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.io.*;
import java.math.BigInteger;
import java.util.StringTokenizer;

import static java.lang.Integer.parseInt;
import static java.lang.Long.MAX_VALUE;
import static java.lang.Long.max;
import static java.math.BigInteger.valueOf;
import static java.nio.charset.StandardCharsets.UTF_8;

public class Main {

    public static void main(String[] args) throws IOException {
        try (BufferedReader in = new BufferedReader(new InputStreamReader(System.in, UTF_8));
             BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out, UTF_8))) {
            int tests = parseInt(in.readLine().trim());
            for (int t = 0; t < tests; t++) {
                StringTokenizer tokens = new StringTokenizer(in.readLine());
                int x = parseInt(tokens.nextToken());
                int y = parseInt(tokens.nextToken());
                int p = parseInt(tokens.nextToken());
                int q = parseInt(tokens.nextToken());
                if (p == 0) {
                    if (x == 0) {
                        out.write("0");
                    } else {
                        out.write("-1");
                    }
                } else {
                    long low = max((x + p - 1) / p, 1);
                    low = max((y + q - 1) / q, low);
                    long high = MAX_VALUE / 2 - low - 1;
                    while (low <= high) {
                        long alpha = (low + high) / 2;
                        BigInteger delta = valueOf(alpha).multiply(valueOf(p)).add(valueOf(-x));
                        BigInteger s = valueOf(alpha).multiply(valueOf(q)).add(valueOf(-y));
                        if (delta.compareTo(s) > 0) {
                            low = alpha + 1;
                        } else {
                            high = alpha - 1;
                        }
                    }
                    long answer = high + 1;
                    if (answer * p - x <= answer * q - y && answer * p - x >= 0) {
                        out.write((answer * q - y) + "");
                    } else {
                        out.write("-1");
                    }
                }
                out.newLine();
            }
        }
    }
}
