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.util.Scanner;

public class roadToZero {
    public static void main(String[] args){
        Scanner ab = new Scanner(System.in);
        int t = ab.nextInt();
        long input[][] = new long[t][4];
        long ans[] = new long[t];

        for(int  i =0; i<t; i++){
            input[i][0] = ab.nextLong();
            input[i][1] = ab.nextLong();
            input[i][2] = ab.nextLong();
            input[i][3] = ab.nextLong();
        }
        for(int  i =0; i<t; i++){
            long x1 = input[i][0];
            long x2 = input[i][1];
            long a  = input[i][2];
            long b  = input[i][3];
            if(Math.abs(x1)>Math.abs(x2)){
                long temp = x1;
                x1=x2;
                x2=temp;
            }
            if(x1==0 && x2==0){
                ans[i]=0;
                continue;
            }
            if(2*a<b){
                ans[i] = (a*Math.abs(x1) + a*Math.abs(x2));
                continue;
            }
            
            if(x1*x2 >0){
                ans[i] = Math.abs(x1)*b + Math.abs(Math.abs(x2)-Math.abs(x1))*a;
                continue;
            }
            else
            {
                ans[i] = (a*Math.abs(x1) + a*Math.abs(x2));
                continue;
            }
        }
        for(long a: ans){
            System.out.println(a);
        }
    }
}