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.
/**
 * Author: Nirav Talaviya
 */

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

public class A1342 {
    static BufferedReader br;

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        int t = readInt();
        while(t-->0){
            String str[] = br.readLine().split(" ");
            long x = Long.parseLong(str[0]);
            long y = Long.parseLong(str[1]);
            str = br.readLine().split(" ");
            long a = Long.parseLong(str[0]);
            long b = Long.parseLong(str[1]);
            if(Math.abs(x-y)>1){

                System.out.println(Math.abs(x-y)*a+Math.min(x,y)*Math.min(b,2*a));
            }else if(Math.abs(x-y)==1){
                System.out.println(Math.min(x,y)*Math.min(b,2*a)+a);
            }else {
                if(x==y && x==0){
                    System.out.println(0);
                }else {
                    System.out.println(Math.min(b,2*a)*x);
                }
            }
        }
    }

    static int readInt() throws IOException {
        return Integer.parseInt(br.readLine());
    }

    static long readLong() throws IOException {
        return Long.parseLong(br.readLine());
    }

    static int[] readintarr() throws IOException {
        String[] ___str___ = br.readLine().split(" ");
        int[] ___arr___ = new int[___str___.length];
        for (int i = 0; i < ___str___.length; i++) {
            ___arr___[i] = Integer.parseInt(___str___[i]);
        }
        return ___arr___;
    }

    static long[] readlongarr() throws IOException {
        String[] ___str___ = br.readLine().split(" ");
        long[] ___arr___ = new long[___str___.length];
        for (int i = 0; i < ___str___.length; i++) {
            ___arr___[i] = Long.parseLong(___str___[i]);
        }
        return ___arr___;
    }
}

    
    
    