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.IOException;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) throws IOException {
    Scanner in = new Scanner(System.in);
    int t = in.nextInt();
    while (t-- > 0) {
      int x = in.nextInt();
      int y = in.nextInt();

      int a = in.nextInt();
      int b = in.nextInt();

      long ans = 0;
      if (x == 0 && y == 0) System.out.println(0);
      else {
        if (x > 0 && y > 0) {
          long min = (long)Math.min(x, y);
          x -= min;
          y -= min;
          long ans_a = 2 * min * (long)a;
          long ans_b = min * b;
          ans += Math.min(ans_a, ans_b);
        } else if (x < 0 && y < 0) {
          int max = -Math.max(x, y);
          x += max;
          y += max;
          long ans_a = 2 * (long)max * (long)a;
          long ans_b = (long)max * (long)b;
          ans += Math.min(ans_a, ans_b);
        }
        if (x <= 0 && y >= 0) {
          long diff = (long)y - (long)x;
          ans += (long)a * diff;
        } else if (x >= 0 && y <= 0) {
          long diff = (long)x - (long)y;
          ans += (long)a * diff;
        }
        System.out.println(ans);
      }
    }
  }
}