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.*;

public class master {
	    
	    
	    public static void solve(InputReader in, PrintWriter out) {
       
	    	int t = in.nextInt();
	    	while(t--!=0)
	    	{
	    		long x = in.nextLong(), y = in.nextLong();
	    		long a = in.nextLong(),b =in.nextLong();
	    		
	    		if(2*a<b)
	    		{
	    			System.out.println(x*a+y*a);
	    		}
	    		else {
	    			long ans = b*Math.min(x, y);
	    			ans = ans + a*(Math.max(x, y)-Math.min(x, y));
	    			System.out.println(ans);
	    		}
	    			
	    	}
	    
	    }
	  
	    
	    public static void main(String[] args) {
	        InputStream inputStream = System.in;
	        OutputStream outputStream = System.out;
	        InputReader in = new InputReader(inputStream);
	        PrintWriter out = new PrintWriter(outputStream);
	        solve(in, out);
	        out.close();
	    }
	  
	    static class InputReader {
	        public BufferedReader reader;
	        public StringTokenizer tokenizer;
	 
	        public InputReader(InputStream stream) {
	            reader = new BufferedReader(new InputStreamReader(stream), 32768);
	            tokenizer = null;
	        }
	 
	        public String next() {
	            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
	                try {
	                    tokenizer = new StringTokenizer(reader.readLine());
	                } catch (IOException e) {
	                    throw new RuntimeException(e);
	                }
	            }
	            return tokenizer.nextToken();
	        }
	 
	        public int nextInt() {
	            return Integer.parseInt(next());
	        }
	        
	        public Long nextLong() {
	            return Long.parseLong(next());
	        }
	        public Double nextDouble() {
	            return Double.parseDouble(next());
	        }
	    }	    
}
