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.
//package EdRound86_Div2;

import java.io.*;
import java.util.*;
public class A {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(in.readLine());
        for (int z = 0; z < t; z++) {
            StringTokenizer st = new StringTokenizer(in.readLine());
            long x = Long.parseLong(st.nextToken());
            long y = Long.parseLong(st.nextToken());
            st = new StringTokenizer(in.readLine());
            long a = Long.parseLong(st.nextToken()); //either
            long b = Long.parseLong(st.nextToken()); //both

            if(2*a <= b){
                System.out.println((x+y)*a);
            }
            else{
                long big = Math.max(x, y);
                long small = Math.min(x, y);
                if(x==y){
                    System.out.println(b*x);
                }
                else{
                    long cost = (big-small)*a + small*b;
                    System.out.println(cost);
                }
            }

        }
    }
}
