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.*;
import java.lang.*;

public class RoadToZero {
    public static void main(String[]args){
        
        
        Scanner in = new Scanner(System.in);
        
        int t = in.nextInt();
        long x,y,a,b;
        long sum;
        long max, min;
        
        for(int i = 0; i < t; i++){
            
            x = in.nextInt();
            y = in.nextInt();
            a = in.nextInt();
            b = in.nextInt();
            
            sum = 0;
            max= Math.max(x, y);
            min = Math.min(x, y);
           
       
            
           if(a*2>b){
               sum += min*b;
               x = max - min;              
               sum += x*a;
           }
           
           else{
               sum+= a*(x+y);
           }
           
           System.out.println(sum);
        }
   }
        
}
