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.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Main m = new Main();

		m.func(new Scanner(System.in));

	}

	long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}

	ArrayList<Integer> get_primes(int limit) {
		ArrayList<Integer> res = new ArrayList<>();
		a:
		for (int i = 2; i <= limit; i++) {
			int temp = (int) Math.sqrt(i);

			for (int j = 2; j <= temp; j++) {
				if (i % j == 0) {
					continue a;
				}
			}
			res.add(i);
		}
		return res;
	}

	ArrayList<Long> get_factor(ArrayList<Integer> ps, long x) {

		ArrayList<Long> res = new ArrayList<>();
		for (int y : ps) {
			boolean enter = false;
			while (x % y == 0) {

				enter = true;
				x /= y;
			}
			if (enter) {
				res.add((long) y);
			}
			if (x == 1) {
				return res;
			}
		}
		res.add(x);
		return res;
	}


	void func(Scanner s) {
		int T = s.nextInt();
		while (T-- != 0) {

			int x = s.nextInt();
			int y = s.nextInt();
			int a = s.nextInt();
			int b = s.nextInt();
			b = Math.min(b, a * 2);
			System.out.println(1L*Math.abs(x - y) * a + 1L*Math.min(x, y) * b);
		}
	}

	int[][] temp = new int[][]{{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
}

class Node {
	int gap;

	int be;

	public Node(int gap, int be) {
		this.gap = gap;

		this.be = be;
	}
}

