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 Abhi {
	
	public static void main(String[] args) {	
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		
		for(int i=0; i<t; i++) {
			long output = 0;
			long x = s.nextInt();
			long y = s.nextInt();
			
			long a = s.nextInt();
			long b = s.nextInt();
		
				if(x>=1 && y>= 1) {
					long n = (int) Math.min(x, y);
					
					if(a*2 < b) {
					     x = x - n;
						 y = y - n;				
						 output += (2*a)*n;		
						 
					}
					else
					{	
						x = x - n;
						y = y - n;				
						output += b*n;
					}	
					
				}
				
			    if(x>0 && y == 0) {
					output += a*x;
					x = 0;	
				}
			    if (x == 0 && y>0) {
					output += a*y;
					y = 0;
				}
			
			System.out.println(output);	
		}
	}		
}
