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;
/**
 * Write a description of class Main here.
 *
 * @author (your name)
 * @version (a version number or a date)
 */
public class Main
{
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int nums = sc.nextInt();
        for(int i = 0; i < nums; i++) {
            long x = sc.nextInt();
            long y = sc.nextInt();
            long a = sc.nextInt();
            long b = sc.nextInt();
            
            long ranVal =(long) (x + y) * a;
            
            if(x == y) {
                long cow = (long)(x * b);
                
                if(cow < ranVal) {
                    System.out.println(cow);
                } else {
                    System.out.println(ranVal);
                }
            } else if( x < y) {
                long diff = (long)(y - x);
                long val = (long)(diff*a + b*x);
                if(val < ranVal) {
                    System.out.println(val);
                } else {
                    System.out.println(ranVal);
                }
                
            } else if( y < x) {
                long diff2 = (long)(x-y);
                long val2 = (long)(diff2*a + b*y);
                if(val2 < ranVal) {
                    System.out.println(val2);
                } else {
                    System.out.println(ranVal);
                }
            } 
            
            
        }
    }
}