#include <iostream>
#include <string>
#include <stack>
#include <map>
#include <queue>
#include <algorithm>
#include <iomanip>
#include <iomanip>
#include <vector>
#include <random>
#include <chrono>

using namespace std;

tuple<long long, long long, long long> gcd(long long a, long long b) {
    if (b == 0)
        return {a, 1, 0};
    auto[d, x1, y1] = gcd(b, a % b);
    return {d, y1, x1 - y1 * (a / b)};
}

pair<long long, long long> diofant(long long a, long long b, long long c) {
    long long k = 1, x, y;


    auto[d, x1, y1] = gcd(a, b);
    if (c % d != 0) {
        return {-1, -1};
    }

    a /= d;
    b /= d;
    c /= d;

    x = x1 * c;
    y = y1 * c;
    k = abs(x) / b;
    x += b * k;
    y -= a * k;

    while (x < 0) {
        x += b;
        y -= a;
    }
    return {x, y};
}

long long inverse(long long a, long long m) {
    if (a == 0) {
        return -1;
    }
    return diofant(a, -m, 1).first;
}

int main() {
    long long n1, a, b, n, m, n_, m_;
    cin >> n1;
    while (n1--) {
        cin >> a >> b >> n >> m;
        int g = get<0>(gcd(a, b));
        if (a % g != b % g) {
            cout << "NO" << '\n';
            continue;
        }
        n /= g;
        m /= g;
        m_ = inverse(m, n);
        n_ = inverse(n, m);
        cout << (a * m * m_ + b * n * n_) % (n * m) << endl;
    }
    return 0;
}