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.*;
//codeforces edu round 86 : A
//Main class start
public class Main {
    // solution starts here!!!
    public void solve() throws IOException {

       int T = in.ni();
       while(T--!=0)
       {
   long x = in.nl();
    long y = in.nl();
           long a = in.nl();
          long b = in.nl();
    if (x==0&&y==0)out.println(0);
    else if(b>2*a){
        out.println((x+y)*a);
    }
   else{
       long diff =(long) Math.abs(y-x);
        if(x<y)
       out.println(diff*a+x*b);
       else out.println(diff*a+y*b);
    }
       }

    } //Solution ENDS Here !!!

    FastScanner in;
    FastWriter out;
    long maxLong = Long.MAX_VALUE  ,  minlong = Long.MIN_VALUE;
    int maxInt = Integer.MAX_VALUE ,  minInt = Integer.MIN_VALUE;
    double PI = 3.141592653589793238462643383279502884197169399;
    int digit(long s){int ans = 0;while(s>0){s/=10;ans++;}return ans;}
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}

    public void run() {
        try {
            in = new FastScanner();
            out = new FastWriter();

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }


    class FastWriter extends PrintWriter {
        FastWriter() throws FileNotFoundException {
            super(System.out);
        }

        void printNext(int i) {
            print(i);
            print(' ');
        }

        void printNext(long i) {
            print(i);
            print(' ');
        }

        void printNext(char ch) {
            print(ch);
            print(' ');
        }


        <T extends Iterable<Integer>> void printIterable(T o) {
            for (Integer t : o) {
                printNext(t);
            }
        }

        void printlnArray(int[] a) {
            for (int i : a) {
                printNext(i);
            }
            println();
        }

        void printlnArray(long[] a) {
            for (long i : a) {
                printNext(i);
            }
            println();
        }


    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;


        boolean ready() throws IOException {
            return (br.ready() || st.hasMoreTokens());
        }

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

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        char nc(){
            return next().charAt(0);
        }

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

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

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

    }

    public static void main(String[] arg) {
        new Main().run();
    }
}
