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.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Random;
import java.util.Scanner;

public class TaskA {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		PrintWriter w = new PrintWriter(System.out);
		int t = Integer.parseInt(in.nextLine());
		while (t-- > 0) {
			StringBuilder sb = new StringBuilder();
//			int n = in.nextInt();
//			long n = in.nextInt();
			long x = in.nextLong();
			long y = in.nextLong();
			long a = in.nextLong();
			long b = in.nextLong();
			if (x == 0 && y == 0) {
				System.out.println(0);
				continue;
			}
			long dif = Math.abs(x - y);
			long min = Math.min(x, y);
			long max = Math.max(x, y);
			long ans1 = min*b + dif*a;
			long ans2 = (x+y)*a;
			System.out.println(Math.min(ans1,ans2));
		}
		w.flush();
		w.close();
	}

	private static void shuffleArray(int[] arr) {
		int n = arr.length;
		Random rnd = new Random();
		for (int i = 0; i < n; ++i) {
			int tmp = arr[i];
			int randomPos = rnd.nextInt(n);
			arr[i] = arr[randomPos];
			arr[randomPos] = tmp;
		}
	}

	private static void shuffleArray(long[] arr) {
		int n = arr.length;
		Random rnd = new Random();
		for (int i = 0; i < n; ++i) {
			long tmp = arr[i];
			int randomPos = i + rnd.nextInt(n - i);
			arr[i] = arr[randomPos];
			arr[randomPos] = tmp;
		}
	}
}
