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.*;
public class Main {
    static FastReader in=new FastReader();
    static StringBuilder Sd=new StringBuilder();
    static List<Integer>Gr[]; 
    static int a[],b[];
    static boolean visit[];
    public static void main(String [] args) {
    	//Dir by MohammedElkady
    	int t=in.nextInt();
    	while(t-->0) {
    		int x=in.nextInt(),y=in.nextInt(),a=in.nextInt(),b=in.nextInt();
    b=Math.min(2*a, b);
    int min=Math.min(x, y),max=Math.max(y, x);
     max-=min;
     long ans=(long)(min)*(long)(b);
     ans+=(long)(max)*(long)(a);
     Soutln(ans+"");
    	}
    	
    Sclose();
    
    }
    static long gcd(long g,long x){
        if(x<1)return g;
        else return gcd(x,g%x);
    }
    //array fill
    static long[]filllong(int n){long a[]=new long[n];for(int i=0;i<n;i++)a[i]=in.nextLong();return a;}
    static int[]fillint(int n){int a[]=new int[n];for(int i=0;i<n;i++)a[i]=in.nextInt();return a;}
    //OutPut Line
    static void Sout(String S) {Sd.append(S);}
    static void Soutln(String S) {Sd.append(S+"\n");}
    static void Soutf(String S) {Sd.insert(0, S);}
    static void Sclose() {System.out.println(Sd);}
    static void Sclean() {Sd=new StringBuilder();}
}
 
class node implements Comparable<node>{
int x,p;
	node(int x,int p){
		this.x=x;
		this.p=p;
	}
	@Override
	public int compareTo(node o) {
       return (x-p)-(o.x-o.p);
	}
}
class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
}
 
class Sorting{
 
 public static int[] bucketSort(int[] array, int bucketCount) {
 
 if (bucketCount <= 0) throw new IllegalArgumentException("Invalid bucket count");
 
 if (array.length <= 1) return array; //trivially sorted
 
 
 
 int high = array[0];
 
 int low = array[0];
 
 for (int i = 1; i < array.length; i++) { //find the range of input elements
 
 if (array[i] > high) high = array[i];
 
 if (array[i] < low) low = array[i];
 
 }
 
 double interval = ((double)(high - low + 1))/bucketCount; //range of one bucket
 
 
 ArrayList<Integer> buckets[] = new ArrayList[bucketCount];
 
 for (int i = 0; i < bucketCount; i++) { //initialize buckets
 
 buckets[i] = new ArrayList();
 
 }
 
 
 
 for (int i = 0; i < array.length; i++) { //partition the input array
 
 buckets[(int)((array[i] - low)/interval)].add(array[i]);
 
 }
 
 
 int pointer = 0;
 
 for (int i = 0; i < buckets.length; i++) {
 
 Collections.sort(buckets[i]); //mergeSort
 
 for (int j = 0; j < buckets[i].size(); j++) { //merge the buckets
 
 array[pointer] = buckets[i].get(j);
 
 pointer++;
 
 }
 
}
 
return array;
 
}
}