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.
//package com.company;

import java.io.FileNotFoundException;
import java.io.FileReader;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

public class Solution {

    public static void main(String[] args) throws FileNotFoundException {
        //Scanner scanner = new Scanner(new FileReader("file.txt"));
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        while (n > 0) {
            n--;
            BigInteger x = scanner.nextBigInteger(), y = scanner.nextBigInteger(),
                    p = scanner.nextBigInteger(), q = scanner.nextBigInteger();
            if (Objects.equals(p, q) && !Objects.equals(x, y)) {
                System.out.println(-1);
                continue;
            }

            if (y.compareTo(q) == 1) {
                if (Objects.equals(y.mod(q), BigInteger.ZERO) && Objects.equals(y.divide(q).multiply(p), x)) {
                    System.out.println(0);
                    continue;
                }
            } else {
                if (Objects.equals(q.mod(y), BigInteger.ZERO) && Objects.equals(q.divide(y).multiply(x), p)) {
                    System.out.println(0);
                    continue;
                }
            }

            BigInteger d;
            BigInteger l = BigInteger.valueOf(1);
            BigInteger r = BigInteger.valueOf(Long.parseLong("10000000000000"));
            while (l.compareTo(r.subtract(BigInteger.valueOf(1))) == -1) {
                BigInteger i = l.add(r.subtract(l).divide(BigInteger.valueOf(2)));
                if (y.compareTo(q.multiply(i)) == 1 || x.compareTo(p.multiply(i)) == 1) {
                    l = i;
                    continue;
                }
                d = q.multiply(i).subtract(y);
                if (x.add(d).subtract(p.multiply(i)).compareTo(BigInteger.valueOf(0)) == 0 || x.add(d).subtract(p.multiply(i)).compareTo(BigInteger.valueOf(0)) == 1)
                    r = i;
                else
                    l = i;
            }
            if ((x.add(q.multiply(l)).subtract(y).subtract(p.multiply(l)).compareTo(BigInteger.valueOf(0)) == 0
                    || (x.add(q.multiply(l)).subtract(y).subtract(p.multiply(l)).compareTo(BigInteger.valueOf(0)) == 1))
                    && (y.compareTo(q.multiply(l)) != 1 && x.compareTo(p.multiply(l)) != 1)) {
                System.out.println(q.multiply(l).subtract(y));
            } else if ((x.add(q.multiply(r)).subtract(y).subtract(p.multiply(r)).compareTo(BigInteger.valueOf(0)) == 0
                    || (x.add(q.multiply(r)).subtract(y).subtract(p.multiply(r)).compareTo(BigInteger.valueOf(0)) == 1))
                    && (y.compareTo(q.multiply(r)) != 1 && x.compareTo(p.multiply(r)) != 1)){
                System.out.println(q.multiply(r).subtract(y));
            }else {
System.out.println(-1);
}
        } 
    }
}