#include <bits/stdc++.h>
using namespace std;
long long l, r, xx, yy, i, j, n, m, k, t, x[1009], y[1009], p[1009], q[1009], d,
    s;
bool ok() {
  xx = p[i] * m;
  yy = q[i] * m;
  if (xx < x[i] || yy < y[i]) return 0;
  if (xx - x[i] > yy - y[i]) return 0;
  return 1;
}
int main() {
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> x[i] >> y[i] >> p[i] >> q[i];
  }
  for (i = 1; i <= n; i++) {
    l = 1;
    r = 10000000000;
    while (l < r) {
      m = (l + r) / 2;
      if (ok())
        r = m;
      else
        l = m + 1;
    }
    m = r;
    if (ok()) {
      s = p[i] * m - x[i];
      t = q[i] * m - s;
      t -= y[i];
      t = max(0LL, t);
      s += t;
      cout << s << endl;
    } else
      cout << -1 << endl;
  }
}

### Prompt

Construct a Cpp code solution to the problem outlined:

You are an experienced Codeforces user. Today you found out that during your activity on Codeforces you have made y submissions, out of which x have been successful. Thus, your current success rate on Codeforces is equal to x / y.

Your favorite rational number in the [0;1] range is p / q. Now you wonder: what is the smallest number of submissions you have to make if you want your success rate to be p / q?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each of the next t lines contains four integers x, y, p and q (0 ≤ x ≤ y ≤ 109; 0 ≤ p ≤ q ≤ 109; y > 0; q > 0).

It is guaranteed that p / q is an irreducible fraction.

Hacks. For hacks, an additional constraint of t ≤ 5 must be met.

Output

For each test case, output a single integer equal to the smallest number of submissions you have to make if you want your success rate to be equal to your favorite rational number, or -1 if this is impossible to achieve.

Example

Input

4
3 10 1 2
7 14 3 8
20 70 2 7
5 6 1 1


Output

4
10
0
-1

Note

In the first example, you have to make 4 successful submissions. Your success rate will be equal to 7 / 14, or 1 / 2.

In the second example, you have to make 2 successful and 8 unsuccessful submissions. Your success rate will be equal to 9 / 24, or 3 / 8.

In the third example, there is no need to make any new submissions. Your success rate is already equal to 20 / 70, or 2 / 7.

In the fourth example, the only unsuccessful submission breaks your hopes of having the success rate equal to 1.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long l, r, xx, yy, i, j, n, m, k, t, x[1009], y[1009], p[1009], q[1009], d,
    s;
bool ok() {
  xx = p[i] * m;
  yy = q[i] * m;
  if (xx < x[i] || yy < y[i]) return 0;
  if (xx - x[i] > yy - y[i]) return 0;
  return 1;
}
int main() {
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> x[i] >> y[i] >> p[i] >> q[i];
  }
  for (i = 1; i <= n; i++) {
    l = 1;
    r = 10000000000;
    while (l < r) {
      m = (l + r) / 2;
      if (ok())
        r = m;
      else
        l = m + 1;
    }
    m = r;
    if (ok()) {
      s = p[i] * m - x[i];
      t = q[i] * m - s;
      t -= y[i];
      t = max(0LL, t);
      s += t;
      cout << s << endl;
    } else
      cout << -1 << endl;
  }
}

```