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 sc = new Scanner(System.in);
        int test = sc.nextInt();

        for (int t = 0; t < test; t++) {
            long x = sc.nextLong();
            long y = sc.nextLong();
            long a = sc.nextLong();
            long b = sc.nextLong();
            long ans1, ans2, ans3;

            //Both opp:
            if(((x<0) && (y>0)) || ((x>0) && (y<0))) {
                x = Math.abs(x);
                y = Math.abs(y);

                ans1 = (x+y)*a;
                System.out.println(ans1);
            } else {
//                System.out.println("Both positive or both negative!");
                x = Math.abs(x);
                y = Math.abs(y);
                long minXY = Math.min(x,y);
                long maxXY = Math.max(x,y);
                long minAB = Math.min(a,b);
                long maxAB = Math.max(a,b);
//                System.out.println(minXY + " "+maxXY+ " "+minAB+" "+maxAB);
                ans2 = (minXY * b) + (x-minXY)*a + (y-minXY)*a;
                ans3 = (x+y)*a;
                System.out.println(Math.min(ans2, ans3));
            }
        }
    }
}
