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.StringTokenizer;

public class EasyCodeforces {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        StringTokenizer stk = new StringTokenizer(in.readLine());
        int t = Integer.parseInt(stk.nextToken());

        while (t-- > 0) {
            stk = new StringTokenizer(in.readLine());
            int x = Integer.parseInt(stk.nextToken());
            int y = Integer.parseInt(stk.nextToken());
            stk = new StringTokenizer(in.readLine());
            long a = Long.parseLong(stk.nextToken());
            long b = Long.parseLong(stk.nextToken());
            if (x == y) {
                if (a + a < b) {
                    out.println((2L) * a * Math.abs(x));
                } else {
                    out.println(b * Math.abs(x));
                }
            } else if ((x <= 0 && y <= 0) || (x >= 0 && y >= 0)) {
                x = Math.abs(x);
                y = Math.abs(y);
                long diff = Math.abs(x - y);
                long ans = diff * a;
                if (a + a < b) {
                    ans += (2L) * a * Math.min(x, y);
                } else {
                    ans += b * Math.min(x, y);
                }
                out.println(ans);
            } else {
                long ans = a * Math.abs(x) + a * Math.abs(y);
                out.println(ans);
            }
        }

        out.close();
        in.close();
    }
}
