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

public class C {
    public static void main(String[] args) throws IOException {
        InputScanner is = new InputScanner();
        int t = is.nextInt();
        for (int i = 0; i < t; i++) {
            long x = is.nextLong();
            long y = is.nextLong();
            long p = is.nextLong();
            long q = is.nextLong();

            if (x < y && p == q) {
                System.out.println("-1");
                continue;
            }

            if (x > 0 && p == 0) {
                System.out.println("-1");
                continue;
            }

            if (x == y && p == q) {
                System.out.println("0");
                continue;
            }

            long low = 0;
            long high = Integer.MAX_VALUE;
            long startP = p;
            long startQ = q;

            long ans = 0;
            while (low < high) {
                long mid = low + (high - low) / 2;
                p = startP * mid;
                q = startQ * mid;
                if (p >= x && q >= y + p - x) {
                    long success = p - x;
                    long failure = q - (y + success);
                    ans = success + failure;
                    high = mid;
                } else low = mid + 1;
            }

            System.out.println(ans);
        }
    }

    static class InputScanner {
        BufferedReader br;
        StringTokenizer st;

        public InputScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() throws IOException {
            if (st == null || !st.hasMoreTokens()) {
                String line = br.readLine();
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            String next = next();
            return Integer.parseInt(next);
        }

        public long nextLong() throws IOException {
            String next = next();
            return Long.parseLong(next);
        }
    }
}

