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.io.InputStreamReader;

public class Roadtozero {

	public static void main(String[] args)throws IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		long t = Long.parseLong(br.readLine());
		while (t-- > 0) {
			String s[] = br.readLine().split(" ");
			long x = Long.parseLong(s[0]);
			long y = Long.parseLong(s[1]);
			s=br.readLine().split(" ");
			long a = Long.parseLong(s[0]);
			long b = Long.parseLong(s[1]);
			long sum = 0;
			if(x==0&&y==0)
			{
				System.out.println("0");
			}else {
				long small=0,big=0;
			
				if(x<y)
				{
					small=x;big=y;
				}else
				{
					small=y;big=x;
				}
				sum+=small*b;
				sum+=(big-small)*a;
				if(b>a)
				{
					long sum1=(big*a)+(small*a);
					sum=Math.min(sum,sum1);
				}
				System.out.println(sum);
			}
			

	}

}
}