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.util.*;

public class Sol2 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		long x[] = new long[t];
		long y[] = new long[t];
		long a[] = new long[t];
		long b[] = new long[t];
		long sum = 0;
	
		
		for(int i=0; i<t; i++) {
			x[i] = s.nextLong();
			y[i] = s.nextLong();
			a[i] = s.nextLong();
			b[i] = s.nextLong();
			
		}
		
		for(int i = 0; i < t; i++) {
			if(x[i] > y[i]) {
				sum += (x[i]-y[i])*a[i];
				if((y[i]*b[i]) < (2*y[i]*a[i])) {
					sum += y[i]*b[i];
				}
				else {
					sum += 2*y[i]*a[i];
				}
				System.out.println(sum);
				sum = 0;
			}
			else {
				sum += (y[i]-x[i])*a[i];
				if((x[i]*b[i]) < (2*x[i]*a[i])) {
					sum += x[i]*b[i];
				}
				else {
					sum += 2*x[i]*a[i];
				}
				System.out.println(sum);
				sum = 0;
			}
		}
			

	}

}