You are given two integers x and y. You can perform two types of operations: 

  1. Pay a dollars and increase or decrease any of these integers by 1. For example, if x = 0 and y = 7 there are four possible outcomes after this operation: 
    * x = 0, y = 6; 
    * x = 0, y = 8; 
    * x = -1, y = 7; 
    * x = 1, y = 7. 

  2. Pay b dollars and increase or decrease both integers by 1. For example, if x = 0 and y = 7 there are two possible outcomes after this operation: 
    * x = -1, y = 6; 
    * x = 1, y = 8. 



Your goal is to make both given integers equal zero simultaneously, i.e. x = y = 0. There are no other requirements. In particular, it is possible to move from x=1, y=0 to x=y=0.

Calculate the minimum amount of dollars you have to spend on it.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of testcases.

The first line of each test case contains two integers x and y (0 ≤ x, y ≤ 10^9).

The second line of each test case contains two integers a and b (1 ≤ a, b ≤ 10^9).

Output

For each test case print one integer — the minimum amount of dollars you have to spend.

Example

Input


2
1 3
391 555
0 0
9 4


Output


1337
0

Note

In the first test case you can perform the following sequence of operations: first, second, first. This way you spend 391 + 555 + 391 = 1337 dollars.

In the second test case both integers are equal to zero initially, so you dont' have to spend money.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.DataInputStream;
import java.io.IOException;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author iavanish
 */
public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ARoadToZero solver = new ARoadToZero();
        solver.solve(1, in, out);
        out.close();
    }

    static class ARoadToZero {

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int t = in.nextInt();

            while (t-- > 0) {
                long x = in.nextLong();
                long y = in.nextLong();
                long a = in.nextLong();
                long b = in.nextLong();

                if (x > y) {
                    long temp = x;
                    x = y;
                    y = temp;
                }

                long ans = (y - x) * a;
                b = Math.min(b, a * 2);
                ans += x * b;

                out.println(ans);
            }
        }

    }

    static class FastReader {

        private final int BUFFER_SIZE = 1 << 16;
        private final InputStream inputStream;
        private final byte[] buffer;
        private int bufferPointer;
        private int bytesRead;

        public FastReader() {
            this.inputStream = new DataInputStream(System.in);
            this.buffer = new byte[BUFFER_SIZE];
            this.bufferPointer = bytesRead = 0;
        }

        public FastReader(InputStream inputStream) {
            this.inputStream = inputStream;
            this.buffer = new byte[BUFFER_SIZE];
            this.bufferPointer = bytesRead = 0;
        }

        public FastReader(String fileName) {
            try {
                this.inputStream = new DataInputStream(new FileInputStream(fileName));
                this.buffer = new byte[BUFFER_SIZE];
                this.bufferPointer = bytesRead = 0;
            } catch (FileNotFoundException e) {
                throw new RuntimeException(e);
            }
        }

        public int nextInt() {
            int nextInt = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean negative = (c == '-');
            if (negative) {
                c = read();
            }
            do {
                nextInt = nextInt * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (negative) {
                return -nextInt;
            }
            return nextInt;
        }

        public long nextLong() {
            long nextLong = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean negative = (c == '-');
            if (negative) {
                c = read();
            }
            do {
                nextLong = nextLong * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (negative) {
                return -nextLong;
            }
            return nextLong;
        }

        private void fillBuffer() {
            try {
                bytesRead = inputStream.read(buffer, bufferPointer = 0, BUFFER_SIZE);
                if (bytesRead == -1) {
                    buffer[0] = -1;
                }
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        private byte read() {
            if (bufferPointer == bytesRead) {
                fillBuffer();
            }
            return buffer[bufferPointer++];
        }

    }

}

