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.math.BigInteger;
import java.io.*;
import java.math.BigInteger;
import java.util.Arrays;


public class Main {

    static BufferedReader reader = new BufferedReader ( new InputStreamReader ( System.in ) );
    static long[] output = null;
    public static void main(String[] args) throws IOException {

        int n = g_int ();
        output = new long[n];
        for(int i=0;i<n;i++){

            perform(i);

        }

        for(long a: output){
            System.out.println (a );
        }


    }

    public static void perform(int counter) throws IOException{
        long[] xy = ga_long (  );
        Arrays.sort(xy);

        long[] dollars = ga_long ();

        long p1 = xy[0]*dollars[1] + ((xy[1]-xy[0])*dollars[0]);
        long p2 = (xy[0]+xy[1])*dollars[0];

        output[counter] = Math.min(p1,p2);


    }





    // initial code
    public static long[] ga_long() throws IOException {
        long[] numbers = Arrays.stream(reader.readLine ().split(" ")).mapToLong (Long::parseLong).toArray();
        return numbers;

    }

    public static int g_int() throws IOException {
        return Integer.parseInt ( reader.readLine () );
    }

    public static long g_long() throws IOException {

        return Long.parseLong(reader.readLine());
    }

    public static int[] ga_int() throws IOException {
        int[] numbers = Arrays.stream(reader.readLine ().split(" ")).mapToInt (Integer::parseInt).toArray();
        return numbers;

    }

    public static String[] ga_string() throws IOException {

        return reader.readLine ().split ( " " );
    }

    public static String g_string() throws IOException {

        return reader.readLine ();
    }
}

