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.*;
public class cpsolve {
    static long calc(long x ,long y ,long a,long b){
        if(x==0 && y==0){
            return 0;
        }
        if(x==y){
            long ans1=b*x;
            long ans2=a*x+a*x;
            return Math.min(ans1,ans2);
        }
        if(x>0 && y<0 || x<0 && y>0){
            return a*x +a*y;
        }
        if(x>0 && y>0){
            long ans1=Math.min(x,y)*b+(Math.max(x,y)-Math.min(x,y))*a;
            long ans2=x*a+y*a;
            return Math.min(ans1,ans2);
        }
        if(x==0 && y>0 || x>0 && y==0){
            return x*a + y*a;
        }
        return 0;
    }
    public static void main(String[] args){
        Scanner in=new Scanner(System.in);
        int T=in.nextInt();
        for(int t=0;t<T;t++) {
            long x = in.nextLong();
            long y = in.nextLong();
            long a = in.nextLong();
            long b = in.nextLong();
            System.out.println(calc(x,y,a,b));
        }
    }
}
