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.*;
import java.math.*;

public class Main {

	private static FastReader fastReader = new FastReader();
	public static void main(String[] args) {
		Task solver = new Task();
		solver.solve();
	}
 
	static class Task{
		public void solve() {
			int nt = fastReader.nextInt();
			StringBuilder result = new StringBuilder();
			
			while(nt-- > 0){
				long x = fastReader.nextLong();
				long y = fastReader.nextLong();
				long priceA = fastReader.nextLong();
				long priceB = fastReader.nextLong();
				if (x == y) result.append(String.valueOf(x*Math.min(priceA*2, priceB))+"\n");
				else{
					long diff = (Math.max(x, y) - Math.min(x, y));
					long val = Math.min(Math.min(x, y)*priceB, Math.min(x, y)*priceA*2) + diff*priceA;
					result.append(val+"\n");
				}
			}
			System.out.println(result);
		}
	}
 
	static class FastReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
 
		public FastReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
			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 String readLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}
	}
}