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 template{

    public static void main(String[] args) throws FileNotFoundException {
        FastScanner fs=new FastScanner();

        int t = fs.nextInt();

        while(t!=0){
            long x=fs.nextInt();
            long y=fs.nextInt();
            long a=fs.nextInt();
            long b=fs.nextInt();

            if(a*2<b){
                long ans=(x+y)*a;
                System.out.println((x+y)*a);
            }else{
                long df = Math.abs(x-y);
                long ans = df*a + (long)Math.min(x,y)*b;
                System.out.println(ans);
            }


            t--;
        }
    }

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


    static class FastScanner {

        //File f = new File("C:\\Users\\Sagar Vats\\IdeaProjects\\Competetive\\src\\com\\Contest\\input.txt");
        //BufferedReader br=new BufferedReader(new FileReader(f));
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st=new StringTokenizer("");

        FastScanner() throws FileNotFoundException {
        }

        public String next() {
            while (!st.hasMoreElements())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) {
                a[i]=nextInt();
            }
            return a;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }

}
