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.math.BigInteger;
import java.util.Arrays;
import java.util.Scanner;

public class Solution
{

    public static void main( String[] args )
    {
        Solution solution = new Solution();
        Scanner scanner = new Scanner( System.in );
        int N = scanner.nextInt();
        for (int i = 0; i < N; i++) {
            int x = scanner.nextInt();
            int y = scanner.nextInt();
            int a = scanner.nextInt();
            int b = scanner.nextInt();

            BigInteger amount = solution.computeAmount(x, y, BigInteger.valueOf( a ), BigInteger.valueOf( b ) );
            System.out.println(amount);
        }
    }

    private BigInteger computeAmount( int x, int y, BigInteger a, BigInteger b )
    {
        int max = x > y ? x : y;
        int min = x > y ? y : x;

        BigInteger result = BigInteger.ZERO;
        BigInteger aX2 = a.multiply( BigInteger.valueOf( 2 ) );
        BigInteger delta = b.min( aX2 );
        result = result.add( delta.multiply( BigInteger.valueOf( min ) ) );

        max -= min;
        result = result.add( a.multiply( BigInteger.valueOf( max ) ) );

        return result;
    }

}
