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.InputStreamReader;

public class Main {

    public static void main(String[] args) throws Exception {
	// write your code here]
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int tc = Integer.parseInt(br.readLine());
        while (tc-->0){
            String[] xy =  br.readLine().split(" ");
            long x =  Long.parseLong(xy[0]);
            long y = Long.parseLong(xy[1]);

            String[] ab = br.readLine().split(" ");
            long a = Long.parseLong(ab[0]);
            long b =Long.parseLong(ab[1]);

           if(2*a<=b){
               System.out.println(a*(x-0)+(a*(y-0)));
           }
           else{
               long cost = (Math.min(x,y)-0)*b;
               cost+=(Math.max(x,y)-Math.min(x,y)-0)*a;
               System.out.println(cost);
           }
        }
    }
}
