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.io.*;
import java.util.*;
import java.math.*;

public class A {

	public void realMain() throws Exception {

		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in), 1000000);

		String in = fin.readLine();

		String[] ar = in.split(" ");

		int T = Integer.parseInt(ar[0]);
	for(int t = 0; t < T; t++) {

		in = fin.readLine();
		ar = in.split(" ");
		long x = Long.parseLong(ar[0]);
		long y = Long.parseLong(ar[1]);

		in = fin.readLine();
		ar = in.split(" ");
		long a = Long.parseLong(ar[0]);
		long b = Long.parseLong(ar[1]);

		if(a*2 <= b) {
			System.out.println( (long)a * (Math.abs(x) + Math.abs(y)) );
			continue;
		}

		if( (x > 0 && y > 0) || (x < 0 && y < 0) ) {
			x = Math.abs(x);
			y = Math.abs(y);

			long bops = Math.min(x, y);

			long ans = bops * b;

			ans += (Math.max(x, y) - bops) * a;
		
			System.out.println(ans);
			continue;
		}

		
		System.out.println( (long)a * (Math.abs(x) + Math.abs(y)) );

	}





	}


	public static void main(String[] args) throws Exception {
		A a = new A();
		a.realMain();
	}
}