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 codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

import java.math.BigInteger;

public class test
{

	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner in=new Scanner(System.in);
		int t=in.nextInt();
		while(--t>=0)
		{
			long x=in.nextLong();
			long y=in.nextLong();

			long a =in.nextLong();
			long b=in.nextLong();

			if (x*y>=0)
			{
				long ans1 = Math.abs((x+y)*a);
				long ans2 = Math.abs(Math.min(x,y)*b + (Math.max(x,y)-Math.min(x,y))*a);

				System.out.println(Math.min(ans1,ans2));
			}
			else
			{
				long ans = (Math.abs(x)+Math.abs(y))*a;
				System.out.println(ans);
			}
			
		}

		
	}
}
