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

public class Road{
    static Integer[]strToIntArr(String s){
	//	s = s.substring(1,s.length()-1);
	//	String[] sArr = s.split(",");
	String[] sArr = s.split(" ");	
	int len = sArr.length;
	Integer[] retArr = new Integer[len];
	for(int i=0;i<len;i++){
	    retArr[i] = Integer.parseInt(sArr[i]);
	}
	return retArr;
    }

    long getCost(int x, int y, int a, int b){
	long retV = 0L;
	if(b>=2*a){
	    retV = (long)a*((long)x+y);
	}else{
	    retV = (long)a*Math.abs((long)x-y)+(long)b*Math.min(x,y);
	}
	return retV;
    }
    public static void main(String[]args) throws Exception{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

	String tLn = br.readLine();
	Road r = new Road();
	int t = Integer.parseInt(tLn);
	for(int i=0;i<t;i++){
	    String xyLn = br.readLine();
	    String abLn = br.readLine();
	    Integer[]xyArr = strToIntArr(xyLn);
	    Integer[]abArr = strToIntArr(abLn);
	    long cost = r.getCost(xyArr[0],xyArr[1],abArr[0],abArr[1]);
	    bw.write(Long.toString(cost));
	    bw.newLine();
	    bw.flush();
	}
    }
}
