A13419. Road To Zero

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.

The first line contains one integer $t$ ( $1 \le t \le 100$ ) — the number of testcases.

The first line of each test case contains two integers $x$ and $y$ ( $0 \le x, y \le 10^9$ ).

The second line of each test case contains two integers $a$ and $b$ ( $1 \le a, b \le 10^9$ ).

For each test case print one integer — the minimum amount of dollars you have to spend.

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.