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.*;

public class Solution {

    BigInteger gcd(BigInteger a, BigInteger b, BigInteger[] c) {
        if (a.equals(BigInteger.ZERO)) {
            c[0] = BigInteger.ZERO;
            c[1] = BigInteger.ONE;
            return b;
        }
        BigInteger[] k = new BigInteger[2];
        BigInteger d = gcd(b.mod(a), a, k);
        c[0] = k[1].subtract(b.divide(a).multiply(k[0]));
        c[1] = k[0];
        return d;
    }

    private void run() throws IOException {
        Scanner scanner = new Scanner(System.in);
        int tc = scanner.nextInt();
        for (int i = 0; i < tc; i++) {
            BigInteger X, Y, P, Q;
            X = scanner.nextBigInteger();
            Y = scanner.nextBigInteger();
            P = scanner.nextBigInteger();
            Q = scanner.nextBigInteger();
            BigInteger a = Q.subtract(P);
            BigInteger b = P.negate();
            BigInteger c = Y.multiply(P).subtract(X.multiply(Q));
            BigInteger[] xy = new BigInteger[2];
            BigInteger g = gcd(a.abs(), b.abs(), xy);
            if (!c.mod(g).equals(BigInteger.ZERO)) {
                System.out.println(-1);
                continue;
            }
            BigInteger x = xy[0];
            BigInteger y = xy[1];
            x = x.multiply(c.divide(g));
            y = y.multiply(c.divide(g));
            if (a.compareTo(BigInteger.ZERO) < 0) {
                x = x.negate();
            }
            if (b.compareTo(BigInteger.ZERO) < 0) {
                y = y.negate();
            }
            a = a.divide(g);
            b = b.divide(g);
            BigInteger sign_a = BigInteger.valueOf(a.signum());
            BigInteger sign_b = BigInteger.valueOf(b.signum());

            BigInteger ans = BigInteger.valueOf(-1);
            if (!b.equals(BigInteger.ZERO)) {
                BigInteger cnt = x.negate().divide(b);
                x = x.add(cnt.multiply(b));
                y = y.subtract(cnt.multiply(a));
                if (x.compareTo(BigInteger.ZERO) < 0) {
                    cnt = sign_b;
                    x = x.add(cnt.multiply(b));
                    y = y.subtract(cnt.multiply(a));
                }
                if (x.compareTo(BigInteger.ZERO) >= 0 && y.compareTo(BigInteger.ZERO) >= 0 && (ans.compareTo(BigInteger.ZERO) < 0 || ans.compareTo(x.add(y)) > 0)) {
                    ans = x.add(y);
                }
            }
            if (!a.equals(BigInteger.ZERO)) {
                BigInteger cnt = y.divide(a);
                x = x.add(cnt.multiply(b));
                y = y.subtract(cnt.multiply(a));
                if (y.compareTo(BigInteger.ZERO) < 0) {
                    cnt = sign_a.negate();
                    x = x.add(cnt.multiply(b));
                    y = y.subtract(cnt.multiply(a));
                }
                if (x.compareTo(BigInteger.ZERO) >= 0 && y.compareTo(BigInteger.ZERO) >= 0 && (ans.compareTo(BigInteger.ZERO) < 0 || ans.compareTo(x.add(y)) > 0)) {
                    ans = x.add(y);
                }
            }
            System.out.println(ans);
        }
    }

    public static void main(String[] args) throws IOException {
        new Solution().run();
    }
}