//#include "testlib.h"
//#include <spoj.h>

#include <iostream>
#include <stdio.h>
#include <vector>
#include <string>
#include <algorithm>
#include <math.h>
#include <assert.h>
#include <time.h>
#include <memory.h>
#include <set>
#include <numeric>
#include <map>
#include <queue>
#include <stack>
#include <bitset>
#include <unordered_map>

using namespace std;

int main() {
    ios::sync_with_stdio(0);
    int t;
    long long a, b, c, d, g;
    cin >> t; assert(1 <= t && t <= 1e4);
    while (t --> 0) {
        cin >> a >> b >> c >> d;
        assert(1 <= a && a <= 1e14);
        assert(1 <= b && b <= 1e14);
        assert(1 <= c && c <= 1e14);
        assert(1 <= d && d <= 1e14);
        g = __gcd(c, d);
        a = abs(a - b);
        cout << min(a % g, g - (a % g)) << "\n";
    }
    return 0;
}