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.
//package CodeForces;

import java.util.Scanner;

public class RoadToZero {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner(System.in);
		int t=s.nextInt();
		while(t>0)
		{
			int x=s.nextInt();
			int y=s.nextInt();
			int a=s.nextInt();
			int b=s.nextInt();
			if((x>=0&&y>=0)||(x<=0&&y<=0))
			{
				x=Math.abs(x);Math.abs(y);
				long sum=0;
				if(2*a>b)
				{
					int temp=Math.min(x,y);
					x=x-temp;y=y-temp;
					sum=(long)temp*(long)b+(long)Math.max(x,y)*(long)a;
				}
				else
				{
					sum=(long)(x+y)*(long)a;
				}
				System.out.println(sum);
			}
			else
			{
				long sum=0;
				sum=(long)Math.abs(x)*(long)a+(long)Math.abs(y)*(long)a;
				System.out.println(sum);
			}
			
			t--;
		}

	}

}
