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.
#! /usr/bin/python3

import sys

def main():
    input_list = get_input()
    for i in range(len(input_list)):
        if i > 0:
            if i % 2 == 1:
                x_pos = int(input_list[i].split(" ")[0])
                y_pos = int(input_list[i].split(" ")[1])
            elif i % 2 == 0:
                a_cost = int(input_list[i].split(" ")[0])
                b_cost = int(input_list[i].split(" ")[1])
                print(func(x_pos, y_pos, a_cost, b_cost))

def get_input():
    input_list = []
    for line in sys.stdin:
        """
        if line.rstrip("\n") == "exit":
            break
        """
        input_list.append(line.rstrip("\n"))
    return input_list

# x_pos, y_pos are integers
def func(x_pos, y_pos, a_cost, b_cost):
    if x_pos > 0 or y_pos > 0:
        if 2 * a_cost < b_cost:
            return a_cost * (abs(x_pos) + abs(y_pos))
        else:
            return a_cost * (abs(x_pos - y_pos)) + b_cost * min(x_pos, y_pos)
    else:
        return 0

if __name__ == "__main__":
    main()
