#include <cstdio>
#include <vector>
#include <map>
#include <stdlib.h>
#include <string.h>
#include <algorithm>
using namespace std;
typedef long long ll;
static char _buffer[1024];
static int _currentChar = 0;
static int _charsNumber = 0;
static inline int _read() {
if (_charsNumber < 0) {
exit(1);
}
if (!_charsNumber || _currentChar == _charsNumber) {
_charsNumber = (int)fread(_buffer, sizeof(_buffer[0]), sizeof(_buffer), stdin);
_currentChar = 0;
}
if (_charsNumber <= 0) {
return -1;
}
return _buffer[_currentChar++];
}
static inline ll _readll() {
int c, s; ll x;
c = _read();
while (c <= 32) c = _read();
x = 0;
s = 1;
if (c == '-') {
s = -1;
c = _read();
}
while (c > 32) {
x *= 10;
x += c - '0';
c = _read();
}
if (s < 0) x = -x;
return x;
}
ll a, b, p, q;
map <ll, ll> d;
ll lim2 = 1e18, lim = 1e15 + 9;
inline ll f(ll x, ll y) {
if (x == 0 || y == 0) return 0;
ll X = x*lim + y;
if (d.count(X)) return d[X];
ll d1 = f(y, x%y) + p, d2 = lim2, m;
if (x >= y) {
m = x / y;
if (m <= d1 / q) d2 = f(x - m*y, y) + m*q;
}
else {
m = y / x;
if (m <= d1 / q) d2 = f(x, y - m*x) + m*q;
}
if (d1 > d2) d1 = d2;
d[X] = d1;
return d1;
}
int main() {
int T;
for (scanf("%d", &T); T--; ) {
a = _readll(); b = _readll(); p = _readll(); q = _readll();
d.clear();
printf("%lld\n", f(a, b));
}
}
