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.BufferedReader;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.StringTokenizer;


public class Main {


    public static class node {
        public BigInteger val;

    public node() {
        this.val = BigInteger.ZERO;
    }
}

    static BigInteger one = new BigInteger("-1");
    public static BigInteger extend_gcd(BigInteger a, BigInteger b,
                                        node x, node y, BigInteger d) {
        if (b.equals(BigInteger.ZERO)) {
            x.val = d.divide(a);
            y.val = BigInteger.ZERO;
            return a;
        }
        else {
            BigInteger r = extend_gcd(b, a.mod(b), y, x, d);
            y.val = y.val.subtract(x.val.multiply(a.divide(b)));
            return r;
        }
    }

    public static void main(String args[]) throws Exception {

        BufferedReader buf=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer s=new StringTokenizer(buf.readLine());

        int t = Integer.parseInt(s.nextToken());
        for(int i=0;i<t;i++) {
            s = new StringTokenizer(buf.readLine());
            BigInteger a = new BigInteger(s.nextToken());
            BigInteger b = new BigInteger(s.nextToken());
            BigInteger p = new BigInteger(s.nextToken());
            BigInteger q = new BigInteger(s.nextToken());
            if (p.equals(BigInteger.ZERO)) {
                if (a.equals(BigInteger.ZERO)) System.out.println(0);
                else System.out.println(-1);
                continue;
            }
            if (p.equals(q)) {
                System.out.println(a.equals(b) ? 0 : -1); continue;
            }

            BigInteger g = b.multiply(p).subtract(a.multiply(q));
            node X = new node();
            node Y = new node();
            BigInteger x=BigInteger.ZERO,y=BigInteger.ZERO;
            extend_gcd(q,p,X,Y,g);
            x = X.val;
            y = Y.val.multiply(one);

            x = x.mod(p);
            if (x.compareTo(BigInteger.ZERO) < 0) x= x.add(p);
            y = q.multiply(x).subtract(g).divide(p);
            if (y.compareTo(BigInteger.ZERO) < 0) {
                y=y.mod(q); if (y.compareTo(BigInteger.ZERO) < 0) y=y.add(q);
                x = p.multiply(y).add(g).divide(q);
            }
            if (y.compareTo(x)<0) {
                BigInteger lk = x.subtract(y).divide(q.subtract(p));
                x=x.add(lk.multiply(p));
                y=y.add(lk.multiply(q));
                if (y.compareTo(x) < 0) {
                    x=x.add(p); y=y.add(q);
                }
            }
            System.out.println(y);
        }
    }


}
