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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class E {

	public static void main(String[] args) throws NumberFormatException, IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	      int t = Integer.parseInt(br.readLine());
	      while(t--!=0)
	      {
	    	  String[] str = br.readLine().split(" ");
	    	  
	    	 
	    	  
	    	  Long x = Long.parseLong(str[0]);

	    	  Long y = Long.parseLong(str[1]);
	    	  
             String[] str1 = br.readLine().split(" ");
	    	  
	    	  Long a = Long.parseLong(str1[0]);

	    	  Long b = Long.parseLong(str1[1]);
	    	  
	    	  
	    	  if(x==0 && y==0)
	    	  {
	    		  System.out.println(0);
	    		  continue;
	    	  }
	    	  
	    	  if(x==0 || y==0)
	    	  {
	    		  x = Math.max(x, y);
	    		  
	    		  Long ans = a*x;
	    		  System.out.println(ans);
	    		  continue;
	    	  }
	    	  
	    	  else {
	    		  
	    		  if(2*a>b)
	    		  {
	    			  Long l = Math.min(x,y);
	    			  Long u = Math.max(x,y);
	    			  Long ans = 0L;
	    			  ans = ans + l*b;
	    			  u=u-l;
	    			  ans = ans + u*a;
	    			  System.out.println(ans);
	    		  }
	    		  
	    		  else {
	    			  Long ans =  ((x+y)*a);
	    			  System.out.println(ans);
	    		  }
	    		  
	    		  
	    	  }
	    	  
	    	
	    		    	    	  
  	  }
	    	  
	    	  
	    	  
	    	  

  }
}