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 Main {
	
	public static long count = (long)0;
	
	public static void main(String[] args) {
		
		Scanner in = new Scanner( System.in );
		int number = in.nextInt();
		
		for( int sa = 0; sa < number; sa ++ ) {
			
			int x = in.nextInt();
			int y = in.nextInt();
			int a = in.nextInt();
			int b = in.nextInt();
			
			long shaobing = (long)a * b;
			
			if(shaobing <= 0 ) {
				count = (long)Math.abs( x - y ) * a;
			}
			else {
				count = (long)Math.abs( x + y ) * a;
				
				int min = Math.abs( x );
				if( Math.abs( x ) > Math.abs( y ) ) {
					min = Math.abs( y );
				}
				count = Math.min( count, (long)min * b + (long)( Math.abs( y - x ) ) * a );
			}
			
			System.out.println( count );
			
		}
		
	}

}