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.*;
import java.util.*;


public class A {
    static int modulo = 1000000007;
    public static void main(String[] args) throws IOException {
        BufferedReader inp = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

        int t = Integer.parseInt(inp.readLine());
        while (t-->0){
            String[] s1 = inp.readLine().split(" ");
            long x = Integer.parseInt(s1[0]);
            long y = Integer.parseInt(s1[1]);

            s1 = inp.readLine().split(" ");
            long a = Integer.parseInt(s1[0]);
            long b = Integer.parseInt(s1[1]);

            long min = Math.min(x,y);

            long cost = 0;

            if(2*a<b){
                cost = 2l*min*a;
            }
            else {
                cost = min*b;
            }

            x -=min;
            y-=min;

            long max = Long.max(x,y);
            cost+= a*max;
            out.write(cost+"\n");


        }


        out.flush();

        //print(tree);
    }

    static void print(int[] array){
        for(int j=0;j<array.length;j++){
            System.out.print(j+":"+array[j]+", ");
        }
        System.out.println();
    }
    static void print(int[][] array){
        for(int i=0;i< array.length;i++) {
            for (int j = 0; j < array[0].length; j++) {
                System.out.print(array[i][j] + " ");
            }
            System.out.println();
        }
    }
    static void print(boolean[] array){
        for(int j=0;j<array.length;j++){
            System.out.print(array[j]+" ");
        }
        System.out.println();
    }
    static void print(boolean[][] array){
        for(int i=0;i< array.length;i++) {
            for (int j = 0; j < array[0].length; j++) {
                System.out.print(array[i][j] + " ");
            }
            System.out.println();
        }
    }
    static void print(long[] array){
        for(int j=0;j<array.length;j++){
            System.out.print(array[j]+" ");
        }
        System.out.println();
    }
    static void print(long[][] array){
        for(int i=0;i< array.length;i++) {
            for (int j = 0; j < array[0].length; j++) {
                System.out.print(array[i][j] + " ");
            }
            System.out.println();
        }
    }
    static void print(String[] array){
        for(int j=0;j<array.length;j++){
            System.out.print(array[j]+" ");
        }
        System.out.println();
    }
    static void print(String[][] array){
        for(int i=0;i< array.length;i++) {
            for (int j = 0; j < array[0].length; j++) {
                System.out.print(array[i][j] + " ");
            }
            System.out.println();
        }
    }



}