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.util.*;

public class C {
    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);


        int t = fs.nextInt();
        tests:
        for(int tt = 0; tt < t; tt++) {

            long x = fs.nextInt(), y = fs.nextInt();
            long p = fs.nextInt(), q = fs.nextInt();


            long lo = 1, hi = (long)1e9;
            long res = -1;

            for(int bs = 0; bs < 100 && lo <= hi; bs++) {
                long mid = (lo + hi) / 2;


                long np = p * mid;
                long nq = q * mid;

                //Is it even possible to get here?

                if(x > np || y > nq) {
                    //go higher
                    lo = mid+1;
                    continue;
                }

                long nx = x, ny = y;
                long change = 0;
                change += Math.abs(nx - np);
                if(ny + change > nq) {
                    //go higher
                    lo = mid+1;
                    continue;
                }

                ny += change;
                change += Math.abs(ny - nq);

                //everything here worked so I'm gonna try a smaller fraction

                if(res < 0) res = change;
                else res = Math.min(res, change);


                hi = mid-1;

            }


            out.println(res);

        }

        out.close();
    }

    public static long gcd(long a, long b) {
        while (b> 0) {
            long temp = b;
            b = a%b;
            a = temp;
        }
        return a;
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            try	{
                br = new BufferedReader(new InputStreamReader(System.in));
                //                br = new BufferedReader(new FileReader("testdata.out"));
                st = new StringTokenizer("");
            } catch (Exception e){e.printStackTrace();}
        }

        public String next() {
            if (st.hasMoreTokens())	return st.nextToken();
            try {st = new StringTokenizer(br.readLine());}
            catch (Exception e) {e.printStackTrace();}
            return st.nextToken();
        }

        public int nextInt() {return Integer.parseInt(next());}

        public long nextLong() {return Long.parseLong(next());}

        public double nextDouble() {return Double.parseDouble(next());}

        public String nextLine() {
            String line = "";
            try {line = br.readLine();}
            catch (Exception e) {e.printStackTrace();}
            return line;
        }

        public Integer[] nextIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for(int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for(int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        public char[] nextCharArray() {
            return nextLine().toCharArray();
        }
    }

}