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