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.util.*;
import java.io.*;

public class Main {

    /**
     */


    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        while (t-->0) {
            long x = sc.nextLong();
            long y = sc.nextLong();
            long a = sc.nextLong();
            long b = sc.nextLong();
            long min = Math.min(x, y);
            long max = Math.max(x, y);
            System.out.println(Math.min(min * b + (max-min)*a, (x+y)*a));
        }
    }

    private static int[] isPrime(int num) {
        for (int i = 2; i <= (int)Math.sqrt(num); i++) {
            if (num % i == 0) return new int[]{i, num/i};
        }
        return null;
    }

    private static int sign(long num) {
        if (num < 0) return -1;
        return 1;
    }

    private static class Pair {
        int x;
        int y;
        public Pair(int x, int y) {
            this.x=x;
            this.y=y;
        }
    }




    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

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

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}

/**
 * 7 3
 * 3 1 5
 * 9 6 5
 *
 * i = 1: 1
 * i = 2: 2
 * i = 3: 3
 *
 *
 * 1 2 3 3 3 3 3
 */


/**
 *
 *  1+1
 **/