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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 * 
 * @author Kajal
 *
 */
public class RoadToZero {
	
	public static void main(String[] args) {
		int testCases;
		long x, y, a, b;
		String input[];
		StringBuilder out = new StringBuilder();
		BufferedReader br = null;
		
		try {
			br = new BufferedReader(new InputStreamReader(System.in));
//			br = new BufferedReader(new FileReader("in.txt"));
			testCases = Integer.parseInt(br.readLine().trim());
			for (int t = 1;t <= testCases;t++)
			{
				input = br.readLine().split(" ");
				x = Long.parseLong(input[0]);
				y = Long.parseLong(input[1]);
				
				input = br.readLine().split(" ");
				a = Long.parseLong(input[0]);
				b = Long.parseLong(input[1]);
				long dollarsSpent = 0;
				boolean remaining = false;
				if (b <= 2*a) {
					if (x < y) {
						dollarsSpent += x * b;
					} else {
						dollarsSpent += y * b;
					}
					remaining = true;
				} 
				if (!remaining) {
					dollarsSpent += a * (x+y);
				} else {
					dollarsSpent += a * Math.abs(x-y);
				}
				out.append(dollarsSpent).append("\n");
			}	
			System.out.println(out);
			
		} catch (NumberFormatException | IOException e) {
			e.printStackTrace();
		} finally {
			try {
				if (br != null)
					br.close();
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
	}

}
