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.
import java.math.BigInteger;
import java.util.Scanner;

/**
 * Created by akatkov on 5/7/17.
 */
public class C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            BigInteger x = sc.nextBigInteger();
            BigInteger y = sc.nextBigInteger();
            BigInteger p = sc.nextBigInteger();
            BigInteger q = sc.nextBigInteger();

            if (p.equals(q) && !x.equals(y) || p.equals(BigInteger.ZERO) && x.compareTo(BigInteger.ZERO) > 0) {
                System.out.println("-1");
                continue;
            }

            BigInteger start = BigInteger.ZERO;
            BigInteger end = BigInteger.valueOf(Long.MAX_VALUE); //Long.MAX_VALUE; //(long) 10E18;
            end = end.multiply(end);
            while (true) {
                if (start.equals(end)) {
                    break;
                }
                BigInteger midpoint = start.add(end).divide(BigInteger.valueOf(2)); // start + end) >>> 1;
//                System.err.println(start + " " + end + " " + midpoint);

                BigInteger diff = midpoint.divide(q);
                BigInteger denomDiff = q.multiply(diff).subtract(y);
                BigInteger numerDiff = p.multiply(diff).subtract(x);
                if (numerDiff.compareTo(denomDiff) > 0 || numerDiff.compareTo(BigInteger.ZERO) < 0) {
                    start = midpoint.add(BigInteger.ONE);
                } else {
                    end = midpoint;
                }
            }
            System.out.println(start.subtract(y));
        }
    }
}
