#include <bits/stdc++.h>

using namespace std;

#define int long long
// #define x first
// #define y second
#define File(a) freopen(a".in", "r", stdin), freopen(a".out", "w", stdout)

inline void debug() { cerr << '\n'; }
template<typename Type, typename... Other>
inline void debug(const Type& x, const Other&... y) { cerr << x << ' '; debug(y...); }
#define DEBUG(a...) cerr << "[" << #a << "] = ", debug(a);

typedef long long LL;
typedef pair<int, int> PII;

const int N = 200010;
const int INF = 2e18;

template<typename Type>
inline void read(Type &res)
{
    res = 0;
    int ch = getchar(), flag = 0;
    while (!isdigit(ch)) flag |= ch == '-', ch = getchar();
    while (isdigit(ch)) res = (res << 3) + (res << 1) + (ch ^ 48), ch = getchar();
    res = flag ? -res : res;
}
template<typename Type, typename... Other>
inline void read(Type &res, Other&... y) { read(res), read(y...); }

int X, Y, P, Q, ans;

int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }

int exgcd(int a, int b, int &x, int &y)
{
	if (b == 0)
	{
		x = 1, y = 0;
		return a;
	}
	int d = exgcd(b, a % b, y, x);
	y -= a / b * x;
	return d;
}

void solve()
{
    ans = INF;
    read(X, Y, P, Q);

    int a = 0, b = 0;
    int gcd = exgcd(2 * (X + Y), P + Q, a, b);

    for (int i = 0; i < Y; i ++)    // i stands for n
    {
        for (int j = 0; j < Q; j ++)    // j stands for m
        {
            if ((P + j - (i + X)) % gcd != 0) continue;
            int base = (P + j - (X + i)) / gcd, fc = (P + Q) / gcd;
            int ansx = a * base, ansy = b * base;

            ansx = (ansx % fc + fc) % fc;
            ans = min(ans, 2 * (X + Y) * ansx + X + i);
        }
    }
    cout << (ans == INF ? -1 : ans) << '\n';
}

signed main()
{
    int T; read(T);
    while (T --) solve();
    return 0;
}