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.BufferedWriter;
import java.io.FileWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;

public class A {

	static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
	static BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));

	static int x, y, a, b;
	
	static void process() throws Exception {
		long cost = 0;
		long diff = 0;
		if (x != y) {
			diff = Math.abs(x - y);
			cost += diff * a;
		}
		long rem = Math.max(x, y) - diff;
		long a_cost = (long) 2*rem*a;
		long b_cost = (long) rem*b;
		if (a_cost < b_cost) {
			cost += a_cost;
		} else {
			cost += b_cost;
		}
		long t_cost = (long) x*a + (long) y*a;
		if (t_cost < cost) {
			writer.write(String.format("%d", t_cost));
		} else {
			writer.write(String.format("%d", cost));
		}
		writer.newLine();
	}

	public static void main(String[] args) throws Exception {
		//		writer = new BufferedWriter(new FileWriter("output.txt"));
		String data[], input;
		int t = Integer.parseInt(reader.readLine());
		while (t-- != 0) {
			data = reader.readLine().split(" ");
			x = Integer.parseInt(data[0]); y = Integer.parseInt(data[1]);
			data = reader.readLine().split(" ");
			a = Integer.parseInt(data[0]); b = Integer.parseInt(data[1]);
			process();
		}
		writer.close();
	}

}
