Road To Zero

1000ms

262144K

Description:

You are given two integers $$$x$$$ and $$$y$$$. You can perform two types of operations:

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:
- $$$x = 0$$$, $$$y = 6$$$;
- $$$x = 0$$$, $$$y = 8$$$;
- $$$x = -1$$$, $$$y = 7$$$;
- $$$x = 1$$$, $$$y = 7$$$.
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 $$$t$$$ ($$$1 \le t \le 100$$$) — 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 $$$b$$$ ($$$1 \le a, b \le 10^9$$$).

Output:

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

Sample Input:

Sample 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.

Informação

Provedor Codeforces

Código CF1342A