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.io.*;
public class Main{
    
    public static void main(String[] args) throws Exception {
       Scanner s = new Scanner(System.in);
       
       
       int t = s.nextInt();
       
       while(t-->0){
            long x = s.nextLong();
            long y = s.nextLong();
            long sum = 0;
            
            long a = s.nextLong();
            long b = s.nextLong();
            
            if(x==0 && y==0)
            System.out.println(0);
            else if(x==0 && y!=0){
                System.out.println(a*y);
            }else if(y==0 && x!=0){
                System.out.println(a*x);
            }
            else if( y!=0 && x!=0){
                if(x==y){
                    if(x*2*a > x*b)
                System.out.println(x*b);
                else 
                System.out.println(x*2*a);
                }
                else{
                    
                    long m = 0;
                    if(x>y)
                     m = y;
                     else 
                     m = x;
                    long k = Math.abs(x-y);
                    sum = sum + k*a;
                    
                    
                        if(m*2*a > m*b)
                            sum = sum+(b*m);
                        else 
                            sum = sum +(m*2*a);
                    
                 System.out.println(sum);   
                }
                
            }
            
        }
    }
}
   