q)
{
long long cand = howMany * q + getAns(a % b, b);
ret = min(cand, ret);
}
}
else
{
long long howMany = b / a;
if(howMany <= ret / (double)q)
{
long long cand = howMany * q + getAns(a, b % a);
ret = min(cand, ret);
}
}
return ret;
}
int main(void)
{
int T;
scanf("%d", &T);
while(T--)
{
scanf("%lld %lld %lld %lld", &a, &b, &p, &q);
nodes.clear();
preproc(a, b);
int ind = 0;
hash_.clear();
for(auto v: nodes) hash_[v] = ind++;
memset(dp, -1, sizeof(dp));
printf("%lld\n", getAns(a, b));
}
return 0;
}
